Quantitative studies of the nucleation of recrystallization in metals

Quantitative studies of the nucleation of recrystallization in metals
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Quantitative studies of the nucleation of recrystallization in metals utilizing
microscopy and X-ray diffraction
Larsen, Axel Wright
Publication date:
2005
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Publisher final version (usually the publisher pdf)
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Citation (APA):
Larsen, A. W. (2005). Quantitative studies of the nucleation of recrystallization in metals utilizing microscopy and
X-ray diffraction. Risø National Laboratory. (Risø-PhD; No. 9(EN)).
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Risø-PhD-9(EN)
Quantitative studies of the nucleation of
recrystallization in metals utilizing
microscopy and X-ray diffraction
Axel Wright Larsen
Risø National Laboratory
Roskilde
Denmark
September 2005
Author: Axel Wright Larsen
Title: Quantitative studies of
the nucleation of recrystallization in
metals utilizing microscopy and X-ray diffraction
Department: Materials Research Department
Risø-PhD-9(EN)
September 2005
This thesis is submitted in partial fulfilment of the requirements for
the Ph.D. degree at the University of Copenhagen and Risø
National Laboratory
Abstract :
This thesis covers three main results obtained during the project:
A reliable method of performing serial sectioning on metal samples
utilizing a Logitech polishing machine has been developed.
Serial sectioning has been performed on metal samples in 1 µm
steps utilizing mechanical polishing, and in 2 µm steps when
electrochemical polishing was needed.
A method by which reliable EBSP line scans may be performed by
scanning three parallel lines has been developed. This method
allows lines of the order of 1 cm in length to be characterized with a
1 µm or better spatial resolution. The method is proven to be a good
way of determining microstructural parameters, which are
important when studying recrystallization dynamics.
The nucleation of recrystallization at triple junctions has been
studied by 3 dimensional X-ray diffraction (3DXRD), allowing for
the first time the deformed and recrystallized microstructures to be
compared at a given nucleation site in the bulk of a metal sample.
From an experiment three nuclei were identified, their respective
crystal orientations were determined, and growth curves were
obtained for two of them.
Resume :
Denne afhandling dækker tre resultater opnået i løbet af projektet:
En pålidelig metode til at udføre seriel sektionering på
metalprøver vha. en Logitech poleringsmaskine er blevet
udviklet. Seriel sektionering er blevet udført på
metalprøver i 1 µm skridt ved brug af mekanisk polering og i
2 µm skridt hvor elektropolering var nødvendigt.
En metode hvormed pålidelige EBSP-linieskans kan udføres ved
at skanne tre parallelle linjer er blevet udviklet. Denne metode
tillader linjer, med længder af størrelsesorden 1 cm, at
blive karakteriseret med en rumlig opløsning på 1 µm. Metoden er
blevet påvist at være en god metode til at bestemme de
mikrostrukturelle parametre, som er vigtige ved studier af
dynamikken i rekrystallisation.
Kimdannelse ved tripelgrænser er blevet studeret vha. 3
dimensional røntgendiffraktion, hvilket for første gang tillod
de deformerede- og rekrystalliserede mikrostrukturer at blive
sammenlignet ved et kimdannelsessted i det indre af en
metalprøve. Tre kim blev identificeret i et eksperiment, deres
respektive krystalorienteringer blev bestemt, og vækstkurver
blev bestemt for to af dem.
ISBN 87-550-3417-9
Cover :
The images on the cover
show respectively:
(centre) a typical X-ray
diffraction image obtained
from a deformed sample, but
including two reflections
from a nucleus;
(top left) an image obtained
from copper by optical
microscopy utilizing
polarized light;
(top right) a single Vickers
hardness indentation;
(bottom left) EBSP from
silicon; and
(bottom right) an EBSP
orientation image map of a
sample for X-ray studies.
Pages: 133/193
Tables: 8
Figures: 45
References: 119
Risø National Laboratory
Information Service Department
P.O.Box 49
DK-4000 Roskilde
Denmark
Telephone +45 46774004
[email protected]
Fax +45 46774013
www.risoe.dk
Abstract
This thesis covers three main results obtained during my Ph.D. project:
A reliable method of performing serial sectioning on metal samples utilizing a Logitech PM5D polishing machine has been developed. Serial sectioning
has been performed on metal samples in 1 µm steps utilizing mechanical polishing, and in 2 µm steps when electrochemical polishing was needed, such
as for electron backscatter pattern (EBSP) studies. It is proven possible to
polish down from the sample surface to a pre–specified target depth with an
accuracy of 1–2 µm, and in all cases, the height difference across the sample
surface was not more than 1–2 µm.
A method by which reliable EBSP line scans may be performed by scanning three parallel lines has been developed. This method allows lines of
the order of 1 cm in length to be characterized with a 1 µm or better spatial resolution, in the same time that it takes to acquire a standard EBSP
map consisting of 173×173 data points, thus drastically improving the sampling statistics. The method is proven to be a good way of determining the
microstructural parameters: the volume fraction recrystallized; the free surface area density separating recrystallized and deformed material; and the
mean intercept length of the recrystallized grains, which are important when
studying recrystallization dynamics.
The nucleation of recrystallization at triple junctions has been studied
by 3 dimensional X–ray diffraction (3DXRD), allowing for the first time the
deformed and recrystallized microstructures to be compared at a given nucleation site in the bulk of a metal sample. From an experiment three nuclei
were identified, their respective crystal orientations were determined, and
growth curves were obtained for two of them. Two nuclei were found to
exhibit orientations corresponding to 1st order twins of one of the deformed
grains. The third nucleus was however found to appear with a new orientation, neither present in any of the deformed grains associated with the triple
junction or 1st order twin–related to any of them.
The images on the cover show respectively:
(centre) a typical X–ray diffraction image obtained from a deformed sample,
but including two reflections from a nucleus; (top left) an image obtained from
copper by optical microscopy utilizing polarized light; (top right) a single
Vickers hardness indentation [1]; (bottom left); EBSP from silicon [2]; and
(bottom right) an EBSP orientation image map of a sample for X–ray studies.
1
Abstract in Danish
Denne afhandling dœkker tre resultater opnået i løbet af mit ph.d.-projekt:
En pålidelig metode til at udføre seriel sektionering på metalprøver vha.
en Logitech PM5D poleringsmaskine er blevet udviklet. Seriel sektionering er
blevet udført på metalprøver i 1 µm skridt ved brug af mekanisk polering og i
2 µm skridt hvor elektropolering var nødvendigt, som f.eks. ved studier vha.
EBSP. Det er blevet bevist, at det er muligt at polere ned fra prøveoverfladen
til en prœdefineret dybde med en nøjagtighed på 1-2 µm, og i alle tilfœlde
har højdeforskellen henover overfladen ikke overskredet 1-2 µm.
En metode hvormed pålidelige EBSP-linieskans kan udføres ved at skanne
tre parallelle linjer er blevet udviklet. Denne metode tillader linjer, med
lœngder af størrelsesorden 1 cm, at blive karakteriseret med en rumlig opløsning
på 1 µm eller bedre på den samme tid, som det tager at optage et standard
EBSP-kort bestående af 173x173 datapunkter, og derved drastisk forbedre
målestatistikken. Metoden er blevet påvist at vœre en god metode til at
bestemme de mikrostrukturelle parametre: volumenbrøkdelen af rekrystalliseret materiale; densiteten af frit areal, som adskiller deformeret og rekrystalliseret materiale; samt den gennemsnitlige interceptlœngde af de rekrystalliserede korn, som er vigtige ved studier af dynamikken i rekrystallisation.
Kimdannelse ved tripelgrœnser er blevet studeret vha. 3 dimensional
røntgendiffraktion, hvilket for første gang tillod de deformerede- og rekrystalliserede mikrostrukturer at blive sammenlignet ved et kimdannelsessted i
det indre af en metalprøve. Tre kim blev identificeret i et eksperiment, deres
respektive krystalorienteringer blev bestemt, og vœkstkurver blev bestemt for
to af dem. To kim blev fundet med orienteringer, der svarede til førsteordens
tvillinger af en af de deformerede korn, og det tredje kim havde en ny orientering, der hverken svarede til orienteringen af en af de deformerede korn
ved en triplegrœnse og heller ikke var førsteordens tvillingerelateret til nogen
dem.
Billederne på forsiden viser respektivt:
(midten) et typisk røntgendiffraktionsbillede optaget af en deformeret prøve,
men som også inkluderer to reflekser fra et krystalkim; (øverst t.v.) billede
optaget af kobber vha. optisk mikroskopi med polariseret lys; (øverst t.h.)
et enkelt Vickers hårdhedsindtryk [1]; (nederst t.v.) EBSP fra silicium [2]; og
(nederst t.h.) et EBSP orienteringskort af en prøve brugt til røntgenstudier.
2
Preface
This thesis is submitted in partial fulfilment of the requirements for obtaining the Ph.D. degree at the University of Copenhagen. The research
presented here was carried out within the Center for Fundamental Research:
Metal Structures in Four Dimensions (Metals–4D center), at
Risø National Laboratory, under the supervision of Jens Als–Nielsen at the
University of Copenhagen, and Dorte Juul Jensen and Henning Friis Poulsen
both at the Metals–4D center.
The work presented here was done during the period from September 1.
2001 until August 31. 2004, and included are six publications (including a
technical report) by the author, of which four have the author as first author.
The author gratefully acknowledges the Danish Research Foundation for
supporting the Center for Fundamental Research: Metal Structures in Four
Dimensions, within which this work was performed. This work was also
partly supported by the Danish Natural Science Research Council
(via Dansync), and the ESRF is acknowledged for provision of beamtime.
The author wishes to thank everyone associated with the Metals–4D center
for ideas, help, discussions, and simply for making the time spent on this
PhD–project a pleasant one. Dorte Juul Jensen in particular is thanked for
her guidance, support, trust, and general wonderful personality, which has
been a great source of inspiration.
The author would also like to thank Jørgen Bilde–Sørensen and
Christian Mammen for many good discussions on respectively electron
microscopy and X–ray physics, and Kristofer Hanneson for his contributions
to developing the serial sectioning technique.
Lastly, a special thank you must go to the three technicians Preben Olesen,
Palle Nielsen, and Helmer Nilsson, who have been of tremendous help during
this PhD project, and with whom I have shared many a good laugh.
3
Contents
1 Introduction
1.1 Metallurgical background . . . . . . . . . .
1.2 Nucleation theories . . . . . . . . . . . . .
1.2.1 Strain–induced boundary migration
1.2.2 Subgrain coalescence . . . . . . . .
1.2.3 Subgrain coarsening . . . . . . . .
1.2.4 Inverse Roland . . . . . . . . . . .
1.2.5 Twinning . . . . . . . . . . . . . .
1.2.6 Particle stimulated nucleation . . .
1.3 Experimental techniques . . . . . . . . . .
1.3.1 Hardness indents . . . . . . . . . .
1.3.2 Optical microscopy . . . . . . . . .
1.3.3 Electron microscopy . . . . . . . .
1.3.4 X–ray diffraction . . . . . . . . . .
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11
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2 Techniques employing microscopies of various kinds
30
2.1 Optical microscopy . . . . . . . . . . . . . . . . . . . . . . . . 30
2.2 Electron microscopy . . . . . . . . . . . . . . . . . . . . . . . 31
2.3 Serial sectioning . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3 Recrystallizing microstructures studied by stereology
3.1 Studies of recrystallizing microstructures . . . . . . . .
3.2 LSGRAINS . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Results and discussion . . . . . . . . . . . . . . . . . .
3.3.1 Validation of the LSGRAINS technique . . . . .
3.3.2 Depth–dependent nucleation kinetics . . . . . .
4
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35
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4 Nucleation of recrystallization studied by X–ray diffraction
4.1 The 3DXRD microscope . . . . . . . . . . . . . . . . . . . . .
4.1.1 Governing equations and scattering geometry . . . . .
4.1.2 X–ray source . . . . . . . . . . . . . . . . . . . . . . .
4.1.3 High energy X–ray focusing . . . . . . . . . . . . . . .
4.1.3.1 Focusing by a bent Laue crystal . . . . . . . .
4.1.3.2 Multilayer focusing . . . . . . . . . . . . . . .
4.1.4 Detectors . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.5 The furnace . . . . . . . . . . . . . . . . . . . . . . . .
4.2 The nucleation experiment . . . . . . . . . . . . . . . . . . . .
4.2.1 Samples used for the 3DXRD study . . . . . . . . . . .
4.2.2 Preliminary studies . . . . . . . . . . . . . . . . . . . .
4.2.2.1 3DXRD feasibility study . . . . . . . . . . . .
4.2.2.2 Vickers hardness testing . . . . . . . . . . . .
4.2.2.3 Investigations by microscopy . . . . . . . . .
4.2.3 The 3DXRD experiment . . . . . . . . . . . . . . . . .
4.2.3.1 Image processing . . . . . . . . . . . . . . . .
4.2.3.2 Volume calibration . . . . . . . . . . . . . . .
4.2.3.3 Identifying nuclei . . . . . . . . . . . . . . . .
4.2.3.4 Determining the exact position of the nuclei .
4.2.3.5 Determining the crystal orientations of the
nuclei . . . . . . . . . . . . . . . . . . . . . .
4.2.3.6 Nucleus–to–parent grain orientation relationships . . . . . . . . . . . . . . . . . . . . . . .
4.2.3.7 Growth kinetics of the nuclei . . . . . . . . .
4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.1 Nucleus 1 . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.2 Nucleus 2 . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.3 Nucleus 3 . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 Discussion and outlook . . . . . . . . . . . . . . . . . . . . . .
4.4.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . .
50
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5 Conclusions
107
88
A Crystal orientations
109
A.1 Twin–orientations . . . . . . . . . . . . . . . . . . . . . . . . . 111
A.2 The X–ray diffraction equation . . . . . . . . . . . . . . . . . 113
5
B Crystallographic textures
115
B.1 Pole figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
B.2 The orientation distribution function . . . . . . . . . . . . . . 117
C Beamline specifics
118
D Publications
121
References
122
6
List of Tables
1.1 Stacking fault energy of various common metals. . . . . . . . . 21
3.1 LSGRAINS — validation of algorithm by visual comparison
on short scans. . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.2 LSGRAINS — comparing extracted line scans. . . . . . . . . . 47
3.3 LSGRAINS — 3×1000+ data point line scans. . . . . . . . . 47
C.1 The ID11 in–vacuum undulator. . . . . . . . . . . . . . . . . . 118
C.2 Technical specifications for the 2D Frelon CCD–detector. . . . 119
C.3 The asymmetrically cut and cylindrically bent perfect Si(111)–
Laue monochromator crystals. . . . . . . . . . . . . . . . . . . 120
C.4 The elliptically shaped and laterally graded W/B4 C–multilayer.120
7
List of Figures
1.1 Micrographs showing the microstructure during different stages
of thermomechanical processing. . . . . . . . . . . . . . . . . .
1.2 Critical embryo creation by SIBM. . . . . . . . . . . . . . . .
1.3 Embryo creation by subgrain coalescence. . . . . . . . . . . . .
1.4 Embryo creation by subgrain coarsening. . . . . . . . . . . . .
1.5 A stacking fault in an fcc lattice leading to twinning. . . . . .
1.6 Strained and misoriented zone around a rigid interstitial particle.
1.7 Vickers hardness indentation. . . . . . . . . . . . . . . . . . .
1.8 High–quality EBSP image from silicon. . . . . . . . . . . . . .
1.9 X–ray penetration in selected elements. . . . . . . . . . . . . .
14
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26
28
29
2.1 Illustration of the geometry of an EBSP system. . . . . . . . . 32
3.1 EBSP OIM showing a partially recrystallized microstructure
with two random lines drawn through it. . . . . . . . . . . .
3.2 Orientation image map of 3–line scans. . . . . . . . . . . . .
3.3 LSGRAINS — connectivity around the i’th data point. . . .
3.4 Flow diagram of the LSGRAINS algorithm. . . . . . . . . .
3.5 LSGRAINS — comparing long manual and automatic scans.
3.6 SV vs. VV curve from article A5. . . . . . . . . . . . . . . . .
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4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
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The 3DXRD microscope. . . . . . . . . . . . . . . . . . . .
Example of experimental 3DXRD data. . . . . . . . . . . .
3DXRD scattering geometry. . . . . . . . . . . . . . . . . .
Example of ID–11 undulator spectrum. . . . . . . . . . . .
The X–ray monochromating and focusing optical elements.
Setup with focus point in front of the sample. . . . . . . .
Rowland circle for a focusing with a bent Laue crystal. . .
Schematics of focusing with a bent Laue crystal. . . . . . .
8
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4.9
4.10
4.11
4.12
4.13
4.14
4.15
4.16
4.17
4.18
4.19
4.20
4.21
4.22
4.23
4.24
4.25
4.26
Reflection from a multilayer mirror. . . . . . . . . . . . . . . . 61
Vickers hardness tests on the copper sample material. . . . . . 68
X–ray sample geometry. . . . . . . . . . . . . . . . . . . . . . 70
Sample A: OIM of the surface microstructure and the location
of the X–ray grid. . . . . . . . . . . . . . . . . . . . . . . . . . 72
Sample B: OIM of the surface microstructure and the location
of the X–ray grid. . . . . . . . . . . . . . . . . . . . . . . . . . 73
Sample C: OIM of the surface microstructure and the location
of the X–ray grid. . . . . . . . . . . . . . . . . . . . . . . . . . 74
Background subtraction using the Bowen et al. method. . . . 76
Spatial correction of 2D diffraction images. . . . . . . . . . . . 77
Nuclei detected in the diffraction images. . . . . . . . . . . . . 84
Sample A nucleus triangulation geometry. . . . . . . . . . . . 86
Sample C nucleus triangulation geometry. . . . . . . . . . . . 87
Diffraction spots simulated and plotted on images from the
deformed microstructure. . . . . . . . . . . . . . . . . . . . . . 90
Evolution of the nucleus 1 (002)–reflection with annealing time. 92
Evolution of the nucleus 2 (1̄11̄)–reflection with annealing time. 93
Nucleus growth curves. . . . . . . . . . . . . . . . . . . . . . . 94
Pole figures — nucleus 1 superimposed on the recovered microstructure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Pole figures — nucleus 2 superimposed on the deformed microstructure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
Pole figures — nucleus 3 superimposed on the deformed microstructure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
A.1 The rolling geometry. . . . . . . . . . . . . . . . . . . . . . . . 109
A.2 The Euler angles. . . . . . . . . . . . . . . . . . . . . . . . . . 110
B.1 Pole figure of rolled sheet. . . . . . . . . . . . . . . . . . . . . 116
9
List of Abbreviations
3DXRD
AI
bcc
BF
CCD
CMS
EBSP
ECD
EM
ESRF
fcc
FWHM
HAGB
LAGB
ML
ND
ODF
OFHC
OIM
OM
PSN
RD
SEM
SFE
SIBM
TD
TEM
Three–dimensional X–ray diffraction
Area of Interest
body centered cubic
Bormann fan
Charge–Coupled–Device
Centre of Mass
Electron Backscatter Patterns
Equivalent Circle Diameter
Electron Microscopy
European Synchrotron Radiation Facility
face centered cubic
Full–Width–at–Half–Maximum
High Angle Grain Boundary
High Angle Grain Boundary
Multilayer
Normal direction (rolling geometry)
Orientation Distribution Function
Oxygen–Free High Conductivity
Orientation Image Map
Optical Microscopy
Particle Stimulated Nucleation
Rolling direction (rolling geometry)
Scanning Electron Microscope
Stacking Fault Energy
Strain–Induced Boundary Migration
Transvers direction (rolling geometry)
Transmission Electron Microscope
10
Chapter 1
Introduction
This PhD thesis deals with the nucleation of recrystallization, which is the
initial step of discontinuous recrystallization (see section 1.1). The aim of the
PhD project was to spatially and crystallographically characterize nucleation
in metals using various experimental techniques (see section 1.3).
This thesis is divided into 5 chapters:
1. a general introduction to the nucleation of recrystallization, including
nucleation theories, and the relevant experimental techniques;
2. an introduction to stereology, a stereological technique (LSGRAINS)
developed by the author, and scientific results obtained using this technique;
3. an introduction to microscopical techniques (both optical and electron),
with special detail given to the electron backscatter pattern technique;
4. an introduction to 3 Dimensional X–Ray Diffraction (3DXRD), followed by the in situ study of nucleation of recrystallization, which was
performed using this technique, will be covered in detail;
5. an overall conclusion based on the results obtained in the previous three
chapters, as well an outlook on their potential impact.
This chapter includes an introduction to the thesis, as well as three sections
dealing with respectively: (i) an introduction to basic metallurgy relevant for
the nucleation of recrystallization; (ii) an introduction to current nucleation
theories; (iii) and an introduction to experimental techniques used to study
recrystallization, as well as the ones used in this PhD project.
11
Typically, it is assumed that the nuclei (the new grains when they initially
appear) are formed from cells in the deformed/recovered structure, which
grow especially fast, i.e., that the nuclei have the same crystallographic orientation as the deformed microstructure they nucleate from. However, new
experimental results have indicated that nuclei can form with orientations
not observed in the deformed microstructure [3, 4, 5, 6, 7, 8], and therefore
that simple growth mechanism models are inadequate to fully describe the
nucleation process. Examples of such models are given in references [9, 10].
Nucleation of recrystallization is not an easy process to study, as the size
of nuclei are of the order of ∼1 µm (samples are sized 103 –104 µm), the nuclei
may be heterogeneously distributed within the material, and as the nuclei
grow into a deformed grain they consume the parent microstructure, thereby
”erasing” any trace of it, and thus making it impossible to determine which
physical mechanism resulted in the creation of the nuclei, because we, so to
speak, have only half the picture.
One reason why precise incontrovertible experimental data of the nucleation of recrystallization is so difficult to obtain is because it has so far been
impossible to characterize both a bulk nucleus and its parent microstructure
in a nucleation event. Either dynamic information has been obtained from
the surface, which can not necessarily be viewed as representative of the
bulk kinetics and there is also the uncertainty of whether the nucleus grew
up to the surface from the sample bulk below [3, 11], or nuclei have been
located on polished sections, where it is not possible to determine the exact
microstructure, which was previously present at the nucleation sites [8].
In recent years, a new technique utilizing high energy X–rays has been developed, which allows studies of exactly the desired nature (see section 1.3) [4].
The main focus of this PhD project was to design and perform an experiment, which allowed in situ studies bulk of nucleation before, during, and
after annealing. However, this PhD project also involved other experimental
methods relevant for studying recrystallization.
12
1.1
Metallurgical background
The vast majority of metal components used for industrial purposes are
polycrystalline. That is, they are typically conglomerates of crystal grains
with a size of the order of 1–1000 µm, which can be considered as individual
single crystals with a low mosaic spread1 , and each with its own crystallographic orientation2 [13, 14]. For a general overview of metallurgy the reader
is referred to the following references [10, 15, 16, 17].
When a metal or alloy is plastically deformed at a relatively low temperature microstructural changes occur (see figure 1.1) [18]:
• the grain shape is deformed, according to the imposed deformation.
• point defects (mainly vacancies) are generated from jogs on the dislocation lines.
• line defects (dislocations) are generated and pile up, creating boundaries in cell–forming metals.
This results in an increase of stored energy, and changes the mechanical
properties of the metal or alloy. In recent years, much knowledge of these
processes has been gleaned, particularly from studies of the build up of dislocation structures by electron microscopy [19, 20].
When the plastically deformed metal or alloy is subsequently heated (annealed), the energy stored by the deformation processes is released in three
(usually overlapping) processes.
Recovery is the process, which occurs first at lower temperatures, and according to Cotterill & Mould it refers to all the various annealing phenomena,
which occur during annealing, but prior to the appearance of new strain–free
grains [22]. It is dominated by the removal of excess vacancies to [23]: free
surfaces; grain boundaries; and dislocation, which leads to climb, and the
sharpening of the dislocation substructure, often referred to as polygonization. After the onset of recovery, it is more correct to speak of the deformed
microstructure as the recovered microstructure. The energy released during
recovery generally represents less than 10% of the total stored energy.
1
The mosaic spread of a single crystallite corresponds to its spread of crystal orientations, the so–called mosaic distribution [12].
2
In this context crystallographic orientation is understood as: the orientation of the
crystal lattice of the grain with respect to the main axis of deformation imposed on the
metal sample (see appendix A).
13
Figure 1.1: Micrographs showing the microstructure during different stages of
thermomechanical processing. In the figure on the left the microstructure is fully
recrystallized. It is subsequently deformed and dislocation tangles are seen to appear, and after additional deformation the microstructure is subdivided into distinct
cells. Lastly, during annealing new strain–free grains nucleate and grow [21].
In terms of rising temperature, the next process to occur is recrystallization, of which two types can be identified [24]:
• Continuous recrystallization, where the recovered dislocation substructure keeps on coarsening. It is a homogeneous type–I Gibbs process.
• Discontinuous recrystallization (the most common, and the case of interest in this study), where a new set of strain–free grains nucleate and
grow, and thereby consume the deformed/recovered microstructure. It
is a heterogeneous type–II Gibbs process.
Recrystallization begins at an ill–defined temperature, which is referred to
as the recrystallization temperature. This temperature also distinguishes the
cold work region (of interest in this study), which takes place below the recrystallization temperature [25, 26, 27]. The recrystallization temperature is
affected by the initial stored energy that is in the metal, and the amount of
recovery that has taken place prior to recrystallization — it is in fact possible to recover samples so much that recrystallization will not set in at any
temperature [22].
The process of discontinuous recrystallization (simply referred to as recrystallization from now on) is divided into two steps: (i) critical embryos, present
in the deformed/recovered microstructure, that nucleate as new grains; and
(ii) the new grains that grow until they impinge upon each other and thus
consume all the deformed/recovered material in the microstructure (the micrograph on the right in figure 1.1 shows a partially recrystallized microstructure).
14
The final annealing process to take place is grain growth, also called grain
coarsening. When the entire deformed/recovered microstructure has been
consumed by the recrystallizing grains, large grains generally continue to
grow at the expense of smaller grains, which increases the mean grain size,
and leads to a reduction in the total grain boundary area and therefore the
total grain boundary energy [28]. Once again, homogeneous coarsening may
be thought of as a type–I Gibbs process.
This study is concerned with the fundamentals of the nucleation of recrystallization. It is however important to note the industrial/commercial
importance of recrystallization, because the recrystallized grains determine
to a large extent the properties of the annealed metal or alloy, and it is
therefore of great importance to understand the nucleation of recrystallization, both from a scientific as well as from an applied point–of–view. Thus
in forming car body steel sheet from a cast billet or aluminium sheet stock
many of tens of recrystallization steps may be involved.
The recrystallization process (often repeated): a) controls the crystallographic texture of the metal (see appendix B), which is important e.g. to
obtain an isotropic deformation when bodies are stamped from sheet material; b) breaks up segregation within the casting and homogenizes the chemistry. This is because migrating grain boundaries are able to redistribute
solutes over very large distances compared with bulk diffusion; c) removes
any undesirable columnar grain structure and replaces it with the more desirable equiaxed grain shape; d) allows a suitable grain size to be selected.
For most applications, a fine grain size is preferable, giving high strength
(σ ∝(grain size)−1/2 ), high fatigue strength, toughness and corrosion resistance. However, where good creep properties are required, a coarse–grained
microstructure (or even large single crystals) may be grown by a process
referred to as the ”strain–anneal” method, where repeated critical strains
(deformations) and anneals are given to selectively reduce the number of
recrystallization nuclei which form [22].
In essence, discontinuous recrystallization is a solid state phase transition,
where there is no change of composition or crystal lattice [29]. However, there
is a significant difference between this type of phase transition and other
phase transitions, such as the liquid–to–solid phase transition, precipitation
within a solid, or the change from one phase to another, eg. the austinite–
to–ferrite transition in iron, where the crystal structure changes from the
fcc to the bcc lattice. In the other cases the nucleus size is relatively small,
involving a few tens of atoms, and this can be formed (homogenously and
15
heterogeneously) by statistical fluctuations within the system [29, 24]. This
is not the case for the nucleation of recrystallization, where calculations show
that a critical nucleus has a size in the micrometre range [24, 30].
1.2
Nucleation theories
In this section we will focus on what is known about the nucleation process, and the most common nucleation theories will be summarized. Nucleation is a process, where small regions, known as critical embryos, nucleate
as new strain–free grains in the deformed/recovered microstructure. The nuclei are typically heterogeneously distributed within the bulk of the material.
Nucleation is also a rare event considering that the size of a critical embryo
is ∼1 µm, and if the material is allowed to fully recrystallize with an average grain size of ∼100 µm, this estimate hints that much material must be
characterized in order to locate nuclei early in the nucleation process.
In single–phase materials3 it has been shown that the critical embryo size
cannot be achieved by atom–by–atom construction through thermal fluctuations [24]. It is instead accepted that nuclei grow from subgrains in the
deformed structure through a thermally activated process, and that in order
to become a nucleus a subgrain must have a minimum size and a high angle
boundary (HAGB) of high mobility [7, 30]. Also, the number of successful
nucleation events increases with increasing stored energy, and the nucleation
rate increases with increasing temperature above the recrystallization temperature.
1.2.1
Strain–induced boundary migration
One mechanism by which nucleation is thought to proceed is strain–
induced boundary migration (SIBM). It involves a part of a pre-existing
high angle boundary bulging, and leaving a relatively dislocation–free region
behind the migrating boundary (see figure 1.2). This region will become a
nucleus if the bulge is sufficiently large. Two different scenarios can occur,
in which either multiple subgrains make up the bulge (fig. 1.2b), or a single
large subgrains makes up the bulge (fig. 1.2c). An interesting point about the
SIBM mechanism is that it appears to have no incubation time if a suitably
3
single–phase is defined as a material consisting of one chemical species or compound
(eg. NaCl) without concentration gradients (i.e., a constant crystal lattice).
16
(a)
(b)
(c)
Figure 1.2:
Critical embryo creation by strain–induced boundary migration
(SIBM). A part of the HAGB bulges out into the grain with the higher stored
energy (E1>E2 ), and if the driving force is big enough it will keep bulging until it
reaches the size of a critical embryo. (a) Initial bulge on a HAGB; (b) multiple
subgrain SIBM; and (c) single subgrain SIBM [11].
sized subgrain is available at a grain boundary at the start of annealing,
as opposed to other recovery driven nucleation mechanisms. If however a
subgrain of suitable size must first be produced by other recovery mechanisms
there is of course an incubation time [22].
The driving force is the difference in stored energy at the two sides of the
HAGB (EV = E1−E2 ). The boundary energy of a spherical bulge with radius
R, and boundary energy γB [J/m2 ] is [11]:
EB = 4πR2 γB
=⇒
dEB
= 8πRγB
dR
(1.1)
In the early stages of bulging, i.e., before the dislocation density drops within
the bulge, the driving force is given by the energy difference EV between the
microstructures:
dE
= 4πR2 EV
(1.2)
dR
B
In order for the bulge to grow we must have dE
> dE
, and if the critical
dR
dR
point is taken to be when the bulge is a hemisphere (R=L), then from equations 1.1 and 1.2, which contain the conditions for a HAGB bulge developing
17
into a nucleus:
dE
dEB
>
dR
dR
R>
2 γB
EV
=⇒ L >
=⇒
2 γB
EV
(1.3)
By inserting typical values (γB ≈0.5 Jm−2 , and EV ≈106 Jm−3 ) into eq. 1.3 we
find the minimum radius of an embryo to be L ≈1 µm, which is in concurrence
with what is observed experimentally [11].
1.2.2
Subgrain coalescence
Subgrain coalescence is a mechanism that allows two or more subgrains
in the deformed microstructure to merge into one larger subgrain, which may
then be a potential embryo (see figure 1.3). It is based on the rotation of a
subgrain, so as to reduce the grain boundary energy of a low angle subgrain
boundary (LAGB) separating two subgrains.
(b)
(a)
Figure 1.3: Embryo creation by subgrain coalescence. The LAGB (B to C) disappears due to the rotation of a subgrain: (a) Two subgrains divided by a LAGB;
(b) The subgrains have coalescenced into one bigger subgrain (embryo) [11].
For a low angle tilt boundary with a misorientation angle θ, the boundary
energy γ may readily be calculated from the Read–Shockley equation [11]:
θ
θ
γ(θ) = γm
1 − ln
(1.4)
θm
θm
18
where the parameters γm and θm are respectively the energy and misorientation as the boundary becomes a high angle boundary (HAGB). θm is typically
set to 15◦ .
The rate by which subgrain reorientation can occur by dislocation climb of
a single tilt boundary has been studied, first by Li and later by Doherty & Szpunar,
who arrived at an expression for the rate of subgrain rotation [31, 32]:
3γm θBb
dθ
θm
=
(1.5)
ln
dt
L2 θm
θ
where L is the height of the boundary, b is the Burger’s vector of the dislocations, and B is the mobility of the dislocations.
During a coalescence event in a recovered microstructure, the reorientation of a subgrain affects all of the N (∼12) surrounding subgrain boundaries.
The total driving force for reorientation of a subgrain is the contributions
from all its boundaries [11]:
F =
N
i=1
dγ
L2i
dθ
=
N
γm
L2i
θm
i=1
θm
ln
θ
(1.6)
From eq. 1.6 it is evident that the largest driving force will come from the
boundary with the smallest θ and the largest L, which from eq. 1.5 will have
the lowest rate of rotation. It can therefore be argued that the lowest rate
of rotation is to a first approximation the controlling rate of rotation of the
entire subgrain. It should be noted that θ and L refer not to
average
θthe
2
m
properties of the subgrain, but to the largest value of (L ln θ ), which
means that to determine the kinetics of subgrain rotation we need to know
the initial distribution of subgrain sizes and orientations, and also how these
parameters evolve as the coalescence event progresses. The usual modelling
method is to equate θ with the mean misorientation between subgrains, and
to assume that all subgrains with a diameter less than L have coalesced at
the time t, so that L2 is proportional to t [11].
The limited experimental evidence of subgrain coalescence is inconclusive.
Direct evidence of subgrain rotation has been observed , but this was from
in situ transmission electron microscopy heating experiments, where surface
effects could not be ruled out, and at a temperature close to the melting
temperature (T ≈0.9 Tm ) [11], which is a much higher temperature than the
recrystallization temperature. So far, all bulk experiments have been post
19
mortem experiments, where it is not possible to distinguish between whether
a LAGB is forming or disappearing. However, post mortem studies have
shown that the subgrain size adjacent to HAGB is larger than in the interior
of the grain, which correlates well with simulation data that predicts that
coalescence is roughly 2.5 times more likely to occur adjacent to a HAGB
than within the interior of a recovered grain (see fig. 1.2) [11].
1.2.3
Subgrain coarsening
Subgrain coarsening is an alternative mechanism by which neighboring
subgrains may merge into a critical embryo. The mechanism is believed to
be the migration of a LAGB, which can then be absorbed in another grain
boundary (see figure 1.4).
(a)
(b)
Figure 1.4: Embryo creation by subgrain coarsening: The LAGB (line from B to
C) moves (see arrow) through the left subgrain, eventually being absorbed in the
left boundary. (a) Two subgrains divided by a LAGB; (b) The two subgrains have
coarsened into one bigger subgrain (embryo) by LAGB migration [11].
Experimental evidence suggests that this process occurs primarily within
regions with large orientation gradients. In such regions statistical studies
show an increase in the mean misorientation across boundaries, and an increase in the mean subgrain size with annealing time [11].
20
1.2.4
Inverse Roland
The inverse Roland nucleation mechanism has been proposed to explain
the strong ’cube’ annealing texture (i.e., {100}<001>) in cold rolled face centered cubic (fcc) material specimens (see appendix A and B). Experimental
evidence indicates invariably that the ’cube’ texture forms during recrystallization when the rolling texture is of the ’copper’–type (i.e., {112}<111>).
The proposed mechanism was that twins produced during deformation,
could coalesce by cooperative glide on <111>–planes, i.e., glide of partial
dislocations, and the proposed twin orientations were of the {112}<111>
orientation [33]. In the absence of large (>1 µm) interstitial particles within
the microstructure (see section 1.2.6), the inverse Roland mechanism is the
only proposed nucleation mechanism, which predicts nuclei forming with
orientations, which are not already present in the parent microstructure.
However, this mechanism is not thought to work for high stacking fault
energy (SFE) metals, such as aluminium, which is also known to produce
the ’cube’ texture. Also, several materials that where predicted to produce
strong ’cube’ texture failed to do so during investigations, which has generally
caused the inverse Roland nucleation mechanism to be rejected [33]. Instead,
experimental evidence suggests that the ’cube’ annealing texture should be
explained by ’cube’ grains having a higher growth rate [34]. In general, there
has been a very long argument about the relative importance of oriented
nucleation vs. oriented growth (eg. Lücke vs. Verbraak), which has yet to be
fully resolved [35, 36, 37].
A stacking
a
fault is a rigid translation of a portion of the crystal lattice
by the 6 [112̄] –vector, where a is a crystal lattice vector. This can be
produced by plastic glide during deformation or a growth accident during
grain growth [38]. The stacking fault energy (SFE) is the energy associated
with a stacking fault on a {111} plane, and it depends on the specific volume
of the metal, and the atomic bonding. For further details, the author refers
to Haasen [15]. A short list of the SFE of various common metals is given in
table 1.1:
Ag Co
20 25
Au
40
Cu
60
Ni Al Zn
130 200 250
Table 1.1: Stacking fault energy of various common metals. The values are in
mJ/m2 , at a temperature of 300 K, and for the stable microstructure [39].
21
1.2.5
Twinning
Twinning is not a proposed nucleation mechanism in its own right, but
rather it is a process, by which recrystallizing grains may develop orientations not previously present in the parent microstructure [8, 39]. Twinning
consists of a 60◦ rotation of the crystal lattice
about a {111}–axis (equivalent
to forming a coincidence site lattice with
3), which is envisaged to occur
via a growth accident on a {111}–plane (see fig. 1.5), and it produces orientations not previously present in the parent microstructure. The possible new
orientations produced by a twinning event are discussed in appendix A.1.
During recrystallization of certain materials, particularly in fcc metals with
(a)
(b)
Figure 1.5: A stacking fault in an fcc lattice leading to twinning.
The perfect fcc ABC/ABC/. . . stacking of (a) is turned into (b) if a stacking fault
occurs, such that an expected C layer becomes an A layer instead [38].
low–to–medium SFE such as copper, annealing twins are formed.
A proposed model for the formation of annealing twins in low–to–medium
SFE metals, which is what would be seen after nucleation events, is based on
the nucleation of Shockley partial dislocation loops on consecutive {111}–
planes by growth accidents on moving {111}–steps on a migrating grain
boundary [40]. In short, the model only predicts twinning in low–to–medium
SFE metals, because the Shockley partial dislocation loops are stable there.
Furthermore, the probability of growth accidents occurring rises with increas22
Figure 1.6: Strained and misoriented zone around a rigid interstitial particle. The
zone extends ∼2d around a particle of diameter d [41].
ing grain boundary mobility, so alloying elements have a role too, since they
both lower the SFE and lower the grain boundary mobility in general.
1.2.6
Particle stimulated nucleation
Interstitial rigid particles within the microstructure can have one of two
effects on the nucleation behavior. If the particles are present as a fine dispersion of fine particles (∼0.1 µm), they will actually retard the nucleation
process, as the fine particles act as inhibitors to the movement of both dislocations and grain boundaries.
