Low Temperature Austenite Decomposition in Carbon Steels Albin Stormvinter

Low Temperature Austenite Decomposition in Carbon Steels Albin Stormvinter
Low Temperature Austenite Decomposition
in Carbon Steels
Albin Stormvinter
Doctoral Thesis
KTH Royal Institute of Technology
School of Industrial Engineering and Management
Department of Materials Science and Engineering
Division of Physical Metallurgy
SE-10044 Stockholm, Sweden
Stockholm 2012
Albin Stormvinter
Low Temperature Austenite Decomposition in Carbon Steels
KTH Royal Institute of Technology,
School of Industrial Engineering and Management,
Department of Materials Science and Engineering,
Division of Physical Metallurgy,
SE-10044 Stockholm,
ISBN 978-91-7501-449-4
Akademisk avhandling som med tillstånd av Kungliga Tekniska högskolan i Stockholm framlägges
till offentlig granskning för avläggande av teknologie doktorsexamen 27 september 2012, kl. 10.00 i
sal F3, Lindstedsvägen 26, Kungliga Tekniska högskolan, Stockholm.
© Albin Stormvinter, August 2012
Printed by Universitetsservice US-AB, Stockholm, Sweden
To Emma
Martensitic steels have become very important engineering materials in modern society. Crucial parts
of everyday products are made of martensitic steels, from surgical needles and razor blades to car
components and large-scale excavators. Martensite, which results from a rapid diffusionless phase
transformation, has a complex nature that is challenging to characterize and to classify. Moreover the
possibilities for modeling of this phase transformation have been limited, since its thermodynamics
and kinetics are only reasonably well understood. However, the recent development of
characterization capabilities and computational techniques, such as CALPHAD, and its applicability
to ferrous martensite has not been fully explored yet.
In the present work, a thermodynamic method for predicting the martensite start temperature (Ms)
of commercial steels is developed. It is based mainly on information on Ms from binary Fe-X
systems obtained from experiments using very rapid cooling, and Ms values for lath and plate
martensite are treated separately. Comparison with the experimental Ms of several sets of commercial
steels indicates that the predictive ability is comparable to models based on experimental information
of Ms from commercial steels.
A major part of the present work is dedicated to the effect of carbon content on the morphological
transition from lath- to plate martensite in steels. A range of metallographic techniques were
employed: (1) Optical microscopy to study the apparent morphology; (2) Transmission electron
microscopy to study high-carbon plate martensite; (3) Electron backscattered diffraction to study the
variant pairing tendency of martensite. The results indicate that a good understanding of the
martensitic microstructure can be achieved by combining qualitative metallography with quantitative
analysis, such as variant pairing analysis. This type of characterization methodology could easily be
extended to any alloying system and may thus facilitate martensite characterization in general.
Finally, a minor part addresses inverse bainite, which may form in high-carbon alloys. Its coupling to
regular bainite is discussed on the basis of symmetry in the Fe-C phase diagram.
Keywords: Carbon steels, Electron backscattered diffraction, Martensite, Microscopy,
Microstructure, Thermodynamic modeling.
In the present doctoral thesis I would like to share my knowledge gained during the past four years,
as a PhD student in physical metallurgy at the Department of Materials Science and Engineering at
KTH Royal Institute of Technology, Sweden. The work has mainly been carried out within the
martensite formation project (Supplements 1-5) which runs within the Hero-m research center,
although Supplement 6 addresses inverse bainite and hence belongs to the bainite formation project
within Hero-m. A large part of the characterization work on martensite is the result of two research
stints conducted by the present author: at INP-Grenoble (France) in the spring of 2010 and at
Tohoku University (Sendai, Japan) in the summer of 2011. In particular this doctoral thesis will
discuss the following challenges, which are related to low temperature austenite decomposition in
carbon steels:
 Thermodynamically based prediction of the martensite start temperature (Ms)
 Quantitative microstructure characterization: The effect of carbon content on the martensite
morphology with emphasis on the transition from lath to plate martensite.
 Inverse bainite in hypereutectoid Fe-C alloys.