If however, the particles are sized d>1 µm they can give rise to high
local concentrations of stored energy and large misorientations in the surrounding microstructure when the particle–containing material is deformed
(see fig. 1.6), and can thus act as favorable nucleation sites. These zones of
high stored energy tend to extend ∼2d from the particle itself, which means
that the size of the zone is determined by the size of the particle [41]. There
is experimental evidence that the microstructure tends to rotate around the
particles when the particle–containing material is deformed, which depending
on strain, can create a local misorientation of 10◦ or higher to the surrounding
microstructure.
Thus if the strained region, which depends on the particle size, is larger
than the critical nucleus size, nuclei can form in these strained regions and
immediately start growing due to the misorientation to the surrounding mi23
crostructure. For elongated particles, the misorientations are greatest at the
ends of the particles, which means that any nucleation is likely to occur
there [41]. This can then give rise to nuclei with orientations not previously
present in the deformed grains away from the particles. However, truly new
orientations are not created, as the nuclei are envisaged to grow from the
highly misoriented subgrains within the strained region around the particles [23, 25, 41, 42].
1.3
Experimental techniques
A wide variety of experimental techniques have been applied to study the
processes involved in annealing and recrystallization. Macroscopically, since
recovery largely involves elimination of vacancies, the recovery process as well
as the recrystallization process may be followed by monitoring the change in
electrical resistivity [22]. The main hardness changes taking place during the
regime of recrystallization can be studied directly by hardness indentation
(see section 1.3.1) [43], and since the whole annealing process involves the
release of stored energy, calorimetry can be used to good effect throughout
all three stages of annealing [22].
Many forms of microscopy have been employed in studying recrystallization (see section 1.3.3), and much of what is known about the detailed mechanisms of recrystallization has been gleaned from studies using transmission
electron microscopy (TEM). This has been particularly useful in following
the evolution of dislocation substructures from the cold worked state to the
recovered state and then on to the nucleation of recrystallization [44]. Optical microscopy (especially using polarized light for enhanced contrast) has
been used to identify nucleation sites. Until 20 years ago scanning electron
microscopy has had only a minor role to play in recrystallization studies, but
with the advent of channelling diffraction [45], and more recently automatic
characterization of electron backscatter patterns [46, 47], one has a technique
well suited to recrystallization studies of the surfaces of metals.
X–ray and neutron diffraction have also long been used in metallurgy, but
their use has always been limited by various factors. The penetration depth
of X–rays generated by a copper or molybdenum anode is of the order of µm,
which has severely limited their usefulness for bulk studies, and in the case
of neutrons, the mm spatial resolution has limited studies to mostly strain
and texture analysis [17, 48, 49]. However, with the advent of synchrotron
24
X–ray sources, higher fluxes and energies have become available, and it has
thus become possible to perform non–destructive in situ experiments on bulk
single–phase metal and alloy samples using X–ray diffraction, due to the
massive increase in penetration depth, which is now of the order of mm (see
section 1.3.4) [50].
In order to perform a study of the nucleation of recrystallization, of the
form described in the introduction, it is necessary to characterize the deformed microstructure within a suitably large volume, so as to be reasonably
sure that at least one nucleation event will take place within that given
volume during recrystallization. Also, the characterization of the deformed
microstructure must be non–destructive, so as to not effect the subsequent
mechanism of the nucleation event(s). This basically means that we must be
able to non–destructively probe volumes sized up to 1 mm3 within a reasonable amount of time and still be able to detect and characterize new nuclei
sized ∼1 µm3 , which translates as being able to detect volume fractions down
to 10−9 .
The choice was made to study nucleation (recrystallization) using both
well tested metallurgical techniques (hardness indentation, optical and electron microscopy), and a newly–developed technique (3 Dimensional X–Ray
Diffraction). The classical approaches are to study the polished surface, or
very thin sections of samples using optical or electron microscopy. This allows a wealth of information to be obtained, but only from the surface or
thin section, and if heating experiments are involved, it is not possible to rule
out surface effects. The new technique is to use high energy synchrotron radiation to non–destructively characterize the bulk of a sample before, during
and after heating, and thus follow nucleation in situ.
1.3.1
Hardness indents
A classical way of studying recrystallization is by hardness indents, which
gives a direct measure of the recrystallization–induced softening in the material. A hardness test measures the resistance of a material to penetration
by a harder test body. Many different hardness tests exist, but they mainly
differ in the shape of the object, which is pressed into the sample. For this
PhD project, the Vickers hardness indentation test was used [43].
A Vickers hardness test consists of pressing a pyramidal diamond indentor
with an apex angle of 136◦ into the sample surface with an accurately controlled load (see fig. 1.7a) for a specific dwell time (typically 10–15 s). After
25
(a)
(b)
Figure 1.7: Vickers hardness indents. (a) the Vickers hardness indentation system [1]; (b) a single Vickers hardness indentation seen from above [51].
the pyramid is removed an indentation is left in the surface, which appears
square shaped (see fig. 1.7b). Its size is determined optically by measuring
the two square diagonals of the indentation. Because the indentation size is
measured optically, the sample surface must be pre–polished in order to get
an accurate measurement of the diagonals. The Vickers hardness HV [N/m2 ]
is a function of the test load divided by the surface area of the indentation,
which is calculated from the mean of the two diagonals. Thus HV is given
by [1, 15]:
test force
(1.7)
HV = C1 ×
(indent diagonal)2
where C1 is a function of the pyramid geometry, and the units of load and
diagonal. It is usually tabulated for a given hardness indentor. Generally,
the mean width of several indentions are used to calculate the hardness.
By annealing samples at different temperatures and for different lengths
of time, the resulting hardness curve allows one to determine at which temperature material softening (eg., recrystallization) sets in, and how quickly
it progresses. This is possible because the flow stress of a metal is the sum
of the flow stress of all its constituents, so a dramatic softening corresponds
to the transformation of the harder deformed/recovered material into softer
recrystallized material.
26
Thus from Hansen &Ṽandermeer [52]:
σf − σ0 = σr VV + σd (1 − VV )
(1.8)
where VV is the volume fraction recrystallized of material, σf , σ0 , σr , and σd
are respectively the flow stress, the lattice friction stress, the flow stress of the
recrystallized material, the flow stress of the deformed/recovered material.
1.3.2
Optical microscopy
Optical microscopy consists of studying back–reflected light from polished
(and often chemically etched) surfaces of metal samples. By using polarized
light, after anodization of the polished surface, it is often possible to clearly
distinguish between regions of different crystallographic orientation. The
size, shape, and location of individual grains or groups of grains may be
determined, but the crystallographic orientation of the individual grains is
not determined directly.
1.3.3
Electron microscopy
Scanning electron microscopy (SEM) has been used extensively to characterize the microstructure of metal samples in this thesis. In SEM an electron
beam impinges upon the surface of a sample, and information is obtained
from the backscattered electrons as well as the emitted X–ray photons. In
modern scanning electron microscopes, the spatial resolution may be as good
as ∼10 nm.
The microscopy technique of choice during this PhD project has been the
electron backscatter patterns (EBSP) technique, where the electron beam is
diffracted according to Bragg’s law (see eq. 2.1). It is a technique by which a
scanning electron microscope may be used to characterize the microstructure
of a sample based on crystallographic analysis, and it is based on analyzing
the electrons elastically scattered, from different crystal planes, onto a 2D
detector. A beautiful example of an EBSP image can be seen on figure 1.8.
It is a quantitative technique that reveals grain size, grain boundary character, grain orientation, texture, and phase identity from the polished surface
of metallurgical, ceramic, and geological samples. Depending on the scanning
electron microscope used, the technique enables analysis of up to cm–sized
27
Figure 1.8: High–quality EBSP image from silicon [2].
samples with grains varying in size from the nm to mm range, and the angular resolution can be as good as ∼0.5◦ [47, 53]. For an overview of the EBSP
technique the author refers to the following references [46, 47, 54, 55, 56].
1.3.4
X–ray diffraction
3 dimensional X–ray diffraction (3DXRD) has been used for in situ studies of nucleation. 3DXRD is a technique developed in recent years by the synchrotron group within the Center for Fundamental Research: Metal Structures in Four Dimensions 4 (Metals–4D center) [21, 57].
It is based on diffraction of high energy (40–100 keV) X–rays. Within this
energy range, kinematical scattering theory (i.e., X–rays are only scattered
once within the sample) generally applies. Furthermore a 10% transmission through metal samples is possible in mm–sized samples (see figure 1.9),
which is generally the minimum acceptable transmission in order to perform
scattering experiments on bulk samples [58].
4
http://www.metals4d.dk
28
Figure 1.9: 10% transmission of X–rays through matter at 50 keV and 80 keV for
selected elements. The penetration data for elements symbolized by refer to the
use of an X–ray energy just below the absorption K–edge of the element [58].
Since X–ray diffraction is a non–destructive technique, 3DXRD allows us
to non–destructively probe the bulk of metal samples, and thus follow bulk
kinetics in situ. For an overview of X–ray diffraction and absorption the
author refers to the following references [12, 21, 38, 49, 59, 60].
A considerable number of different studies have so far been performed using the 3DXRD microscope including strain analysis, grain boundary mapping, 3D grain maps, deformation studies, grain growth during recrystallization, subgrain growth, recovery, phase transformations, and spatial and
crystallographic characterization of single grains [4, 50, 61, 62, 63, 64, 65, 66,
67, 68, 69].
3DXRD microscopy is perfectly suited for in situ studies of nucleation,
which is a ”needle–in–the–haystack” problem, as the fractional volume detection limit can be as low as 10−9 , which would allow the detection of a
1 µm3 nucleus within the bulk of a 1 mm3 volume.
29
Chapter 2
Techniques employing
microscopies of various kinds
Optical microscopy (OM) and electron microscopy (EM) of polished surfaces have been instrumental in studying metal microstructures since the
beginning of modern metallurgy. Both have been used extensively during
this PhD project.
This chapter is divided into three parts: an introduction to optical microscopy; an introduction to the electron backscatter patterns (EBSP) technique; and lastly, an introduction to serial sectioning, as well as results obtained.
2.1
Optical microscopy
Optical microscopy (OM) amounts to studying samples in a microscope
under visible light. Preparing surfaces for optical microscopy is a much simpler process than for electron microscopy (see section 2.2), and much larger
areas may be observed. However, the best achievable theoretical spatial resolution is limited by the wavelength of visible light (∼0.5 µm), and the crystal
orientation of the observed grains is not determined directly.
OM has been used for many studies were it was not important to know
the crystal orientations within the sample. It is typically also an important
step in sample preparation, as the sample surface is inspected by optical
microscopy after each polishing step.
30
The optical microscope used was a Leitz Aristomet reflection microscope.
It had a choice of six objective lenses, which together with the ocular gave a
magnification range of ×10 to ×1583, which allows the distance between lines
(on a scale inserted into the microscope) to be as small as 1 µm. Halogen or
zenon light (top or bottom incidence) was available, as well as a polarizing
filter, phase contrast, and darkfield imaging. A Leica DC300 V2.0 CCD–
camera controlled by Leica IM500 framegrabber software, is installed on the
microscope.
2.2
Electron microscopy
The electron microscopy (EM), which has been performed during this
PhD project has almost exclusively been scanning electron microscopy (SEM),
where the technique of choice has been the electron backscatter pattern
(EBSP) technique, which will be described below. A short overview of EBSP
will be given here, but for further reading the following references are recommended [53, 70, 71]. The set–up of a typical EBSP system can be seen in
figure 2.1.
In the SEM, the electron beam is brought to impinge on the specimen
surface at a sharp angle ∼20◦ . The primary electrons from the electron beam
penetrate into the sample and are subject to diffuse inelastic scattering in all
directions, and in a crystalline sample a fraction of these electrons will have
an angle of incidence to the atomic planes, which satisfies Bragg’s law:
nλ = 2 dhkl sin θ
(2.1)
where n (positive integer) is the order of the reflection, λ is the electron
wavelength, dhkl is the distance between crystal lattice planes with Miller
indices {hkl}, and θ is the diffraction angle. The energy loss of the electrons
due to the inelastic scattering is negligible (of the order of 100 eV), so we
may to a first approximation assume that the energy of the electrons is
unchanged, and thus the wavelength of the electrons is given by the de Broglie
wavelength [17, 38]:
12.3
h
≈√
λ=
(2.2)
mv
V + 10−6 V 2
where λ is the wavelength (in Å), h is Planck’s constant, m is the electron
mass, v is the electron speed, and V is the accelerating voltage (in V ). Thus,
31
electron beam
phospherous screen
dhkl
Kikuchi cone
2θ
set of lattice planes
crystal
b
R
Figure 2.1: Illustration of the geometry of a typical EBSP system. 2θ is the
opening angle of a Kikuchi band, dhkl is the distance between the crystal lattice
planes, R is the sample to screen distance, b is the distance between two Kikuchi
lines from the same band, and the dashed line is the intersection of the crystal
lattice plane with the screen [70].
for an accelerating voltage of 20 kV, the electrons will have a wavelength of
0.085 Å, and from eq. 2.1 we see that diffraction angles are of the order of 1◦ .
Since the electrons initially exhibit all directions, the diffraction from a
set of parallel planes will have a fixed angle θ to the planes and therefore be
in the form of the two Kikuchi cones emitted from the diffracting volume (see
fig. 2.1). Because of the low Bragg angles (∼1◦ ), the two cones will appear
as a pair of Kikuchi lines (also called a band) on the screen instead of as
hyperbolas.
Each pair of lines are the result of electrons being diffracted from one
particular set of atomic planes in the crystal, and the intersection of the plane
with the screen is a line, which is located very close to the center between the
two Kikuchi lines. The distance b between two Kikuchi lines on the screen
is roughly proportional to the diffraction angle θ and the sample–to–screen
distance R (b = 2R sin θ ≈ 2Rθ), which readily allows the {hkl}–family of the
diffracting plane to be determined from equation 2.1. Also, the intensity of a
particular band relative to the intensities of the other bands can be predicted
32
from the structure factor of the material (I ∝ |Fhkl |2 ), which is used along
with the diffraction angle when assigning Miller indices (hkl ) to the observed
Kikuchi bands in the EBSP.
Experimentally, a video camera or a CCD–detector is coupled to the
phosphorous screen, generating a digitized EBSP image. The EBSP are extracted from the images by an image analysis technique known as the Hough
transform [72]. If several sets of bands are obtained and indexed (i.e., their
(hkl)–values are determined) from the same spot, it is possible to determine
the crystal orientation of the volume struck by the electron beam. In order
to reliably determine the crystal orientation of a volume by the use of successfully indexed Kikuchi bands, experience dictates that at least 5 out of 8
eight detected bands are successfully indexed with the same orientation [72].
The electrons forming the EBSP originate from a small volume below the
surface, where its depth below the surface is of the order of 20 nm for an
accelerating voltage of 20 kV, so the information obtained is basically from
the surface region. This thin layer must be clean and with a relatively low
dislocation density, which requires the surface to be mechanically polished,
and often electrochemically polished as well, to remove any surface deformation. By scanning over the surface of the sample it is possible to produce 2
dimensional crystallographic orientation image maps [73], which clearly show
the surface microstructure of the sample (see fig. 3.1). This technique is a
”workhorse” in modern metallurgy, where the EBSP data is often complimented by energy dispersive spectroscopy, where characteristic X–ray peaks
are generated by the interaction of the electron beam with the sample and
the relative intensities of the peaks gives the concentrations of each element
in the material being studied. These systems, coupled to computer materials
data bases, can be used to yield phase maps of inspected samples [47].
2.3
Serial sectioning
Serial section is a method by which 3 dimensional microstructures may
be reconstructed from data obtained by surface techniques, such as OM and
EBSP. This is important, because the structures (eg. grains) are really 3 dimensional objects, which are generally studied by microscopy on 2 dimensional surfaces. In serial sectioning, stacks of closely–spaced parallel surfaces
(sections) are inspected by microscopy, and by using purpose–written software, it is possible to layer the sections on top of one another and thus
reconstruct the 3D microstructure [74, 75, 76].
33
The biggest challenge in performing serial sectioning is in producing polished sections, which are parallel enough and where the distance between
sections is small and constant enough. Typically, the required flatness and
depth control is 1–2 µm [77, 78]. It was the task of the author to device a
system, which could satisfy these criteria, as well as polish a sample down
to any target depth with the same precision. The polishing system of choice
was the ’Logitech PM5D polishing and lapping system’, who’s construction
guaranteed the sample flatness, and which included the ’PSM1 position sample monitor’ that determines the amount of material removed during lapping [79]. The user manual, written by the author, is inclosed in this thesis
as reference [A3].
It has been proven possible to polish samples down to a pre–specified target depth with an accuracy of 1–2 µm and the same degree of flatness, and it
has also been proven possible to consistently serial section samples in 2 µm
steps. After electrochemical polishing the resulting surfaces have then been
suitable for EBSP studies. However, flawless mirror–like surfaces have been
somewhat harder to obtain through mechanical polishing alone, due to the
fact that the Logitech PM5D is placed in a normal laboratory, and contamination of the polishing surface by hard particles can therefore be a problem.
Sectioning of copper samples at an early stage of recrystallization has
shown that volumes around triple junctions are the dominant nucleation
sights in non–particle containing metals, which is also supported by the literature [3, 11, 30]. Sectioning of aluminium samples has shown that nucleation
kinetics might vary slightly near the surface from that in the bulk [A5].
Serial sectioning and EBSP 2D mapping with a group of students from
Roskilde University has created 3D grain maps [80]. This work was a successful preliminary study, which has lead to a direct mapping of the same
microstructure by both EBSP and 3DXRD [81].
Also, the author has collaborated with a European group studying precipitates in supercooled liquids containing 58% Cu and 42% Co [82]. The
author’s task was to instruct and supervise S. Curiotto, a PhD student from
the University of Turin, Italy, who performed serial sectioning on Cu–Co samples. Optical microscopy was used to observe the structures, which consisted
of Co spheres and dendrites.
34
Chapter 3
Recrystallizing microstructures
studied by stereology
Stereology is an efficient tool for statistical studies of recrystallization
kinetics, based on traditional techniques employing microscopy on polished
surfaces. ”Stereology is a mathematical science, which deals with inferring
(n+1) dimensional information from observation at the n’th level” [83], or
in other words, it establishes 3-dimensional properties of a material from
0, 1, or 2–dimensional measurements performed on polished planar surfaces
(eg. volume fractions, grain size, grain shape etc.) [84].
Recrystallization kinetics can be studied by studying the polished surfaces of samples, cut from the bulk of a series of specimens and heat treated
to various fractions of recrystallization. From these surfaces, critical microstructural properties can be determined stereologically:
VV — the volume fraction recrystallized;
SV — the interfacial area (grain boundary) density separating recrystallizing
grains from deformed volumes;
<λ> — the mean recrystallized grain intercept length.
These properties are of special interest, because the average growth rate
of the recrystallizing grains may be determined by using for example the
Cahn–Hagel method (see section 3.1) [85]. Also, it may be possible to determine the nucleation rate as a function of time using microstructural growth
path modelling [86, 87].
35
The properties are often determined by the linear intercept method (see
section 3.1), and if EBSP (see section 2.2) is used, the properties of the individual texture components may be determined. Generally, EBSP studies
have been performed by experts using subjective means to distinguish between different recrystallized grains, and the deformed material [34]. Also,
previously an automatic technique based on EBSP, utilizing line scans consisting of one scanned line was found to yield a precise determination of VV ,
but SV was typically an order of magnitude off [88]. A new automatic technique based on EBSP has been envisaged, and developed by the author [A1].
It is based on quasi–line scans consisting of 3 parallel lines of equal length,
and with a mutual distance equal to the line scan step size. This method
has the advantages of only scanning lines (short measuring times, and good
statistics), while being automatic (i.e., objective) and making use of the
principle of connectivity to avoid errors [89]. An other advantage of scanning
random lines is that this takes microstructural anisotropies into account.
Another line scan method for quantifying recrystallization using EBSP
has recently been published [90]. It is based on measuring the fractional
changes of the HAGB–fraction of boundaries along a line through the microstructure. It can be used to determine VV , but no information is provided
about SV and <λ>.
The chapter is divided up into three parts and is largely based on reference
A1. The first part deals with how critical parameters, which describe the
recrystallizing microstructure, may be determined by line scans through the
microstructure. The second part describes the automatic line scan method,
which was developed by the author. It consists of an alternative way of
performing line scans, and a data analysis program called LSGRAINS, which
interprets the experimental data. The third part deals with the validation of
the 3–line technique, and various results obtained using it.
3.1
Studies of recrystallizing microstructures
An efficient way of studying the microstructural properties described in
the previous section by stereology, is by scanning the microstructure along
random lines through the microstructure, using the linear intercept method.
Random lines are drawn through the microstructure, and the intersections
between different recrystallized grains, and between grains and the deformed
microstructure are noted. An example of this can be seen on figure 3.1, which
is an EBSP orientation image map (OIM) [73].
36
Recrystallized grains
Deformed matrix
Grain grain interface
Deformed recrystallized
interface
Figure 3.1: EBSP OIM showing a partially recrystallized microstructure with two
random lines drawn through it. Examples of recrystallized and deformed grains
are identified by the red arrows, and where the drawn lines cross an interface this
is marked: orange for a recrystallized–recrystallized interface, and white for a
deformed–recrystallized interface. The colour of the individual grains corresponds
to their crystal orientation [A1].
With the linear intercept method it is easy to determine the three parameters VV , SV , and < λ >, described in the previous section, which are
important when studying recrystallizing microstructures [34]:
Lrex
L
2×nint
SV =
L
N
1 λi
<λ> ≡
N i=1
VV
=
(3.1)
(3.2)
(3.3)
where L is the total length of the scanned line, Lrex is the total length of
37
the line in recrystallized material, nint is the number of interfaces between
recrystallized and deformed material crossed by the line, N is the number
of grains intersected by the line, and λi is the intersect length of the i’th
recrystallized grain.
If these parameters are determined for a series of samples, annealed for
different periods of time at the same temperature, it is possible to study
the recrystallization kinetics at that temperature. Following the work of
Cahn & Hagel, the overall deformed–to–recrystallized material transformation rate may be written as [85]:
dVV
= <G> ·SV
dt
(3.4)
where <G> is the average growth rate of the recrystallizing grains (G = dR/dt),
and R is their radius. If the recrystallized grains are distinguished based on
which crystallographic texture component they belong to (see appendix B),
as is possible by EBSP, the average growth rate for the texture components
is also determined [34].
The main difficulty related to using the linear intercept method is insufficient statistics, since ideally hundreds of different grains scattered over a large
area must be probed in order for the approach to be statistically viable. The
demand for different grains is often a problem, since the typical approach is
to perform a 2 dimensional scan, and then trace random lines across it while
noting down changes in the microstructure. However, the number of sampled
grains remains relatively low. This difficulty is aggravated when individual
texture components are studied, because doing so only uses a fraction of all
the intercepted grains.
Line scans can be performed by optical microscopy on polished surfaces,
which may be photographed, and the linear intercept method may be applied
with a ruler and a pencil. However, the crystal orientations of the intercepted
grains are not determined directly. An alternative way, is by using the EBSP
system in a SEM (see section 2.2). The EBSP are monitored on the computer
screen while the sample is translated beneath the electron beam. This form
of data acquisition is slow, subjective, and tiresome in the extreme, but
the crystal orientation is also determined. A fast, automatic, and objective
method, which consisted of a data acquisition procedure, and a corresponding
analysis program, was developed by the author (see section 3.2).
38
3.2
LSGRAINS
The automatic method, which will be denoted as the LSGRAINS method,
for obtaining quantitative recrystallization parameters, is a line scan method
based on the EBSP technique, scanning not one but three parallel lines, with
a mutual separation equal to the line scan step size. Examples of the form
of 3–line scans can be seen in figure 3.2a–c.
(a)
(b)
(c)
Figure 3.2: Orientation image map of 3–line scans (3×50 steps, 1 µm step size)
of AA1050–aluminium sample at various annealing times. The black lines indicate
misorientations θ with θ≥1.0◦ between neighboring data points, and black spots are
”bad” data points. The colour of the individual grains corresponds to their crystal
orientation. The samples were annealed in an oil bath at 250◦ C for respectively:
(a) 300; (b) 2,000; and (c) 28,000 s [A1].
The method has the advantage of scanning lines (i.e., short measuring
time, or alternatively good statistics), while making use of the principle of
connectivity, where adjacent data points of the same crystal orientation are
grouped together into grains, to avoid errors [89]. Two adjacent data points
are considered connected if their orientations are equivalent, i.e., their misorientation θ is lower than some cut–off angle, which is usually set to the resolution of the EBSP system (normally θ≤1◦ ). The 3–line data is interpreted
by the computer program LSGRAINS, which was developed specifically for
3–line EBSP scans. The LSGRAINS algorithm is described in detail in article A1, but in this section an overview of the most important concepts will
be given.
39
The LSGRAINS algorithm interprets EBSP data in the form of 3–line
scans, and the central line is the main source of data, while the upper and
lower lines are auxiliary lines, which assist the computer algorithm in calculating which parts of the microstructure are recrystallized and which are
deformed, based on data point connectivity. The data points on the central line are compared to all their surrounding data points (see the arrows
on figure 3.3), and comparisons between data points are used to group data
into recrystallized grains and deformed material. When the data points have
finally been grouped into individual recrystallized grains and deformed regions, the recrystallization parameters are calculated using eq. 3.1–3.3, giving
a reliable and time–efficient measuring technique.
A[0,i-1]
n.n.n.
A[1,i-1]
n.n.
A[2,i-1]
n.n.n.
A[0,i]
n.n.
A[1,i]
A[2,i]
n.n.
A[0,i+1]
n.n.n.
A[1,i+1]
n.n.
A[2,i+1]
n.n.n.
Figure 3.3: Connectivity around the i’th data point on the central line. The arrows
indicate which neighboring data points are compared with the i’th data point. If
the i’th and (i-1)’st data points are both recrystallized and of the same orientation,
then they are connected, and both data points thus belong to the same grain. nn and
nnn are respectively the nearest and next nearest neighboring data points adjacent
to the i’th data point [A1].
More specifically, the algorithm runs through a series of iterations (see
fig. 3.4), which test for/implement the various criteria that recrystallized
grains must fulfill, as set down by the operator of the program. The algorithm
has been made to run with all the routines, but some may be omitted at the
discretion of the operator (see sec. 3.3.1a). From figure 3.4 it is seen that the
data is run through some of the iterations more than once, which constitutes
a refining process of the microstructure derived from the experimental data.
40
1.
2.
4.
Read and validate data.
Do connectivity for all data
points on the central line.
Repairs ‘bad’ data
points (where possible).
3.
Combine data points into
individual recrystallized
grains and deformed regions.
6.
Discard too short
recrystallized grains
and deformed areas.
5.
Check if grain boundaries
are of high angle.
7.
Final subdivision into invidual recrystallized grains
and deformed regions.
8.
Determine Lrex , λi , and nint
based on the interfaces
in the microstructure.
9.
Sort recrystallized grains
into texture components:
‘cube’, ‘rolling’, ‘random’
Calculate statistics for
the microstructure:
* Vv
* Sv
* <λ>
9.
Calculate statistics for
the texture components :
* Vv
* Sv
* <λ>
9.
Figure 3.4: Flow diagram of the LSGRAINS algorithm. The iterations are numbered for easy reference.
1. Initially, the EBSP data is read from a long string file and ordered into
an array with dimensions (3 × npoints ), and every data point is checked
to see if it satisfies the minimum acceptable successfully indexed EBSP
Kikuchi bands (normally 5). Those that do are considered indexed and
are termed ”good”, while those that do not are considered non–indexed
and are termed ”bad”. The first and the last data point on the lines
are not used!
41
2. All ”good” data points (see above) are checked for equivalence with all
their neighboring data points (see arrows in fig. 3.3). Data points,
which have the acceptable minimum number of neighbors (normally
4), are considered as belonging to a recrystallized grains (”rex”), and
those that do not are considered as belonging to the deformed matrix
(”def”). Every data point is then given an ID–number to define its
status: ”rex” (positive integer), ”def” (-1), or ”bad” (0). Note that
when iteration 2 is run again after the repair routine (iteration 4, see
below), only ”good” data points exist (i.e., ”rex” or ”def”).
3. ”rex” data points (positive ID–number) are combined into recrystallized
grains if they are adjacent to each other and their orientations are
equivalent (i.e., the misorientation is smaller than ∼1◦ ), while data
points with ID–number equal to -1 and 0 are grouped into deformed
regions between the recrystallized grains. This gives a first rudimentary
picture of the microstructure.
4. This iteration attempts to repair every ”bad” data point (ID–number=0)
on the central line, by allocating a new good orientation to the data
point, with preference to the orientation of a neighboring grain. This
is done by using the rudimentary picture of the microstructure from
iteration 3. If a dominant orientation exists around a ”bad” data point
(see arrows in fig. 3.3), the ”bad” data point assumes this orientation
and becomes a ”good” data point (ID–number=positive integer). In
order to be able to define a dominant orientation surrounding the ”bad”
data point, a minimum number of neighboring data points with the
same orientation (normally 2) must exist. If this is not the case, the
”bad” data point becomes a ”def” data point (ID–number=-1).
5. This iteration checks the boundaries of each grain to ascertain if at least
one them is of high angle (normally, θ ≥15◦ for grain–deformed or θ ≥2◦
for grain–grain boundaries). A grain that does not satisfy this criteria
is rejected as a large sub–grain, and the data points of the grain are
relabelled to ID–number=-1.
42
6. To limit fictitious interfaces arising from small grains and deformed regions, which are considered too small (normally smaller than 3 times
the scan step size), are relabelled. Based on mutual misorientations
(normally, if θ <2◦ ) small grains are joined into larger grains or relabelled as deformed, and small deformed regions are added to the
adjacent grains. This iteration is necessary to avoid adding fictitious
grain–grain and grain–deformed interfaces to the microstructure, which
is a critical parameter for calculating SV and <λ>.
7. The final subdivision into recrystallized grains and deformed regions is
determined in the same fashion as in iteration 3. From this the location
and nature of all the boundaries of the grains are determined, as well
as which of the texture components ’cube’, ’rolling’, or ’random’ the
grains belong to (see appendix B).
8. The nature and location of the grain boundaries are used to calculated
the number of grain–grain and grain–deformed interfaces, the number
of grains, as well as the intercept length of each grain, and the total
summed length of the recrystallized grains.
9. Lastly, from equations 3.1–3.3 the recrystallization parameters VV , SV ,
and < λ > are calculated for the full microstructure and for each of
the texture components, as well as grain contiguity, grains size distribution, and a distribution of the length of deformed material between
recrystallized grains.
The following are the user–set parameters in the algorithm. These parameters have default settings, but the parameters need to be set and tested
for each series of experiments if a different material is used. This can be done
by comparing the algorithm’s results with what is obtained from inspecting
the OIM of a 3–line scan (see section 3.3.1). Below is a list of the parameters,
their capital letter codes, and their default values for aluminium:
M — min indexed bands: minimum number of correctly indexed Kikuchi
bands from the EBSP required for a data point to be ”good” (default: M=5).
C — min data point connectivity : minimum number of equivalent data
points around and including data point A[1, i] required for a data point
to be termed ”rex” (default: C=5).
43
D — max misorientation: maximum allowed point–to–point misorientation between data points of the same orientation (default: D=1.0◦ ).
X & Y — min boundary misorientation: minimum accepted misorientation across a ’high’ angle boundary (default: X=15.0◦ for grain–
deformed, and Y=2.0◦ for grain–grain boundaries).
L — min grain intercept length: minimum accepted intercept length in
data points of a recrystallized grain along the line
(default: L=3 for 1 µm steps).
I — min deformed region intercept length: minimum accepted intercept length in data points of a deformed region along the line
(default: I=3 for 1 µm steps).
N — min equivalent neighbors: minimum number of neighboring data
points of equivalent orientation needed to repair a ’bad’ data point
(default: N=2 data points).
R — repair : should LSGRAINS try to repair ’bad’ data points (default: R=YES).
B — check boundaries: should LSGRAINS check the grain boundaries
of each grain to see if it has at least one is of high angle (default: B=YES).
In general, the stricter the requirements that are placed on data to be
accepted as coming from recrystallized grains, the lower VV will of course
be. Discarding grains may cause SV to go either up or down, generally
depending on the degree of recrystallization in the scanned material. This is
because the number recrystallized–deformed interfaces depends on the local
microstructure around the discarded grains, so discarding a grain may do
anything in between removing or creating two interfaces. < λ > generally
goes up with stricter requirements because only bigger and more developed
grains are likely to satisfy stricter criteria.
44
3.3
Results and discussion
In this section the 3–line technique, with its corresponding analysis program LSGRAINS, is validated by comparison with three different techniques
(see section 3.3.1). Also included is an experimental investigation of recrystallization kinetics at the surface and in the bulk, which was performed using
LSGRAINS (see section 3.3.2) [A6].
3.3.1
Validation of the LSGRAINS technique
The automatic LSGRAINS line scan technique was validated by comparing the results obtained using the LSGRAINS method with results obtained
by using other and significantly slower manual scanning methods, who’s results are considered correct, on the same specimens. One–to–one comparisons, and the resulting graphs were used to determine whether the automatic
method gives viable results.
The material used in the validation studies was AA1050–aluminium (99.5%
pure), and was chosen because it had previously been used for extensive characterization and modelling [91]. In cases (a) and (c), the material was cold
rolled 90%, and then annealed in a 250◦ C oil bath for 300, 2,000, 11,000,
20,000, 28,000, 38,000, 55,000, 72,000, and 86,400 seconds. In case (b), the
aluminium was cold rolled 60%, and then annealed for 1 hour in an air furnace
at 550◦ C, producing a fully recrystallized sample.
After annealing the RD–ND surface (see appendix A) of the samples was
mechanically and electrochemically polished to produce a surface suitable
for EBSP measurements. For long scans (length=1000+ µm), the flatness of
the sample surface is critical, as a non–flat surface may move out of focus in
the SEM. The samples were therefore mechanically lapped and polished on
a Logitech PM5D lapping and polishing machine, giving a height difference
of only 1–2 µm across the sample surface. Finally, the samples were electrochemically polished for 40 seconds at 12 V. The sample was used as anode,
aluminium was used as cathode, and an A2–solution was used as electrolyte1
before they were studied by EBSP [92, 93]. In all cases a JEOL–840 scanning
electron microscope with a LaB6 –filament was used to collect the EBSP data.
The working distance was 22 mm, the electron beam current was 280 µA,
and the voltage was 20 kV.
1
A2: 12% H2 O, 70% ethanol, 10% ethylene glycol monobutyl ether, and 7.8% HCl.
45
Three different comparisons were performed to validate LSGRAINS:
(a) To test that the LSGRAINS algorithm performed as required, short
(200 steps) scans were performed on samples annealed for 300, 2,000, and
28,000 seconds. Their OIMs were plotted on paper, and misorientations with
θ≥1◦ were marked by black lines (see figure 3.2). Other plots were made with
lines drawn for misorientations greater than 2◦ and 15◦ so as to allow high
angle boundaries to be identified. The identification of recrystallized grains
could then be performed both by the algorithm, and by visually performing the same calculations, as the algorithm would do, on the OIM. Diagonal
data point connectivity is very difficult to visually discern on OIMs, so it was
chosen to omit repair of bad data points, and not to ignore short deformed
regions. This ensured that exactly the same criteria were used to define a
recrystallized grain with the two procedures. The results of the comparison show excellent agreement (see table 3.1). The very slight scatter in VV
and < λ > comes from the slight uncertainty when measuring longer grain
lengths on the paper printouts. Also, only grains intersected by all three
lines were indexed by the algorithm as recrystallized grains. This indicates
that the chance of accidentally indexing cells within the deformed matrix as
recrystallized grains is very low.
Time (s) VV vis
300 0.05
2,000 0.04
28,000 0.66
VV auto
0.04
0.04
0.67
SV vis
0.05
0.04
0.11
SV auto
0.05
0.04
0.11
<λ>vis
3.5
3.5
14.6
<λ>auto
4.0
4.0
14.8
Table 3.1: Short line scans — 3×200 data point line scans with a step size of 1 µm
were performed on the 300; 2,000; and 28,000 s samples. The chosen parameters
were: M=5, D=1.0◦ , C=5, L=3, I=1, R=NO, B=YES, Y=2◦ , X=15◦ [A1].
(b) Two 3–line scans were extracted from a large 2 dimensional EBSP
map, which was performed on a fully recrystallized microstructure, where it
was possible to identify the recrystallized grains by direct visual inspection of
the OIM. This allowed a more direct comparison than in (a), and importantly
allowed a test of how well the method handled samples with VV =1.0 and
SV =0.0 (fully recrystallized). The results generated by the algorithm were
compared directly with the results of the visual inspection (see table 3.2),
and the results again show excellent agreement.
(c) For the chosen material (see below), a previous stereological study
had supplied values for VV , SV , and <λ> for a large range of annealing times
46
Scan
middle
top
VV OIM
0.98
1.00
VV auto
0.99
1.00
SV OIM
0.01
0.00
SV auto
0.01
0.00
<λ>OIM
48.2
59.6
<λ>auto
45.8
59.6
Table 3.2: Extracted line scans — 3×169 data point line scans with a step size
of 5 µm were performed on the 300; 2,000; and 28,000 s samples. The chosen parameters were: M=5, D=1.0◦ , C=5, L=1, I=2, R=YES, B=YES, Y=2◦ ,
X=15◦ [A1].
using the manual line scan method [91]. The corresponding parameter values
obtained with the LSGRAINS technique therefore needed to be statistically
viable to allow a comparison between the two methods. For practical reasons, the criteria for a statistically viable data set was set to 100+ detected
recrystallized grains. When single scans did not yield a 100+ grains, additional scans were performed, and the weighted average of the scans was used
(based on the scan length for VV and SV , and the number of grains for <λ>).
The results of the automatic method on the same specimen were compared
to the results of the manual scans (see table 3.3 and fig. 3.5).
Time (s) VV man
300
0.02
2,000
0.07
11,000
0.22
20,000
0.60
28,000
0.21
38,000
0.37
55,000
0.78
72,000
0.96
86,400
0.87
VV auto
0.03
0.05
0.22
0.89
0.43
0.43
0.93
0.64
0.89
SV man
0.02
0.05
0.09
0.06
0.05
0.05
0.03
0.02
0.05
SV auto
0.02
0.03
0.08
0.05
0.09
0.08
0.03
0.10
0.05
<λ>man
2.6
3.5
5.8
14.2
6.9
13.5
23.8
18.1
16.7
<λ>auto
3.7
4.3
7.1
12.8
8.5
14.5
16.7
13.1
15.2
Table 3.3: Long line scans — 3×1000+ data point line scans with a step size of
1 µm were performed on all the samples. The table shows the automatic vs. the
manual results. The automatic results were based on the following choice of parameters: M=5, D=1.0◦ , C=5, L=3, I=3, R=YES, B=YES, Y=2◦ , X=15◦ [A1].
47
Sv_man
Sv vs. Vv
0.12
Sv_auto
0.10
0.08
Sv
Vv
Vv vs. time
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0.06
0.04
Vv_man
0.02
Vv_auto
0.00
0
20000
40000
60000
Time (seconds)
80000
0
0.2
0.4
Vv
0.6
0.8
1
(b)
(a)
<L>_man
<L> vs. time
25.0
<L>_auto
<L> (microns)
20.0
15.0
10.0
5.0
0.0
0
20000
40000
60000
80000
Time (seconds)
(c)
Figure 3.5: The results from comparing long manual and automatic scans.
(a) VV vs. time; (b) SV vs. VV ; (c) < λ > vs. time. Parameters were: M=5,
D=1.0◦ , C=5, L=3, I=3, R=YES, B=YES, Y=2◦ , X=15◦ [A1].
3.3.2
Depth–dependent nucleation kinetics
The 3–line scanning technique has been used in studies of possible differences between nucleation close to the surface and in the bulk of 90% cold
rolled Al–2S aluminium [A6].
The VV and < λ > curves were identical in both samples. However, in
the bulk microstructure samples, the maximum of the SV vs. VV curve was
located at VV =0.47, and in the surface microstructure samples, it was found
that the maximum of the SV vs. VV curve was located at about VV =0.5 (see
fig. 3.6). The difference between a maximum in SV at a VV –value of 0.47
48
and 0.5 may not be significant, or it might perhaps suggest that there is a
slight difference in the nucleation kinetics at the surface and in the bulk, as
a maximum SV at lower VV generally implies clustered nucleation, whereas
a VV value near 0.5 is typical for a random distribution of the nuclei. This
could indicate that the nuclei in the bulk are clustered, while the nuclei at
the surface are more randomly distributed.
Sv
Sv vs Vv
0,25
Bulk
0,20
Surface
0,15
0,10
0,05
0,00
0
0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9
1
Vv
Figure 3.6: SV vs. VV curve from article A5. The large scatter in the data, due to
limited sampling statistics, is quite normal in metallurgy. The solid lines indicates
fits to the data. The maximum of SV is located at respectively 0.47 and 0.5 in the
bulk and surface microstructure samples [A6].
49
Chapter 4
Nucleation of recrystallization
studied by X–ray diffraction
This chapter on 3 dimensional X–ray diffraction (3DXRD) studies is divided into four main sections. The first deals with the general properties
of the 3DXRD microscope. The second deals with the nucleation experiment, which was carried out by the author, and where the primary weight
of this PhD project lies. The third deals with the results obtained from the
nucleation experiment, and the fourth contains a discussion of the results
obtained.
In this thesis no distinction will be made between the terms diffraction
spot and reflection. Also, the term pole will often be used in short for a
diffraction spot/reflection arising from one of the deformed parent grains.
When dealing with Miller indices, the following notation is traditionally applied and will be used here [68]: (hkl) is a specific direction; {hkl} is a set of
equivalent lattice planes; and <hkl> is a set of equivalent directions.
3DXRD is based on the rotational diffraction method, where the sample is irradiated by a monochromatic X–ray beam, which is diffracted as it
passes through the sample [21, 38]. The sample is rotated around an axis
perpendicular to the X–ray beam (the vertical axis), and at each angular
position, the sample is oscillated around the rotation axes while a diffraction image is collected on a 2 dimensional detector oriented perpendicular to
the beam (see fig. 4.1). Using the in–house software GRAINDEX [94], the
individual crystal orientations of up to thousands of crystal grains may be
determined at the same time (see section 4.2.3.5). Due to the high X–ray
50
Illuminated volume
NSNS N SN
e
reflection
reflection
X-ray beam
-
S NS N SN S
Sample
electron beam
crystallite
reflection
Slit #1
Slit #2
Focal Point
Furnace
white
X-ray beam
Bent Laue crystal
Curved multilayer
2θ
ω
z
sample
ω
ω
y
y
η
x
z
beam
stop
x
2 dimensional
detector
(undulator)
-5400 cm
-2600 cm
-210 cm
-150 cm
-25 cm
-10 cm
0 cm
34 cm
Figure 4.1: The 3DXRD microscope. The white beam was monochromated and
focused vertically by a bent Laue-crystal, and then focused horizontally by a curved
graded multilayer. In the experiment, the beam focus was in front of the sample
and the beam profile was defined by slit # 2.
energies, kinematical scattering theory1 may be used, even in mm–sized bulk
samples, and because the scattering angles are small, it is possible to obtain
sufficient structural information for most experiments with a fixed position
of a flat detector.
The experimental data from 3DXRD is very similar to that obtained from
X–ray powder diffraction (see figure 4.2a–c). Each crystal grain gives rise to
a set of reflections, and since a polycrystal is essentially a coarse powder
fused together, the reflections from the differently–oriented grains produce a
basic powder diffractogram (see fig. 4.2a), but which is made up of discrete
discernable diffraction spots (see fig. 4.2c). If the sample is deformed, the
mosaic spread of the grains increases and the diffraction spots spread out
1
In kinematical scattering theory, individual X–rays are assumed to be scattered only
once within the sample [12].
51
(a)
(b)
(c)
Figure 4.2: Example of experimental 3DXRD data. Diffraction images showing
the six first fcc Debye–Scherrer rings: (a) drawn Debye–Scherrer rings; (b) reflections from a heavily deformed sample lying on the powder rings; and (c) individual
reflections from strain free grains lying on the powder rings.
over the rings, but without filling them completely (see fig. 4.2b). In the
case of a material with a face centered cubic (fcc) structure this is much
simplified, and only the first five powder rings, which are allowed in the fcc–
structure, are normally necessary to determine the crystal orientation of a
grain: {111}, {200}, {220}, {311}, and {222}.
As already mentioned in chapter 1, the big challenge in studying nucleation of recrystallization is the fact that it is not possible to predict exactly
where a new grain will nucleate, which means that large volumes must be
characterized with a spatial resolution of at least 1 µm in order to properly
characterize all possible nucleation sites before annealing. This same volume must then be characterized post–annealing, so that the before and after
microstructure at a nucleation site can be compared. Ideally, the ”birth”
and subsequent growth of a nucleus should be followed in situ, so that the
nucleation mechanism can be identified. Lastly, the microstructures and nuclei studied should be away from the sample surfaces, so as to avoid possible
surface effects.
The criteria placed on a suitable experimental technique for studying bulk
nucleation in situ, exclude all techniques based on microscopies of various
kinds, as they either study the surface or thin sections. 3DXRD, which has
a penetration power of the order of mm in most metals (see fig. 1.9), and the
ability to detect volumes sized ∼1 µm3 within volumes sized up to 1 mm3 ,
52
on the other hand satisfies all these criteria, and it would seem that this
technique is the natural technique for studying in situ bulk nucleation.
The primary motivation for performing the experiment was to perform a
feasibility study to determine whether it was possible to study bulk nucleation in situ in suitable detail using 3DXRD, and what information could
actually be gleaned from such an experiment. It was for example known that
we would only be able to detect nuclei, which appeared with orientations on
the tails of the orientation spread of a deformed grain or with a completely
new orientation. Whether such nuclei would actually appear was not known
prior to the experiment, even though copper’s tendency to produce annealing twins, with new and detectable orientations, made this more likely (see
section 1.2.5).
4.1
The 3DXRD microscope
The 3DXRD microscope is an unique instrument, located in the second
experimental station at beamline ID11 at the European Synchrotron Radiation Facility (ESRF), which is a 6 GeV third generation X–ray source located
in Grenoble, France [95]. The experimental hutch is 10 m long and is centered
at 56 m from the undulator source. The lead shielding provides sufficient radiation protection to allow 1 mm2 of the white beam to be accepted into
the hutch [58]. With white beam we mean the quasi–monochromatic X–ray
beam, which is emitted by the undulator (see fig. 4.4). The experiments are
remotely controlled from the outside using ’SPEC’ control software, and ’Image Pro’ image processing software is used to capture the diffraction images.
The specific parameters of the undulator, the monochromating–focusing optical elements, and the 2D detector can be found in appendix C.
4.1.1
Governing equations and scattering geometry
In the tilted coordinate system, within which the 3DXRD microscope operates (see Appendix A.2), the governing equation is Bragg’s law (see eq. 4.1),
which relates the diffraction angle to the spacing between the diffracting lattice planes, and the wavelength of the X–rays for elastic coherent scattering
from a periodic lattice [12, 59]:
nλ = 2 dhkl sin θ
53
(4.1)
where n is an integer number, λ is the wavelength, dhkl is the spacing of the
diffracting lattice planes, and θ is the diffraction angle. Also [12]:
λ=
hc
Ephoton
=
12.398
Ephoton [keV]
(4.2)
where Ephoton is the photon energy, and λ is in Å. Further:
dhkl(cubic) = √
h2
a
+ k 2 + l2
(4.3)
where a is the lattice vector, and {hkl} are the Miller indices of the lattice
plane. Please note that in this thesis only cubic lattices will be dealt with,
and only kinematical scattering will be assumed.
0
ω
6
2θ
X-ray beam
sample
R
x R
dist(s,d)
detector
zdet
ydet
Figure 4.3: 3DXRD scattering geometry. The X–ray beam is along the x–axis,
and is scattered with an angle 2θ, the azimuthal angle is η ∈ [0◦ , 360◦ ], the sample–
to–detector distance is dist(s, d), the horizontal scattering angle is ψ=(2θ sin η),
the vertical scattering angle is κ=(2θ cos η), and R=dist(s,d) tan(2θ). ydet and zdet
are respectively the y and z–coordinates on the detector.
54
4.1.2
X–ray source
The radiation source for beamline ID11 is either an in–vacuum undulator (U23) or a wiggler2 [12], where the in–vacuum undulator is used for
experiments with the 3DXRD microscope (see table C.1 for specifics).
A wiggler/undulator is a device that is inserted into the electron beam
on a straight section of a storage ring. It consists of powerful magnets of
alternating polarity, which causes the electrons to move in a sinusoidal manner while in the device. Since radiation is emitted when a charged particle
is accelerated, radiation is emitted at each sinusoidal ”wiggle”, and if the
dimensions of the insertion device are constructed such that the radiation
emitted at one wiggle is in phase with the radiation emitted from the other
wiggles, the insertion device is called an ”undulator”, which is currently the
most intense X–ray source available to man.
It should be noted that the spectrum produced by the ID–11 undulator
(see fig. 4.4) is somewhat different from what is expected from ideal circumstances, and that which can be modelled by undulator spectrum simulation
software such as XOP (available at ESRF) [96].
4th
5th
6th harmonic
7th
8th
9th
50.77
Figure 4.4: Example of ID–11 undulator spectrum. A complete undulator spectrum
is only available for a motor gap of 8 mm. This is shown here including the
locations of the various harmonics. Note the non–ideal shape of the undulator
spectrum [97, 98].
2
http://www.esrf.fr/exp facilities/ID11/handbook/welcome.html
55
The spectrum is instead fitted with a beamline ID–11 in–house program,
which gives a quadratic fit to the gap motor position. A user defines which
X–ray energy he or she wishes to work at, and the program calculates which
gap motor positions correspond to which harmonics. For the experiment, a
motor gap of 7.219 mm was used, placing the energy 50.77 keV in the 7th
harmonic [98], which would place the ideal fundamental energy at 7.25 keV
(λ=1.7 Å). The beam divergence was 0.5 mrad at the sample position.
4.1.3
High energy X–ray focusing
The quasi–monochromatic white X–ray beam is generated in the undulator (see section 4.1.2), passes slit#1 (see fig. 4.1), and then enters the experimental hutch, where the 3DXRD microscope is located, through a 1 × 1 mm2
pinhole.
The 3DXRD microscope is constructed to operate in the energy range of
40–100 keV (λ=0.12–0.31 Å), and two optical elements are used to monocromate and focus the X–beam. These are an asymmetrically cut cylindrically
bent perfect silicon (Si) crystal in transmission mode, and an elliptically
shaped laterally graded W/B4 C–multilayer in reflection mode (see figure 4.1
and 4.5) [58].
(a)
(b)
Figure 4.5: The X–ray monochromating and focusing optical elements:
(a) Vertical: asymmetrically cut cylindrically bent Si[111]–Laue crystal;
(b) Horizontal: elliptically shaped and laterally graded W/B4 C–multilayer [58].
The sample phases are generally known in 3DXRD experiments, and the
angular resolution may therefore be relatively relaxed compared to other
condensed matter studies, such as structural determination, and reciprocal
space mapping. Hence, by focusing in two dimensions, and increasing the
56
energy bandwidth to ∆E/E∼1 %, a flux increase for micrometre–sized beams
of the order of 106 can be obtained (102 from the increased bandwidth, and
104 from the focusing) compared to ’standard’ X–ray optics, where the beam
is monocromated by two flat Si crystals, and subsequently narrowed to the
required size by slits.
For experiments with the 3DXRD microscope, three different X–beam
cross sections are generally used: a box beam, where the cross section is
much larger than the structural elements (5×5 µm2 to 1×1 mm2 ); a line
beam, where the cross section is confined as much as possible to the ω–
plane (1×1000 µm2 ); and a pencil beam, where the beam is confined in both
directions to dimensions smaller than the structural elements (2×5 µm2 ) [21].
When a box beam is required, such as for the nucleation experiment
described in section 4.2, the X–ray focus is located in front of the sample.
From experience, the most homogeneous box–like beams, where the tails are
very small and the maximum intensity variation across the beam is ∆I
∼10%,
I
are obtained when the focus is placed in front of the sample, and the beam
size itself is defined by slits placed between the focusing optics and the focus
point (see figure 4.6). It could be argued that even better results could be
obtained by placing the slits between the focus point and the sample, but
this option is not practical due to space restrictions.
sample
slit #2
hslit
X-ray
beam
hsample
focus point
Figure 4.6: Setup with focus point in front of the sample. Slit #2 was 15 cm
in front the focus point, which was 10 cm in front of the sample, and the beam
divergence was 0.5 mrad.
4.1.3.1
Focusing by a bent Laue crystal
The incident X–ray beam is monocromated and focused in the vertical
direction by reflection from the [111]–plane of an asymmetrically cut cylindrically bent perfect Si–crystal in transmission mode (a Laue crystal). In
57
ρ
q
θq θp
p
Ω
e-
Figure 4.7: Rowland circle for focusing with bent Laue crystal. The X–ray beam
is incident on the convex side of the bent crystal. θp is the angle of incidence, θq
is the exiting angle, and√both are related through |θq −θp | = 2θB , where θB is the
Bragg angle. Ω(≈ K/γ N ) is the opening angle of the undulater, and ρ is the
bending radius of the crystal lattice planes [100].
this geometry, the X–ray beam is nearly perpendicular to the surface of the
Si(111)–crystal, which gives a small footprint on the crystal, limits the beam
absorption, crystal heating, and necessary crystal size.
Only a brief introduction to the focusing mechanisms will be given here,
and for a more detailed account the author refers to the following references [58, 99, 100], which the following introduction is based on. Focusing
with a bent Laue crystal corresponds to solving the lens equation for a geometrically focusing crystal (see fig. 4.7), which is [101]:
2
sin θq sin θp
1
=
+
=
ρ
q
p
f
(4.4)
where q is the geometric focus to crystal distance, p is the source to crystal
distance, ρ is the radius of curvature of the lattice planes, and f is the focal
length of the crystal (for p → ∞), which is seen to be half that of the radius
of curvature. The big difference from normal optical focusing is that the
paths of the X–rays are changed by Bragg reflection, and not by refraction.
It is however not that simple, as the polychromatic X–ray beam propagates through the bent crystal, rays of different energies follow different
trajectories inside an area known as the ”Borrmann fan” (BF). This causes
the different energies to be spread out over the BF at the exit surface
(see figure 4.8). Due to the concave curvature of the inner crystal surface,
these rays will all meet in one point known as the polychromatic focus qpoly ,
which in general does not coincide with the geometric focus qgeom (see figure
58
4.8). However, for a given energy, these foci can be brought to coincide by
giving the diffracting planes of the crystal a specific angle to the surface normal, known as the asymmetry angle χ. Different energies therefore require
different asymmetry angles [99].
q geom
ly
∆θ po
BF
p
Spoly
to so
u
q poly
geom.
focus
polych.
focus
rc e
T
Figure 4.8: Schematics of focusing with a bent Laue crystal. p is the source to
crystal distance, qgeom is the geometric focal length, and the polychromatic focus
qpoly is where all wavelengths of the Bormann fan (BF) coincide [102].
Bending a perfect crystal entails an (often dramatic) increase in its angle
of acceptance. This is due to changing reciprocal lattice vector orientations,
as well as variations in dhkl –spacing and asymmetry angle. For a cylindrically
bent asymmetrically cut Laue crystal, the angular acceptance is increased
by [99]:
1/2
cos(χ ∓ θB )
T tan χ
×
∆θgeom = ±
ρ cos2 θB
cos(χ ± θB )
1
s13 + s15 cot χ
1 + (cos(2χ) + cos(2θB )) 1 −
(4.5)
2
s11
where T and ρ are respectively the thickness and bending radius of the crystal, θB is the Bragg angle, sij are the elastic compliances for the given crystal
orientation, and χ is the asymmetry angle. The lower sign of the ±/∓ corresponds to a X–ray beam incident between the surface normal and the lattice
plane. In the hard X–ray range, the intrinsic angular acceptance of the crystal (the absolute Darwin width) is of the order of 10−6 radians, which is
negligible compared to the geometric acceptance, so we may take:
1/2
2
2
+ ∆θgeom
≈ ∆θgeom
(4.6)
∆θ0 = ∆θDW
59
The total angle of acceptance is the result of the geometric as well as the
polychromatic focusing ∆θpoly , which is [99]:
cos(χ ∓ θB )
BF
(4.7)
∆θpoly = 1 +
∆θ0 +
cos(χ ± θB )
ρ
where ∆θ0 is the rocking–curve width of the crystal, and BF is the length of
the Borrmann fan. Via the differential Bragg’s law (see eq. 4.8), this directly
gives the energy bandwidth of the bent Laue crystal:
∆θpoly
∆E
=
E
tan θB
(4.8)
The bandwidth of an asymmetrically cut bent Si[111]–Laue crystal (∼10−2 )
is considerably larger than the natural bandwidth of a perfect Si[111]–crystal
(the relative Darwin width: ∼10−4 ), which allows focusing and greatly increases flux. The geometric and the polychromatic focal lengths are given
by [99]:
qgeom =
qpoly
ρ | cos(χ ∓ θB )|
2 − ρ cos(χ ± θB )/p
BF
=
cos(χ ∓ θB )
∆θpoly
(4.9)
(4.10)
and these may be brought to coincide for a suitable choice of χ.
In practice, the energy tunability of a Si[111]–Laue crystal is only about
10%, because the geometric and the polychromatic foci must be brought
to coincide appreciably to obtain a good result. The 3DXRD microscope
therefore has two identical focusing set–ups, with nominal energies of 50 keV
and 80 keV, which allows most of the 40–100 keV energy range to be covered.
For specifics on the two crystals, see table C.3.
4.1.3.2
Multilayer focusing
After the beam has been monocromated and focused in the vertical direction by the bent Laue crystal, it is focused in the horizontal direction
by a 30 cm long elliptically shaped and laterally graded periodic W/B4 C–
multilayer (ML), used in reflection mode at grazing angle (see figure 4.5b,
and table C.4 for specifics).
60
In the 3DXRD setup, the ML is used solely to focus the X–ray beam in the
horizontal plane. The reason for using a graded ML, as opposed to a curved
mirror, is that the ML may be made considerably shorter, especially at higher
energies, where the angle of total reflection is impractically small (αc ∼mrad)
for mirrors. This is due to the fact that while mirrors work by total specular
reflection, while a ML works by Bragg reflection from the periodic layers,
which works at much higher angles of incidence, thus reducing the length
necessary to accommodate the footprint of the X–ray beam on the surface.
θ
....
dML=21 Å
2{
N{
θ
θ
W
B 4C
W
B 4C
W
B 4C
W
B 4C
θ
dML=19 Å
ΓΛ
Λ
Buffer layer (Cr)
Substrate (Si)
Figure 4.9: Reflection from a multilayer mirror. The reflection angle θ varies
with the periodic layer spacing dM L , through equation 4.11. Λ is the thickness
of one bilayer, ΓΛ is the thickness of one W-layer, k and k are respectively the
wavevectors of the incident and reflected beams, and Q is the wavevector transfer.
The two reflected beams shown have the same energy, but different incident angles.
Periodic multilayers are stacks of alternating periodic layers of materials
of high and low electron density, which are grown on highly polished substrates. At each layer interface a fraction of the incident intensity is reflected
and large reflectivities are obtained when the Bragg condition is fulfilled (see
fig. 4.9):
nλ = 2 dM L sin θB
(4.11)
where λ is the X–ray wavelength, n is the order of the reflection, dM L is
the periodic layer spacing, and θB is the corresponding Bragg angle. Due to
eq. 4.11, ML may also be used as monochromators.
61
Focussing is obtained by giving the surface an elliptical shape, where
the source and focus points coincide with the focal points of an ellipse (see
fig. 4.5b). In elliptical geometry, the incidence angle of the X–ray beam
changes along the the footprint, and the periodic layer thicknesses are therefore changed correspondingly to prevent a further increase of the bandwidth [58]. The energy bandwidth of periodic multilayers is of the order
of 1%, which is of the same order as the bandwidth of the bent Laue crystal
(see tables C.3 and C.4) [58, 97].
The multilayer consists of 100 consecutive layers of W and B4 C, with a
Γ–factor (W/B4 C–thickness ratio) of 0.1455. They are deposited on a polished Si–substrate, with a 100 Å chromium–buffer layer. The elliptical curvature of the multilayer corresponds to a major radius of 25 m, and the periodic
spacing dM L at the centre of the multilayer is 20 Å, and this spacing falls from
21 Å at the edge furthest from the focal point to 19 Å at the edge closest to
the focal point (see figure 4.5). The substrate dimensions are 30×4×1.5 cm.
4.1.4
Detectors
For the 3DXRD experiment, two different types of detectors was used:
A solid state silicon pin diode was used to align the experimental setup
and characterize the X–ray beam. The active area of the diode is 20×20 mm,
and the detector efficiency as a function of X–ray energy is known.
Diffraction images were recorded on an ESRF–developed 14–bit 2D Frelon
CCD detector with anti–blooming coupled by an image intensifier to a fluorescence screen of area 160×160 mm2 (see table C.2 for specifics). The
X–rays strike a spherical phosphorous screen, where some are absorbed and
generate visible light, which is then reflected up onto a CCD–chip (Charge
Coupled Device) with 1024×1024 pixels. The CCD–chip has a dynamic
range of 14 bits, which means that it saturates at 214 (∼16,000) counts,
where counts is the number of detected photons within the exposure time.
Anti–blooming limits electrical charge ’seeping’ from intense to less intense
areas on the CCD–chip, but also lowers the maximum dynamic range of the
chip to about 14,000 counts.
The spatial resolution of a detector depends mainly on the thickness of the
fluorescence screen, where a thinner screen gives a better resolution. However, for too thin screens, the absorption becomes small, which is detrimental
to the detector efficiency. The Frelon detector has a relatively high efficiency,
62
but also a large point spread function (the size of a perfectly collimated infinitely thin beam on the detector) of 200–300 µm, which means that the
Frelon detector does not have a high spatial resolution, and therefore does
not preserve the shape of the diffracting volumes. The spatial resolution is
therefore defined by the volume illuminated by the X–ray beam, and the
diffraction images are solely used to determine the crystallographic orientation and size of the individual diffracting volumes (see fig. 4.1). Due to the
relatively large size of the detector, it can be placed at some distance to the
sample, and a good angular resolution (∼0.1◦ ) is obtained.
4.1.5
The furnace
The furnace used in the experiment can provide a maximum stable temperature of 500◦ C. It is mounted on the sample stage, and can be rotated
360◦ around the ω–axis (see figure 4.1). The sample is mounted in a groove
on a copper sample stub and fastened with a screw, and a thermocouple is
in direct contact with the bottom of the sample through a hole drilled in the
sample stub.
The sample is surrounded by a quartz cylinder with an outer diameter of
20 mm, which allows sample sizes up to 1 cm. The quartz cylinder has been
chemically etched down to a thickness of approximately 0.1 mm, thereby
giving rise to negligible absorption and minimizing diffuse scattering. The
furnace allows a controlled atmosphere.
The furnace temperature is controlled by a ’EuroTherm’ control box,
which is controlled by the computer interface ’iTools’ and the ’Set Point
Editor’ software3 . This software allows very quick heating up to a target
temperature without overshooting. Please note that this requires that a
comparable sample is initially used to calibrate the temperature set points
of the EuroTherm–furnace system.
3
Manuals can be found at http://www.risoe.dk/afm/synch/furnace.htm
63
4.2
The nucleation experiment
This section is concerned with the design and carrying out of the 3DXRD
experiment. It follows and elaborates on what is written in publications [A2,A5,A7],
and is divided up into three subsection covering the following topics:
4.2.1 the choice of sample material and the sample preparation.
4.2.2 the preliminary studies carried out before the 3DXRD experiment.
4.2.3 the 3DXRD experiment.
It was decided to limit our X–ray study of nucleation to triple junctions
of grains (i.e., where three grains meet) within the material. Previous investigations [3, 30, 74], as well as a study by optical microscopy (see section 2.3)
had shown that triple junctions are preferred nucleation sites in light to moderately deformed large particle–free single–phase metals.
4.2.1
Samples used for the 3DXRD study
The sample material was oxygen–free high conductivity (OFHC) copper
99.995% pure, which was relatively free of large interstitial particles. The
Metals–4D center has considerable experience in working with aluminium,
but copper was chosen for the 3DXRD experiment, because we wanted to
focus on nucleation at triple junctions, which requires a material relatively
free from large particles in order to avoid particle stimulated nucleation (see
section 1.2.6). We chose not to use high purity aluminium because it recrystallizes at very low temperatures, thus making it impossible to characterize
the deformed state in the 3DXRD microscope. Additional advantages when
using copper for the experiment is that copper recrystallizes at relatively
low strains, and has a X–ray scattering power, which is greater than that of
aluminium, allowing us to detect smaller volumes (see section 4.2.3.2). Also,
copper routinely produces annealing twins (see section 1.2.5), which greatly
improves the chances of a nucleus appearing with an orientation not present
in the parent grains, and therefore facilitates its detection significantly. However, we must also bear this in mind when comparing the orientation of nuclei
with the available parent grains (see section 4.2.3.6). It should be noted that
on a timescale of months the OFHC copper was found to recover at room
temperature. This was however not deemed a problem, since all studies were
64
performed within 1–2 weeks of cold rolling, and here no dramatic recovery
effects were observed.
In a previous study by Poulsen et al. [4], it was observed that an aluminium single crystal, channel die deformed to 78% reduction in thickness
at room temperature, fills 30–40% of the orientation space available in a
{200}–pole figure (see appendix B), which contains the {hkl}–family of lowest multiplicity (m200 =6). From this it is clear that a smaller deformation
must be used in order to characterize the microstructure at triple junctions,
where it must be possible to distinguish the reflections of at least three grains
at the same time, and some free orientation space must also be present to
allow nuclei with new orientations to be detected. At low to moderate deformation (10–40%), pre–existing grain boundaries should act as the dominant nucleation sites [30], and reduce the number of potential nucleation
events [103].
The chosen solution was to use a moderately deformed material
(20% deformed) with a relatively large grain size, and to limit spot–overlap
(overlap of diffraction spots from different grains) as much as possible, it
was chosen to polish the sample down to a small thickness (0.3 mm), so
that the surface grains would generally continue throughout the thickness
of the sample. It was then deemed that there was good chance that only
three grains would be irradiated by the X–ray beam as it penetrated the
samples at a triple junction, and as the sample thickness was two orders
of magnitude larger than the average cells in the deformed microstructure
(see section 4.2.2.3), as well as the expected initial size of the nuclei (see
section 1.2), the nucleation dynamics were therefore expected to exhibit bulk
properties.
It should be noted that the sample thickness was not chosen to maximize
the diffracted flux I(x) from the full thickness of the sample, which is [12]:
I(x) = xe−µx =⇒
1
Imax = I(x= )
µ
(4.12)
(4.13)
where x is the thickness of the sample, and µ is the linear absorption coefficient. From eq. 4.13, the total diffracted intensity from the sample is at
maximum for a thickness of 0.43 mm (at 50 keV)4 , and at a thickness of
0.3 mm, 95% of the maximum possible diffracted intensity is obtained.
4
The linear absorption coefficient of copper at 50 keV is: µ = 2.31 mm−1 [104].
65
The starting material was annealed for 2 hours in an air furnace at 600◦ C,
then cold rolled 20%, and lastly, annealed for 8 hours at 700◦ C. This resulted
in a grain size distribution with an average grain size of about 500 µm. This
starting material was then additionally cold rolled to a 20% reduction in
thickness — from a thickness of 32.0 mm to 25.6 mm (see figure A.1a).
During cold rolling, where the roll radius was 170 mm, the L/h–ratio was
1.2 (see eq. 4.14), and the deformation is therefore expected to be uniform
throughout the thickness of the material [105]:
r(h0 − h1 )
L
=
(4.14)
h
(h0 − h1 )/2
where r is the radius of the rolls, h0 and h1 are respectively the specimen
thickness before and after rolling, L=|AB|≈|AB|= r(h0 − h1 ) is the contact
length between the rolls and the specimen, and h = (h0 − h1 )/2 is the average
thickness of the specimen.
From this material thin 10 × 10 mm2 RD–ND (see appendix A) sections were cut out. The sections were mechanically lapped (with 9 and
3 µm Al2 O3 ) and polished (with colloidal silica) down to a thickness of
0.3 mm. The lapping and polishing was performed on both sides using a
Logitech PM5D polishing and lapping machine with a PSM1 sample monitor [A3]. Additionally, to remove any remaining surface deformation or
sub–micrometre scratching (i.e., surface nucleation sites), the samples were
electrolytically polished for 5 seconds at a voltage of 10 V. The sample was
used as anode, platinum was used as cathode, and a D2–solution5 was used
as electrolyte [92, 93].
5
D2: 500 ml H2 O, 250 ml H3 O4 P, 500 ml ethanol, 50 ml propanol,
5 g (crystalline uric acid), and 2 ml Dr . Vogels Sparbeize :
’Dr. Vogels Sparbeize’ is a chemical solution, who’s exact recipe is unknown. It acts as
an inhibitor that allows electrochemical polishing of copper surfaces without corrosion.
Known contents are: ≤ 20% H2 SO4 , ≤ 1% H3 PO4 , 40–50% 1–methoxy–2–propanol,
5–7% nonylphenol–ethoxylate, 3–5% thio–uric acid.
66
4.2.2
Preliminary studies
Several preliminary studies were performed with various experimental
techniques prior to the 3DXRD nucleation experiment. These studies were
essential in order to maximize the probability of the experiment being a
success.
Firstly, it was necessary to ascertain whether the diffraction spots from
three large grains located at a triple junction in a 20% cold deformed sample
could be distinguished from each other, and whether they left enough free
space in the diffraction images for any new diffraction spots, which might
appear, to be observed. Also, several studies were performed on the sample
material using hardness indentations and microscopies of various kinds, so as
to determine the approximate recrystallization temperature, whether triple
junctions were the dominant nucleation sites, and the surface positions of
triple junctions suitable for study by 3DXRD on the samples used in the
experiment.
4.2.2.1
3DXRD feasibility study
At an earlier beamtime, a short feasibility study was performed at the
3DXRD microscope on a sample identical with those used in the actual
experiment. This was done in order to confirm that the reflections from
three adjacent grains, cold deformed 20%, would not completely fill all of
orientation space, which would make the experiment impossible to perform
with the chosen amount of deformation.
Before the X–ray study, an area of the surface was characterized by optical
microscopy, so as to determine the surface location of all triple junctions
suitable for 3DXRD study. This feasibility study confirmed that spot–overlap
was at an acceptable level for the deformed grains at a triple junction, and
that there was still plenty of available space in the diffraction images.
4.2.2.2
Vickers hardness testing
The recrystallization temperature (see section 1.1) was estimated by annealing several identical samples at different temperatures for 1 hour, and
then performing Vickers hardness tests on them. The Vickers hardness vs.
annealing temperature curve (see figure 4.10a) was used to estimate the minimum temperature for the onset of nucleation. The recrystallization temperature was estimated to be around 290◦ C, and this was chosen for the experi67
100
100
Exp. Temp.
90
80
80
70
70
60
60
2
Hv [N/m ]
Hv [N/m2]
90
50
40
50
40
fully Rex
fully Rex
30
30
20
20
10
0
0
10
100
200
290
400
500
0
600
o
Temp [ C]
0
50
100
150
200
250
300
350
Time [min]
(a)
(b)
Figure 4.10: Vickers hardness tests on the copper sample material. The material was cold rolled 20%, the samples were heated in an air furnace, and the test
load was 5 kg. (a) samples were annealed for 1 hour at different temperatures;
(b) samples were annealed at 300◦ C for different periods of time.
ment, to make sure that the softening was not caused solely by recovery and
that nucleation would occur from the onset of annealing (see section 1.1).
A series of samples were annealed at 300◦ C, which was slightly above the
recrystallization temperature, for varying periods of time to ascertain how
fast recrystallization proceeds at this temperature. The resulting hardness
curve can be seen on figure 4.10b). The hardness curve shows that recrystallization does not occur very rapidly at 300◦ C, taking more than 5 hours to
be complete, which indicated that it would be possible to follow the kinetics
of a growing nucleus if one was identified in the experiment. From the large
scatter in hardness, it could also be concluded that not all regions of the
sample material would initially recrystallize at an experimental temperature
of 290◦ C.
68
4.2.2.3
Investigations by microscopy
Previously a detailed TEM study of pure copper had been performed by
Huang et al. [106]. In this study it was found that the minimum distance
between cell boundaries with a misorientation of 1◦ or greater was 1–2 µm
in pure copper deformed 17% by cold rolling and 36% in tension. According
to Huang, the minimum subgrain size within the sample material should
therefore be 1–2 µm [107]. This may be compared with the classical critical
nucleus size that can be determined from equation 4.15 [30]:
RC >
2γ
ES
(4.15)
where RC is the classical critical radius of curvature, which allows a nucleus to
grow, γ is the boundary energy, and ES is the stored energy of cold work. For
copper we have γ=0.625 Jm−2 [11], and for copper 20% cold deformed we have
ES =2.20·106 Jm−3 [108]. By inserting these into equation 4.15, we find
ECDC =2RC >1.14 µm.
After electrochemical polishing, a 1.820 × 1.800 mm2 area on each sample was inspected by EBSP, with a step size of 20 µm. From this an OIM
was produced to allow easy identification of all triple junctions within that
surface area. Figure 4.11 shows an example of the area on the samples characterized by EBSP — the upper right edge of the inspected area was 2 mm
below the top edge, and 2 mm left of the right edge (see also fig. 4.12–4.14).
A JEOL JSM–840 scanning electron microscope, with a LaB6 –filament was
used to collect the EBSP data. The working distance was 22 mm, the electron
beam current was 270 µA, and the accelerating voltage was 20 kV.
69
Figure 4.11: X–ray sample geometry. Note that the relative size of the OIM has
been slightly exaggerated to make the microstructure more easily discernable. The
white squares indicate the surface locations of selected triple junctions, and the
alignment notch was made to ensure that the the sample was mounted correctly in
the X–ray study.
4.2.3
The 3DXRD experiment
An X–ray energy of 50.77 keV (λ=0.2442 Å) was used for the 3DXRD
experiment, thus giving a transmission of 50% through the 0.3 mm thick
copper samples. This energy was not chosen specifically for the experiment,
but was to be used for an experiment directly following the one described
in this section. However, using this energy was not a drawback. During the
experiment, the synchrotron ring was in 16–electron bunch mode, giving a
maximum synchrotron ring current of 90 mA, and a maximum monochromated flux6 of 3.6 · 106 photons/s at 50.77 keV was measured with the pin
diode behind the multilayer, which corresponds to a flux of the order of
1010 photons/s [98].
6
Should be corrected for Si–diode efficiency at the X–ray energy.
70
For the experiment, a 800×800 µm2 sized white X–ray beam was monochromated and focused onto the sample. The focal point was located 10 cm in
front of the sample, and the beam dimensions were defined by using slit #2
(see fig. 4.6). The resulting X–ray box beam had a flat profile ( ∆I
≤10%) and
I
a size of 49×49 µm2 at the sample position. The X–ray beam size, defined
as the full width at half maximum (FWHM) at the sample position, was
determined by scanning the Si–diode through the beam. While it is possible
to focus the X–ray beam down to a size of roughly 2×5 µm on the sample
(see tables C.3 and C.4), a considerably larger beam was used in order to
characterize a relatively large volume in a reasonable amount of time.
It should be noted that specific details pertaining to the setup and alignment have been omitted from this section, except where doing so has been
deemed of great importance. Also, before performing the actual experiment,
the calibration data utilized in sections 4.2.3.1 and 4.2.3.2 was collected.
To characterize the microstructure of a volume, defined by the beam size
and the sample thickness, diffraction images were obtained by CCD exposures made for a number of equally spaced values of the rotation axis ω, equal
to the angular range in degrees. To ensure an even sampling of integrated
intensities, the sample was rotated by ±0.5◦ during each exposure, which
lasted for 1 second. To further increase the volume characterized by the
X–ray beam, exposures were made at a set of sample positions. For all
samples this corresponded to an (y, z)–grid, where the distance between
grid nodes was 40 µm.
The experiment could basically be divided into two parts. First, a volume
(grid area × sample thickness) centered on a suitable triple junction was
characterized in the deformed state at room temperature (25◦ C). Secondly,
the sample was heated to 290◦ C in a helium atmosphere (1.3 bar), and once
at temperature, the same volume was continually characterized, so as to
follow the nucleation kinetics. The same volume was located again in the
hot sample by utilizing its (y, z)–distance to the upper right sample corner,
who’s change with heating was negligible on the length scales and precision
of the experiment.
Three samples (A, B, and C) were studied during the experiment, and on
each sample a grid, of varying size and centered on a triple junction, was
characterized as described below. Figures 4.12–4.14 show the X–ray grid
superimposed on the EBSP OIMs obtained from the preliminary study (see
section 4.2.2.3). The samples were characterized in the following order:
71
Sample A: a 2×2 grid centered at a triple junction, with (y, z)–motor positions = (0.769, 138.460), was characterized within an ω–range of [-10◦,11◦ ].
The sample was subsequently heated to 290◦ C, and upon reaching temperature, an identical 2×2 grid was then continually characterized with
a time resolution of ≈6 minutes. During annealing a reflection originating from a nucleus was identified in the diffraction images, and it
was therefore decided to quench the sample back to room temperature
after only 45 minutes of annealing, in order to determined the exact
(x, y, z)–position of the nucleus, as well as to increase the ω–range, to
determine the crystal orientation of the nucleus with greater accuracy.
The exact position of the nucleus was determined, and the nucleus was
subsequently translated into the centre of rotation, allowing exposures
to be made for an ω–range of [-45◦,46◦ ] without risk of the nucleus
moving out of the X–ray beam as the sample was rotated. Afterwards,
the sample was once again heated to 290◦ C, and the growth kinetics of
the nucleus were followed.
100 µm
Figure 4.12: Sample A: OIM of the surface microstructure and the location of the
X–ray grid (marked in red). A 2×2 grid was characterized, within the ω–range of
[-10◦ ,11◦ ], in the deformed state and continuously during annealing with a time resolution of ≈6 minutes. A nucleus (nucleus 1) was detected in the white grid area.
72
Sample B: a 2×2 grid centered at a triple junction, with (y, z)–motor positions = (1.431, 138.806), was characterized within an ω–range of [-20◦,21◦ ].
However, to increase the sensitivity of the characterization of the deformed microstructure, the exposure time was increased to 15 seconds
and the ω steps between exposures was reduced to 0.5◦ , giving a sampling rotation of ±0.25◦ . This increased the intensity diffracted into a
given reflection during an exposure by a factor of 30 (see eq. 4.17). After the initial high sensitivity characterization, the sample was heated
to 290◦ C, and upon reaching temperature, an identical 2×2 grid with
an ω–range of [-20◦ ,21◦ ] was continually characterized during annealing, which lasted for 11.1 hours. Note that the exposures made during
annealing were made with normal sensitivity (i.e., 1◦ ω–steps, rotated
±0.5◦ for 1 second), giving a time resolution of ≈8.5 minutes.