The outline of this thesis is as follows; In the first chapter, introduction, the topic low temperature
austenite decomposition and the aims and purposes related to the three challenges listed above are
introduced. In Chapters 2-4 my intention has been to condense selected works on three important
subjects related to this work: Phase transformations, Characterization techniques, and
Thermodynamics. I make no claim that these chapters would advance the understanding of low
temperature austenite decomposition further; instead they should be viewed as either an introduction
to the different topics for the novice or as an interpretation of the dense literature on the subjects
done by the present author. The readers are referred to the cited works for more details. The expert
reader may in fact skip Chapters 2-4 and move on to Chapters 5-7 where I summarize the results
from the supplements and discuss them in relation to existing literature.
Albin Stormvinter
Stockholm, 2012-08-01
Appended papers
Investigation of Lath and Plate Martensite in a Carbon Steel
A. Stormvinter, P. Hedström and A. Borgenstam
Solid State Phenomena, 172-174, (2011), p. 61-66.
Thermodynamically Based Prediction of the Martensite Start Temperature for Commercial
A. Stormvinter, A. Borgenstam and J. Ågren
Metallurgical and Materials Transactions A, Online first, 2012,
DOI: 10.1007/s11661-012-1171-z
A transmission electron microscopy study of plate martensite formation in high-carbon low
alloy steels
A. Stormvinter, P. Hedström and A. Borgenstam
Submitted manuscript
Effect of Carbon Content on the Orientation Relationship between Austenite and bctMartensite in Fe-C Alloys resolved by Electron Backscattered Diffraction
A. Stormvinter, G. Miyamoto, T. Furuhara, and A. Borgenstam
Submitted manuscript
Effect of Carbon Content on the Variant Pairing of Martensite in Fe-C alloys
A. Stormvinter, G. Miyamoto, T. Furuhara, P. Hedström and A. Borgenstam.
Submitted manuscript
On the Symmetry Among the Diffusional Transformation Products of Austenite
A. Borgenstam, P. Hedström, M. Hillert, P. Kolmskog, A. Stormvinter and J. Ågren
Metallurgical and Materials Transactions A, 42(6), (2010), p. 1558-1574.
* The appended papers will be referred to as [1–6] in the present thesis
My contribution to the appended papers
Major part of: literature survey, experimental work, and writing.
Major part of: literature survey, modeling work, and writing.
Major part of: literature survey, experimental work, analysis, and writing.
Major part of: literature survey, experimental work, analysis, and writing.
Major part of: literature survey, experimental work, analysis, and writing.
Part of experimental work, contributed to discussions and took part in the writing.
Other related reports not included in the thesis
A. On the Three-Dimensional Microstructure of Martensite in Carbon Steels
Peter Hedström, Albin Stormvinter, Annika Borgenstam, Ali Gholinia, Bartlomiej Winiarski,
Philip J. Withers, Oskar Karlsson and Joacim Hagström
Proceedings of the International Conference on 3D Materials Science 2012.
Parts of this work have been presented at the following international conferences
1. “Investigation of the Transition from Lath to Plate Martensite in Fe-C”,
Albin Stormvinter, Peter Hedström and Annika Borgenstam,
Solid-Solid Phase Transformations in Inorganic Materials (PTM2010),
6 - 11 June 2010, Avignon, France.
2. “A Phenomenological Model for the Prediction of Martensite Start Temperature in Steels”,
Albin Stormvinter and Annika Borgenstam,
The TMS Annual Meeting & Exhibition 2011 (TMS2011),
27 February - 3 March 2011, San Diego, USA.
3. “Thermodynamically Based Prediction of the Ms Temperature for Commercial Steels”,
Albin Stormvinter and Annika Borgenstam,
International Conference on Martensitic Transformations 2011 (ICOMAT2011),
4 - 9 September 2011, Osaka, Japan.
4. “Martensitic Meso- and Nanostructures in High-Carbon Low-Alloyed Steels”,
Albin Stormvinter, Peter Hedström, and Annika Borgenstam,
The TMS Annual Meeting & Exhibition 2012 (TMS2012),
11 - 15 March 2012, Orlando, USA.