100 µm
Figure 4.13: Sample B: OIM of the surface microstructure and the location of the
X–ray grid (marked in white). A 2×2 grid was characterized, within the ω–range
of [-20◦ ,21◦ ], before and continuously during annealing with a time resolution of
≈8.5 minutes. No nuclei were identified in this sample.
73
Sample C: a grid centered at a triple junction, with (y, z)–motor positions
= (0.776, 138.646), was characterized within an ω–range of [-20◦,21◦ ].
For this sample it was chosen to expand the grid into a 4×4 grid,
in order to increase the probability of a nucleation event occurring
within the characterized volume. The deformed sample was characterized with the 4×4 grid described above, after which the sample was
heated to 290◦ C. Once the sample had reached the desired temperature, the central 2×2 grid areas of the 4×4 grid were continually characterized within an ω–range of [-20◦ ,21◦ ] during annealing with a time
resolution of ≈8.5 minutes. Towards the end of annealing (after 3–
3.5 hours), the grid was once again expanded into a 4×4 grid, so as to
characterize the same volume as was initially characterized within the
deformed sample.
100 µm
Figure 4.14: Sample C: OIM of the surface microstructure and the location of the
X–ray grid (marked in black). The 4×4 grid was characterized before and at the
end of annealing, within the ω–range of [-20◦ ,21◦ ]. During annealing the red 2×2
grid was characterized continuously with a time resolution of ≈8.5 minutes. Two
nuclei (nucleus 2 and nucleus 3) were detected in respectively the top and bottom
white grid areas. Nucleus 2 was also faintly observed in the top left red grid area.
74
4.2.3.1
Image processing
The 2D Frelon detector produces raw digital images in the .EDF–format,
roughly 2 MByte in size. Before the images can be used for quantitative
crystallographic analysis, the background intensity must be subtracted and
the images must be spatially corrected.
Background subtraction
The typical background subtraction method, is to record X–ray images without the sample present (raw background image), and without any X–rays
(darkfield image). The darkfield image (the internal noise in the CCD–chip,
which is only exposure–time dependant) is initially subtracted from both the
diffraction and the background image, which are then scaled to the same
synchrotron current (i.e., the same X–ray flux), and the background image
is then subtracted from the diffraction image.
However, in this case a considerable effort was made to obtain a low
volume detection limit (i.e, an intense X–ray beam), so the reflections from
the large deformed grains gave rise to high intensities, which subsequently
saturated the Frelon detector, which saturates at ∼14,000 counts (see section 4.1.4). Even with anti–blooming on the detector (see section 4.1.4), some
charge from intense poles was seen to leak out onto the surrounding areas of
the CCD–chip, and thus to surrounding areas of the diffraction image. This
leakage can be seen as the streaks on figure 4.15a.
It was chosen to use the background subtraction method developed by
Bowen et al. [109]. In the algorithm, an image is divided up into a grid, and
each grid area is further subdivided into more subgrid areas. The standard
deviation of the intensity in each subgrid area is calculated, and those in
which the standard deviation is above a specified limit are ignored, while
those that are below are used to interpolate the background intensity of the
full grid area, which is in turn used to interpolate the background intensity
of the entire image. The results were very good, with the pixel intensity
often falling to zero between the Debye–Scherrer rings. Note that this procedure is performed on every single diffraction image, and that the calculated
background is valid for that image only.
Figure 4.15 shows examples of diffraction images before and after background subtraction using the Bowen et al. method. Due to the nature of the
interpolation function, the background is not subtracted from the outer edge
of the image.
75
(a)
(b)
(c)
Figure 4.15: Background subtraction using the Bowen et al. method. Diffraction
images showing respectively: (a) a raw image; (b) a background subtracted image; and (c) a background subtracted, and spatially corrected image (see below).
Note that (a) and (b)&(c) are not on the same intensity scale.
Spatial correction
Because the diffraction cones are not scattered onto a flat surface
(the phosphorous screen is spherical), the diffraction images are distorted
and must be spatially corrected. This is done by mounting a flat 1.5 mm
thick copper plate, with a regular grid of 65×65 holes, on the front surface of
the detector. The holes have a diameter of 1.5 mm, and the centre–to–centre
distance is 2.5 mm. Using the recorded transmission image of this grid (see
figure 4.16b) and the software package ’FIT2D’7 [110], it is possible to produce a spline function, which corrects the spatial distortion on the diffraction
images (see figures 4.15c and 4.16c) [111].
The specifics of the scattering geometry (eg. sample–to–detector distance,
detector tilt angle, effective detector pixel size, etc.), which are necessary to
create the spline function, are determined by placing a LaB6 –powder sample
in the beam and recording diffraction images from this. LaB6 is used because
it produces many well defined powder rings (see figure 4.16a), which allows
an accurate fitting of the scattering geometry to be performed in FIT2D,
using a fitting routine specifically developed for LaB6 –powder. This fitting
is carried out twice. First, with the distorted raw LaB6 –image, which then
7
http://www.esrf.fr/computing/expg/subgroups/data analysis/FIT2D/
76
(a)
(b)
(c)
Figure 4.16: Spatial correction of 2D diffraction images. Diffraction images showing respectively: (a) the LaB6 –powder rings (distorted); (b) image of grid (spatially distorted); and (c) image of grid (spatially corrected).
yields rough parameters for the scattering geometry. These parameters are
then used to produce a first spline function, which is then applied to the raw
LaB6 –image. The resulting corrected parameters are subsequently used to
determine the final spline function.
The spatial correction of the images using the spline function was also
carried out using FIT2D, and the transmission images of the grid before and
after the spatial correction has been applied can be seen on figure 4.16b–c.
During image processing, the background subtraction was performed before
the spatial correction, due to strict mathematical requirements imposed on
the dimensions of the image file by the Bowen et al. background subtraction
method.
4.2.3.2
Volume calibration
In this investigation of nucleation, the size of the nuclei was of interest,
as well as their the crystal orientations. This is because if the size of the
nuclei can be determined at different annealing times, it is possible to follow
the growth kinetics of the nuclei. Also, of great importance was to determine the smallest detectable diffracting volume (the detection limit), because
this determines with what sensitivity the deformed microstructure could be
characterized, and the smallest nuclei that could be detected.
77
In 3DXRD, the size of a diffracting volume is determined by scaling the
scattered intensity from the volume with the scatter from an accurately
known volume of known scattering factor. By scaling the intensity of a
reflection from a diffracting volume to the intensity of the known volume,
the size of the diffracting volume may thus be determined.
An aluminium foil of 53 µm thickness and random texture was placed in
the X–ray beam, with surface normal parallel to the beam, thus illuminating
a channel through the foil, with a volume equal to the beam area × the foil
thickness (49 × 49 × 53 µm3). The foil produced a powder diffraction pattern, and the total intensity of the {200} Debye–Scherrer ring was integrated,
giving an intensity–to–volume conversion factor (see below). This conversion
factor can readily be applied to other materials, but must then be corrected
for differences in scattering factors and diffraction angles.
By placing aluminium attenuators in the X–ray beam, it was possible
to perform long exposures without saturating the Frelon detector. 1 second
counts with the Si–diode gave respectively 2059 counts and 389,000 counts
for respectfully the attenuated and unattenuated X–ray beam, giving an
attenuation factor of Iatten /I0 ≈1/189. Diffraction images were obtained at
20 adjacent y–positions. For each image, the exposure time was 4 seconds,
and the sample was rotated by ±5◦ , so as to achieve an even sampling and
as homogeneous a powder diffraction image as possible.
The intensity of these 20 images was averaged using FIT2D, and from this
average image, the average integrated intensity of the {200}–ring, and the average background were determined. The true intensity of the {200}–ring was
determined by subtracting the average background (255 photons/pixel/4s)
× the area covered by the ring (42,000 pixels). Scaling this intensity to 1 second exposures, and multiplying by the attenuation factor (≈189), the total
diffracted intensity of the {200}–ring was found to be 18.4 ·106 photons/s at
a synchrotron ring current of 77.2164 mA.
We may also calculate this from Warren [59], where (for a monochromatic
X–ray beam) the total energy scattered into a {hkl}–Debye–Scherrer ring by
a perfect texture–free powder of volume V is given by:
Epowder =
1
I0 t 2 λ3 |F u.c. (hkl)|2 V mhkl
r0
u.c.
2
4
(v )
sin θ sin 2θ
(4.16)
where I0 is the intensity of the X–ray beam, λ is the X–ray wavelength,
r0 =2.82 · 10−5 Å is the electronic scattering cross section, F u.c. (hkl) is the
structure factor of the atomic unit cell, v u.c. is the volume of the unit cell,
78
t is the integration time, V is the volume of the illuminated powder, θ and η
are defined on fig. 4.3, and mhkl is the multiplicity of the {hkl}–family.
This must be related to the intensity of a single reflection, which we may
also calculate from Warren [59], where (for a monochromatic X–ray beam)
the energy scattered by a crystallite of size δV into a single (hkl)–reflection is:
Esingle =
P
I0 2 λ3 |F u.c.(hkl)|2 δV
r0
u.c.
2
∆ω
(v )
sin 2θ | sin η|
(4.17)
where ∆ω is the rate of rotation of the crystallite in the X–ray beam, and P
is the polarization factor.
By determining the intensity of a single reflection, and the intensity of
a full powder ring, it is possible to find the ratio of Esingle to Epowder by
dividing eq. 4.17 by eq. 4.16. Note that if the same X–ray wavelength is
used in both cases, there is no need to know the absolute value of I0 , or the
detector efficiency for that matter. Below, the subscripts s and p refer to
respectively a single reflection from a crystallite, and a full powder ring, so
that comparisons between different materials may be made:
Esingle
δV |Fsu.c.(hkl)|2 (vpu.c. )2 P sin θp sin 2θp
4
=
Epowder
∆ω t V mhkl |Fpu.c.(hkl)|2 (vsu.c. )2 sin 2θs | sin ηs |
(4.18)
By isolating δV in eq. 4.18, we obtain an equation for δV , based on the
illuminated volume of the powder, and the ratio of Esingle to Epowder , which
may be substituted by the ratio of Isingle to Ipowder , and thus:
|Fpu.c.(hkl)|2 (vsu.c. )2 sin 2θs | sin ηs |
∆ω t Is
V mhkl u.c.
δV =
4 Ip
|Fs (hkl)|2 (vpu.c. )2 P sin θp sin 2θp
(4.19)
Specifically for the experiment, the synchrotron X–ray beam was horizontally polarized, i.e., P=cos2 ψs [12], where ψs=2θ sin ηs (see figure 4.3). From
eq. 4.17 we can deduce that Esingle is at minimum for ηs =90◦ , and therefore the ”worst–case” detection limit is also to be found there. The angular
rotation rate, and the integration time were respectively set to ∆ω=1◦ and
t=1 s, which were used in the experimental exposures. From the diffraction
images the signal–to–noise limit (the minimum detectable scatter) from an
aluminium {200}–reflection at η=90◦ was estimated to 400 photons/s This
signal–to–noise limit counts for every pixel, so the minimum detectable scatter corresponds to 400 photons/s on a single pixel.
79
Furthermore, we had Vf oil =49×49×53 µm3 , and the multiplicity (i.e., the
number of reflections of the {hkl}–family) was m200 =6. Aluminium and
copper both have the fcc–structure, so instead of comparing the scattering
factors of their respective lattices |F u.c.(hkl)|2 (given in eq. 4.20), it is enough
to compare the scattering factors fatom of the two elements [12]:
4·fatom if all (hkl) are even or odd.
u.c.
(4.20)
Ff cc (hkl) =
0
otherwise.
(4.21)
fatom = f (Q) e−M (T )
sin θ is the wavevector transfer, f (Q) is the atomic scatwhere |Q| = 4π
λ
tering factor, and e−M (T ) is the temperature dependent Debye–Waller factor. The values of f (Q) were obtained from appropriate tables [104], and
the Debye–Waller factors were calculated by the method of Als–Nielsen &
McMorrow [12]. Thus:
2
sin θ
M = BT
λ
2, 873
11, 492 T [K]
2
BT [Å ] =
· φ(Θ/T ) +
2
2
A Θ [K ]
A Θ[K]
1 x ξ
dξ
φ(x) =
x 0 eξ − 1
(4.22)
(4.23)
(4.24)
where λ is the wavelength, θ is the scattering angle, T is the temperature (in
Kelvin), A is the atomic weight (AAl =27.0, and ACu =63.5), Θ is the Debye
temperature (ΘAl =394 K, ΘCu =343 K [112]), and x = Θ/T .
The scattering factors at 25◦ C (298 K) were respectively found to be
fAl =7.9, and fCu =20.0. The lattice parameters are respectively aAl =4.05 Å,
aCu =3.61 Å [112], which directly gives the volumes of the respective unit cells
u.c.
u.c.
vAl
=(4.05 Å)3 and vCu
=(3.61 Å)3 . Lastly, the wavelength was λ=0.2442 Å,
which gave the respective Bragg angles (see eq. 4.1): θAl =3.46◦ , and θCu =3.88◦ .
Entering all the above parameter values into equation 4.19, we obtain an
80
equation for the minimum detectable scattering copper volume δVmin
at 25◦ C:
u.c. 2
f 2 (vCu
)
sin 2θs | sin ηs |
∆ω t Imin
Vf oil m200 Al
(4.25)
2
u.c. 2
4 Ip {200}
fCu (vAl ) cos2 ψs sin θp sin 2θp
6
2
400 phot/sec
π
7.9
3.61 Å
3
(49 × 49 × 53 µm ) · 6
=
720 18.4 ·106 phot/sec
20.0
4.05 Å
◦
◦
sin(2·3.88 ) | sin(90 )|
×
cos2 ((2·3.88◦) sin(90◦ )) sin(3.46◦ ) sin(2·3.46◦)
= 0.107 µm3
=
δVmin
For equation 4.25 to yield the correct value in any situation, three corrections must be applied to the volume determined from the integrated intensity:
Firstly, there may be a change in the synchrotron ring current ISC , to which
the X–beam flux is proportional: I = I0 ×(ISC /ISC,0), where ISC,0 =77.2164 mA
is the reference current.
Secondly, the Debye-Waller factor in the atomic scattering factor decreases
with increasing temperature: f (T ) = f (T0)×(e−M (T ) /e−M (T0 ) ), where M(T )
is given by eq. 4.22, and T0 =25◦C and T =290◦ C are respectively the cold
and hot experimental temperatures.
Thirdly, the diffracted beam is attenuated as it travels the distance x through
the sample, which is approximately equal to the sample thickness, and the
attenuation is: ICu = IAl ×(e−µCu·xCu /e−µAl·xAl ), where the linear attenuation
lengths are µAl =0.09 mm−1 and µCu =2.31 mm−1 at E≈50 keV [58], and the
sample thicknesses are xAl =53 µm and xCu =300 µm.
We may correct for these three effects, by scaling the volume determined from
eq. 4.25 correspondingly with the parameters given above (see eq. 4.26):
e−M (T0 )
e−M (T )
2
e−µAl·xAl
=
e−µCu·xCu
0.183 µm3 at 25◦ C
0.223 µm3 at 290◦ C
(4.26)
where the maximum synchrotron ring current ISC,M =90 mA has been used.
Please note, that there exists a ’cold’ and a ’hot’ value for δVmin , but to
simplify things δVmin is defined to be at 25◦ C.
δVmin =
δVmin
ISC,0
ISC,M
81
Using δVmin and Imin , we may scale the intensity of any given copper
{hkl}–reflection, with scattering angle θ and azimuthal angle η , to a volume:
V = δVmin
I
Imin
sin(2θ)
ISC,M
cos2 (2θ sin η )
2
cos (2θ)
sin(2θ )| sin η | ISC
e−M (T0 )
e−M (T )
2
(4.27)
The structure factor for all non–vanishing reflections from an fcc–lattice is
F u.c.=4·fatom , so no extra term is needed.
Due to the large point spread function of the Frelon detector (see section 4.1.4), it is not possible to determine the shape of the nucleus. However,
based on the volume of the nucleus, we may define an equivalent circle diameter (ECD), which is the diameter of a spherically shaped nucleus of volume
V . Here the diameter is used, because this is what is measured with other
microscopy techniques. Thus:
1/3
3
=⇒
ECD = 2×
V
4π
0.70 µm at 25◦ C
ECDmin =
0.75 µm at 290◦C
(4.28)
(4.29)
which gives the smallest length that can be detected within the microstructure, and ECDmin is therefore defined as the detection limit of the experiment.
For sample B, the characterization of the deformed microstructure was
performed with a lower detection limit. This was achieved by decreasing the
sample rotation rate to ∆ω=0.5◦s−1 , and increasing the integration interval
to t=15
level is equal
√ seconds. Assuming Poisson statistics, where the noise
√
to ∼ I, this gave an increase in volume resolution of × 30 ≈×5.5. Thus
giving a minimum detectable volume of δVmin =0.033 µm3 , which is equal to
ECDmin =0.40 µm.
An important observation to make is that even at the highest volume detection limit of the experiment (i.e., ISC ≈62 mA and T=290◦ C),
ECDmin ≈0.85 µm was still smaller than the size of the smallest subgrains
observed in the deformed microstructure (see section 4.2.2.3). We may therefore conclude that, at no time during the experiment were we unable to detect
the volume of the smallest subgrains.
82
4.2.3.3
Identifying nuclei
This was the single biggest challenge of the experiment, and was by no
means a guarantied success. Sections 4.2.1 and 4.2.2 described all the steps
taken to improve the chances of observing nuclei in their early stages of
growth. Due to the high intensity of the large reflections from the deformed
parent grains, any diffraction spots originating from the nuclei within the
central regions of the poles will not be detectable. Only intense diffraction
spots on the tails of the poles, or completely removed from them will be
detectable (see fig. 4.17).
In practice, finding the diffraction spots originating from a nucleus is
very much a ”needle–in–the–haystack” problem. As of yet, no automatic
method has been developed, which would be 100% certain of finding all nuclei in the diffraction images. The solution was to manually inspect each
diffraction image for spots, which could be diffraction spots originating from
a nucleus, Unlike the deformed/recovered parent grains, the nuclei exhibit
only very limited mosaic spread, and the diffraction from the nuclei appear
as distinct spots, as opposed to the broad reflections originating from the
deformed grains. During data acquisition, the diffraction images were continually monitored on the computer screen in order to detect the nuclei during
the in situ annealing. This was of course also done post–experiment.
During the in situ annealing of sample A, one nucleus was identified. This
allowed us to follow the growth kinetics of the nucleus (see section 4.2.3.7).
No nuclei were identified in sample B during annealing or the post–experiment
data analysis. However, one important detail was gleaned from the images
obtained from the deformed state of this sample — no reflections were observed outside the large poles, even with a detection limit of ECDmin =0.40 µm.
No nuclei were identified in sample C during annealing, but two nuclei were
identified in the post–experiment data analysis.
4.2.3.4
Determining the exact position of the nuclei
Determining the 3 dimensional positions of the nuclei was of high importance, since it was critical to the following discussion of the results, whether
the nucleation events had occurred in the sample bulk or at the surface. The
(x, y, z)–directions can be seen on figure 4.11, and the coordinate values are
defined as follows: x is zero at the sample surface struck by the X–ray beam;
and the (y, z)–coordinates are set equal to their corresponding motor positions. Positions are given in mm, and (y, z) are accurate to within 0.001 mm.
83
(a)
(b)
(c)
(d)
(e)
(f)
Figure 4.17: Nuclei detected in the diffraction images. The nuclei reflection appeared within the white squares (intensity≥400): (a)&(b) nucleus 1 — the deformed and annealed sample; (c)&(d) nucleus 2 — the deformed and annealed
sample; (e)&(f ) nucleus 3 — the deformed and annealed sample.
84
Here we have to distinguish between the two different degrees of available
experimental information. The nucleus in sample A was identified during
the experiment, which allowed a much more precise determination of its
position, whereas the two nuclei in sample C were identified during the post–
experiment data analysis (see section 4.2.3.3), and no special effort could be
made to determine their positions.
Nucleus in sample A
In the case of sample A, a nucleus (called nucleus 1) was located during the
annealing part of the experiment, and it was therefore possible to perform a
superscan (see below) in the y, z, and ω–directions to determine it’s exact
location in these directions, after the sample had been quenched back down
to room temperature.
A superscan consists of defining an area of interest (AI) in Image Pro
around a reflection with little or no mosaic spread, and scanning the intensity
of the AI in small steps between two motor positions for one motor at a time,
which allows the centre–of–mass (CMS) position of a grain to be determined
for the motors scanned (i.e., y, z, and ω). During superscans, the slits are
generally narrowed to increase precision, so that the beam size is ideally
smaller than or at least comparable with the size of the grain being scanned.
By performing superscans on two different reflections, their (y, z)–positions
as well as their ω–angles are determined. With these sets of coordinates, it
is possible to perform a triangulation in the (x, y)–plane to determine the
distance from the nucleus to the centre–thickness of the sample, which is
150 µm from the surface, and whether it in front of or behind the centre
line. This, in turn, yields the 3 dimensional position of the nucleus. The
triangulation geometry is visualized on figure 4.18, and based on this, the
following equation can be used to determine the maximum distance R from
the nucleus to the sample centre–thickness in the (x,y)–plane:
|y2 − y1 | = |R sin ω2 − R sin ω1 | ⇐⇒
−
y
y
2
1
R = sin ω2 − sin ω1 (4.30)
where R (defined to be positive) is the nucleus–to–centre thickness distance.
85
y0 y1
ω=0
o
d
y2
nucleus
ω
x
1
ω
2
y
R
O
Sample (x,y)-plane
Figure 4.18: Sample A nucleus location triangulation geometry in the (x,y)–plane
of the sample: y0 , y1 , and y2 are the y–coordinates of the nucleus, and 0◦ , ω1 , and
ω2 are the corresponding ω–angles. d is the half–thickness of the sample, O is the
x-coordinate of the half–thickness, and R is the distance from the nucleus to O in
the (x, y)–plane.
Nuclei in sample C
The two nuclei in sample C (called nucleus 2 and nucleus 3) were identified
post–experiment, and it was therefore not possible to perform superscans
on them to determine their precise (x, y, z)–positions within the sample.
Their positions must instead be inferred from the grid area, where they gave
rise to diffraction spots, and the maximum distance the nuclei can have to the
sample centre–thickness in order to still give rise to the observed reflections.
We may therefore confine the (y, z)–position of the nuclei within a grid area
(40×40 µm2 ) on the sample surface, and the x–position within a distance R
from the centre–thickness. However, due to the fact that the actual beam
size (49×49 µm2 ) used in the experiment was accidentally larger than the
grid areas (40×40 µm2 ), the nuclei in sample C gave rise to reflections in
diffraction images from more than one grid area. The grid areas, where the
nuclei were located, were taken to be the ones, where the integrated intensity
of the reflections from the nuclei were highest.
The triangulation from sample A was not possible, but there is an alternative method of determining whether the nuclei nucleated in the sample bulk
or at the surface. Since every observed reflection from the nuclei originated
from within the volume illuminated by the X–ray beam, we can use the rota86
reflection
2θ1
reflection
2θ2
nucleus
ω=0
o
d
x
ω1 ω2
R
y
O
Sample (x,y)-plane
b
Figure 4.19: Sample C nucleus location triangulation geometry in the (x,y)–plane
of the sample: ω1 and ω2 are respectively the maximum negative and positive
ω–values (ω ∈[-20◦ ,21◦ ]), which give rise to observed reflections.
tion angle between reflections to calculate the maximum distance R, which
the nucleus may be from the centre–thickness in the (x, y)–plane in order for
it not to rotate out of the X–ray beam when the sample is rotated. When the
ω–values of the outermost reflections are known, the y–offset they represent
may be used to calculate the maximum distance R, which the nucleus can
be from the sample centre–thickness (see figure 4.19):
b < |R sin ω1 | + |R sin ω2 | ⇐⇒
b
R <
| sin ω1 | + | sin ω2 |
(4.31)
where b=49 µm is the horizontal width of the X–ray beam, R is the maximum distance from the centre–thickness, and ω1 and ω2 are respectively
the maximum (negative and positive) ω–values, which give rise to observed
reflections.
87
4.2.3.5
Determining the crystal orientations of the nuclei
The crystallographic orientations of the nuclei were determined using
GRAINDEX, which is an in–house general–purpose multi–grain indexing
routine for powder and polycrystalline samples [94], running on the Windows
platform. It utilizes the commercial software Image Pro Plus for visualization
and some image analysis tasks. Especially the ’Spot Finder’, where individual
diffraction spots are identified on the diffraction images, is used. In order
to utilize only real diffraction spots, the minimum accepted intensity, the
min/max accepted spot size, and the maximum accepted (y, z) aspect–ratio
of a spot must be defined.
By rotating the sample around its vertical axis and recording diffraction
images on a 2D detector at several ω–values (typically one image per 1◦
rotation), it is possible to locate several reflections from each grain, and using
GRAINDEX, the individual crystal orientations of up to 5,000 bulk grains
within a sample may be determined from the same data set. GRAINDEX
works by assigning Miller indices (hkl) to the identified reflections, and fitting
them to different crystal orientations, i.e., different grains. It is assumed that
the crystal structural type (eg. fcc), such as may be determined by powder
diffraction, is known prior to using GRAINDEX.
The accuracy of this indexing is dependant on the size of the ω–range,
within which the diffraction images were obtained, and it is also very dependent on how much the sample has been deformed. This is because
the mosaic spread of the grains increases with increasing deformation, and
quickly leads to the diffraction spots from different grains overlapping for
even moderate plastic deformation (10+%) [67]. However, for an undeformed
powder sample, the data was good enough to allow Schmidt et al. to successfully perform structural refinement on a single Al2 O3 –grain [67].
The orientations of nucleus 1 and nucleus 2–3 were determined from
respectfully ω–ranges of ω ∈ [−45◦ , 46◦ ] and ω ∈ [−20◦ , 21◦ ] with ∆ω=1◦ .
For all nuclei, some of the expected reflections were hidden behind the poles,
but where this was not the case, it was possible to locate the reflections from
the nucleus with the GRAINDEX ’spot finder’, using the following settings:
the minimum accepted diffraction spot intensity was 600 counts (ignores noise);
the maximum diffraction spot area was 500 pixels (ignores the large reflections from the parent grains); and the maximum diffraction spot aspect–ratio
was 2 (the nucleus reflections were generally circular in shape).
88
4.2.3.6
Nucleus–to–parent grain orientation relationships
The reflections of the deformed grains all had a mosaic spread in the range
of ±5–20◦ on either side of a diffraction peak (measured in the azimuthal direction). Calculating the misorientation between the orientation of a given
nucleus, and the mean orientation of the grains in the deformed microstructure, was therefore not sufficient to prove whether the nucleus emerged with
an orientation previously present in the deformed microstructure, a 1st order
twin orientation of an orientation in the microstructure, or a new orientation
entirely.
Consideration was given to generating orientation distribution functions
(ODFs) for the deformed microstructure, as is possible from 3 pole figures
(see appendix B.2), and plotting the orientations of the nuclei into the ODFs
for a direct comparison. Unfortunately, this was impossible due to the saturation of the poles in the diffraction images, so another way of comparing
the orientations of the nuclei and those of the deformed microstructure had
to be envisaged.
Using pole figures was also considered (see appendix B.1), but was rejected as being too inaccurate. Pole figures, however, are a very good way
of showing the orientations. Figures 4.24–4.26 show the orientations of a
nucleus and its 1st order twins superimposed on the orientations present in
the deformed microstructure. The pole figures were obtained by first using
FIT2D to extract the azimuthal variations in intensity (intensity vs. η–angle)
for the {111}, {200}, and {220} Debye–Scherrer rings for every diffraction
image obtained from the deformed microstructure. The pole figures were
then calculated by the method of Mishin et al. [113].
The chosen method of comparing the orientations of the nuclei with their
possible parent orientations was to simulate the diffraction spots of the nuclei
directly onto the diffraction images recorded from the deformed microstructure before annealing. On figure 4.20 the methodology of the simulation can
be seen, as well as examples of spots lying within and outside the orientation
spread of the deformed microstructure. The procedure was to run through
the diffraction images obtained from the full ω–interval obtained from the
deformed sample one orientation at a time, i.e., one time for the nucleus
orientation, and one time for each of its four 1st order twin orientations.
In order for an orientation to lie within the orientations of the deformed
microstructure, no simulated diffraction spots for a given nucleus or twin
orientation were allowed to lie outside the poles of the deformed grains in
the diffraction images.
89
(a)
(b)
Figure 4.20: Diffraction spots simulated and plotted on images from the deformed
microstructure. The diffraction image is colour scaled to intensity (black to yellow),
and the white squares (indicated by arrows) are the simulated diffraction spots:
(a) orientation within the poles of the deformed grains; (b) orientation not within
the poles of the deformed grains.
4.2.3.7
Growth kinetics of the nuclei
By following the intensity of the diffraction spots arising from a nucleus
as a function of annealing time it is possible to follow its growth. This was
possible for nucleus 1 and nucleus 2, where a suitable diffraction spot was
found at all intermediate annealing time steps. No diffraction spots were
obtained from nucleus 3 at intermediate annealing times. For nucleus 1 and
nucleus 2, the volume was determined from respectively a (002) and (1̄11̄)–
reflection at the latest available annealing time step using equation 4.27.
At each time step, the intensity of the chosen reflection was determined
by integrating the intensity within an area–of–interest (AI) centered on the
reflection, and subtracting the background not due to the reflection. This was
determined by integrating the intensity within an identical AI on four sides
of the central AI, and the mean of these was defined to be the background.
Instead of applying equation 4.27 to find the size of the nuclei at every
time step, the intensity of the reflection relative to the reference intensity (see
above) was used to determine the size of the nucleus at all earlier time steps.
90
This was done because the intensity at the latest time step was considered
less effected by whatever fluctuations might affect the integrated intensity of
the reflection.
Estimating the uncertainties on the derived ECD was difficult since the
intensities of the different reflections arising from the same nucleus could vary
by nearly a factor 3. However, for the most intense reflections, the maximum
error in the intensities is thought to be about a factor 2. Error bars have on
purpose not been drawn on the nucleus growth curves in figure 4.23a–b, as
their size would at best be quite arbitrary.
Nucleus 1
This nucleus was identified in sample A, where a time resolution of
≈6 minutes was obtained. Note that, because the sample edges of the hot
specimen had to be realigned in situ during annealing, data was not acquired
at early annealing times. The first exposure obtained during annealing was
at 28.4 minutes after the annealing temperature had been reached.
Figures 4.21a–f show the evolution of the nucleus 1 (002)–reflection as
a function of annealing time. Good intense diffraction spots were obtained
throughout the dynamic study from the white square indicated on figure 4.12,
and the integrated intensities of the diffraction spots were scaled directly with
that obtained from the same diffraction spot in the GRAINDEX scan, where
the nucleus was centered in the X–ray beam (see section 4.2.3.5).
We were able to follow the growth of the nucleus for a full additional hour.
There was however considerable sample drift, which caused the nucleus to
drift nearly completely out of the X–ray beam, so that only a very week signal
was obtained from the otherwise intense (002)–reflection for the first 35–40
minutes. It was therefore not possible to reliably determine the integrated
intensity of (002)–reflection, past the first annealing step, without making
a considerable number of assumptions. It was therefore chosen to omit the
additional data from the nucleus 1 kinetics curve (see figure 4.23a). However, for reasons of interest, the last recorded image of the reflection (after
106.5 minutes of annealing) has been included in figure 4.21 as figure 4.21f.
Nucleus 2
During annealing of sample C, only the red 2×2–grid shown on figure 4.14
was characterized, so as to improve the time resolution by a factor of four
(≈8.5 minutes), but because the area (and possible tails) of the X–ray beam
extended from the top left red grid area into the top white grid area, where
91
(a)
(b)
(c)
(d)
(e)
(f)
Figure 4.21: Evolution of the nucleus 1 (002)–reflection with annealing time:
(a) 0 min; (b) 28.4 min; (c) 34.1 min; (d) 38.7 min; (e) 43.3 min;
(f ) 106.5 min.
nucleus 2 was located, the nucleus also gave rise to (weak) diffraction spots
in the top left red grid area.
Figures 4.22a–f show the time evolution of the nucleus 2 (1̄11̄)–reflection
as a function of annealing time. That we actually have dynamic data for this
nucleus is due to the X–ray beam vs. grid area mismatch, which was described
in the sample C–part of section 4.2.3.4. As can be seen from the images the
contrast between the nucleus reflection and the surrounding background was
minimal, and of the same order of magnitude.
It was therefore chosen not to use the full integrated intensity of the
single usable reflection, which was found to fluctuate considerably. Rather,
for the reflection, the highest measured single–pixel intensity was used to
92
(a)
(b)
(c)
(d)
(e)
(f)
Figure 4.22: Evolution of the nucleus 2 (1̄11̄)–reflection with annealing time:
(a) 0 min; (b) 2.5 min; (c) 72 min; (d) 124.5 min; (e) 167.8 min; (f ) 180 min.
Note that images (a) and (f ) are obtained from the top white grid area, and
(b)–(e) are obtained from the top left red grid area in figure 4.14.
assign a size to the nucleus. This maximum pixel intensity was then scaled
to the maximum pixel intensity observed in the same reflection in the white
grid area, giving a rough intensity conversion factor for the maximum pixel
intensity in the red and white grid areas (Iwhite ≈40 · Ired ). The integrated
intensity of the reflection could be reliably determined in the white grid area,
and this was then scaled to the maximum pixel intensity. Thus, the maximum
pixel intensity of the reflection in the red grid area was scaled linearly to an
integrated intensity through the conversion factor. The resulting ”integrated
intensities”, which were of course corrected for changes in the synchrotron
ring current, were then be converted into volumes using equation 4.27.
93
4.3
Results
In this section we will focus on the results obtained from the 3DXRD
nucleation experiment. Three samples were investigated, and to summarize
the results: three nuclei were identified (one in sample A, and two in sample C), all of which were located within the bulk; the crystal orientations of
the nuclei were determined, and compared to the parent microstructure; and
lastly, growth curves were determined for two of the nuclei (see figure 4.23).
10
7
9
6
8
5
ECD [µm]
ECD [µm]
7
6
5
4
3
4
3
2
2
1.14
0.72
0
0
Critical nucleus size
1.14
0.83
Critical nucleus size
Detection limit
Detection limit
10
20
30
40
0
0
50
50
100
150
200
Time [minutes]
Time [minutes]
(a)
(b)
Figure 4.23: Nucleus growth curves. The equivalent circle diameter (ECD) of the
nuclei are plotted as a function of annealing time. The annealing temperature was
290◦ C, and all values above ECD>0 were scaled from the intensity of an intense
reference reflection: (a) nucleus 1; (b) nucleus 2.
At t=0, the ECD of both nuclei was smaller than the detection limit (∼0.70 µm),
and are plotted as ECD=0 µm. No error bars have been plotted on the growth
curves for reasons discussed in section 4.2.3.7.
This section is divided into a subsection for the results obtained from
each nucleus, and all begin with a short summary of the results obtained
from that specific nucleus.
94
4.3.1
Nucleus 1
The (x, y, z)–position of nucleus 1 within the bulk of the sample was determined. The crystal orientation of this nucleus corresponded to a 1st order
twin orientation of one of the deformed grains. Lastly, a growth curve was
obtained for the nucleus, following its ECD from 5.1–9.4 µm during an annealing time space of 28.4–45.5 minutes (see fig. 4.23a).
The (x, y, z)–position of nucleus 1 was determined by the method detailed
for sample A in section 4.2.3.4. From superscans, the CMS–positions of two
{200}–reflections were found to be at ω1 =2.87◦ and ω2 =10.51◦ , and these
were found to have respectively the following (y, z)–coordinates:
(y1 , z1 )=(0.803 mm, 137.460 mm) & (y2 , z2 )=(0.792 mm, 137.458 mm)
By inserting these coordinates into eq. 4.30, the distance from the nucleus
to the centre–thickness in the (x, y)–plane is determined to be 83 µm, and
because ∆y=y2 −y1 is negative, it was also determined that the position is to
the right of ω=0◦, and therefore that it lies after the sample centre–thickness
(see fig. 4.18). Since the sample centre–thickness is 150 µm from the surface
in the x–direction, the nucleus was therefore located 150–83 µm=67 µm from
the sample surface, thus making it a bulk nucleus.
The (x,y,z)–position of the nucleus was (0.233 mm, 0.799 mm, 137.456 mm),
with negligible uncertainty, and from the EBSP study, the surface position of
the triple junction was (y, z)=(0.769 mm, 137.460 mm). When determining
the distance from the triple junction in the (y, z)–plane, we must take the
EBSP step size of 20 µm into account, which infers an uncertainty of ±10 µm
on the (y, z)–position of the triple junction in the (y, z)–plane, giving an overall uncertainty of ±14 µm. The nucleus was thus located 20±14 µm from
the (y, z)–surface location of the triple junction in the (y, z)–plane.
From the set of diffraction images within an angular range of ω∈[-45◦,46◦ ],
an orientation was fitted to the experimental diffraction spots using
GRAINDEX. The χ2 of the least–squares fit was 0.24, and the completeness was 0.63, which corresponds to the successful indexing of 17 out of 27
expected reflections. The 10 missing reflections were all expected in areas
covered by the poles of the deformed grains, and the fit was therefore considered to be a good representation of the orientation of the nucleus.
95
The orientation of the nucleus was found to be:
⎡
⎤
0.767 −0.629 −0.124
U(nucleus 1) = ⎣ −0.031
0.157 −0.987 ⎦
0.641
0.761
0.101
(4.32)
which is 41◦ from the ’cube’, and 35◦ from the ’rolling’ texture components
(see appendix B for details).
By using the diffraction spot simulation routine described in section 4.2.3.6,
the orientation of the nucleus was found to correspond to a 1st order twin
orientation of one of the deformed grains, i.e., that the embryo nucleated with
the orientation of one of the deformed grains, and subsequently twinned during its early growth. Before twinning, the orientation of the nucleus was:
⎡
⎤
0.384 −0.890 −0.246
0.454 −0.564 ⎦
Û([11̄1̄], −60◦ ) = ⎣ 0.690
(4.33)
0.641
0.047
0.788
where the crystal lattice of the nucleus is rotated -60◦ around the [11̄1̄]–axis.
The centre–of–mass (CMS) orientation of the deformed grains was determined from the images of the recovered microstructure (ω ∈ [−45◦ , 46◦ ])
using GRAINDEX. Three individual grain CMS–orientations were identified
with a completeness varying between 0.52 and 0.92. The CMS–orientation
of the deformed nucleus–parent grain was:
⎡
⎤
−0.231
0.390 −0.891
0.695
0.450 ⎦
U(parent grain) = ⎣ −0.560
(4.34)
0.795
0.604
0.058
By comparing the fitted orientation of the nucleus with the CMS–orientation
of the deformed parent grain, it was determined that the pre–twinning nucleus was misoriented by 38◦ from the CMS–orientation of the grain.
On figure 4.24, the orientations of nucleus 1 and its 1st order twins are
superimposed onto the {111}, {200}, and {220}–pole figures of the annealed
(not deformed) microstructure. Note that it was chosen to use the annealed
(i.e., recovered), rather than the deformed microstructure, as this allowed the
ω–range to be increased from [-10◦ ,11◦ ] to [-45◦ ,46◦ ], and thus much more
complete pole figures could be displayed. That a 1st order twin orientation
() of the nucleus lies within a pole in each pole figure is still evident.
96
TD
TD
{111}
{200}
RD
RD
TD
(a)
(b)
{220}
RD
(c)
Figure 4.24: Pole figures — nucleus 1 superimposed on the recovered microstruc-
∗
ture. The green marker ( ) is the orientation of the nucleus, and the red markers
(, ♦, , ) are the 1st order twins of the nucleus orientation.
The ω–range was [-45◦ ,46◦ ], and the intensities are ordered by colour:
[ black=400, blue=1,000, cyan=2,500, magenta=5,000, yellow=10,000 counts].
Reflections used in the pole figures were: (a) {111}; (b) {200}; and (c) {220}.
4.3.2
Nucleus 2
Nucleus 2 was located within a specific volume in the bulk sized 40×40×164 µm.
The crystal orientation of this nucleus did not correspond to the orientation
of any of the deformed grains, nor a 1st order twin orientation of any of
the deformed grains. Lastly, a growth curve was obtained for the nucleus,
following its ECD from 4.8–6.1 µm during an annealing time space of 2.5–
182.0 minutes (see fig. 4.23b).
97
The (y, z)–position of nucleus 2 was determined to be within the grid
area, where the reflections had the highest intensity, which was the grid
area centered at (y, z)=(0.716, 138.586). The maximum nucleus–to–centre–
thickness distance was determined by the method detailed for sample C in
section 4.2.3.3. The two outermost reflections, which were observed from
nucleus 2, were at ω1 =-14◦ , and ω2 =21◦ , and by substitution into eq. 4.31 we
find that R<82 µm, and thus that nucleus 2 is 150−82 µm >68 µm from the
sample surface. We may therefore conclude that nucleus 2 is a bulk nucleus.
The uncertainty on the (y, z)–position of the nucleus is set to half the
grid node distance (±0.020 µm), and we may thus place nucleus 2 within
the volume (0.150±0.082, 0.716±0.020, 138.586±0.020). In the (y, z)–plane,
we have an uncertainty of ±14 µm on the position of the triple junction
from section 4.3.1, and to this must be added the uncertainty ±28 µm on
the position of the nucleus. In the (y, z)–plane, the nucleus was located
85±42 µm from the surface position of the triple junction.
From the set of diffraction images within an angular range of ω∈[-20◦,21◦ ],
an orientation was fitted to the experimental diffraction spots using
GRAINDEX. The χ2 of the fit was 0.15, and the completeness was 0.91,
which corresponds to the successful indexing of 10 out of 11 expected diffraction spots, which is a very good fit of the nucleus orientation:
⎡
⎤
−0.412
0.428 0.804
U(nucleus 2) = ⎣ 0.174 −0.830 0.531 ⎦
(4.35)
0.895
0.358 0.267
which is 40◦ from the ’cube’, and 14◦ from the ’rolling’ texture components.
When the diffraction spot simulation routine described in section 4.2.3.6
was utilized, the orientation of the nucleus was neither found to correspond to
any of the deformed grains, or to a 1st order twin orientation of any of them.
Nucleus 2 was therefore of special interest, because it exhibited a completely
new orientation. Please note that twin–relations were not investigated to
further than 1st order.
It was not possible to confidently determine the CMS–orientations of the
deformed grains (or recovered grains for that matter) using GRAINDEX, due
to considerable spot–overlap in the diffraction images, which yielded no less
than 17 different individual grain orientations with completeness between
0.40 and 0.70. Of these orientations, no more than five could be discarded
by manually inspecting the diffraction images.
98
TD
TD
{200}
{111}
RD
RD
TD
(a)
(b)
{220}
RD
(c)
Figure 4.25: Pole figures — nucleus 2 superimposed on the deformed microstruc-
∗
ture. The green marker ( ) is the orientation of the nucleus, and the red markers
(, ♦, , ) are the 1st order twins of the nucleus orientation.
The ω–range was [-20◦ ,21◦ ], and the intensities were ordered by colour:
[ black=400, blue=1,000, cyan=2,500, magenta=5,000, yellow=10,000 counts].
Reflections used in the pole figures are: (a) {111}; (b) {200}; and (c) {220}.
On figure 4.25, the orientations of nucleus 2 and its 1st order twins are
superimposed onto the {111}, {200}, and {220}–pole figures of the deformed
microstructure. Note that for none of these orientations did all the reflections
lie fully within the poles of the deformed grains.
99
4.3.3
Nucleus 3
Nucleus 3 was located within a specific volume in the bulk sized 40×40×164 µm.
The crystal orientation of this nucleus corresponded to a 1st order twin orientation of one of the deformed grains. Lastly, its ECD was determined to
7.0 µm after 3.4 hours of annealing.
The (y, z)–position of nucleus 3 was determined to be within the grid
area, where the reflections had the highest intensity, which was the grid
area centered at (y, z)=(0.716, 138.706). The maximum nucleus–to–centre–
thickness distance was determined by the method detailed for sample C in
section 4.2.3.3. The two outermost reflections, which were observed from
nucleus 3, were at ω1 =-20◦, and ω2 =15◦ . By substitution into eq. 4.31 we
find that R<82 µm, and thus that nucleus 3 is 150−82 µm >68 µm from the
sample surface. We may therefore conclude that nucleus 3 is a bulk nucleus.
The uncertainty in the (y, z)–position of the nucleus is set to half the
grid node distance (±0.020 µm), and we may thus place nucleus 3 within the
volume (0.150±0.082, 0.716±0.020, 138.706±0.020).
In the (y, z)–plane, we have from section 4.3.1, an uncertainty of ±14 µm on
the position of the triple junction, and to this must be added the uncertainty
±28 µm on the position of the nucleus. In the (y, z)–plane, the nucleus was
located 85±42 µm from the surface position of the triple junction.
From the set of diffraction images within an angular range of ω∈[-20◦,21◦ ],
an orientation was fitted to the experimental diffraction spots using
GRAINDEX. The χ2 of the fit was 0.08, and the completeness was 0.53,
which corresponds to the successful indexing of 8 out of 15 expected diffraction spots. 6 of the missing reflections were all expected in areas covered by
the poles of the deformed grains, and the fit was therefore considered to be
a good representation of the orientation of the nucleus.
⎡
⎤
0.955 −0.236
0.181
0.167 −0.960 ⎦
U(nucleus 3) = ⎣ 0.223
(4.36)
0.196
0.957
0.212
which is 21◦ from the ’cube’, and 26◦ from the ’rolling’ texture components
(see appendix B for details).
100
By using the diffraction spot simulation routine described in section 4.2.3.6,
the orientation of the nucleus was found to correspond to a 1st order twin
orientation of one of the deformed grains, i.e., that the embryo nucleated with
the orientation of one of the deformed grains, and subsequently twinned during its early growth. Before twinning, the orientation of the nucleus was:
⎡
⎤
0.595
0.540
0.596
Û([1̄1̄1], −60◦ ) = ⎣ 0.733 −0.060 −0.677 ⎦
(4.37)
−0.330
0.839 −0.431
where the crystal lattice of the nucleus is rotated -60◦ around the [1̄1̄1]–axis.
The centre–of–mass (CMS) orientations of the deformed grains were determined from the images of the recovered microstructure (ω ∈ [−20◦ , 21◦ ])
using GRAINDEX. Five individual grains were identified with completeness
varying between 0.69 and 1.00. By utilizing the simulation routine, the nucleus orientation was found to originate from one of the grains, even though
it was misoriented 32◦ from the CMS–orientation of the grain, which was:
⎤
⎡
0.572 −0.597 −0.563
(4.38)
0.685 −0.722 ⎦
U(parent grain) = ⎣ −0.070
0.779
0.506
0.371
On figure 4.26, the orientations of nucleus 3 and its 1st order twins are
superimposed onto the {111}, {200}, and {220}–pole figures of the annealed
(not deformed) microstructure. That a 1st order twin orientation (♦) of the
nucleus lies within a pole in each pole figure is evident.
101
TD
TD
{111}
{200}
RD
RD
TD
(a)
(b)
{220}
RD
(c)
Figure 4.26: Pole figures — nucleus 3 superimposed on the deformed microstruc-
∗
ture. The green marker ( ) is the orientation of the nucleus, and the red markers
(, ♦, , ) are the 1st order twins of the nucleus orientation.
The ω–range was [-20◦ ,21◦ ], and the intensities were ordered by colour:
[ black=400, blue=1,000, cyan=2,500, magenta=5,000, yellow=10,000 counts].
Reflections used in the pole figures were: (a) {111}; (b) {200}; and (c) {220}.
4.4
Discussion and outlook
The main aim of the 3DXRD study was to investigate whether it was possible to relate the orientation of any identified nuclei with those orientations
existing in the deformed microstructure at the nucleation site prior to annealing.
The secondary aim was to investigate if the nuclei could be detected at the
time when they nucleated, and if possible, follow their growth as a function
of annealing time.
102
4.4.1
Discussion
Three nuclei were detected in the experimental diffraction images: two
exhibited orientations corresponding to 1st order twin orientations (nucleus 1
and nucleus 3); and of particular interest, one exhibited an orientation neither
corresponding to any of the deformed grains, nor a 1st order twin of any of
them (nucleus 2). Orientations obtained through the use of GRAINDEX are
generally accurate to within ∼1◦ .
The copper sample material was assumed to be free of large particles, as
no particles were observed in the OIMs, and no diffraction spots from second
phase particles sized above (>1 µm) the detection limit were observed in
the X–ray diffraction images, which at a deformation of 20% rules out PSN
according to Sandström (see section 1.2.6) [42]. Fine particles sized ∼0.1 µm
could not be resolved in the diffraction images. However, according to Jones
& Hansen any such dispersion of fine particles does not lead to PSN, but
leads instead to a retardation of the nucleation of recrystallization [23].
The next question to be addressed must be whether it is possible that
the nuclei grew from volumes, which were smaller than the detection limit.
A TEM–study had shown that the minimum subgrain size was 1–2 µm, and
further the classical critical nucleus size was found to be ECDC >1.14 µm
(see section 4.2.2.3), both of which were well above the detection limit of the
experiment. We may therefore conclude that any subgrains present outside
the poles would be detected in the diffraction images.
Lastly, there is the question of whether the orientation of nucleus 2 is
twin–related to any of the deformed grains. In this study we have limited
ourselves to comparing the orientation of the deformed grains with that of the
nucleus and its 1st order twins. Based on the results of nucleus 2, it would
seem that new orientations do occur. However, Haasen found up to 5th
order twin–relationships while investigating nucleus–matrix orientation relationships in TEM [8, 39], so this could indicate that the above conclusion is in
fact inconclusive. It should however be noted that no diffraction spots from
any twin orientations were observed, which has two possible explanations:
(i) either nucleus 2 does not have any twin–relation to the deformed/recovered
microstructure, i.e., it is a new orientation; or alternatively, (ii) multiple twinning occurred so rapidly on the migrating high angle boundary of the nucleus
that the intermediate twins are smaller than the detection limit. However,
according to Leffers this is unlikely [114].
103
Other authors have reported nuclei with new orientations [3, 5, 6, 115],
and have in each case noted a rotation about a <111>–axis with respect to
one of the deformed parent grains. It was however not possible to determine
any such relationship between the possible new orientation of nucleus 2 and
the deformed grains. This was due to the fact that the X–ray beam was
diffracted by all orientations lying within the volume traced out by the beam,
while it would be necessary to know the exact orientations present at the
nucleation site to determine whether the new orientation corresponded to a
rotation about a <111>–axis.
It was possible to follow the kinetics of two of the three nuclei during
annealing, and in one case the nucleus was detected after only 2.5 minutes
of annealing at 290◦ C. The estimated error in the intensity of the most intense reflections is estimated to be a factor 2 at most. For the ECD, this
gives a maximum relative error of 26%. The growth curves were plotted
showing ECD as a function of time. However, given the fact that the nuclei most likely nucleated on triple junctions or grain boundaries, a more
realistic nucleus shape would be saucer–like, which would result in a geometrically modified ECD. However, as it was not possible to obtain conclusive
data indicating for or against a spherical nucleus shape (see section 4.1.4),
determining this must be a task for the future.
104
4.4.2
Outlook
To summarize, a method which allows in situ studies of the nucleation
of discontinuous recrystallization within diffracting bulk materials has been
envisaged and realized. Depending on the data obtained, the following information about an observed bulk nucleus may be obtained: its deformed
parent microstructure; its crystal orientation; its exact or approximate position; and its growth kinetics. To the knowledge of the author, this is the first
technique to provide all this information, without the ambiguity of resorting
to dynamic surface investigations.
As well as the scientific results obtained, this experiment should mainly
be viewed as a feasibility study. In outlook, the method presented can
be applied to almost any problem in nucleation, such as phase transitions
and solidification, and should therefore find broad application. The spatial
resolution of the deformed microstructure was rather crude in this study
(49×49×300 µm3 ), but this may be significantly improved at the discretion
of the user, eg. by narrowing the X–ray beam and/or reducing the thickness of the sample, as has been successfully done by both Poulsen et al. and
Gundlach et al. [4, 66].
In future experiments, the volume detection limit may if necessary be
lowered significantly by a combination of several factors:
an additional undulator has been installed at ID–11 since the experiment,
which means that the X–ray flux has been increased by a factor of 2–3 [97];
if the storage ring is run in normal (992 electron bunch) mode, the ring
current is 200 mA (it was 90 mA during the experiment), and additionally,
there are plans to upgrade the storage ring to running at 250 mA, which
gives a relative flux increase of 2.2–2.8 [95];
the X–ray beam may be focused to a smaller size, eg. using a 25×25 µm2
beam will increase the relative flux by a factor of 4;
and lastly, the detection limit may also be lowered by choosing to study a
metal with a higher X–ray scattering factor (roughly proportional to Z), such
as silver (Z=47) or gold (Z=79).
105
Lastly, a method which allows the actual nucleation mechanisms to be
studied directly by 3DXRD is envisaged. This is done by locating and characterizing the strained zone surrounding elongated rigid interstitial particles
of micrometre size in situ within the bulk of a deformed sample, because
rigid particles are very likely nucleation sites (see section 1.2.6). Also, the
strained zone around a rigid particle is generally misoriented relative to the
surrounding microstructure, and may thus be distinguished from this with
3DXRD. By characterizing the strained zone surrounding a particle before
and during annealing, there is a good chance that nucleation may be followed
on the subgrain level, due to the relatively small size of the deformation
zone (∼10 µm), which may then be characterized in great detail, and with a
X–ray beam of slightly larger size the annealing process may thus be followed
with a single beam position.
The particle–containing sample should preferably be a deformed single
or bi–crystal of small thickness, and consist of a metal with high stacking
fault energy (such as aluminium), to avoid twinning as much as possible.
Choosing a metal with a well–defined deformation microstructure will help
as well. The initial detection of suitable particles can be performed with a
large box beam, and a suitable particle may then be translated into the centre
of rotation, after its precise position has been determined with a superscan
on one of its reflections. Characterization of the strained zone around a
particle may afterwards be performed with a X–ray beam focused to small
size (eg. 10×10 µm2 ).
This approach follows closely that of Gundlach et al. [66], but here a likely
nucleation site is chosen for study, in the hope that nucleation will occur at
that specific site, as opposed to simply following subgrain growth. If a bi–
crystal is chosen the chances of nucleation occurring at the chosen particle
may be further increased by choosing a particle situated at the grain boundary, due to the high local orientation gradients present at grain boundaries
in deformed metals.
106
Chapter 5
Conclusions
In this PhD project the nucleation of recrystallization has been studied
in a broad sense using various experimental techniques. This has lead to:
• Development of an experimental method, which allows reliable automatic line scans to be performed utilizing the EBSP technique.
The program LSGRAINS represents a fast and efficient way of obtaining the recrystallization parameters VV , SV , and <λ>, which are
important when studying recrystallization dynamics. The method has
been compared to three different manual EBSP line scan methods and
has been found to be in good agreement with these, and is now used
for studies of recrystallization kinetics within the Metals–4D center.
• A reliable method by which serial sectioning of samples may be performed in steps down to 2 µm has been developed. Combined with
OM or EBSP investigations of the sectioned surfaces, a full 3D reconstruction of the microstructure is possible with a spatial resolution
of ∼2 µm. The method also allows polishing of samples down to a
pre–specified target depth with an accuracy of 1–2 µm, and thus allows a direct comparison between surface and bulk sensitive techniques.
Equally important is that this allows the two kinds of techniques to be
combined within one experiment, so as to provide even more detailed
information about the samples studied.
107
• 3DXRD has been proven to be a powerful tool for studying in situ bulk
nucleation of recrystallization, yielding both crystallographic orientations as well as growth kinetics of individual bulk nuclei.
Triple junctions have been proven to be likely nucleation sites, but
also not all triple junctions lead to nucleation, which is in good agreement with previous surface and serial sectioning results.
The first ever experiment using X–ray diffraction to study in situ bulk
nucleation of recrystallization in a metal sample was carried out successfully. The deformed and annealed microstructures around triple
junctions were characterized in three samples, from which three nuclei
were identified, their crystal orientations were determined, and for two
of them growth curves were determined as well.
• A nucleus emerging with a new orientation, not directly or 1st order
twin–related to the deformed microstructure, has been observed growing. It is deemed very unlikely that its orientation should be the result
of multiple twinning reactions, or that it grew from a cell smaller than
the detection limit.
With the LSGRAINS program, obtaining experimental data on recrystallization dynamics is now a much faster and more efficient process. Several
studies have already been performed or are in progress using this technique.
With the development of a reliable serial sectioning technique it has become possible to combine 3DXRD and microscopy, so that interesting microstructural features, such as nuclei, identified using 3DXRD may also be
studied directly by microscopy by polishing the sample down to the depth
of the feature. This should increase the knowledge gleaned from such experiments, as it will be possible to combine the strengths of the various
microscopies.
Finally, it is the opinion of the author that with the various planned
upgrades of the 3DXRD microscope and the experiment outlined in section 4.4.2, it will soon be possible to study in situ the nucleation of recrystallization on a scale and with a time resolution, which will allow the mechanism behind an observed nucleation event to be determined, thus leading to
a breakthrough in the understanding of the nucleation of recrystallization.
108
Appendix A
Crystal orientations
The alignment between the sample geometry and the crystal lattice of a
given crystal grain is called the crystal orientation of the grain. . .
There are several ways to quantitatively represent crystal orientations.
However, to define crystal orientations we must first define the axes of the
sample coordinate system. In this thesis we will focus on the rolling geometry,
where the rolling axes and planes are derived from the deformation process
(see figure A.1):
roll
r
O
specimen
C
A
B
h0
ND
h1
TD
RD
RD-TD
ND-TD
roll
(a)
D
-N
RD
(b)
Figure A.1: The rolling geometry: the rolling direction (RD); the transverse direction (TD); and the normal direction (ND). (a) Rolling mill geometry: r is the
radius of the rolls, and h0 and h1 are respectively the specimen thickness before
and after rolling. (b) Rolling plane geometry: the rolling plane (ND–TD); the
transverse plane (RD–ND); and the normal plane (RD–TD).
109
Of course other deformation modes exist, eg. wire–drawing where only
one axis is defined by the process, but since the samples used in this thesis
have all been deformed by cold rolling the rolling geometry is used. For a
more complete coverage of the topic of crystal orientations the author refers
to Hansen et al. [13].
A frequently used way to represent the orientation of a crystal grain is
to use the Miller indices (hkl)[uvw] to indicate which crystallographic planes
lie in respectively the rolling plane (ND–TD) and along the perpendicular
rolling direction (RD) [13]. The Miller indices {hkl}<uvw> indicate the
family of crystallographic planes, which correspond to the same orientation.
E.g. the ’cube’ orientation has {100}<001>, which means that the axes
of the unit cell are perfectly aligned with the rolling axes (see fig. A.1b).
The main advantages of this representation is its brevity and that it may be
plotted directly onto images of the microstructure, thus giving a visual and
very intuitive understanding of an orientation.
An often used alternative to this representation is the Euler angles (ϕ1 , φ, ϕ2),
which are defined as the three rotations that will bring the sample coordinate
system (xs , ys , zs ) to coincide with the crystal coordinate system (xc , yc , zc ).
For a cubic lattice, the crystal coordinate system is spanned by the three
lattice vectors ([100], [010], [001]). Here the Bunge definition of the Euler
angles has been used [116]. First, (xs , ys , zs ) is rotated around zs by the angle
ϕ1 . Secondly, the rotated sample system (xs , ys , zs ) is rotated around xs by
the angle φ, which brings zs to coincide with zc . Lastly, xs and ys are brought
to coincide with xc and yc by a rotation of ϕ2 around zs /zc .
zc
zs
φ1
φ2
yc
φ2
φ1
ys
xs
φ1
xc
xs’ φ2
Figure A.2: The Euler angles ϕ1 ∈[0,2π], φ∈[0,π], and ϕ2 ∈[0,2π] describe how
the crystal coordinate system (xc , yc , zc ) may be rotated into the sample coordinate
system (xs , ys , zs ).
110
Generally, a 3×3 orientation matrix U is used to fix the crystal lattice to
the sample geometry. This is a very useful representation, since it may be
used directly to calculate the diffraction vector from an X–ray beam diffracted
by a set of crystal planes in a crystal grain within a macroscopic polycrystalline sample (see section A.2) [13].
U may be calculated directly from a set of Miller indices (hkl)[uvw] [13]:
⎡
⎤
V
W
U
⎢
⎢
U((HKL)[UVW]) = ⎢
⎢
⎣
N
N
N
KW−LV
MN
LU−HW
MN
HV−KU
MN
H
M
K
M
L
M
⎥
⎥
⎥
⎥
⎦
(A.1)
√
√
where M = H2 +K2 +L2 and N = U2 +V2 +W2 , or alternatively from the
Euler angles (ϕ1 , φ, ϕ2) [13]:
⎡
cos ϕ1 cos ϕ2 − sin ϕ1 sin ϕ2 cos φ
U(ϕ1 , φ, ϕ2 ) = ⎣ sin ϕ1 cos ϕ2 + cos ϕ1 sin ϕ2 cos φ
sin ϕ2 sin φ
A.1
− cos ϕ1 sin ϕ2 − sin ϕ1 cos ϕ2 cos φ
− sin ϕ1 sin ϕ2 + cos ϕ1 cos ϕ2 cos φ
cos ϕ2 sin φ
⎤
sin ϕ1 sin φ
− cos ϕ1 sin φ ⎦
cos φ
(A.2)
Twin–orientations
Crystallographically, twinning amounts to a 60◦ rotation around a [111]–
axis. The twin–orientations of an orientation are calculated by performing
±60◦ rotations around all eight <111>–axes. The resulting 16 U–matrices
produce a total of 4 different twin–orientations when the symmetrically equivalent orientations (see below) are taken into account.
The orientation resulting from rotating an orientation U by an arbitrary
angle θ around an arbitrary normalized axis vector n̂ = (n̂1 , n̂2 , n̂3 ) is:
Û(n̂, θ) = U R(n̂, θ)
(A.3)
where U is the original orientation, Û(n̂,θ) is the new orientation, and the
rotation matrix R(n̂,θ) is given by eq. A.4 [13]:
⎡
n̂21 (1−cos θ) + cos θ
R(n̂, θ) = ⎣ n̂1 n̂2 (1−cos θ) + n̂3 sin θ
n̂1 n̂3 (1−cos θ) − n̂2 sin θ
n̂1 n̂2 (1−cos θ) − n̂3 sin θ
n̂22 (1−cos θ) + cos θ
n̂2 n̂3 (1−cos θ) + n̂1 sin θ
111
⎤
n̂1 n̂3 (1−cos θ) + n̂2 sin θ
n̂2 n̂3 (1−cos θ) − n̂1 sin θ ⎦
n̂23 (1−cos θ) + cos θ
(A.4)
√
where for a twin–orientation: θ = ±60◦ ; and n̂ = (±1, ±1, ±1)/ 3.
Because |n̂|2 = n̂21 + n̂22 + n̂23 = 1, it is apparent from eq. A.4 that the rotation angle θ may be calculated directly from the trace of the rotation
matrix R(n̂,θ):
Trace(R(n̂, θ)) − 1
θ = arccos
(A.5)
2
Therefore, if two orientations are known, the misorientation angle θ between
them may be determined by calculating R(n̂,θ) from eq. A.6 and inserting
R(n̂,θ) into eq. A.5:
(A.6)
R(n̂, θ) = UT Û(n̂, θ)
where UT is the transpose of U.
However, it should be noted that because of the symmetry of the crystal
lattice, the θ value given by eq. A.5 may not be the lowest misorientation
angle between two orientations. This is found by calculating all symmetric
equivalent orientations (24 in fcc crystals) of the first orientation, and determining the misorientation angle between each of these orientations and the
second orientation. The one with the lowest misorientation angle is chosen
as the misorientation angle between the two orientations.
The symmetric equivalents exist because it possible to perform symmetry
operations (eg. rotations about an i–fold axis, or inversions about mirror
planes), which result in exactly the same crystal lattice and therefore exactly
the same orientation as before the symmetry operation was performed, but
with a different U–matrix [13].
112
A.2
The X–ray diffraction equation
In this section will determine the basic diffraction equation of the 3DXRD
microscope. The derivation follows those of Nielsen and Lauridsen et al. [68, 94].
The experimental coordinate system (xt , yt , zt ), within which the experiment was performed, is tilted slightly from the laboratory coordinate system
(xlab , ylab , zlab ). This is due to the fact that the initially horizontal X–ray
beam leaves the monochromating–focusing optics at an angle. The transformation between the two coordinate systems is described by the following
matrix operation:
⎞⎛
⎛
⎞ ⎛
⎞
xlab
xt
cos(2θm ) cos(2θM L ) − sin(2θM L ) sin(2θm )
⎠ ⎝ ylab ⎠
⎝ yt ⎠ = ⎝
cos(2θM L )
0
sin(2θM L )
zt
0
cos(2θm )
zlab
− sin(2θm )
(A.7)
where θm is the vertical diffraction angle from the monochromator crystal,
and θM L is the horizontal diffraction angle from the multilayer.
Now that the tilted coordinated system is defined, we shall work exclusively in that. The vector Gt for elastic scattering of X–rays in the tilted
system is given by (see fig. 4.3):
⎛
⎞
cos(2θ) − 1
2π ⎝
Gt =
sin(2θ) sin(η) ⎠
(A.8)
λ
sin(2θ) cos(η)
When the sample is rotated, the positive sample rotation Ω is in the anti–
clockwise direction when one observes the sample from above (see fig. 4.3):
Gω = Gt Ω
⎛
⎞
cos(ω) − sin(ω) 0
Ω = ⎝ sin(ω) cos(ω) 0 ⎠
0
0
1
(A.9)
(A.10)
The sample coordinate system (xs , ys , zs ) defines how the sample is mounted
on the rotation stage with respect to the deformation axes of the sample. The
setup of choice was xs =TD, ys =RD, and zs =ND, which gives the S–matrix
(see fig. A.1a):
Gω = S Gs
⎛
⎞
1 0 0
S = ⎝ 0 1 0 ⎠
0 0 1
113
(A.11)
(A.12)
The Cartesian grain system (xc , yc , zc ) is related to the Cartesian crystal axes
by making the crystal orientation transformation:
Gs = U Gc
(A.13)
where U is the orthogonal matrix that relates the sample to the crystal
coordinate system (see eq. A.1 and A.2). Lastly, the Miller indices (hkl),
where the crystal scattering vector is calculated, are directly linked to the
orthonormal crystal scattering axes Gc by the transformation matrix B [38]:
Gc = B Ghkl
Ghkl = (h, k, l)
⎞
⎛ ∗ ∗
c∗ cos(β ∗ )
a b cos(γ ∗ )
B = ⎝ 0 b∗ sin(γ ∗ ) −c∗ sin(β ∗ ) cos(α) ⎠
0
0
c∗ sin(β ∗) sin(α)
cos(β ∗ ) cos(γ ∗ ) − cos(α∗ )
cos(α) =
sin(α∗ ) sin(β ∗)
(A.14)
(A.15)
(A.16)
(A.17)
where (a, b, c, α, β, γ) and (a∗ , b∗ , c∗ , α∗, β ∗ , γ ∗ ) are respectively the lattice parameters in direct and reciprocal space. In the case of a cubic crystal we have
a∗ =b∗ =c∗ =2π/a and α∗ =β ∗ =γ ∗ =π/2, which greatly simplifies B and simply
adds a factor 2π/a in front of Ghkl . When all transformations between the
different coordinate systems are compounded, we get the basic diffraction
equation for the scattering vector Gt :
Gt = Ω S U B Ghkl
(A.18)
which describes all scattering within the tilted laboratory coordinate system.
114
Appendix B
Crystallographic textures
When all possible crystallographic orientations do not occur with the
same frequency in a polycrystalline material, and one or more preferred orientations exist, the material is said to have a texture. Texture is of major
industrial importance, since the properties of a polycrystalline material will
depend on the overall crystallographic orientation of the crystal grains and
much effort is made to control it. The texture of a material is generally represented using either pole figures, which are quite visually intuitive, or orientation distribution functions, which quantify textures better. For further
information about textures the author refers to Hatherley & Hutchinson [14].
In cold rolled fcc metals, the dominant texture components are:
’cube’ {100}<001> — a texture component, which grows from volume fractions close to zero to high values during primary recrystallization.
’rolling’ consisting of ’Brass’ {110}<112>, ’S’ {123}<624>, and
’Copper’ {112}<111> — the dominant texture observed in cold rolled
metals prior to annealing. This is due to the grains rotating in specific
directions during plastic deformation.
’random’ — Generally, any crystal grain not belonging to either of the
above texture components is said to exhibit ’random’ texture.
Depending on the application of the material other texture components (such
as ’Goss’ {110}<001>) may be of interest. Here we have used the first
orientation notation presented in appendix A.
115
B.1
Pole figures
Pole figures are a way to visually represent the orientation of a single
crystal or polycrystal with respect to directions given by the sample geometry
and/or deformation method. The orientation of a single crystal grain in the
sample can be represented by plotting a number of its crystal directions (eg.
three {100} directions) at their appropriate angular positions relative to the
reference direction.
Figure B.1: Pole figure of rolled sheet. The pole figure axes are the ND, RD,
and TD directions, and the displayed plane normals are those of the {100} planes.
(a) the stereographic projection of the {100} planes of a single crystal; (b) pole
figure of an undeformed single crystal; and (c) pole figure of a deformed single
crystal [14].
To produce a pole figure, a single crystal is placed within an unit sphere,
116
who’s axes are set equal to the axis of the imposed deformation (RD, TD, and
ND). The intersections of the normal vectors of a set of crystal lattice planes
(eg. {100}) with the surrounding unit sphere are determined (see fig. B.1a).
The pole figure is the stereographic projection of these intersections.
In short, the stereographic projection consists of drawing lines from the
intersection points on the northern hemisphere of the unit sphere to the
south pole. The positions, where these lines cross the equatorial plane give
a 2 dimensional representation of the orientation of the crystal, which is the
stereographic projection.
In a pole figure the plane normals of one crystal grain will be spots with
an orientation spread around them corresponding to the mosaic spread of
the grain, so a perfect single crystal should give very distinct spots (see
fig. B.1b), while a heavily deformed crystal grain with a large mosaic spread
would produce a large spot centered around the average orientation of the
grain (see fig. B.1c). The pole figure of a polycrystal will simply be the
superposition of all the spots of all the grains onto the equatorial plane.
B.2
The orientation distribution function
When the texture of a polycrystal must be quantitatively described, this
is generally well done using the orientation distribution function (ODF),
which describes the volume fraction of crystal grains with a specific orientation in the 3 dimensional Euler angle space (ϕ1 , φ, ϕ2 ), which is covered in
appendix A. Shortly, the ODF is a function f (g), which is defined in such a
manner that f (g) dg is the volume fraction of orientations within the orientation element dg, and that f (g)=1 for a random distribution of orientations.
This is done by introducing the orientation volume element dg [13]:
dg =
1
sinφ dϕ1 dφ dϕ2
8π 2
where the orientation distribution function f (g) is defined by [13]:
2π π 2π
1
f (g) 2 sinφ dϕ1 dφ dϕ2 = 1
f (g) dg =
8π
0
0
0
(B.1)
(B.2)
ODFs are generally plotted as a series of planes in Euler space, where one
Euler angle (ϕ1 or ϕ2 ) is held constant in each plane.
117
Appendix C
Beamline specifics
Specific information on the X–ray source, monochromating–focusing optics, and the CCD–detector of beamline ID–11 has been placed in this appendix, as it is primarily thought to be of interest for dedicated X–ray scientists, and to be of less interest to the more general audience, with whom
in mind this thesis has been written.
magnet period
Kmax
field Bmax
fundamental wavelength
source size
source divergence
peak brilliance
peak tot. integ. flux
power
power density
beam size at 25 m
total horizontal
angular acceptance
23 mm (69 periods)
1.8995
0.88 T
1.70 Å
57 × 10 µm2 (H×V) FWHM
(incl. source broadening)
88 × 5 µrad2 (H×V) FWHM
5·1019 ph s−1 mrad−2 mm−2 ,
0.1% BW, 0.1 A
16
2.5·10 ph s−1 , 0.1% BW, 0.1 A
3.8 kW (at 0.1 A SR current)
114 Wmm−2
25 × 1.5 mm2
2.2 mrad (FWHM)
Table C.1: Specifics about the ID11 in–vacuum undulator. Properties are for a
gap motor setting of 7.219 mm, which was used for the experiment. Note however,
that fluxes given at a synchrotron ring current of 200 mA [97].
118
Most of the information presented in these tables has already been presented in section 4.1, so they should mainly be viewed as a summary of the
four standard devices used in the 3DXRD experiment.
No further explanation will be given here for the additional information
available in these tables, but keen readers are recommended the book by
Als–Nielsen & McMorrow for further reading [12].
CCD–chip size
1024×1024 pixels
effective pixel size
157×157 µm2
Width of Point Spread Function
200–300 µm
effective active area
160×160 mm2
Phosphor after–glow
< 10−2 s
Dynamic range
14 bits
min. readout time
0.2 sec
sample to detector distance
330 mm
Table C.2: Technical specifications for the 2D Frelon CCD–detector [97].
119
energy
tunability
source–mono distance
mono–focus distance
reflection
asymmetry angle
bending radius
crystal thickness
energy bandwidth
(per 1 mm beam width)
efficiency
focus size
focal length
50 keV
∼10%
51.2 m
2m
(1 1 1)
0.8◦
4m
2 mm
0.8%
80 keV
∼10%
51.2 m
2m
(1 1 1)
0.5◦
4m
1 mm
0.8%
90 %
1.5 µm
2m
90 %
1.5 µm
2m
Table C.3: Specific information about the asymmetrically cut and cylindrically
bent Si(111)–Laue crystals, used for monochromating and focusing the X–ray beam
in the vertical direction [97].
energy
source–ML distance
ML–focus distance
ML materials
number of periods
Γ–ratio
central d–spacing
gradient ∆d/d
curvature (major rad.)
energy bandwidth
efficiency
focus size
50 & 80 keV
52.5 m
1.4 m
W & B4 C
100
0.1455
20 Å
0.10
25 m
1.4 %
50 %
4 µm
Table C.4: Specific information about the elliptically shaped and laterally graded
W/B4 C–multilayer, used to focus the X–ray beam in the horizontal direction [97].
120
Appendix D
Publications
A1:
A. W. Larsen and D. Juul Jensen. Automatic determination of recrystallization parameters in metals by EBSP line scans.
Materials Characterization, 51(4):271–282, 2003.
A2:
A. W. Larsen, H. F. Poulsen, L. Margulies, C. Gundlach, Q. Xing, X. Huang
and D. Juul Jensen. Nucleation of recrystallization observed in situ in the
bulk of a deformed metal. Scripta Materialia, 53:553–557, 2005.
A3:
A. W. Larsen. ’Logitech PM5D precision polishing and lapping system’
user manual. Risø I–report, Risø–I–2051(EN), Risø National Laboratory,
Roskilde, Denmark, September 2003.
A4:
G. Winther, L. Margulies, H. F. Poulsen, S. Schmidt, A. W. Larsen,
E. M. Lauridsen, S. F. Nielsen, and A. Terry.
Lattice rotations of individual bulk grains during deformation.
In Textures of Materials, pts 1 and 2, volume 408–4, pages 287–292, Roskilde,
Denmark, 2002. Materials Science Forum.
A5:
A. W. Larsen, C. Gundlach, H. F. Poulsen, L. Margulies, Q. Xing, and
D. Juul Jensen. In–situ investigation of bulk nucleation by X–ray diffraction.
In 2. International conference on recrystallization and grain growth, pages
81–86, Annecy, France, 2004. Trans Tech Publications Ltd.
A6:
D. Juul Jensen, M. D. Lund, A. W. Larsen, and J. R. Bowen.
Recrystallization kinetics in the bulk and at the surface.
In 2. International conference on recrystallization and grain growth, pages
147–151, Annecy, France, 2004. Trans Tech Publications Ltd.
A7:
D. Juul Jensen and A. W. Larsen.
Orientations of recrystallization nuclei studied by 3DXRD.
In Proceedings of the 14th International Conference on Textures of Materials,
pages 1285–1290, 2005. Materials Science Forum
121
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133
A1
Materials Characterization 51 (2003) 271 – 282
Automatic determination of recrystallization parameters in metals
by electron backscatter pattern line scans
Axel W. Larsen *, Dorte Juul Jensen
Center for Fundamental Research: Metal Structures in Four Dimensions, Risø National Laboratory, PO Box 49,
4000 Roskilde, Denmark
Received 14 December 2003; received in revised form 7 January 2004; accepted 14 January 2004
Abstract
In this paper, a new automatic procedure for determining critical recrystallization parameters, which are important when
studying recrystallization kinetics, is presented. The method is based on electron backscatter patterns (EBSP) line scans
using a scanning electron microscope, where three parallel lines are scanned. The concepts of equivalence and connectivity
are used to group the data points into those originating in recrystallized grains and those originating in the deformed
matrix. The computer program implementing the automatic procedure is tested in three different ways: three short scans are
performed, where the calculations are also done by hand; the results of two long scans are compared to the direct
observation of the microstructure seen in orientation image maps (OIMs) [Mater. Sci. Eng. A. 166 (1993) 59], and the
results of scans from a series of samples are compared to statistical results obtained manually. A good correlation was
achieved in all three cases.
D 2004 Elsevier Inc. All rights reserved.
Keywords: LSGRAINS; EBSP; Line scans; Recrystallization; Metals
1. Introduction
In the characterization of recrystallizing microstructures it is often important to determine the three
parameters: the volume fraction recrystallized (VV),
the interfacial area separating recrystallized grains
from the deformed matrix (SV), and the mean recrystallized grain intercept length (hki) [2].
For example, using the method of Cahn and Hagel,
VV and SV are used for an exact determination of the
average growth rate (hGi) of the recrystallizing grains
in the microstructure [3]:
dVV
¼ hGiSV
dt
* Corresponding author. Tel.: +45-46775783; fax: +4546775758.
E-mail address: [email protected] (A.W. Larsen).
URL: http://www.metals4d.dk.
1044-5803/$ - see front matter D 2004 Elsevier Inc. All rights reserved.
doi:10.1016/j.matchar.2004.01.001
ð1Þ
An efficient way to determine these parameters is
by the linear intercept method, which uses random
line scans through the microstructure, and where the
interfaces between recrystallized grains and the de-
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A.W. Larsen, D. Juul Jensen / Materials Characterization 51 (2003) 271–282
Fig. 1. EBSP OIM showing a recrystallizing microstructure is shown with two lines drawn through it [1]. Examples of recrystallized and
deformed grains are identified by the red arrows, and where the drawn lines cross an interface this is marked orange for a recrystallized –
recrystallized interface and white for a deformed – recrystallized interface.
formed matrix are noted (see Fig. 1) [4]. In this case
VV, SV, and hki can be written as [3,5]:
VV ¼
Lrex
L
ð2Þ
SV ¼
2nint
L
ð3Þ
hkiu
N
1X
ki
N i¼1
ð4Þ
where L is the total length of the scanned line, Lrex is
the total length of the line in recrystallized material,
nint is the number of interfaces between recrystallized
and deformed material crossed by the line, N is the
number of grains intersected by the line, and ki is the
intersect length of the ith grain.
If the orientations of the recrystallized grains are
also determined, as it is possible by electron backscatter patterns (EBSP), VV, SV, and hki may be
determined for the individual orientations. Therefore,
the average growth rate for grains of different crys-
tallographic orientations can also be determined, e.g.,
cube (h100i {001}) oriented grains in fcc metals [6] or
g-fibre grains in bcc metals [7].
This approach to determining the parameters is
adopted in the present work, where the EBSP technique is used. A previous technique, also based on
EBSP, but scanning a single line was found to give an
accurate determination of VV and hki, but SV typically
differed by one order of magnitude from the value
obtained by manual scans (Krieger Lassen, private
communication, 2001). In this paper, we present a
new method based on scanning three parallel lines, the
outer two of which are used solely as auxiliary lines to
support the data points on the central line.
Alternatively, one may consider making the measurement by EBSP in full 2-D, which may even be a
possibility as the EBSP data acquisition rate is constantly increasing (at present, up to 10– 60 patterns/s).1
However, as an efficient method for determination of
1
Numbers from the homepages of: HKL Technology (http://
www.hkltechnology.com), and TSL (http://www.edax.com/TSL/).
A.W. Larsen, D. Juul Jensen / Materials Characterization 51 (2003) 271–282
273
VV, SV, and hki is based on the linear intercept method,
all the data points away from this line are redundant,
and the measuring time is better spent measuring
longer lines, which will intersect more grains than a
2-D scan, thus giving superior sampling statistics.
2. The procedure
The procedure is to scan along a line through the
microstructure collecting EBSP orientation data at
each step along the line. Going through the data,
one of three specifications is allocated to every data
point: recrystallized, deformed, or bad. Based on these
specifications, it is determined which data points
belong to which recrystallized grain and which data
points belong to the deformed matrix.
This indexing is done using an algorithm called
LSGRAINS, which has been specially developed for
three-line scans (see Section 2.1): that is, a central line
with two parallel auxiliary lines (an upper and a
lower). Only the data points on the central line are
considered ‘‘real’’ data points and are thus used to
calculate VV, SV, and hki. The data points on the
auxiliary lines are only used to determine whether a
data point on the central line is a part of a recrystallized grain or the deformed matrix, and to make sure
that the correct orientation is attributed to a given data
point in the case when this data point is incorrectly
indexed (i.e., ‘‘bad’’).
The pivotal part of the algorithm is the concept of
equivalent crystallographic orientation. Two data
points are said to have equivalent orientation if their
mutual misorientation is less than a user-specified
limit—this is normally set to the resolution of the
EBSP system (typically, 0.5 –1.0j).
2.1. The three-line scan
The three-line scans (see Fig. 2) consist of three
parallel lines: a central line with an upper and a lower
auxiliary line. These auxiliary lines have the same step
size as the central line, and are at the same distance to
the central line as the step size. They function as a pair
of reference lines for the central line, helping the
algorithm determine whether a data point belongs to
a recrystallized grain or the deformed matrix (Fig. 5
shows examples of real three-line scans).
Fig. 2. The environment around the ith data point on the central line.
The arrows indicate which neighboring data points are compared
with the ith data point. If the ith and (i 1) data points are both
recrystallized and of the same orientation, then both data points
belong to the same grain.
For a given data point, it is first determined whether
the data point is ‘‘good’’ or ‘‘bad.’’ Bad data points are
data points with less correctly indexed EBSP Kikuchi
bands than a user-preset limit [8]. If a data point is not
bad (i.e., good) then it belongs to either the recrystallized or the deformed microstructure.
A recrystallized data point is a good data point (on
the central line) that has the same crystallographic
orientation as a user-specified minimum number of its
neighboring data points on all three lines (see the
arrows in Fig. 2), while a deformed data point is a
good data point that does not satisfy this condition.
The single data point specifications are then compared from the start of the line and onwards, and built
one on top of each other into a complete picture of the
microstructure (recrystallized grains, deformed
regions, and bad data points) along the central line,
somewhat like beads on a string.
Additional routines, which will be described in
detail in Sections 2.3 and 2.4, exist to improve the
results based on geometry and growth kinetics.
These corrections are applied in an iterative process.
Finally, a routine orders the detected grains into
groups according to which texture component they
belong.
The corrections are to repair bad data points by (if
possible) allocating the most representative orientation surrounding that specific data point, to eliminate
too small deformed areas within/between recrystallized grains, to discard recrystallized grains without
at least one high-angle boundary, and to discard too
small recrystallized grains. An overview of the
application of these corrections can be seen in
Section 2.4.
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2.2. The definition of a recrystallized grain
In order to identify recrystallized grains, it is
essential to first precisely define what criteria we place
on a grain.
A grain starts as a nucleus with a specific orientation. Theory has it that a nucleus must have a
minimum size in order to overcome its surface tension
and start growing [9,10]. Nuclei then grow by grain
boundary migration into the deformed matrix, which
is facilitated by high-angle boundaries of high mobility [2]. It is clear that our definition of grains in threeline scans must mirror these observations.
A data point must exhibit a minimum connectivity
(i.e., number of good neighbors of equivalent crystallographic orientation); the grain must have a minimum intercept length; and at least one of its
encompassing grain boundaries must be of high angle
(generally, 15j for grain-deformed) to be considered
recrystallized.
Using Fig. 3 as an example, we can see what the
preset parameter ‘‘minimum data point connectivity’’
(pixcon) does. It is an integer that is equal to the
number of neighboring data points including the
central data point itself, which are of equivalent
orientation to the central data point. Only properly
indexed (i.e., good) data points have a connectivity.
In Fig. 3, the data point called Equiv has three
equivalent neighbors (shown by the solid arrows)
and also counting itself, it therefore gets a connectivity of 4.
For pixcon z 4, the three central good data points
(coloured dark grey) within the grain boundaries on
the central line are counted as being recrystallized.
The leftmost data point has only a connectivity of 2;
the second from the right is bad, and the rightmost
data point has only a connectivity of 3. If the bad data
point is repaired (see Section 2.3), the rightmost data
point will have connectivity of 4, and will therefore
also belong to the recrystallized grain.
If the distance between the two determined grain
boundaries is less than the user-specified minimum
intercept length kmin, the grain will be rejected as too
small. On Fig. 3 for (pixcon z 4), the unrepaired grain
satisfies kmin = 3, and the repaired grain satisfies
kmin = 5.
If either one of the grain boundaries is of high
angle, i.e., has a misorientation angle of more than the
user-specified limit (generally, 15j for grain-deformed
or 2j for grain –grain interfaces) the grain is accepted
as being a recrystallized grain. For pixcon z 4, it can
be seen that this condition will not be fulfilled unless
we perform the repair, as neither of the boundaries of
the unrepaired grain will be of high angle.
2.3. Repairing bad data
In a data set some of the data points will yield
fewer correctly indexed EBSP Kikuchi bands than the
minimum specified by the user. For a minimum of
five indexed Kikuchi bands, the bad data points
generally number 2– 20% of the data points, but this
Fig. 3. Pixcon = 4, kmin = 2 steps. A recrystallized grain is seen surrounded by the black line. Black squares indicate bad data points. The long
line k is the intercept length of the grain. The arrows around Equiv show which neighboring data points are tested for equivalence with the
central data point (a solid arrow indicates equivalence; and a dashed arrow indicates nonequivalence). Thus, the data point has a connectivity of
4 (itself + 3 equiv. neighbors), and will thus be considered recrystallized. The dark grey area shows which data points initially satisfy a
connectivity of 4.
A.W. Larsen, D. Juul Jensen / Materials Characterization 51 (2003) 271–282
275
minimum number of user-specified neighbors must
have equivalent orientations (normally, two or more).
Secondly, if the bad data point lies next to a grain,
preference is given to the orientation of that grain if it
satisfies the first criteria. Some examples of repairing
a bad data point are given in Fig. 4.
2.4. The algorithm
Fig. 4. Here is shown three different scenarios for repairing a bad
data point. (Upper) Data point within a grain, (middle) data point
outside a grain, and (lower) a nonreparable data point.
varies with the material, the quality of the polished
surface, the grain/subgrain size, the length of the scan
(microscope losing focus), and even the orientation of
the backscattering grains.
The way we repair is by allocating the orientation
(G matrix) of one of the neighboring data points to the
bad data point. This is based on using the most
common orientation amongst all the neighboring data
points of the bad data point (see Fig. 2). Certain
criteria exist for choosing this orientation. Firstly, a
The algorithm goes through a series of iterations,
which steadily refine the data processing by applying
default and user-specified refining procedures.
The data are taken from a string and ordered in a
3 npoints array (see Figs. 2 and 5). The EBSP data
file contains information such as Euler angles, xyz
scan coordinates, the number of indexed EBSP Kikuchi bands, acquisition method, acquisition time, etc.
Before the first iteration, every data point A[1,i] is
checked to see if it satisfies the minimum number of
successfully indexed EBSP Kikuchi bands (normally,
5). A data point that satisfies this condition is termed
‘‘good,’’ and one that does not is termed ‘‘bad.’’
2.4.1. First iteration
Each good data point on the central line is checked
for equivalence with all its good neighbors. This is
done by checking how many of the neighboring data
points are of equivalent orientation (i.e., their misorientation angle is less than the angular resolution of the
EBSP system).
Fig. 5. Orientation plot of three-line scans (3 50 steps, 1-Am step size) of AA1050-aluminium sample at various annealing times. The black
lines indicate a misorientation of H z 1.0j between neighboring data points, and black spots are bad data points. The samples were annealed in
an oil bath at 250 jC for (a) 300, (b) 2000, and (c) 28,000 s, respectively.
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A.W. Larsen, D. Juul Jensen / Materials Characterization 51 (2003) 271–282
If the number of equivalent data points is equal to
or greater than the user-specified limit (normally, 5 or
more), the data point is considered to belong to a
recrystallized grain. Otherwise, it is considered to
belong to the deformed matrix. The individual data
points are allocated an ID number corresponding to
their present status: ‘‘rex’’ (positive integer), ‘‘bad’’
(0), or ‘‘def’’ ( 1).
2.4.2. Second iteration
Each bad (ID number = 0) data point on the central
line is optionally run through a routine that attempts to
allocate a new good orientation to that data point. This
orientation is taken from the most common orientation
amongst the neighboring data points (see Fig. 4), with
preference for the orientation of neighboring grains.
This is done by checking the neighbors for equivalence with each other. The orientations of the data
points (on the line) to the left and right (A[1, i 1] and
A[1, i + 1]) are checked first to see if they are ‘‘rex.’’
This is to ensure that additional grains are not wrongly
introduced into the data set.
If the most representative orientation is shared by a
user-specified minimum number of equivalent data
points (normally 2), the bad data point is termed good
and given that orientation (G matrix). If not, the bad
data point is termed ‘‘def’’ (ID number = 1).
2.4.3. Third iteration
The first iteration is done once more, but this
time all data points are considered to be good or
repaired; that is, data points are only recrystallized
or deformed.
The data points are grouped into individual recrystallized grains, or the deformed matrix, and the
location, type, and misorientation angle of each grain
boundary is determined.
During this grouping, deformed data points belonging to a deformed region, with a smaller intercept
length than a user-specified minimum length and
bounded by recrystallized material, are automatically
assumed to be measurement errors, and are added to
the neighboring recrystallized grain(s).
2.4.4. Fourth iteration
Each grain is then checked to see if it has at least
one high-angle boundary (normally, H z 15j for
grain – deformed or H z 2j for grain – grain bound-
aries). Grains that cannot satisfy these criteria are
rejected and treated as deformed material.
2.4.5. Fifth iteration
Each remaining grain is checked to see if it satisfies
a user-specified minimum grain intersect length hki
(normally, 1– 3 times the step size). Grains that cannot
satisfy this criterion are rejected and treated as cells in
the deformed matrix.
2.5. Parameters
The following are the user-set parameters in the
algorithm. These parameters have default settings, but
the parameters need to be set and tested for each series
of experiments if a different material is used. This can
be done by comparing the algorithm’s results with
what is obtained from inspecting the orientation image
map (OIM) of a three-line scan (see Section 3.1).
Below is a list of the parameters, their capital letter
codes, and their default values for aluminium.
min indexed bands: minimum number of correctly
indexed Kikuchi bands from the EBSP (default:
M = 5).
min data point connectivity: minimum number of
equivalent data points around and including data
point A[1,i] (default: C = 5).
max misorientation: maximum allowed point-topoint misorientation between equivalent data
points (default: D = 1.0j).
min boundary misorientation: minimum accepted
misorientation across a ‘‘high’’ angle boundary
(default: X = 15.0j for grain-deformed, and Y =
2.0j for grain – grain).
min grain intercept length: minimum accepted
intercept length of a recrystallized grain along the
line (default: L = 3 step lengths for 1 Am steps).
min deformed region intercept length: minimum
accepted intercept length of a deformed region
along the line (default: I = 3 step lengths for 1 Am
steps).
min equivalent neighbors: minimum number of
neighboring data points of equivalent orientation
needed to repair a bad data point (default: N = 2
data points).
repair: try to repair bad data points (default:
R = YES).
A.W. Larsen, D. Juul Jensen / Materials Characterization 51 (2003) 271–282
Table 1
Short line scans—3 200 data point line scans with a step size of 1
Am were performed on the 300-, 2000-, and 28,000-s samples
Time (s)
VV,vis
VV,auto
SV,vis
SV,auto
hkivis
hkiauto
300
2000
28,000
0.05
0.04
0.66
0.04
0.04
0.67
0.05
0.04
0.11
0.05
0.04
0.11
3.5
3.5
14.6
4.0
4.0
14.8
The chosen parameters were M = 5, D = 1.0j, C = 5, L = 3, I = 1,
R = NO, B = YES, Y = 2j, X = 15j.
check boundaries: check the grain boundaries of
each grain to see if it has at least one high-angle
boundary.
277
In general, the stricter the requirements that are
placed on data to be accepted as coming from recrystallized grains, the lower VV will of course be. Discarding grains may cause SV to either go up or down,
generally depending on the degree of recrystallization
in the scanned material. This is because the number of
recrystallized – deformed interfaces depends on the
local microstructure around the discarded grains, so
discarding a grain may do anything in between
removing or creating two interfaces. hki generally
goes up with stricter requirements because only bigger
and more developed grains are likely to satisfy stricter
criteria.
Fig. 6. (a) EBSP OIM (169 169 data points in 5 Am steps) of AA1050-aluminium, cold rolled 60%, and annealed for 1 h at 550 jC. The
sample is fully recrystallized; note how the bad data points (the black spots) are largely constrained to the grain boundaries. Three-line scans
were extracted from the topmost three lines and three lines one-fourth of the way down rows of the data file to use as three-line scans (3 169
steps). (b) Three topmost horizontal lines of the 2-D map (black arrow). (c) Three horizontal lines one-fourth of the way from the top of the 2-D
map (red arrow).
278
A.W. Larsen, D. Juul Jensen / Materials Characterization 51 (2003) 271–282
Table 2
Extracted line scans—3 169 data point line scans with a step size
of 5 Am were performed on the 300-, 2000-, and 28,000-s samples
Scan
VV,OIM
VV,auto
SV,OIM
SV,auto
hkiOIM
hkiauto
Middle
Top
0.98
1.00
0.99
1.00
0.01
0.00
0.01
0.00
48.2
59.6
45.8
59.6
The chosen parameters were: M = 5, D = 1.0j, C = 5, L = 1, I = 2,
R = YES, B = YES, Y = 2j, X = 15j.
It has been chosen not to include the quality factor
(Q/A) as a parameter. Previous analysis based on Q/A
has shown that Q/A goes up with increased deformation. However, from many investigations of recrystallizing aluminium and copper, it is our experience that
many other factors affect Q/A, and that Q/A does not
give a good measurement of VV [11].
3. Validation
3.1. Experiment
To test the program it was run on three different
types of scans.
(a) Three short (200 steps) 3 line scans were
performed on three different samples, which
had been annealed for different lengths of time.
By performing short 3 line scans, the OIMs of the
scans could to be printed on paper (see Fig. 5),
allowing us to perform the same calculations as
are performed by the algorithm on the orientation
data by visual inspection and directly compare
the results of the algorithm with the results it
should produce if working properly. The calculations were performed by going through the data
points on the central line and noting how many of
the neighboring data points had orientations
within 1j of the data point being inspected, as
is clearly visible from the plots, where misorientations with H z 1j are marked by black lines.
Additional plots were made with lines drawn for
misorientations greater than 2j and 15j to allow
the identification of boundaries of high angle. By
choosing not to repair bad data points and not to
ignore short deformed regions no error crept in
that way. In addition, the visual inspections
allowed us to determine whether a correctly
functioning routine would misinterpret features
within the microstructure. The results of the
visually based and automatic calculations can be
seen in Table 1.
(b) Two 3 line scans were extracted from the data file
of a large 2-D scan of a fully recrystallized
microstructure, where it was possible to identify
the recrystallized grains by direct visual inspection of the OIM (which can be seen in Fig. 6).
This allowed for a more direct comparison than in
(a), and also allowed us to see that the program
really could produce the crucial parameters
VV = 1.0 and SV = 0.0 for a suitable data set. The
results of the visual inspection and the automatic
calculations can be seen in Table 2.
(c) A series of samples were annealed for different
lengths of time were analyzed. Long (1000+ steps)
3 line scans were performed on these and data
analysis was carried out with LSGRAINS. For
comparison, manual line scans were also performed on the samples. This was done on both a
statistical and a one-to-one basis. The statistical
method consisted of comparing the results of long
manual and automatic scans, where the scans were
made long enough to include of the order of a
hundred recrystallized grains to make the data sets
from the two types of scans statistically comparable. The one-to-one comparisons consisted of
scanning precisely the same line on the two
samples manually and automatically. This allowed
a direct comparison between the two methods, as it
was possible to see what results were obtained
Table 3
Long line scans—3 1000+ data point line scans with a step size of
1 Am were performed on all the samples
Time (s)
VV,man
VV,auto
SV,man
SV,auto
hkiman
hkiauto
300
2000
11,000
20,000
28,000
38,000
55,000
72,000
86,400
0.02
0.07
0.22
0.60
0.21
0.37
0.78
0.96
0.87
0.03
0.05
0.22
0.89
0.43
0.43
0.93
0.64
0.89
0.02
0.05
0.09
0.06
0.05
0.05
0.03
0.02
0.05
0.02
0.03
0.08
0.05
0.09
0.08
0.03
0.10
0.05
2.6
3.5
5.8
14.2
6.9
13.5
23.8
18.1
16.7
3.7
4.3
7.1
12.8
8.5
14.5
16.7
13.1
15.2
The table shows the automatic vs. the manual results. The automatic
results were based on the following choice of parameters: M = 5,
D = 1.0j, C = 5, L = 3, I = 3, R = YES, B = YES, Y = 2j, X = 15j.
A.W. Larsen, D. Juul Jensen / Materials Characterization 51 (2003) 271–282
from exactly the same microstructure. Manually
scanning a sample corresponds to watching the
EBSP on the SEM screen for changes while
manually translating the sample translation stage.
Deformed areas are characterized by a meandering
EBSP, while the EBSP of a recrystallized grain is
279
Table 4
Directly compared manual and automatic line scans
Time (s)
L
VV,man
VV,auto
SV,man
SV,auto
hkiman
hkiauto
11,000
86,400
11,000
86,400
3
3
5
5
0.41
0.87
0.41
0.87
0.51
0.85
0.42
0.81
0.08
0.05
0.08
0.05
0.10
0.06
0.08
0.08
12.4
16.7
12.4
16.7
9.2
15.1
13.1
17.5
A step size of 1 Am was used, and the two samples were annealed
for 11,000, and 86,400 s, respectively. The parameters were: M = 5,
D = 1.0j, C = 5, L = 3 & 5, I = 3, R = YES, B = YES, Y = 2j, X = 15j.
clear and does not move when the sample is
translated. By noting down the changes in the
EBSP, the grain boundaries between both recrystallized grains and between grains and deformed
material are determined, giving the microstructure
of the sample. The results of the long manual and
automatic line scans can be seen in Table 3 and Fig.
7, while the results of the one-to-one comparisons
can be seen in Table 4.
Fig. 7. The results from comparing long manual and automatic
scans. (a) VV vs. time, (b) SV vs. VV, (c) hki vs. time. Parameters
are M = 5, D = 1.0j, C = 5, L = 3, I = 3, R = YES, B = YES, Y = 2j,
X = 15j.
The same material was used for all tests of the
algorithm. The material used in the studies was
AA1050-aluminium (99.5% pure). This material is
chosen because it has previously been used for extensive characterization and modelling [5]. In cases (a)
and (c), the aluminium was cold rolled 90%, and then
annealed in a 250 jC oil bath for 300, 2000, 11,000,
20,000, 28,000, 38,000, 55,000, 72,000, and 86,400 s.
In case (b), the aluminium was cold rolled 60% and
then annealed for 1 h in an air furnace at 550 jC,
producing a fully recrystallized sample.
After annealing the RD-ND surface of the samples
was mechanically and electrochemically polished to
produce a surface suitable for EBSP measurements.
For scans with a length of 1000+ Am a completely
plane sample surface is very desirable. The samples
were therefore mechanically lapped and polished on a
Logitech2 PM5D lapping and polishing machine using
a PSM1 sample monitor, giving a height difference of
only 1 –2 Am across the sample surface [12]. The
samples were electrochemically polished for 40 s at
12 V with an A2 electrolyte (12% H2O, 70% ethanol,
10% ethylene glycol monobutyl ether, 7.8% HCl).
In all cases a JEOL JSM-840 scanning electron
microscope with a LaB6 filament was used to collect
2
Logitech (http://www.logitech.uk.com/).
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A.W. Larsen, D. Juul Jensen / Materials Characterization 51 (2003) 271–282
the EBSP data. The working distance was 22 mm,
the electron beam current was 280 AA, and the
voltage 20 kV.
The three short 3 line scans consisted of 3 200
data points with a step size of 1 Am, thus producing
scans 200 Am long. The resulting scans can be seen
in Fig. 5, where only the last 50 steps have been
plotted to make the form of the data more obvious.
The colors were generated by setting the red, green,
and blue color levels proportional to the Euler angles,
all black spots are bad points, and all point-to-point
misorientations with H z 1.0j are marked with black
lines.
The two 3 line scans extracted from the already
existing data file of a large (169 169 steps) 2-D scan
had the dimensions 3 169. With a step size of 5 Am
the total scan length was 840 Am. The full 2-D OIM
and the two three-line scans extracted from it can be
seen in Fig. 6.
Generally, the long 3 line scans have 3 1000+
data points in 1 Am steps, thus giving a line length of
1000+ Am. Great care was taken when mounting the
samples because long line scans (1000+ Am) cover
such a large horizontal distance that the sample surface
will tend to move out of the microscope’s focus if it is
even slightly tapered. The solution to this problem was
to align the firmly gripped samples in an optical
microscope to get the scanning surface as horizontally
flat as possible. When this is done, it is possible to
perform line scans of lengths of the order of up to 10
mm with a 1 Am step size and down to 10% bad points
(see Section 2.1).
3.2. Results
3.2.1. Short scans
To use a good nonsubjective test method, the three
short scans (see Fig. 5) were analyzed visually and
with LSGRAINS. Exactly the same criteria were used
to define grains in the two procedures. The result of
the short visual inspection and automatic line scans
can be seen in Table 1.
The results show excellent agreement. The very
slight scatter in VV and hki comes from the slight
uncertainty when measuring grain lengths on the
paper printouts. Note that only grains intersected by
all three lines were accepted as recrystallized grains
by the algorithm. This indicates that the chance of
accidentally indexing cells within the deformed matrix
as recrystallized grains is very low.
3.2.2. Lines from large 2-D scans
Two 3 line scans were extracted from a large 2-D
EBSP map. This 2-D map was done on a sample,
which was fully recrystallized. The results are given in
Table 2.
As in Section 3.2.1, the results show excellent
agreement. The very slight scatter in VV and hki again
comes from the slight uncertainty when measuring
grain lengths on the paper printouts. The choice of
L = 1 and I = 2 is based on the step length of 5 Am,
where small recrystallized grains with an intersect
length of less than two step lengths ( < 10 Am) are
very possible. Because of the poor indexing on the
grain boundaries (see Fig. 6a), deformed areas less
than two step lengths long are ignored.
3.2.3. Long scans
All of the comparisons between the manual and
automatic long line scans were done along the rolling
direction (RD) in the RD-ND plane. The long (1000+
data points) manual line scans were performed as
described in Section 3.1. The number of grains
intersected for each sample was in the range 64–
251. The result of the long manual and automatic line
scans can be seen in Table 3 as well as in Fig. 7.
As can be seen, there is some scatter in the data,
but that is unavoidable due to the subjectivity of the
manual method and that different parts of the microstructure are scanned.
The scatter is generally that the automatic method
finds a higher VV and SV, indicating that maybe in the
manual method some small recrystallized grains within the deformed matrix have been neglected (see
Section 3.1).
It has to be noted that differences within the
microstructure intersected by a single RD-ND section
can be very big. Even for scans well above 1000 Am,
the VV measured along the line on the same surface
can vary by as much as an order of magnitude,
depending on how recrystallized the sample is. It is
believed that this is responsible for the large difference between the manual and automatic results on the
72,000-s sample.
Also, there is an immense scatter between samples
of different annealing times; for example, the 20,000-s
A.W. Larsen, D. Juul Jensen / Materials Characterization 51 (2003) 271–282
sample is found (in both the automatic and the manual
scans) to be much more recrystallized than the
28,000-s sample.
The one-to-one comparisons between the manual
and automatic scans (see Table 4) produces some
quite interesting observations: For our standard choice
of parameters (most notably, L = 3), it is observed that
the automatic method finds many more grains for the
11,000-s sample, while an excellent agreement is
found for the 86,400-s sample. Upon choosing L = 5,
a near-perfect match is obtained for the 11,000-s
sample, but the results for the 86,400-s sample dip
below the manual results.
For L = 3, it is noteworthy that for the 11,000-s
sample the manual method overlooks many small
grains within the deformed structure, which are seen
by the automatic method. It is known that within some
nuclei the crystallographic orientation can vary by up
to 6j and that these internal misorientations decrease
as recrystallization progresses [13]. This means that
the EBSP pattern might be seen to wobble a bit while
doing manual scans, causing the nuclei to be considered as deformed material, while they still satisfy the
recrystallized grain criteria defined for the automatic
method, and are thus included here. If these are also
neglected in the automatic method (by setting L = 5),
the two methods match very well, but we conclude
that the correct result must be to include the smaller
recrystallized grains (thus, L = 3).
For L = 5, it is noteworthy that for the 86,400-s
sample, the automatic method neglects small grains
within the deformed structure, which are seen by the
manual method. This indicates that in this case small
recrystallized grains are observed using the manual
method, and thus indicates that rejection of small
grains in the manual method is less of a problem
here. This agrees with the observation in Ref. [13] that
the internal misorientations are reduced when the
sample is annealed for a longer time.
Based on the arguments above, setting the parameter L = 3 is assumed to give the correct description of
the microstructure for the present sample.
4. Conclusions
A new automatic procedure for determining the
critical recrystallization parameters VV, SV, and hki by
281
EBSP line scans has been presented. The concept of
grain connectivity is used and has proven to be a good
method.
The procedure has been tested on aluminium, and
we have obtained a fully satisfactory agreement with
other available techniques. From the results presented
in this paper we can conclude that the method
correctly determines the values of VV, SV, and hki,
with the added advantage of being completely automatic (i.e., objective).
For samples in the latter stages of recrystallization
(i.e., grains have grown to large sizes) considerable
lengths can be covered relatively quickly by increasing the step size without sacrificing precision, as seen
in case (b) in Section 3.1, where the distance 840 Am
is covered in only 169 steps, each 5 Am long.
Acknowledgements
The authors would like to thank Roy Vandermeer
and Brian Ralph for useful discussions and suggestions while writing this paper, and Preben Olesen for
tremendous support when performing the many EBSP
line scans necessary for this study.
The authors gratefully acknowledge the Danish
Research Foundation for supporting the Center for
Fundamental Research: Metal Structures in Four
Dimensions, within which this work was performed.
References
[1] Adams BL. Orientation imaging spectroscopy: application to
measurement of grain boundary structure. Mater Sci Eng, A
1993;166(A):59 – 66.
[2] Juul Jensen D. Orientation aspects of growth during recrystallization, Risø R-report Risø-R-978 (EN), Risø National Laboratory, Roskilde, Denmark; 1997 (April).
[3] Cahn JW, Hagel WC. Theory of the pearlite reaction. Decomposition of Austenite by Diffusional Processes. 1st ed. New
York: Interscience Publishers; 1962. p. 131 – 96.
[4] Underwood EE. Surface area and length in volume.
Quantitative Microscopy. New York: McGraw-Hill; 1968.
p. 77 – 127.
[5] Vandermeer RA, Juul Jensen D. Microstructural path and temperature dependence of recrystallization in commercial aluminium. Acta Mater 2001;49:2083 – 94.
[6] Juul Jensen D. Growth of difference crystallographic orientations during recrystallization. Scr Metall Mater 1992;27:
533 – 8.
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[7] Magnusson H, Juul Jensen D, Hutchinsson B. Growth rates
for different texture components during recrystallization of
steel. Scr Mater 2000;44:435 – 41.
[8] Lassen NCK, Juul Jensen D, Conradsen K. Image procedures
for analysis of electron back scattering patterns. Scanning
Microsc 1992;6(1):115 – 21.
[9] Bay B, Hansen N. Recrystallization in commercially pure
aluminum. Metall Trans 1984;15(A):287 – 97.
[10] Doherty RD. Nucleation of recrystallization of single phase and
dispersion hardened polycrystalline materials. 1st Risø International Symposium on Metallurgy and Materials Science. Roskilde, Denmark: Risø National Laboratory; 1980. p. 57 – 69.
[11] Lassen NCK, Juul Jensen D. Automatic recognition of recrys-
tallized grains in partly recrystallized samples from crystal
orientation maps. Proceedings of the Twelfth International
conference of Textures of Materials, vol. 2. Ottawa, Canada:
NRC Research Press; 1999. p. 854 – 9.
[12] Larsen AW. ‘Logitech PM5 precision polishing and lapping system’’ user manual. Risø I report Risø-I-2051(EN),
Risø National Laboratory, Roskilde, Denmark; 2003
(September).
[13] Sabin TJ, Winther G, Juul Jensen D. Orientation relationships
between recrystallized nuclei at triple junctions and deformed
structures. Acta Mater 2003;51:3999 – 4011.
A2
Scripta Materialia 53 (2005) 553–557
www.actamat-journals.com
Nucleation of recrystallization observed in situ
in the bulk of a deformed metal
Axel W. Larsen a, Henning F. Poulsen a, Lawrence Margulies a,b, Carsten Gundlach a,
Qingfeng Xing a, Xiaoxu Huang a, Dorte Juul Jensen a,*
a
Center for Fundamental Research: Metal Structures in Four Dimensions, Risø National Laboratory, P.O. Box 49, Building 228,
Frederiksborgvej 399, DK-4000 Roskilde, Denmark
b
European Synchrotron Radiation Facility, BP 220, F-38043 Grenoble, France
Received 31 January 2005; received in revised form 18 April 2005; accepted 22 April 2005
Available online 8 June 2005
Abstract
Nucleation of recrystallization is studied in situ in the bulk by three-dimensional X-ray diffraction. Copper samples cold rolled
20% are investigated. The crystallographic orientations near triple junction lines are characterized before, during and after annealing. Three nuclei are identified and it is shown that two nuclei are twin related to their parent grain and one nucleus has an orientation, which is neither present in the deformed parent grains nor first order twin related to any of them. Data on the nucleation
kinetics is also presented.
2005 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Keywords: Nucleation of recrystallization; X-ray diffraction; Copper; Misorientation
1. Introduction
Nucleation is a much debated recrystallization process, whereby upon annealing nearly perfect nuclei form
in a deformed material [1]. One reason for the debate is
that it has been impossible to follow experimentally the
nucleation process in situ, except at a sample surface.
It is characteristic of previous studies of nucleation,
that these have been performed either on the surface
of samples, which is not necessarily representative of
the bulk of the sample, or have been statistical in nature.
In the latter case, the bulk microstructure is characterized in deformed and annealed samples separately. It
is therefore not possible to relate directly a nucleus to
the specific deformation microstructure at the exact site
where it formed. This ‘‘loss of evidence’’ [2] is important,
*
Corresponding author. Tel.: +45 46 77 58 04; fax: +45 46 77 57 58.
E-mail address: [email protected] (D.J. Jensen).
as detailed quantitative analysis by electron microscopy
has revealed that the deformed microstructure in metals
is heavily subdivided into small, typically lm-sized volume elements of different crystallographic orientations
[3]. Furthermore, the orientation of the original grain
in a polycrystalline sample affects its subdivision, leading to heterogeneous deformation microstructures [4,5].
A currently much debated issue is the possible development of nuclei with new orientations compared to the
deformed microstructure. Existing nucleation models
such as strain induced boundary migration [6], nucleation in cube bands [7,8], and particle stimulated
nucleation [9], all predict that orientation should be conserved. In contrast a number of electron microscopy
(EM) investigations suggest that some fraction of the
nuclei do appear with new orientations [10–20]. Such
‘‘odd nuclei’’ would have good growth potentials and
are thus considered very important in the understanding
of the recrystallization microstructures and texture
1359-6462/$ - see front matter 2005 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
doi:10.1016/j.scriptamat.2005.04.053
554
A.W. Larsen et al. / Scripta Materialia 53 (2005) 553–557
development. However, these EM studies can be questioned. In the case of in situ surface studies, the nucleus
might have formed not at the surface characterized, but
at a site below it. Also surface effects may lead to atypical types of nucleation. In the case of statistical studies,
it is essential to note that nuclei are small as well as rare.
To characterize a representative part of the deformed
microstructure, it is necessary to measure volume
fractions of the order of 10 8 or less with a sub-micron
spatial resolution. That is not practical with existing
EM methods.
These experimental limitations do not apply to threedimensional X-ray diffraction (3DXRD) microscopy
[21]––an emerging method based on the use of high
energy X-rays generated by a synchrotron. 3DXRD
enables characterization of the individual embedded
grains in bulk crystalline samples as well as studies of
the dynamics of the grains during processing [22–24].
In a recent publication, a variant of 3DXRD was demonstrated, whereby the microstructure of a channel-die
deformed Al single crystal (e = 1.5) could be characterized with respect to the existence of structural elements
with ‘‘odd’’ orientations [25].
In this paper we extend this method to in situ studies
of the microstructure evolution during annealing of deformed polycrystals. For the first time, a direct correlation between the orientation of the emerging nuclei and
the parent microstructure is obtained in a polycrystalline
sample.
2. Experimental
The material of choice is particle-free, 99.995% pure,
oxygen-free, high conductivity copper. The initial material was prepared by cold rolling to 20% reduction in
thickness and annealing for 8 h at 700 C to give a
microstructure with relatively coarse grains with an
average size of 500 lm. This material was further coldrolled to 20% reduction. The deformed material was
characterized by transmission electron microscopy
(TEM) using a JEOL-2000FX microscope operated at
200 keV. Similar to previous studies [26] the average
distance between dislocation walls exhibiting a misorientation of 1 or more was 1–2 lm, depending on the
orientation of the grain.
From this material three 10 · 10 mm2 plates were cut,
with the plate normal in the TD direction. These samples were thinned from both sides to a final thickness
of 0.3 mm, using a Logitech PM5D polishing and lapping machine. Finally, the sample surfaces were electrochemically polished to remove any remnant surface
scratches, which might act as unwanted surface nucleation sites.
The surface of each of the three samples (to be
referred to as A, B and C) were inspected within a
Fig. 1. An EBSP map of the surface of sample B. Deformed grains are
outlined by black lines. The red square indicates the 160 · 160 lm2
area in the vicinity of a triple junction, which was characterized in the
X-ray diffraction study.
1.8 · 1.8 mm2 area by electron back-scattering pattern
(EBSP) using a JEOL JSM-840 scanning electron microscope (see Fig. 1).
The experiment took place at beamline ID11 at
ESRF, Grenoble, France. A sketch of the experimental
set-up is shown in Fig. 2. The beam was monochromated and focused in two directions by means of a combination of a bent Laue Si crystal and a laterally graded
multilayer [21]. The sample was positioned behind the
focal spot. In combination with the use of an aperture
this set-up resulted in the sample being illuminated by
a nearly homogeneous 51 keV beam of dimensions
49 · 49 lm2. Diffraction studies were performed in
transmission mode by exposing a 14-bit FRELON
CCD coupled by an image intensifier to a fluorescence
screen of area 160 · 160 mm2. Data acquisition times
were typically 1 s.
To increase the volume characterized, exposures were
made at a set of sample positions. For all samples these
corresponded to the four points in a 2 · 2 (y, z)-grid,
while for sample B a larger 4 · 4 (y, z)-grid was also
used. In all cases, the distance between nodes was
40 lm. At each grid point, exposures were made for 22
equally spaced values of the rotation axis x (see Fig.
2) within a range of 42. To ensure an even sampling
of integrated intensities, the sample was rotated by
±0.5 during each exposure. This corresponds to measurements of partial pole figures covering a fan of 42
around TD. As five reflections are recorded simultaneously on the detector this angular-range is sufficient
to determine the crystallographic orientations of the
evolving nuclei.
The data analysis methodology was described in Ref.
[25]. In terms of image analysis, initially a background
A.W. Larsen et al. / Scripta Materialia 53 (2005) 553–557
555
Fig. 2. Schematic diagram of the setup of the 3DXRD experiment, with indication of the angles 2h, x and g.
subtraction method was applied [27]. In the algorithm, a
box of a given size is scanned across each image. The
average and standard deviation of the pixel intensities
within the box are determined as function of position.
Positions with a small standard deviation are then
defined to be in the background. The background level
at each point is then determined by interpolation of
the average values in the background areas. Images were
spatially corrected by the program FIT2D [28].
For each nucleus, the orientation was determined
with an accuracy of 1 by the multi-grain indexing
algorithm, GRAINDEX [29]. In addition, the volume
of the nucleus is readily found, as it is proportional to
the integrated intensity of the associated diffraction
spots. The proportionality constant was estimated from
the integrated intensity of the diffracted signal from a
reference Al powder with known thickness [21,25]. Furthermore, the (x, y, z) position of the nucleus can be estimated by trigonometry, based on information on when
the nucleus ‘‘rotates out of the beam’’ during the x-scan.
To ensure the same volume was illuminated at all times,
the position of the edges of the sample was repeatedly
determined by scanning the sample.
The furnace provides a stable temperature of up to
500 C, with a choice of working in a neutral atmosphere, and can rotate 360 about the z-axis. The sample
is enclosed in a glass capillary tube with a thickness of
0.1 mm, giving rise to negligible absorption and minimizing diffuse scattering.
3. Results and discussion
Nucleation in three 300 lm thick plate shaped samples (A, B and C) was studied by the 3DXRD method.
As a function of rotating the sample around the x-axis,
diffraction images were acquired with a highly efficient
area-detector. Typical data from the as-deformed samples are shown in Fig. 3a. In the corresponding {1 1 1},
{2 0 0} and {2 2 0} partial pole figures, shown in Fig. 4,
the orientations present are enclosed within broad poles
associated with the three deformed grains at the triple
Fig. 3. Examples of 3DXRD images, acquired for sample B. A grey scale is used with white representing the more intense regions. The textured
Debye–Scherrer rings of the {1 1 1}, {2 0 0}, {2 2 0}, {3 1 1} and {2 2 2} reflections are seen. The two images relate to the same position within the
sample and represent (a) the as-deformed microstructure, and (b) the microstructure in the sample annealed for 3 h at 290 C. The white box indicates
the position of a diffraction spot, representing a nucleus.
556
A.W. Larsen et al. / Scripta Materialia 53 (2005) 553–557
Fig. 4. Partial pole figures of sample B measured at the location of the nucleus with the new orientation. The orientations of the deformed
microstructure are shown in colours with [black, blue, light blue, pink, yellow] corresponding to intensities of [400, 1000, 2500, 5000, 10,000] counts/s.
The diffraction pattern from the sample after 3 h of annealing at 290 C is very similar, except for the presence of three sharp diffraction spots, which
are shown as green stars. The orientations of the associated four first order twins are marked by red symbols (squares, diamonds, circles, and stars).
There is a small ‘‘invisible spot’’ in the centre of all pole figures.
junction. No smoothing has been applied. The individual elements in the deformed microstructure associated
with these poles cannot be distinguished. Instead the virtue of the 3DXRD method in this case relates to characterization of the ‘‘empty’’ parts of the partial pole figures
(i.e. within the measured x-range of 42 but away from
major poles). The boundary between the white and colored parts of the pole figures indicates the smallest volume elements that can be observed. This limit of
400 counts/s corresponds to an equivalent circle diameter (ECD) of 0.70 lm. In other words, all volume elements within an illuminated sample volume of 49 ·
49 · 300 lm3 with an ECD larger than 0.7 lm will be
recorded as a significant signal on the detector. It is
characteristic of all three samples that large parts of
the partial pole figures are empty, and furthermore that
the intensities in the ‘‘tails’’ of the poles fall off rapidly
with the distance to the centre of the pole.
The acquisition of such high-sensitivity pole figures
was repeated with a frequency of 10 min, while annealing the samples at 290 C for 1–3 h. During this process,
a few nuclei appeared, easily identifiable in the images as
distinct point-like diffraction spots, see Fig. 3b. Based on
the position and intensity of these spots 3DXRD specific
analysis software was used to determine the orientation
and position of the nuclei [21,25], as well as their volume
as a function of annealing time.
Three nuclei were detected: one in sample A, two in
sample B and zero in sample C––all positioned at least
65 lm from any surface. This result confirms that triple
junctions are potential nucleation sites in this material,
but also that not all junctions lead to nucleation, which
is in good agreement with previous surface [20] and
serial sectioning results [30].
The orientation of the sample A nucleus was identical
to a first-order twin associated with an orientation close
to the centre-of-mass of one of the poles. This nucleus
grew to a size of ECD = 9.4 lm within 45 min. The ori-
entation of one of the sample B nuclei was also identical
to a first-order twin associated with an orientation close
to the centre-of-mass of one of the poles. The results for
the second nucleus in sample B, which is of the main
interest here, is shown in Figs. 3 and 4. In this case six
diffraction spots were observed in the ‘‘empty’’ parts
of the partial pole figures (i.e. within the measured
x-range of 22 but away from the poles of the deformed
parent grain), while another seven were on top of poles.
From the six spots, the orientation of the nucleus was
determined to be neither within the range of orientations
found in the as-deformed sample, nor related to a firstorder twin associated with any of the orientations in this
range (see Fig. 4). This nucleus grew to a size of
ECD = 6.1 lm within 3 h.
There are two explanations to why such a nucleus
could be generated:
1. It emerged by reorientation of parts of the deformed
structure.
2. It emerged from rare parts of the deformed microstructure associated with volume fractions of the
order of 1.5 · 10 7. All elements in the deformed
microstructure associated with such hypothetical
‘‘odd orientations’’ have an ECD of less than
0.70 lm. This number corresponds to the lower limit
of the size-distribution of elements as characterized
by chord–length measurements in TEM [26]. Furthermore, they are substantially below the classical nucleation threshold [31], which in the present case is
ECDclassic > 1.1 lm [1,32]. This explanation thus
seems very unlikely.
A mechanism explaining how and why reorientation of
parts of the deformed microstructure (explanation 1
above) should take place during the early stages of
annealing has not been derived. The present result
together with the previous observations of nuclei with
A.W. Larsen et al. / Scripta Materialia 53 (2005) 553–557
new orientations both at triple junction and away from
them, however, strongly suggests that further detailed
work should be devoted to the understanding of this.
For the experimental part of such work, it appears the
method presented here is an ideal tool. Uniquely, information on nucleation sites, orientation relationships and
kinetics is obtained. The sensitivity of the method can
be increased to ECD = 0.2 lm or better by improved
focusing [33]. Statistics of nuclei characteristics can be
extracted from repeated studies, which in turn is likely
to give insight into the underlying mechanisms. Also,
potential reorientations of emerging nuclei would be
readily observable.
4. Conclusion
A unique method for in situ studies of nucleation in
the bulk has been presented. The method is based on
three-dimensional X-ray diffraction. It has been confirmed that volumes near triple junction lines are potential nucleation sites in 20% cold rolled copper. Three
nuclei have been identified and followed during annealing at 290 C. Analysis of orientation relationships with
their deformed parent grains has revealed that nuclei
may develop with orientations within the orientation
distributions of the parent grains, being twin related
here or with a new orientation that was not detected
in the deformed parent grains.
Acknowledgments
The authors gratefully acknowledge the Danish National Research Foundation for supporting the Center
for Fundamental Research: Metal Structures in Four
Dimensions. This work was also partly supported the
Danish Natural Science Research Council (via Dansync). The ESRF is acknowledged for provision of beam
time. P. Nielsen and P. Olesen performed the pre-experiment sample scanning and testing.
References
[1] Humphreys FJ, Hatherly M. Recrystallization and related annealing phenomena. Oxford: Pergamon; 1995.
[2] Duggan B. Term suggest at international conference on textures
of material. ICOTOM 11, 1996.
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[3] Hansen N. Metall Mater Trans A 2001;32:2917.
[4] Driver JH, Juul Jensen D, Hansen N. Acta Metall Mater
1994;42:3105.
[5] Winther G. Acta Mater 2003;51:417.
[6] Bailey JE, Hirsch PB. Proc Roy Soc A 1962;267:11.
[7] Samajdar I, Doherty RD. Scr Metall Mater 1995;32:845.
[8] Vatne HE, Daaland O, Nes E. ICOTOM 10. Mater Sci Forum
1994;157–162:1087.
[9] Humphreys FJ, Fery M, Johnson C, Paillard P. In: Hansen N
et al., editors. Proceedings of the 16th Risø international symposium on material science: Microstructural and crystallographic
aspects of recrystallization. Roskilde, Denmark: Risø; 1995. p.
87.
[10] Wu GL, Godfrey A, Juul Jensen D, Liu Q. ICOTOM 14. Mater
Sci Forum 2005;495–497:1309.
[11] Kikuchi S, Kimura E, Koiwa M. J Mater Sci 1992;27:4927.
[12] Juul Jensen D. In: Sakai T, Suzuki HG, editors. Proceedings of
the 4th international conference on recrystallization and related
phenomena, 1999;(JIM):3.
[13] Paul H, Driver JH, Maurice C, Jasienski Z. Acta Mater
2002;50:4339.
[14] Inoko F, Okada T, Tagami M, Kashihara K. In: Hansen N et al.,
editors. Proceedings of the 21st Risø international symposium on
material science. Risø National Laboratory; 2000. p. 365.
[15] Godfrey A, Juul Jensen D, Hansen N. Acta Mater 2001;49:2429.
[16] Barett CS. Recrystallization texture of aluminium after compression. Metals Technol 1940:128–49.
[17] Driver JH, Paul H, Glez J-C, Maurice C. In: Hansen N et al.,
editors. Proceedings of the 21st Risø international symposium on
material science. Risø National Laboratory; 2000. p. 35.
[18] Inoko F, Mima G. Scr Metall 1987;21(8):1039.
[19] Okada T, Huang X, Kashihara K, Inoko F, Wert JA. Acta Mater
2003;51:1827.
[20] Sabin TJ, Winther G, Juul Jensen D. Acta Mater 2003;51:3999.
[21] Poulsen HF. Three-dimensional X-ray diffraction microscopy.
Berlin: Springer; 2004.
[22] Margulies L, Winther G, Poulsen HFI. Science 2001;291:2392.
[23] Offerman SE et al. Science 2002;298:1003.
[24] Schmidt S, Nielsen SF, Gundlach C, Magulies L, Huang X, Juul
Jensen D. Science 2004;305:229.
[25] Poulsen HF, Lauridsen EM, Schmidt S, Margulies L, Driver JH.
Acta Mater 2003;51:2517.
[26] Huang X, Leffers T, Hansen N. In: Bilde-Sørensen JB et al.,
editors. Proceedings of the 20th Risø international symposium on
material science. Roskilde, Denmark: Risø National Laboratory;
1999. p. 365.
[27] Teuber J, Bowen J, Lauridsen EM, Private communication.
[28] Hammersley AP, Svensson SO, Hanfland M, Fitch AN, Häuserman D. High Pressure Res 1996;14:235.
[29] Lauridsen EM, Schmidt S, Suter RM, Poulsen HF. J Appl Cryst
2001;34:744.
[30] Vandermeer RA. Trans Metall Soc Aime 1959;215:577.
[31] Doherty R. In: Hansen N et al., editors. Proceedings of the 1st
Risø international symposium on material science. Roskilde,
Denmark: Risø National Laboratory; 1980. p. 57.
[32] Gordon P. Trans AIME 1955;203(9):1043.
[33] Ice GE, Chung JS, Tischler JZ, Lunt A, Assoufid L. Rev Sci
Instrum 2000;71(7):2635.
A3
Risø-I-2051(EN)
'Logitech PM5D Precision Polishing and
Lapping System' User Manual
Axel W. Larsen
Materials Research Department, Building 228
Risø National Laboratory, Roskilde
August 2003
Abstract This internal Risø report is a user manual for the ‘Logitech PM5D precision polishing and
lapping system’. It is not a ‘stand alone’ manual. It is assumed that the user has taken an introductory
course to the PM5D system.
It includes: an introduction to the various components of the system; the necessary steps that must be
taken before lapping/polishing can commence; how to operate that PM5D machine and do lapping and
polishing on it; how to maintain the system in working order, as well as tips on how to achieve good
polishing results are also found within.
Print: Pitney Bowes Management Services Denmark A/S, 2003
Contents
1
Introduction to the PM5D precision polishing and lapping system 5
2
Before getting started 6
2.1
2.2
2.3
2.2
Prepare the sample 6
Bonding the sample 6
Check flatness of the lapping plate 7
Clean components when necessary 8
3
Machine Operation 8
3.1 PM5D controls 8
3.1 Adjusting sample load 8
3.2 Operation procedure 9
4
Lapping with with the PP5D polishing jig and PSM1 sample monitor 9
4.1 Lapping slurries 9
4.2 Material take-off rate 10
4.3 Using the PSM1 sample monitor 10
5
Polishing with the PP5D polishing jig 11
5.1 Polishing slurries 11
5.2 Material take-off rate 12
6
Machine maitenance 13
7
Final Words 13
Risø-I-2051(EN)
3
Preface
This manual is not thought as a booklet to teach prospective users how to use the
‘Logitech PM5D precision polishing and lapping system’.
Rather, it should be seen as useful pre-reading before taking the introductory
course, and after taking the course, the user should view it as a user reference
manual while working with the PM5D system.
It is of course not possible to write a manual explaining everything about all aspects of using the PM5D system, but after the user has taken a introductory
course, the manual should answer any questions he or she might have…
4
Risø-I-2051(EN)
1 Introduction to the PM5D precision
polishing and lapping system
WARNING: Please do not use this equipment
until you have had a user course from one of
the trained staff!!!
The Logitech PM5D polishing and lapping machine is built on the principle of an
rotating lapping plate with a free standing and rotating sample holder on top. This
sample holder is the PP5D Precision Polishing Jig with PSM1 sample monitoring
system. The system includes the following pieces of equipment:
• PM5D Lapping and Polishing Machine with abrasive autofeed cylinder
(see figure 1)
• PP5D Precision Polishing Jig with PSM1 sample monitoring system (see
fig. 3)
• PJ2 two-position thin section bonding Jig (see fig. 2)
• Contact gauge with flat granite master plate.
The PM5D system allows control of the depth of material removal within 1-2 µm,
and sample flatness to within 1-2 µm height difference across the sample.
Figure 1. PM5D precision polishing and lapping machine.
Risø-I-2051(EN)
5
2 Before getting started
This section includes the necessary steps, which must be performed before lapping and polishing can commence.
• Prepare the sample.
• Bonding the sample.
• Check (and correct) lapping plate flatness.
• Clean components when measuring and changing slurries during lapping
and polishing.
2.1
Prepare the sample
Before processing make sure that the sides and edges of the sample are polished
(by hand) to avoid small pieces chipping off the edges, causing scratching on the
sample surface during polishing. Make sure that the sample is cleaned well with
alcohol before starting the lapping.
2.2
Bonding the sample
The sample must be bonded onto the base plate of the PP5D polishing jig (see
figure 2). This is normally done with a quartz wax. It has a melting point of 6669º, which is well below the recovery and recrystallization temperature of most
metals. The bonding is carried out with a hot plate (positioned opposite the
PM5D machine), where a black line indicates the correct temperature, and the
BJ2 two-position bonding jig.
Firstly, find a suitable amount of quartz wax and place this on the PP5D base
plate. The base plate is then placed on the bonding jig, which is placed on the hot
plate. Once the wax is fully melted, the sample is placed on the wax, and the
spring driven piston is used (with a block in between) to press down and flatly
bond the sample(s) to the base plate.
The metallurgy lab only has a very warm hot plate, so in the case of VERY heat
sensitive samples, it is a good idea to find a less warm hot plate or use dissolvable
glue instead. When the sample is bonded to the plate, use a scalpel to remove the
excess wax/glue on the plate around the sample – this gives the most accurate
height measurements afterwards.
Note that, size permitting, several samples of roughly the same height (within a
few hundred micrometers) may be bonded to the base plate at the same time, allowing for the polishing of several samples at once!
In the case of samples mounted on a SEM sample stub, there is an alternative way
to bond the sample. The SEM sample stub can be clamped to the base of the
PP5D polishing jig with a special clamp. This method of bonding makes relatively easy serial sectioning possible if the area of interest is marked with hardness indents, so as to make the area of interest clearly identifiable.
Once bonded, any remaining sharp or ragged edges on the sample should be filed
or cut with a scalpel. If this is not done, pieces of the edges can (and will) break
off and cause scratching on the sample surface, as well as contaminate the polishing plate. If only a limited amount (i.e. a few hundred microns) of material is to
be removed from the sample, pre-polishing the sample’s edges (before bonding)
by hand will do wonders for the resulting surface quality!
6
Risø-I-2051(EN)
Figure 2. BJ2 two-position thin section bonding jig.
2.3
Check flatness of the lapping plate
For all moderately hard materials (i.e. metals, ceramics, composites etc.), the lapping takes place on cast iron lapping plates, which have a diameter of 30 cm. If
the sample diameter is bigger than 50 mm across, the grooved lapping plate is
used. Otherwise the non-grooved plate is used.
If the non-grooved lapping plate is used, the grooved test block is used; and if the
grooved lapping plate is used, the non-grooved test block is used. To ensure that
the lapping plate is perfectly flat. Let the relevant test block (grooved for flat
plate, or flat for grooved plate) lap with a static lapping arm for 20 min at
70 rpm on a 9 µm Al2O3 slurry. This also removes the thin layer of rust that will
often be on the cast iron plates.
The test block is then inspected with a contact gauge (which is first calibrated on
the flat granite master plate) to determine whether it is concave/flat/convex. The
test block surface will have the opposite deviation from flatness that the plate has
test block → lapping plate: concave → convex, flat → flat, convex → concave
This inspection is carried out with a special contact gauge and the flat granite
master plate, which is used to calibrate the contact gauge. If the lapping plate
only deviates 1-2 µm from perfect flatness it is not a problem, but if it deviates
more, the lapping plate will have to be corrected. Remember to clean all surfaces with alcohol when measuring the test block!!!
If the lapping plate is concave, move the sample arm so that the test block only
just extends a few mm over the inner edge; and if the lapping plate is convex,
move the sample arm so that the test block only just extends a few mm over the
outer edge. Let the machine lap as before. The lapping plate will be corrected at a
rate of about 1 µm/hr (at 70 rpm on a 9 µm Al2O3 slurry). This can be sped up by
adding extra weight to the test block.
2.4
Clean components when necessary
Always clean all the components with water and/or alcohol when doing measurements and changing slurries. It is very important to avoid contamination, because
this will normally result in scratching during the polishing process.
Use the differently labeled brushes when removing the different lapping and polishing slurries.
Risø-I-2051(EN)
7
3 Machine operation
The machine works in three ways. In all three different ways the top left screen
indicates the total lapping/polishing time that has passed:
• 100% user controlled. manually pressing ‘ON/OFF’-button.
• the machine runs for a pre-specified period of time and then stops.
• the PSM1 unit can (for lapping) stop the machine when a pre-specified
thickness of material has been taken off.
3.1
PM5D controls
The PM5D (see figure 1) has two main ‘ON’ switches + one on the membrane
touch display, which must be turned on for the machine to function when the
electric power has been turned on. The ‘Emergency Stop’ button is a red
knob on the lower right of the machine — if pressed, it immediately turns off all
power to the machine, and it must be turned clockwise to reactivate the PM5D.
Right next to the emergency stop switch is the ‘Mains Isolator’ switch,
which will light up green when ON. Lastly, the ‘ON/OFF’-button on the membrane touch display must be pressed.
When the display lights up the jig arm will do a self-test, after which you need to
choose between static arm (lapping) or sweeping arm (polishing), and then press
the button under <Systems check>. In the systems check you can adjust the
position of the jig arm (static arm mode), or the outer positions of the jig
arm (sweeping arm mode).
When the machine is first turned on, it will go through a systems check. Unless
you know better, simply press the button under the arrow.
The machine starts when the ‘START’ membrane button is pressed. The lapping
plate will not start rotating until you press the ‘Plate Speed Control’
keys, which increments the plate rotation speed in increments of ±1 rpm within
the interval 0-70 rpm (NB! this speed is not stable if the chosen plate rotation
speed is less than 10 rpm).
The slurry will not start dripping from the cylinder until the ‘ABRASIVE
AUTOFEED ON/OFF’ button is pressed, and the valve on the autofeed cylinder
has been opened. If the slurry does not run properly down the drip wire onto the
plate, use a finger to wet the wire.
3.2
Adjusting sample load
The downward load/pressure that the PP5D polishing jig exerts on the sample can
be adjusted by rotating the collar behind the PSM1. The load on the sample can
thus be varied from 0.1−2.7 kg. If the collar is rotated clockwise, the load is on
the sample increased; and if the collar is rotated anticlockwise, the load on the
sample is decreased.
Load is best adjusted by inspecting how much the sample protrudes from beneath
the base ring of the polishing jig. For well-controlled lapping and polishing, the
sample should protrude 0.1-1 mm, but if many hundred microns of material need
to be lapped off, a larger sample load should be used (see sections 4 & 5).
It should be noted that too much sample load can result in small samples being
forced through the lapping slurry, thus causing them to be scratched on the polishing plate.
8
Risø-I-2051(EN)
3.3
•
•
•
•
•
•
•
•
•
•
Operation procedure
Turn on machine (on all three buttons).
Do systems check (static or sweeping arm).
Place autofeed cylinder or SF1-container on machine and open valve.
(if first use of the day) Run the machine with polishing block for 20 min
with 9 µm Al2O3 at 70 rpm. Check (and correct) flatness.
Adjust sample load.
(if lapping) Turn on the PSM1 and the contact gauge. Reset the contact
gauge and set a target depth on the PSM1. (if polishing) Press ‘SET’ on
the PM5D to set the polishing time.
Press ‘START’, ‘ABRASIVE AUTOFEED ON’, and ‘PLATE SPEED
CONTROL’ keys.
When the slurry is spread out on the lapping plate, place the polishing jig
on the plate, while restraining the sample base plate. Gently lower the
specimen plate down onto the lapping/polishing plate in order to avoid
damaging the sample.
Stand the autofeed cylinder on its end, and wash everything thoroughly
(very thoroughly if SF1 was used).
Carefully clean all the components when changing lapping/polishing slurries, and clean the samples with water and/or alcohol as often as needed.
4 Lapping with the PP5D polishing jig
with PSM1 sample monitor
Lapping is the wearing away of material by liquid abrasion from a free flowing
liquid slurry. The sample aquaplanes on the slurry on the lapping plate.
Lapping causes sub-surface material damage down to a depth of approx. 3 times
the diameter of the abrasive particles (i.e. a 9 µm abrasive will cause damage
down to a depth of approx. 30 µm), and produces a non-reflective surface, with a
surface roughness of several hundred nanometers (a 9 µm Al2O3 abrasive will
result in a surface roughness of approx. 400 nm).
During lapping the sample holder arm is in static mode, and plate speed is 70 rpm.
4.1
Lapping slurries
The Risø PM5D system has two different lapping abrasives. They are on powder
form and need to be mixed with de-ionized water (DI-water) in the ratio given:
3 µm Al2O3
9 µm Al2O3
(20% total slurry volume =
300 ml (full fill))
(10-15% total slurry volume = 150-225 ml (full fill))
DI-water must be used to avoid contamination, and the cylinder should only be
filled up to the halfway-line (it contains 1.5 liters of slurry). If refilling a nonempty cylinder, the above percentage indicates how much abrasive powder
should be added. For example, 1 liter of ‘3 µm Al2O3’ slurry comes from 200 ml
of powder (20%) and 800 ml of DI-water
When the machine is stopped, stand the autofeed cylinders on their ends!
If the valve is kept closed, the slurry can remain in working order for months. If
this is not done the Al2O3-abrasive has a tendency to solidify within the valve of
the cylinder clogging it up, thereby stopping the flow of slurry to the lapping
plate  this has already happened once!!!
Risø-I-2051(EN)
9
Lapping allows in situ control of material removal. The digital contact gauge on
the jig tells the depth of material taken off, and with the PSM1 installed the lapping process will be stopped once the specified depth has been reached. This is in
general accurate within 1-2 µm, which can be checked with a contact gauge. In
general, the majority of the material will be lapped with the 9 µm Al2O3, and only
the last 30 µm (to be lapped) will be taken off with the 3 µm Al2O3, thus leaving
only 10 µm sub-surface damage, which must then be removed during the polishing process. It is important to leave a bit of extra material for accidental overshooting, as the extra material may be taken off in the polishing process.
If surface polishing samples, the 9 µm-step may be omitted, thereby saving sample material and lapping time!
4.2
Material take-off rate
Depending on the material, the surface area being lapped, the PP5D sample load,
and the lapping slurry being used, the material take-off rate can vary from 1
µm/min to 100 µm/min.
In general, the slower the lapping take-off rate, the better the depth control, but
one must decide how long one wants to spend on the lapping stage, which does
not dramatically effect the post-polishing surface. The take-off rate is controlled
by increasing or decreasing the sample load (see section 3.2).
4.3
Using the PSM1 sample monitor
NB! The PSM1 only works properly during lapping!!!
Turn on the PSM1 by pressing the green button (see figure 3). If the PSM1
doesn’t turn on (or only for a few seconds) the batteries are dead, and they should
be replaced with the other set we have – please remember to recharge the old
ones! The PSM1 will first display an error message “E7”, which will disappear
when the contact gauge on the polishing jig is turned on by pressing ‘POWER’.
NB! Don’t turn on the contact gauge without turning on the PSM1, as this will
leech the internal battery in the contact gauge instead of using the rechargeable
PSM1 batteries!
When the polishing jig is placed on the wet lapping surface, it should be allowed
to rotate at least once to allow the slurry to get in under the sample and the ring of
the polishing jig. The contact gauge is reset to 0 by pressing ‘RESET’. If the error
persists, check if the contact gauge is turned on. If this is the case, consult the
Logitech PSM1 manual (which is found in the red plastic case next to the PM5D)
for a complete list of error messages.
When the PSM1 and contact gauge are turned on, the PSM1 display should read
‘P’. To set the desired amount of material to be removed (in microns), press the
‘SET’ button and use the ‘+’/’-‘ buttons to enter the desired value, followed by
‘SET’ once again - all this can be done in advance as long as the contact gauge is
also turned on. When you are ready to start lapping, press ‘RUN’ and the PSM1
will start counting down to the desired depth on the screen. Before leaving the
machine to lap by itself, take a moment to check that the PSM1 is actually counting down  in other words working properly!
When the sample gets within 20% of the desired depth the PSM1 will start beeping
at an rate that increases as the specified depth comes closer. Finally, the PSM1 will
stop the PM5D lapping machine using a continuous infrared signal when the desired depth is reached, and it will continue beeping after the machine has stopped!
Please don’t let the PSM1 stand in beeping mode for too long, as this will drain
the batteries, and greatly annoy all other people in the metallurgy lab. To stop the
beeping, press the red “Off” button on the PSM1, which turns it off. The contact
gauge will turn off on its own.
10
Risø-I-2051(EN)
Figure 3. PP5D precision polishing jig with PSM1 sample monitoring system.
5 Polishing with the PP5 polishing jig
Polishing is the removal of surface material by the grinding of small hard particles against the surface. It produces a reflective surface, with a surface roughness
down to a few nanometers (or even lower if great care is taken).
During polishing the sample holder arm is in sweeping mode, and the plate
speed is around 40 rpm.
In general, to get good results, keeping the working area as clean as possible and
using a low sample loading weight is essential. If the resulting surface is to be
used for EBSD analysis without additional to electro-chemical polishing, great
care must be taken to ensure that the entire deformed surface layer from the lapping process (see previous section) is removed during the polishing.
Before starting, the edges of the samples should be visibly inspected for bits that
might crack off, as these will cause surface scratching during the polishing process.
5.1
Polishing agents
The Risø PM5D system has two different polishing slurries:
1 µm synthetic polycrystalline diamond
1 µm colloidal silica (SF1)
When working with soft materials, such as annealed aluminium, diamond yields
the best results. When working with hard materials, such as deformed nickel,
SF1 works very well, but this does vary from material to material. The SF1 solution does not seem to be very effective for polishing aluminium, but it gives very
good results for materials such as cupper and steal.
Risø-I-2051(EN)
11
Synthetic polycrystalline diamond (1 µm)
The diamond powder must be mixed with ethane diol polishing fluid. For standard research size samples 2 g diamond/cylinder fill will be a suitable concentration. It uses the expanded polyurethane (or the DP DUR) polishing cloths. The
polishing cloths must be glued (they are self-adhesive) to the flat metal polishing
plate. When applying the polishing cloth, make sure that the base plate is clean
and that no air bubbles are left under the cloth.
The DP DUR cloths are both durable and chemically resistant, so the use of OPS
(the finest mechanical polishing slurry available in the metallurgy lab) is also
possible – if everything is cleaned quickly with water and washing up liquid immediately after polishing is finished.
SF1 colloidal silica (1 µm)
The SF1 colloidal silica is supplied in a ready blended SF1 polishing suspension, and it uses a (pink) hyprocel pellon polishing cloth. This cloth is a permanent polishing cloth, not to be confused with the expendable polishing cloths used
with diamond polishing.
When using the SF1 suspension, it is very important to remember that the silica
crystallizes very quickly, so about 5 minutes before stopping the plate it should
be doused with DI-water to remove most of the SF1 . Immediately after removing
the jig from the polishing plate, the sample and jig should be thoroughly rinsed
with water, and be placed in a shallow bowl of DI-water with a soft cloth to soak
for a while. The plate should be doused with plenty of DI-water and be kept rotating at 10-15 rpm, so the silica does not crystallize on the plate’s surf
ace. In general, all components in contact with the SF1 solution should quickly be
thoroughly cleaned after use, so as to avoid SF1 crystallizing on them.
5.2
Material take-off rate
Measuring material take-off while polishing is done in a somewhat different way
than for lapping. Because the polishing plates are covered with a soft material, the
sample penetrates somewhat into them making an accurate in situ sample take-off
measurement with the PSM1 unit impossible!
Good quality polishing is generally a slow business, with a maximum material
removal rate of 1 µm/min. The sample load should be as low as possible when
polishing.
To get the polishing take-off rate. The sample thickness is measured with a contact gauge before polishing is begun and then again after 10-15 minutes of polishing. Dividing the amount of removed material with the polishing time gives the
material removal rate (µm/min), which is used to calculate how long the sample
must be polished for in order to reach the desired sample depth.
For this take-off “calibration” to be correct, it is very important not to change the
polishing parameters: i.e. sample load; plate speed; and sample arm positions/speed. Always err on the side of safety!!!
A digital contact gauge can be found in the SOFC lap on the ground floor of
Nordlab (building 227). Talk to Ebtisam Abdellahi (tel. 5750, e-mail:
[email protected]) about borrowing it. It is recommended to use this
instead of our own mechanical contact gauge at the metallurgy lab.
12
Risø-I-2051(EN)
6 Machine maintenance
Please leave the PM5D system in as good (or better) a state as you hope to find it!
When not in use, place the slurry cylinders up on their ends AND close the valve.
This prolongs the lifetime of the slurry. If stored on its end and out of direct
sunlight, the slurry in a cylinder can last up to a year.
Rinse and scrub all the removable components with DI-water and a brush. Give
the machine a good clean, using some alcohol on the more difficult spots. Don’t
forget to clean the drip tray with a brush in the sink. Give the drip tube (the sink
of the PM5D machine) a good rinse, using the water tube to the right of the machine. This is to prevent the slurry from drying in the tube and congesting it during and after use.
Whenever you’re changing lapping/polishing slurries make sure to rinse the lapping plate and scrub the surface and gullies with a heavy brush. Also make sure
that the slurry chute and drip wire are cleaned as well, since slurry contamination
can cause scratching.
7 Final words
Please note that reading this manual is NO SUBSTITUTE for taking an introductory course on the PM5D system!!!
This course and copies of this manual, as well as the full Logitech PM5D
system CD-ROM are available from Helmer Nilsson (tel. 5714, e-mail:
[email protected]) & Axel Larsen (tel. 5787, e-mail:
[email protected]).
Finally, if something goes disastrously wrong or badly malfunctions contact
Helmer Nilsson (5714) or Axel Larsen (5787).
Risø-I-2051(EN)
13
Bibliographic Data Sheet
Risø-I-2051(EN)
Title and authors
’Logitech PM5D precision polishing and lapping system’ user manual
Axel W. Larsen
ISBN
ISSN
xx-xxx-xxxx-x
xxxx-xxxx
Department or group
Date
Center for Fundamental Research:
Metal Structures in Four Dimensions
AFM
21.08.03
Groups own reg. number(s)
Project/contract No(s)
Sponsorship
Danish Research Foundation
Pages
Tables
Illustrations
References
13
0
3
0
Abstract (max. 2000 characters)
This internal Risø report is a user manual for the ‘Logitech PM5D precision
polishing and lapping system’. It is not a ‘stand alone’ manual. It is assumed
that the user has taken an introductory course to the PM5D system.
It includes: an introduction to the various components of the system; the necessary steps that must be taken before lapping/polishing can commence; how to
operate that PM5D machine and do lapping and polishing on it; how to maintain
the system in working order, as well as tips on how to achieve good polishing
results are also found within.
Information Service Department: 2 copies
A4
Mater. Sci. Forum vols. 408-412, 287-293
Lattice Rotations of Individual Bulk Grains during Deformation
G. Winther1, L. Margulies1,2, H.F. Poulsen1, S. Schmidt1, A.W. Larsen1,
E.M. Lauridsen1, S.F. Nielsen1 and A. Terry2
1
Materials Research Department, Risø National Laboratory, DK-4000 Roskilde, Denmark
2
ESRF, BP 220, F-38043 Grenoble Cedex, France
Keywords: polycrystal deformation; X-ray Diffraction; Synchrotron Radiation
Abstract. Three-dimensional X-ray diffraction has been applied to measure in-situ lattice rotations
of individual grains deeply embedded in a 2 mm thick copper sample during 6% elongation. The
tensile axis of seven grains initially close to <111> all rotated towards this orientation. This
common rotation behaviour indicates a limited influence of grain interaction at low strains. Minor
variations in the rotation of the tensile axis did not exceed the spread in the predictions by the
classic Sachs and Taylor models.
Introduction
Polycrystal plasticity models for prediction of texture evolution during deformation are based on
prediction of active slip systems in individual grains and calculation of the resulting grain rotation.
Only bulk textures before and after deformation can be measured by standard techniques. The field
has therefore been severely impeded by lack of data on the grain level. All models consequently
rely on assumptions concerning the factors controlling the behaviour of individual grains. The
earliest models, i.e. those proposed by Sachs [1] and Taylor [2], assume that the rotation of a grain
is determined by its crystallographic orientation. Limitations of these models, especially when it
comes to prediction of the rate of texture evolution, have lead to models which consider the detailed
interaction between a grain and its neighbours as an important factor [3, 4].
Experimental studies of individual grains have mostly been limited to surfaces. A clever
experiment where two metal surfaces were pressed tightly together during deformation to mimic
bulk conditions has also been devised [5, 6]. It is however unclear to what extent these data are
representative of true bulk grains.
Recently, in-situ studies of structural changes in individual grains deeply embedded in a
polycrystal have become possible with the 3-Dimensional X-Ray Diffraction (3DXRD) microscope
situated at the European Synchrotron Radiation Facility. The first application of this microscope to
measure lattice rotations during straining was performed on four grains in a polycrystalline
aluminium sample with 300 µm sized grains [7]. The number of measured grains was however too
small to allow solid conclusions and the grain size was also rather large.
This paper presents data from a study of seven grains in copper with an average grain size of 35
µm. Only grains having the tensile axis close to the crystallographic <111> direction were
monitored. In particular, some grains with nearly identical orientations were picked, in order to shed
light on the relative importance of the initial crystallographic grain orientation and interaction with
different neighbouring grains.
Mater. Sci. Forum vols. 408-412, 287-293
Fig. 1. Sketch of the experimental set-up, including definition of angles 2θ (Bragg angle) and ω
(sample rotation).
Experimentals
The experimental set-up is sketched in Fig. 1. The material is 99% pure copper with an average
grain size of 35 µm. Sample dimensions are 55 mm x 8 mm x 2 mm. The sample is mounted in a
stress rig not shown in Fig. 1 so that tension can be carried out on-line. Data are acquired before
deformation and after 0.5, 1, 2.5, 4, and 6% elongation. Dimensions of the X-ray beam are 13 x 6
µm2 and the energy is 61.62 keV. Position and intensity of diffracted spots are recorded by the
detector. At each deformation step an ω-range from –10° to +12° is scanned to obtain diffraction
spots from different crystallographic planes in each grain in the sample volume probed.
A conical slit is placed between the sample and the detector. The conical slit contains 6 conically
shaped openings, placed in accordance with the {111}, {200}, {220}, {222}, {331} and {422}
reflections of copper. For each ring the conical slit ensures that only diffraction spots arising from a
small intrinsic gauge volume are seen by the detector. For general information on the three
dimensional X-ray microscope see refs. [8-13]. Specific information on its application to lattice
rotations can be found in refs. [7] .
Indexing of the spots to derive the crystallographic orientation of individual grains is carried out
as described in ref. [13]. For crystallographic reasons, the number of measured diffraction spots for
each grain varies between 7 and 15 in the scanned ω-range. Typically, 2-3 of these are lost during
straining because they rotate to positions outside the ω-range or overlap with other spots. To assure a
uniform sampling for each grain crystallographic orientations are derived from a fixed set of 5
reflections.
Results
A total of 7 grains were found with initial orientations near the <111> corner. The measured grain
rotations are plotted with respect to the tensile axis and one transverse axis in Fig. 2 and Fig. 3,
respectively. The tensile axis of all grains rotates significantly towards the <111> orientation. The
initial orientation of the transverse axis is not the same. The rotations in Fig. 3 therefore cannot be
compared directly.
Mater. Sci. Forum vols. 408-412, 287-293
111
4
5
7
6
1,2,3
100
1
2
3
110
Fig. 2. Stereographic triangle showing the rotation of the tensile axis. All grains rotate towards the
<111> corner. Enlargements of grains 1-3 relative to the <110>-<111> line are shown to the right.
111
4
5
3
2
6
1
7
100
110
Fig. 3. Sterographic triangle showing the rotation of one of the transverse axis for
all grains.
Mater. Sci. Forum vols. 408-412, 287-293
Discussion and modelling
The tendency for rotations towards <111>, i.e. the dominant component of tensile fcc textures, was
also observed in the previous study of four aluminium grains. These data indicate that the
interaction between an individual grain and its specific neighbours does not have a dominant
influence on the rotation at least at low strains. The initial orientation spread of the present copper
data is insufficient to judge the strength of the correlation between rotation behaviour and the initial
crystallographic orientation of a grain. A more comprehensive investigation is currently being
carried out.
Although the grains share a common main rotation direction, they do not rotate in completely the
same way. The minor variations may be attributed to either grain interaction or to ambiguity in the
activation of slip systems so that different slip system combinations accompanied by different
rotations are equally likely.
One would expect grain interaction to be more dominant in polycrystals with small grain sizes
than in large grained samples. The data available so far, which covers about a factor of ten in grain
size, do not reveal significant grain size effects. The number of grains and the range of initial grain
orientations studied are however too limited to reliably assess the effect of grain size.
Due to the fact that grain interaction does not seem to have a dominant influence on the
rotations, the measured rotations are compared with predictions obtained with the Sachs and Taylor
models. Measured and predicted rotations of the tensile axis are shown in Figs. 4 and 5. For the
Taylor model all the different solutions with five active slip systems are shown. Linear
combinations of these solutions are of course also valid. For the Sachs model the rotation was
calculated as the antisymmetric part of the deformation tensor. The Sachs prediction always heads
more towards the <100>-<111> line than the two Taylor predictions. The experimental data show
that no grains rotate further towards the <100>-<111> line than the Sachs prediction and only a
single grain rotates slightly more towards the <110>-<111> line than predicted by the Taylor
model. The two models thus represent the extremes well and the experimental rotation paths span
the orientation space between them.
There is a good correlation between the rotation direction and the magnitude of the rotation:
Grains lying close to the Sachs prediction rotate faster than those lying close to the Taylor
prediction. This is an indication of significant multislip in grains rotating more towards the <110><111> line as the rotation contribution from one slip system may be partly counterbalanced by
contributions from other systems.
Comparison of the rotation of the transverse axis instead of the tensile axis does not give as clear
a conclusion. Only in a few cases rotation of both tensile axis and transverse axis rotate consistently
with respect to the model predictions. The best correlation between rotation of tensile and
transverse axes is found for the three grains close to <221>. One of these grains almost perfectly
follows the paths predicted by the Sachs model but rotates significantly less than predicted. Another
of the grains follows the Taylor prediction closest to the <110>-<111> line nicely, both with respect
to direction and distance. The third grain has a tensile axis which rotates as predicted by assuming
double slip on the two equally stressed systems. The Taylor model predicts a tensile axis rotation in
the same direction but too small. Neither of these models predicts the observed rotation of the
transverse axis for this grain.
The conclusion is that the tensile axis of grains initially close to <111> appears to rotate in a
reasonably well-behaved manner which lies in between the predictions of the Sachs and Taylor
models while rotation of the transverse axis appears harder to predict.
Mater. Sci. Forum vols. 408-412, 287-293
4
5
7
1
6
2
3
Fig. 4. Prediction with the Sachs model. To allow sufficient enlargement the stereographic triangle
itself is not drawn. Grains 1-3 and 4-7 are shown separately.
4
5
7
6
1
2
3
Fig. 5. Prediction with the Taylor model. To allow sufficient enlargement the stereographic triangle
itself is not drawn. Grains 1-3 and 4-7 are shown separately. The two lines for each grain represent
two different solutions with the Taylor model, each having five active slip systems.
Mater. Sci. Forum vols. 408-412, 287-293
Summary
•
•
•
•
Three-dimensional X-ray diffraction has been applied to monitor lattice rotations of individual
grains deeply embedded in a copper polycrystal during tensile straining.
Seven grains with approximately the same orientation of the tensile axis (close to <111>) were
studied.
All grains exhibited the same main rotation of the tensile axis, indicating a limited influence of
grain interaction.
Variations in rotation of the tensile axis with respect to both direction and speed lie within the
predictions of Sachs and Taylor.
Acknowledgments
The authors gratefully acknowledge the Danish National Research Foundation for supporting the
Center for Fundamental Research: Metal Structures in Four Dimensions, within which this work
was performed. Additional support for this work was provided by the Danish research council SNF
(via Dansync). The authors thank P.B. Olesen, P. Nielsen, A. Goetz and M. Nicola for technical
assistance, U. Lienert and R.V. Martins for help in setting up the experiment and N. Hansen and D.
Juul Jensen for fruitful discussions.
References
[1] G. Sachs: Z. Ver. Deu. Ing. Vol. 72 (1928), p. 734
[2] G. J. Taylor: Journal of the Institute of Metals Vol. 62 (1938), p. 307
[3] U. F. Kocks, C. N. Tomé and H.-R. Wenk: Texture and anisotropy: Preferred orientations in
polycrystals and their effect on materials properties (Cambridge University Press 1998)
[4] D. P. Mika and P. R. Dawson: Materials science and engineering A Vol. 257 (1998), p. 62
[5] C. S. Barrett and L. H. Levenson: TMS-AIME Vol. 137 (1940), p. 112
[6] R. Becker and S. Panchanadeeswaran: Acta metallurgica et materialia Vol. 43 (1995), p. 2701
[7] L. Margulies, G. Winther and H. F. Poulsen: Science Vol. 291 (2001), p. 2392
[8] D. Juul Jensen, Å. Kvick, E. M. Lauridsen, U. Lienert, L. Margulies, S. F. Nielsen and H. F.
Poulsen: Materials research society symposium proceedings Vol. 590 (2000), p. 227
[9] U. Lienert, H. F. Poulsen and Å. Kvick: Proceedings of 40th conference of AIAA on structures,
structural dynamics and materials, St. Louis, USA 1999
[10] U. Lienert, C. Schulze, V. Honkimäki, T. Tschentscher, S. Garbe, O. Hignette, A. Horsewell,
M. Lingham, H. F. Poulsen, N. B. Thomsen and E. Ziegler: Journal of synchrotron radiation Vol. 5
(1998), p. 226
[11] S. F. Nielsen, A. Wolf, H. F. Poulsen, M. Ohler, U. Lienert and R. A. Owen: Journal of
synchrotron radiation Vol. 7 (2000), p. 103
[12] H. F. Poulsen, S. F. Nielsen, E. M. Lauridsen, U. Lienert, R. M. Suter and D. J. Jensen: Journal
of applied crystallography Vol. 34 (2001), p. 751
[13] E. M. Lauridsen, S. Schmidt, R. M. Suter and H. F. Poulsen: Journal of applied crystallography
Vol. 34, p. 744
A5
Mater. Sci. Forum vols. 467-470, 81-86
In-Situ Investigation of Bulk Nucleation by X-Ray Diffraction
A.W. Larsen1, C. Gundlach1, H.F. Poulsen1,
L. Margulies1+2, Q. Xing1, D. Juul Jensen1
1
Center for Fundamental Research: Metal Structures in Four Dimensions,
Materials Research Department, Risoe National Laboratory, DK-4000 Roskilde, Denmark
2
ID11, ESRF, 38043 Grenoble Cedex 9, France
Keywords: Nucleation, Triple junctions, 3DXRD, X-Ray Diffraction, Orientation measurements
Abstract. A new method for in-situ studies of nucleation in bulk metals based on high energy
synchrotron radiation is presented. Copper samples cold rolled 20% are investigated. The
crystallographic orientations near triple junctions are characterized using non-destructive 3DXRD
microscopy before, during, and after annealing for 1 hour at 290°C. This method allows in-situ
identification of new nuclei and the deformed material, which spawns the nuclei. Also, since data is
acquired during annealing nucleation kinetics can be studied.
Introduction
Studies of bulk nucleation have always been hampered by the fact that it has been impossible to
know the exact microstructure at the exact nucleation sites before the nuclei emerged.
It is possible to perform microscopic scanning electron microscopy (SEM) and transmission
electron microscopy (TEM) studies of nucleation, where the starting structure is known [1,2]. But
in both cases it is not possible to rule out surface effects. In SEM studies there is also the added
problem of grains growing up from the hidden bulk sample below the surface.
With high X-ray energies (50 keV) a 10% transmission through a thickness of 25 mm of Al, 1.5 mm
of Fe, and 1 mm of Cu is obtained, thus allowing non-destructive probing of the bulk of metal
samples. By using samples of a suitable thickness it is possible to characterize the microstructure
within a column through the sample, which is representative of the bulk microstructure. Depending
on the X-ray beam spot size, the measurement time, and the material being investigated, a submicron volume resolution can be achieved.
Poulsen et al have shown that it is possible to perform in-situ studies of recovery in a deformed Al
single crystal using 3DXRD microscopy [3].
Earlier studies of nucleation have shown that areas near triple junctions are likely sites for
nucleation [2,4], so in this study we limit ourselves to volumes near triple junctions. The purpose
of this paper is to explain in detail the experimental procedure and illustrate it’s potentials, by
showing the first results obtained with the method.
The 3DXRD microscope
The 3D X-ray diffraction (3DXRD) microscope1 works in the X-ray energy regime of 40-100 keV
[5]. It is installed in the second hutch of ID11, which is a high energy beamline at the ESRF2
(Grenoble, France). The X-ray beam can be focused down to a 2x5 µm2 spot, using double focusing
1
2
http://www.risoe.dk/afm/synch/3dxrd.htm
http://www.esrf.fr/exp_facilities/ID11/handbook/welcome.html
Mater. Sci. Forum vols. 467-470, 81-86
from a bent Laue Si-111 crystal and a bent multilayer, giving a maximum flux of Φ0=1.5⋅1010
(photons/sec/µm2) on the sample with an energy bandwidth of 0.06-1%.
A schematic diagram of the 3DXRD microscope can be seen on Fig. 1.
The 3DXRD microscope allows static and dynamic studies of the microstructure of solid bulk
samples. The high transmission and photon flux allows the reflections from individual
crystallographic grains to be detected, and specialized software allows these reflections to be
indexed back to the individual grains, thus allowing individual grains to be followed in-situ.
Slits placed right in front of the sample precisely define the spot size, and several different detectors
of varying resolution are available. It is possible to mount a furnace (used in this study), a cryostat,
a tensile stress rig, or a torsion device on the sample stage, thus allowing in-situ studies of phase
transformations, annealing, and deformation.
Figure 1: Schematic diagram of the 3DXRD microscope. The 1×1 mm2 white X-ray beam enters
from the left, where it is monochromated and focused in the vertical plane using a bent Laue Si-111
crystal. Horizontal focusing is performed with a bent multilayer. A slit in front of the sample defines
the size of the beam on the sample. The sample can be translated in the x, y, z-direction, ω is the
sample rotation around the z-axis, and it is possible to tilt the sample around the x and y-direction.
Sample preparation
The sample material is 99.995% Vol. pure copper, which is initially cold rolled 20%, and then
annealed for 8 h at 700°C. This results in an inhomogeneous grain size distribution with an average
grain size of about 500 µm. This starting material is additionally cold rolled 20% to a thickness of
25.6 mm. During cold rolling the l/h ratio is equal to 1.2, and the deformation is therefore expected
to be uniform throughout the thickness of the material [6]. Here l is the cordal length of the contact
area with the rolls, and h is the sample thickness.
From the rolled material a thin 10×10 mm2 sample is cut out, and the sample surface (the RD/ND
plane) is polished down to a thickness of 0.3 mm (see Fig. 2), using a Logitech PM5D polishing and
lapping machine with a PSM1 sample monitor3 [7], where polishing is performed from both sides.
Lastly, the sample is electrochemically polished, with a D2-electrolyte4 for 5 seconds at 10 V, to
remove any remnant surface deformation or sub-micron scratching (i.e., surface nucleation sites).
An illustration of the sample geometry can be seen on Fig. 2.
3
http://www.logitech.uk.com/
D2: 500 ml H2O, 250 ml H3O4P, 250 ml ethanol, 2 ml Vogel’s Sparbeize, 50 ml propanol, and 5 g H2N CO NH2
(urea)
4
Mater. Sci. Forum vols. 467-470, 81-86
Initially, the surface microstructure of the sample is studied to determine the surface positions of the
triple junctions within a chosen area on the surface. The surface microstructure of a 1.8×1.8 mm2
area is characterized by electron backscatter patterns (EBSP), producing an orientation image map
(OIM) of the area in studied [8,9]. A JEOL JSM-840 scanning electron microscope, with a
LaB6-filament is used to collect the data, and the step size is 20 µm. From the OIM, an area
containing one or more well defined triple junctions is chosen for 3DXRD studies (see Fig. 2).
Figure 2: Sample geometry. Side lengths are
less than 10 mm, and thickness is 0.3 mm. The
RD, ND, and TD-directions are respectively
oriented along the y, z, and x-axis in the
3DXRD microscope (see Fig. 1).
The upper right corner of the OIM is located
2 mm below the top edge and 2 mm to the left
of the right edge. Note that the relative size
of the OIM has been exagerated to make the
microstructure more easily discernable. The
white squares indicate the position of suitable
triple junctions.
A TEM foil is taken parallel to the RD/ND plane, and prepared by electro polishing. From this the
average distance between dislocation boundaries (the cord length) within the deformed material is
determined using a JEOL-2000FX transmission electron microscope, operating at 200 kV. The
average cord length is found to be about 0.5 µm, and the smallest length is ∼0.15 µm.
3DXRD experiment
For the 3DXRD experiment, an energy of E=50.77 keV (λ=0.2442 Å) is chosen, giving a
transmission of 50% through the 0.3 mm thick copper samples. A 1024×1024 pixel Frelon5 CCDdetector was placed 333 mm from the sample, allowing for the simultaneous full recording of the
four Debye-Scherrer rings of lowest multiplicity: [111], [200], [220], and [311].
The sample is mounted within a furnace (see Fig. 1), with the RD/ND plane perpendicular to the Xray beam (see Fig. 2). It is possible to heat and cool the sample within the furnace, which consists
of a 0.1 mm thick glass capillary tube with a thermocouple in the middle. This can be done in
vacuum or in an argon atmosphere.
The approach is in detail to map a 100×100×300 µm3 volume (grid area × sample thickness),
centered on a triple junction in the as-deformed sample. The sample is then heated to 290°C, and
data is continually collected from the same volume with a time resolution of 6 min. After 1 hour,
the sample is cooled to room temperature, and the same 100×100×300 µm3 volume is mapped
5
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Mater. Sci. Forum vols. 467-470, 81-86
again. By comparing the post-annealed with the pre-annealed data, it is possible to locate new
nuclei, and the microstructure from which it grew. If the new nuclei yields more than one
diffraction spot, it is possible to determine the nuclei’s maximum distance from the sample center
by triangulating the positions of the diffraction spots.
To avoid spot-overlap (different sample volumes diffracting into the same position on the detector),
it was decided to limit the number of grains intersected by the X-ray beam penetrating through the
sample. The solution is to make the grain size and the sample thickness comparable, while keeping
the sample thick enough for the microstructure to have true bulk properties. This lead to the chosen
0.3 mm sample thickness. Also, the sample is cold rolled 20%, only creating a moderate
deformation and therefore only a moderate broadening of the poles. With this approach, it is
typically possible to observe all the broadened reflections (poles) from the 3 grains at a triple
junction without spot-overlap.
The time and ω resolutions are chosen as 1 second and 1° respectively. To make sure that the
sensitivity of the 3DXRD microscope is high enough to detect the deformed cells, a small X-ray
beam size is chosen: the beam is horizontally and vertically focused down to a 49x49 µm2 spot.
To detect a cell, the diffracted intensity from that cell must be at least twice that of the background
noise. A textureless aluminium foil of known thickness is used to calibrate the volume detection
limit, and from that a volume detection limit of (0.26 µm)3 is determined for copper.
For the experiment, the microstructure of a 2×2 grid (100x100 µm2 area), centered on a triple
junction, which is chosen from the OIM, is characterized at different time steps. At each grid point
a 1 second ±0.5° rocking curve scan is performed at ω positions from -20° to 20° in 1° increments.
This angular range is sufficient to cover all crystallographic orientations.
The as-deformed triple junction is characterized at room temperature, after which the sample is
heated to 290°C. When at temperature, identical 2×2 grid scans are continually performed at the
same sample position. Each grid point contains 42 rocking curve scans (each taking ∼2 seconds),
and since there is 4 of these, it corresponds to a complete 2×2 grid scan roughly once every 6
minutes, thus allowing us to follow nucleation in-situ as a function of time with that time resolution.
The choice of a 49x49 µm2 spot size is a compromise between spatial and time resolution. It is
possible to focus the X-ray beam as far down as a 2x5 µm2 spot, but since studying in-situ
nucleation is a ‘needle in the haystack’ problem, a larger area would still have to be covered,
requiring many more grid points, and the corresponding time resolution would make dynamical
studies impossible.
Because the smallest observed cells (∼0.15 µm) in the deformed structure are just smaller than the
volume detection limit (0.26 µm)3, an additional high sensitivity measurement on an as-deformed
sample is also performed. This measurement has a time and ω resolution of respectively 15 seconds
and 0.5°, giving a volume detection limit of (0.15 µm)3, and thus allowing us to see the smallest
length/cells observed in the TEM study.
Mater. Sci. Forum vols. 467-470, 81-86
Results
In the diffraction images from the as-deformed samples, the reflections are seen as elongated poles,
as would is seen in the diffraction patterns from deformed crystals. Due to the moderate
deformation (20%), even when all three grains diffract into the same image, the Debye-Scherrer
rings are still not fully filled with reflections (see Fig. 3a). As heating progresses, nuclei are seen to
appear as sharp diffraction spots with very low mosaic spread and intensity increasing with time
(see Fig. 3b).
In Fig. 3, diffraction images from the same volume of the sample before and after annealing can be
seen. In this case, the nucleus clearly forms with an old (already existing) orientation.
Triangulating the positions of the diffraction spots from the nuclei shows where the nuclei are
inside the sample. It is therefore possible to determine whether a detected nucleus has formed in the
sample bulk or on the sample surface.
(a)
(b)
Figure 3: Example of experimental data. The two figures show the raw X-ray diffraction data as
seen on the detector. (a) in the as-deformed state; and (b) after annealing for 3 hours at 290°C.
The white square indicates where in the diffraction images a nucleus can be seen to appear.
In general, the nuclei are observed primarily within the existing crystallographic orientations
(the poles, see Fig. 3b), but some nuclei are also seen to form with orientations not previously found
within the poles of the as-deformed sample.
In this case, the high sensitivity images of the as-deformed sample confirm that no diffraction spots
are observed in the space between the crystallographic poles. This means that before the onset of
annealing, no cells of volumes larger than (0.15 µm)3 have orientations outside the poles.
Further analysis will show if these new orientations are within annealing-twin orientations, results
of grain rotations, or if they are indeed completely new orientations inherent to the annealing
process itself.
Mater. Sci. Forum vols. 467-470, 81-86
Conclusion
A new method for in-situ studies of bulk nucleation has been presented. The method has allowed
for the in-situ detection of new bulk nuclei, while they formed and therefore, the nucleation kinetics
could be followed. It has been confirmed that triple junctions are good nucleation sites.
With this method, there is no ‘lost evidence’, i.e., the parent bulk microstructure is fully
characterized before the nuclei form.
In the present preliminary investigation: Nuclei with crystallographic orientations corresponding to
the orientations already observed in the deformed structure are seen (see Fig. 3); but some nuclei,
which form with orientations not previously observed in the microstructure are seen as well.
Acknowledgements
The authors gratefully acknowledge the Danish Research Foundation for supporting the Center for
Fundamental Research: Metal Structures in Four Dimensions, within which this work was
performed.
References
[1] T.J. Sabin, G. Winther and D. Juul Jensen: Orientation relationships between recrystallization
nuclei at triple junctions and deformed structures (Acta Mat. Vol. 51 (2003), p. 3999-4011)
[2] H. Hu: Recovery and recrystallization in Metals (Interscience, New York (1963), p. 311)
[3] H.F. Poulsen, E.M. Lauridsen, S. Schmidt, L. Margulies and J.H. Driver: 3D-characterisation
of microstructure evolution during annealing of a aluminum single crystal of the S-orientation
(Acta Mat. Vol. 51 (2003), p. 2517-2529)
[4] R.A. Vandermeer and P. Gordon: Edge-nucleated, growth controlled recrystallization in
aluminum (Met. Trans. Vol. 215 (1957), p. 577-588)
[5] H.F. Poulsen and D. Juul Jensen: From 2D to 3D microtexture investigations, 13. International
conference on textures of materials (ICOTOM 13), Seoul (KR), 26-30 August 2002.
(Mat. Sci. Forum 408-412 (2002), p. 49-66)
[6] M. Holscher, D. Raabe and K. Lucke: Relation between rolling textures and shear textures in
fcc and bcc metals (Acta Metall. Mater. Vol. 42:3 (1994), p. 879-886)
[7] A.W. Larsen: ‘Logitech PM5D Precision Polishing and Lapping System’ user manual (Risø-I2051(EN), Risoe National Laboratory, Roskilde, Denmark (2003))
[8] N.C.K. Lassen, D. Juul Jensen and K. Conradsen: Image-processing procedures for analysis of
electron back scattering patterns (Scanning Microscopy Vol. 6:1 (1992), p. 115-121)
[9] B.L. Adams: Orientation Imaging Microscopy: Application to measurement of grain boundary
structure (Mat. Sci. Eng. Vol. 166(A):59 (1993), p. 2517-2529)
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A6
Mater. Sci. Forum vols. 467-470, 147-151
Recrystallization Kinetics in the Bulk
and at the Surface
D. Juul Jensen1, M.D. Lund1+2, A.W. Larsen1 and J.R. Bowen1
1
Center for Fundamental Research: Metal Structures in Four Dimensions,
Risø National Laboratory, Roskilde, Denmark
2
Geological Institute, University of Copenhagen, Copenhagen, Denmark
Keywords: Growth rates, nuclei distribution, stereology, 3DXRD, EBSP
Abstract. Possible variations in recrystallization kinetics from the sample surface to the center have
been investigated in 90% homogeneously cold rolled aluminium (AA1050). It was found that
whereas the average growth rates are quite similar, the nucleation characteristics are different at the
surface and in the bulk.
Introduction
In-situ investigations of recrystallization and grain growth near the surface of samples are
relatively straightforward. Recently in particular the X-Ray Interface Continuous Tracking
technique [1] has provided key results on grain boundary motion during grain growth but also
results from in-situ SEM heating experiments are starting to appear [2, 3].
In-situ investigations of microstructural changes within the bulk of samples are much more
complex. With 3 Dimensional X-Ray Diffraction (3DXRD) microscopy, it is possible to map the
microstructure with a spatial resolution in the micrometer range and a time resolution of the order
of minutes [4-8]. However, 3DXRD measurements can only be performed at high energy
synchrotron sources, the measurements are typically not easy and the data analysis is demanding as
the data sets almost always are very large and new software often has to be developed to treat the
“state-of-the-art” data.
The purpose of the present work is to investigate recrystallization occurring near the surface and
in the bulk of a rolled aluminium plate and to analyze if the nucleation characteristics and growth
rates are similar at the two locations. It is well known that inhomogeneously rolled plates can
exhibit quite large through-thickness differences [e.g. 9, 10]. Therefore, a plate rolled at
intermediate draughts is chosen for the present work, and to be able to compare with previous work,
it is rolled to a relatively high rolling reduction (90%).
In the investigation focus is on the average recrystallization behaviour. Therefore, stereological
characterization of a series of partly recrystallized samples is chosen as the basis for the analysis
instead of in-situ investigations, which more envisage the individualism of the various grains.
Experimental
Commercial purity aluminium (AA1050) heat treated to minimize the amount of iron in solid
solution and with an initial grain size of 80 µm was used for the investigation. This starting material
is similar to that used in a series of previous studies [e.g. 11 - 13]. The starting material was cold
rolled to 90% reduction in thickness. In order to obtain a maximum degree of homogeneity through
the sample thickness, the rolling was done at intermediate draughts [e.g. 9, 10] with l/h ratios in the
range 1-2. Here l is the chord length of the contact arc with the rolls and h is the sample thickness.
Mater. Sci. Forum vols. 467-470, 147-151
From the rolled plate samples were cut out. These were paired in sets of two, which were kept
together during the subsequent anneal at 280° in a molten tin bath. Annealing times ranged from
125 seconds to 6 hours, giving a series of partly recrystallized samples.
After the anneal, one of the two samples in each pair was sectioned to half thickness using a
Logitech PM precision polishing and lapping system [14]. The other sample was just slightly
polished to reveal the near surface microstructure.
All samples, both surface and bulk (half sample thickness), were inspected in the rolling plane
by EBSP in a JEOL 840 SEM, to determine the following microstructural parameters:
Vv,
Sv,
<λ>
volume fraction of recrystallized material
the grain boundary area density separating recrystallized grains from the deformed
matrix.
the mean intercept-free cord length of recrystallized grains.
In previous works these parameters have been determined by manual EBSP inspection [e.g. 12,
13]. In the present work an automatic method is used based on EBSP recordings of 3 parallel lines 1
µm apart. An example of such a 3 line EBSP scan is shown in Fig. 1. The two outer lines are used
as auxiliary lines to support the analysis of the center line. It has been proven that for the present
material, this automatic method is in good agreement with the manual inspections [15].
Fig. 1. Example of a section within a 3 line EBSP scan through a partly recrystallized structure. The step size is 1 µm
and the distance between the lines is also 1 µm.
The length of the 3 line EBSP scans was in all cases 1000 µm, but in some cases several series of
scans were performed on a sample to reduce the experimental scatter. This was in particular
necessary for intermediate annealing times, where the microstructure is rather inhomogeneous;
some large regions can be almost fully recrystallized, whereas others remain deformed.
Results and Discussion
The mean cord lengths of the recrystallizing grains are plotted as a function of annealing time in
Fig. 2. Each 3 line EBSP scan is represented by one point. The figure shows that the grains on
average grow to become 12-14 µm in the fully recrystallized state, which is in good agreement with
our previous result of 14.8 µm [13]. The figure further reveals that the grain sizes in the bulk and at
the surface are indistinguishable. Also when the complete grain size distributions are compared,
there is no obvious difference between surface and bulk.
Figure 3 shows, how the volume fraction of recrystallized material evolves with time. A
significant scatter is observed in particular for surface samples at about 50% recrystallization.
Despite this scatter, the data show that the surface samples in general are more recrystallized than
the bulk samples at a given annealing time. The difference is largest at short and intermediate
annealing times.
Mater. Sci. Forum vols. 467-470, 147-151
Mean length vs time
17
<λ> [µm]
15
13
11
9
7
Bulk
5
Surface
3
0
4000
8000
12000
16000
Annealing time [sec]
Fig. 2. Evolution in the grain size as a function of annealing time.
The evolution in free unimpinged surface area Sv is shown as a function of Vv in Fig. 4. For both
the surface and bulk, the typical curve shape is observed with an initial increase in Sv at low Vv a
maximum near Vv = 0.5 and then a decrease to Sv = 0 at Vv = 1.0. In the early stages of
recrystallization new grains nucleate and grow, whereby the surface area Sv increases. Then the
grains start to impinge and with increasing Vv a larger and larger fraction of the grain surface areas
are neighboring other recrystallized grains (and not deformed matrix material) whereby Sv
decreases.
Vv vs time
1
0,8
Vv
0,6
0,4
0,2
Bulk
Surface
0
0
4000
8000
12000
16000
Annealing time [sec]
Fig 3. Evolution in the volume fraction of recrystallized material as a function of annealing time.
When the Sv results for the bulk and surface samples are compared (Fig. 4), it is seen that the Sv
values for the surface samples are higher than those for the bulk, and the fitted maximum is at Vv =
0.5 for the surface, whereas it is at Vv = 0.47 for the bulk. A maximum Sv at lower Vv generally
implies clustered nucleation, whereas a value near 0.5 is typical for a random distribution of the
nuclei [16]. That the nuclei in the bulk are clustered is in good agreement with earlier more detailed
investigations [13]. Here it was found by microstructural path modeling that linearly clustered
nucleation fits the experimental data well [13]. That the present observations reveal more random
nucleation near the surface may be an effect of some extra nucleation sites introduced by the
proximity of the rolls.
From the measured Sv and Vv values the true average growth rate of the grains <G> can be
calculated using the Cahn-Hagel approach:
d Vv
= G Sv
dt
Mater. Sci. Forum vols. 467-470, 147-151
Sv
Sv vs Vv
0,25
Bulk
0,20
Surface
0,15
0,10
0,05
0,00
0
0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9
1
Vv
Fig. 4. Evolution in the free unimpinged surface area of the recrystallizing
grains as a function of the volume fraction of recrystallized material.
The result is shown in Fig. 5. The curves show a transition: First the grains grow rapidly, but this
high growth rate quickly reduces to a lower quite constant growth rate. This is in good agreement
with the earlier observations [8]. No difference between bulk and surface is observed (see Fig. 5).
So the differences observed for Vv and Sv “normalizes” out resulting in identical growth rates.
<G> vs Vv
1,0E-01
Bulk
<G> [µm/sec]
Surface
1,0E-02
1,0E-03
1,0E-04
0,00
0,20
0,40
0,60
0,80
1,00
Vv
Fig. 5. The average growth rate determined by the Cahn-Hagel method as
a function of the volume fraction of the volume fraction of recrystallized material.
Conclusions
The stereological parameters <λ>, Vv and Sv were used to evaluate possible differences in
recrystallization near the surface of a 90% homogeneously cold rolled Al plate and in the bulk at
the center of the plate. It was found that the average grain size and the recrystallization growth rate
were identical at the two locations. The distribution of nuclei, however, appeared to be more
random at the surface than in the bulk.
Acknowledgement
The authors gratefully acknowledge the Danish National Research Foundation for supporting the
Center for Fundamental Research: Metal Structures in Four Dimensions, within which this work
was performed.
Mater. Sci. Forum vols. 467-470, 147-151
References
[1] D.A. Molodov: Grain Boundary Character – A key factor for Grain Boundary Control. Proc
Recrystallization and Grain Growth, ed. G. Gottstein and D.A. Molodov, Springer Berlin
(2001), p. 21- 38
[2] I.M. Fielden, J. Cawley, J.M. Rodenburg: Backscattered SEM Imaging of High Temperature
Samples for Grain Growth Studies in Metals. Proceedings of Physics Electron Microscopy
and Analysis Group Conference, Ed. S. McVitie, in print.
[3] F.J. Humphreys, www2.umist.ac.uk/material/staff/academic/fjh/SEM-PSN.htm
[4] H.F. Poulsen and D. Juul Jensen: From 2D to 3D microtexture investigations, 13.
International conference on textures of materials (ICOTOM 13), Seoul (KR), 26-30 August
2002. (Mat. Sci. Forum 408-412 (2002, p. 49-66)
[5] A.W. Larsen, C. Gundlach, H.F. Poulsen, L. Margulies, Q. Xing and D. Juul Jensen: In situ
Investigation of Bulk Nucleation by X-ray Diffraction (In these Proceedings)
[6] S. Schmidt and D. Juul Jensen: In-situ measurements of growth of nuclei within the bulk of
deformed aluminium single crystals. (In these Proceedings).
[7] R.A. Vandermeer, E.M. Lauridsen and D. Juul Jensen: Growth Rate Distrubutions During
Recrystallization of Copper (In these Proceedings)
[8] H.F. Poulsen: 3DXRD – Mapping grains and their dynamics in 3 dimensions (In these
Proceedings)
[9] O.V. Mishin, B. Bay and D. Juul Jensen: Through-Thickness Texture Gradients in Cold
Rolled Aluminium (Metall Mater Trans. A. Vol 31A (2000), p. 1653-1662).
[10] W. Truszkowski, J. Krol and B. Major: On Penetration of Shear Texture into the Rolled
Aluminium and Copper (Metall Trans, Vol 13A (1982), p. 665-669).
[11] E.M. Lauridsen, H.F. Poulsen S.F. Nielsen and D. Juul Jensen: Recrystallization Kinetics of
Individual Bulk Grains in 90% Cold Rolled Aluminium (Acta mater. vol. 51 (2003) p. 44234435).
[12] D. Juul Jensen: Growth Rates and Misorientation Relationships Between Growing
Nuclei/Grains and Surrounding Deformed Matrix During Recrystallization (Acta Mater. Vol
43 (1995), p. 4117-4129).
[13] R.A. Vandermeer and D. Juul Jensen: Microstructural Path and Temperature Dependence of
Recrystallization in Commercial Pure Aluminium (Acta Mater. Vol 49 (2001), p. 2083-2094).
[14] A.W. Larsen: Logitech PM5D Precision Polishing and Lapping System’ user manual (Risø-I2051(EN), Risø National Laboratory, Roskilde Denmark (2003))
[15] A.W. Larsen and D. Juul Jensen: Automatic determination of recrystallization Parameters in
metals by EBSP line scans, Materials Characterization. in print.
[16] D. Juul Jensen and R.A. Vandermeer: Effect of Anisotropic Impingement on Recrystallization
Texture, Microstructure and Kinetics (Proc. ICOTOM11, eds. Z. Liang et al. Int. Acad.
Publisher Beijing (1996), p. 490-496)
[17]
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A7
Mater. Sci. Forum vols. 495-497, 1285-1290
Orientations of recrystallization nuclei studied by 3DXRD
D. Juul Jensena and A.W. Larsenb
Center for Fundamental Research; Metal Structures in Four Dimensions,
Risø National Laboratory, Roskilde Denmark
a
[email protected], [email protected]
Keywords: Nucleation, recrystallization,3DXRD, orientation relationships.
Abstract: recent results on nucleation of recrystallization are reported. This includes previously
published data, obtained by EBSP and new results obtained by the 3 dimensional X-ray diffraction
method. Focus is on the orientation relationship between nuclei and parent grains. It is demonstrated
that nuclei may well form with orientations different from their parent grains.
Introduction
A critical point in the understanding of recrystallization textures is the development of
crystallographic orientations of the nuclei. Here an issue, which has been debated much recently
[eg. 1], is if nuclei have orientations identical to those of the deformation microstructures from
which they originate or not. Traditional nucleation mechanisms like strain induced boundary
migration [2] and particle stimulated nucleation [3] operate with nuclei orientations identical to the
“parent” deformation microstructure. This is also what is commonly incorporated in
recrystallization modeling. However, a number of studies have found recrystallization nuclei in
orientations that were not expected from measurements on deformed structures. Some of these
results are reviewed and discussed in this paper, and new in-situ results obtained by the 3
dimensional X-ray diffraction (3DXR) method are presented.
Electronmicroscopy Observations
Within recent years there have been a number of investigations into the local orientation is
deformed metals and the development of recrystallization nuclei [4-22]. In these studies nuclei with
orientations identical to the “parent” orientations in the deformed state are always observed.
However, also nuclei of new orientations, which could not be directly identified in the deformed
state, are generally reported. For example for recrystallization of deformed single crystals studied
by TEM and EBSP before and after annealing, Godfrey et al. [17] found nuclei with orientations
beyond and at the very far end of the orientation scatter observed in the deformed state in % channel
die deformed (ε=1.5) S oriented aluminium crystals. Okada et al. [18] found new recrystallized
grains which a twin relationship to crystal orientations present in the deformation microstructure in
a 70% uni-axial tensioned aluminium single crystal. A twin relationship between a nucleus and its
parent deformation microstructure may not sound too surprising even in aluminium [23], but in the
paper by Okada et al. [18] the new twinned nucleus orientation is reported not to be a growth effect,
but originating from a boundary dissociation process. Concerning the work by Godfrey et al. [17],
nuclei with orientations at the far end of the deformation orientation scatter agree well with standard
expectations as nuclei with such rare orientations compared to the deformed microstructure would
have better growth potentials [24]. More interesting are the nuclei with orientations beyond the
orientational scatter observed in the deformed state. Because of the indirect nature of the
observation (measured separately before and after annealing, (it can, however, not be ruled out that
these nuclei originated from volumes in the deformed microstructure with orientations rotated even
further, which are just so rare that the (although very detailed) TEM and EBSP measurements did
not record them.
Nuclei with new orientations are reported more frequently in deformed polycrystals. For
example Sabin et al. [19] found that about half the nuclei in a 40% or coarse-grained aluminium
Mater. Sci. Forum vols. 495-497, 1285-1290
sample had orientations away from the parent deformed grains. In this work triple junctions were
examined by EBSP before and after annealing. In Fig. 1 is shown a triple junction that produced
two nuclei. One of these has the parent orientation whereas the other is rotated approximately 10°
about a <111> pole from another parent grain. All nuclei with new orientations were observed to be
rotating about a pole close to <111> relative to their parent grains [19]. As these results are based
on surface observations, it could be that the nuclei grew upwards from deformed grains (with the
nuclei orientations) positioned below the investigated surface. This was, however, concluded
unlikely in [19], because such growth from below should not give only <111> rotations.
A smart way to avoid the uncertainty discussed above concerning “below-surface grains”
possibly leading to nucleation of grains with orientations not seen at the surface is to work with
columnar grained sample – i.e. samples where the surface grains extend through the entire sample
thickness. Data from such an experiment is presented elsewhere in these proceedings and do reveal
that also in this condition nuclei of new orientations may form [20].
Fig. 1. {111} pole figure showing the orientation relationship between 2 nuclei and their parent
deformed grains at a triple junction in 40% cold rolled aluminum annealed for 2.5 h at 300 °C. The
contours indicate the extent of scatter in orientations from the deformed grains. The nucleus marked
by “X” has the parent grain orientation, whereas the nucleus marked by “O” is rotated about 10°
around a <111> pole from another grain [19].
3DXRD observations
The 3 dimensional X-ray diffraction (3DXRD) method allows in-situ studies of bulk microstructural
changes non-destructively [21, 25, 26]. This method has been used for studies of nucleation. The
channel die deformed aluminium single crystal discussed above in the work of Godfrey et al. [17]
was characterized by 3DXRD before and after 5 minutes annealing at 300°C [21]. These 3DXRD
measurements confirmed that new orientations could develop upon the annealing [21].
In the most recent 3DXRD experiment on nucleation a 20% cold rolled polycrystalline copper
samples were studied in-situ while annealing. The orientations in volumes (100x100x300 µm3) near
selected triple junction lines were characterized in detail before annealing. For experimental details
see [22]. Then while annealing at 290°C, data were continually collected from the same sample
volume with a time resolution of 6 min. Examples of the diffraction images are shown in Fig. 2.
The reflections from the deformed grains are seen as elongated poles whereas nuclei have sharp
diffraction spots (see Fig. 2). By integrating the intensities within the diffraction spots from nuclei,
their kinetics can be followed. Two examples are shown in Fig. 3. The nucleus in Fig 3a was only
found after about 30 minutes annealing when it had a size of about 5 µm. In the following 30
Mater. Sci. Forum vols. 495-497, 1285-1290
minutes it grew fairly steadily to about 10 µm in size. On the contrary the nucleus shown in Fig. 3b
very rapidly (within the first few minutes at temperature) grew to about 5 µm after which it only
grew very little to about 6 µm in a following 3h anneal. This variety in growth kinetics agrees well
with previous 3DXRD observations of growth during recrystallization [27].
Fig. 2. Examples of signals recorded on the 3DXRD detector. a) Cu deformed 20%. b) as a) but
annealed for3 hours at 290 °C. [22].
Also orientation relationships between nuclei and parent deformation structure were analyzed for
3 nuclei. It was found that 1 nucleus had an orientation within the deformation orientation spread, 1
was first order twin related to it and 1 had a new orientation. Focusing on the latter nucleus, one
could speculate that it could have evolved from a surface imperfection. However, by a triangulation
method using all recorded diffraction spots from the nucleus, was determined that the nucleus was
at least 68 µm from the surface and thus is a true bulk nucleus. Another explanation could be that it
originated from a small part of the deformation microstructure, which could not be differentiated
from the background in the 3DXRD measurements. However, the experiment was set-up to record
all volume elements larger than 0.7 µm. This value corresponds to the lower limit of cell sized
recorded by TEM the deformed microstructure [28] and is significantly below the expected critical
nucleation size which is calculated to be 1.1 µm for the present sample. This explanation thus seems
very unlikely and it is believed that the nucleus has emerged by some reorientation of part of the
deformed structure.
Mater. Sci. Forum vols. 495-497, 1285-1290
Fig. 3. 3DXRD results for the growth of individual nuclei. Sample and annealing conditions as
given in Fig. 2.
Concluding remarks
Many independent studies using different experimental methods and different types of samples have
shown that nuclei with crystallographic orientations different from those in the parent deformation
microstructures can form during recrystallization. No realistic mechanism(s) explaining this
phenomenon is yet available. The optimal experiment giving direct information to derivation of
such a mechanism would be to characterize in detail and in 3D the deformation microstructure cell
by cell and then follow its evaluation in-situ during recovery until nucleation occurs. The 3DXRD
method offers potentials for this type of measurements in particular if the spatial resolution can be
improved.
Acknowledgements
This work was supported by the Danish National Research Foundation through the “Center for
Fundamental Research: Metal Structures in Four Dimensions” and by the Danish Natural Research
Council via Dansync. Beam time at ESRF is also gratefully acknowledged.
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Mission
To promote an innovative and environmentally sustainable
technological development within the areas of energy, industrial
technology and bioproduction through research, innovation and
advisory services.
Vision
Risø’s research shall extend the boundaries for the
understanding of nature’s processes and interactions right
down to the molecular nanoscale.
The results obtained shall set new trends for the development
of sustainable technologies within the fields of energy, industrial
technology and biotechnology.
The efforts made shall benefit Danish society and lead to the
development of new multi-billion industries.
www.risoe.dk
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