Table of Contents
Abstract ................................................................................................................................................................ v
Preface ................................................................................................................................................................ vii
1 Introduction ..................................................................................................................................................... 1
1.1 Aim of the present work ........................................................................................................................ 2
2 Low temperature austenite decomposition ................................................................................................. 5
2.1 Martensite ................................................................................................................................................. 6
2.1.1 Lattice orientation relationship ...................................................................................................... 7
2.1.2 The habit planes ............................................................................................................................... 8
2.1.3 Martensite – A hierarchic structure ............................................................................................... 8
2.2 Bainite and inverse bainite ................................................................................................................... 10
3 Characterization techniques......................................................................................................................... 13
3.1 Optical microscopy ............................................................................................................................... 13
3.2 Electron microscopy ............................................................................................................................. 15
3.2.1 Scanning electron microscopy ..................................................................................................... 15
3.2.2 Transmission electron microscopy.............................................................................................. 18
4 Thermodynamics ........................................................................................................................................... 21
4.1 Measuring the martensite start temperature ...................................................................................... 23
4.2 Predicting the martensite start temperature....................................................................................... 24
5 Martensite characterization in carbon steels ............................................................................................. 29
5.1 High-carbon martensite investigated by TEM and ASTAR ........................................................... 35
5.2 EBSD – Variant pairing tendency of martensite in Fe-C alloys ..................................................... 41
5.3 Transition between lath and plate martensite.................................................................................... 51
6 Discussion on inverse bainite ...................................................................................................................... 53
7 Thermodynamically based prediction of the martensite start temperature .......................................... 57
8 Concluding remarks and future prospects ................................................................................................ 61
9 Acknowledgments ......................................................................................................................................... 63
10 Bibliography ................................................................................................................................................. 65
1 Introduction
Steels are by far the most widely-used metallic material and worldwide the crude steel production
reached 1,527 megatons (Mt) for the year of 2011 [7]. The world production has almost doubled in
ten years (851 Mt crude steel in 2001) and it is the demand from fast developing countries, in
particular China, that drives this expansion [7]. This ever-growing demand for steel is certainly due to
its attractive combination of high strength and high toughness with a low cost and easy recycling.
These material properties make steel ideal for most engineering applications, although unlocking
these inherent properties may not be trivial. It is the basic insight in physical metallurgy that allows
for tailoring of steel properties, such as strength and toughness, by tuning alloying content and heat
treatment processes [8].
The vast majority of engineering steels belong to the category carbon steels, these are steels that are
often loosely classified according to carbon content. The manufacturing of carbon steels relies on
controlling the decomposition of austenite, the high-temperature allotrope of iron. Austenite is not a
stable phase at ambient temperature for carbon steels so it will decompose into ferrite and cementite
on cooling. Figure 1.1 displays the well-known Fe-C phase diagram, which may be used to predict
this decomposition. The phase diagram concept is best applied for phase transformations with fairly
rapid kinetics, i.e. at relatively high temperatures, since diffusion is needed to reach equilibrium.
However, the present work is dedicated to low temperature austenite decomposition. This might
occur by some diffusional process as in the case of bainite formation. On the other hand, it might
also be a diffusionless transformation as in the case of martensite formation. It all depends on the
alloying content and the processing. Regardless whether the austenite decomposition results in
bainite or martensite, phase transformations at low temperatures offer many challenges from a
scientific point of view. These challenges include, but are not limited to: (1) Assessing the
thermodynamics of important alloying systems, since there are very few experimental data available
at such low temperatures. (2) Controlling and analyzing the kinetics of the phase transformations. (3)
Characterizing and analyzing the complex microstructures which the phase transformations give rise
Figure 1.1: The Fe-C phase diagram calculated by Thermo-Calc [9], [10]. Solid lines represent the metastable phase
diagram with cementite. Dotted lines represent the stable phase diagram with graphite.
1.1 Aim of the present work
The major part of this work has been dedicated to the effect of carbon on the martensitic
microstructure in carbon steels. This is usually referred to as “well-known”, even though there is no
standardized quantitative method to objectively evaluate this microstructure. Recent advances in
electron microscopy have enabled quantitative characterization based on crystallographic
information. Such techniques are electron backscatter diffraction (EBSD) [11] in the scanning
electron microscope (SEM) and automatic phase and orientation mapping (ASTAR) [12], [13] in the
transmission electron microscope (TEM). Here, these techniques have been applied to martensite
formed in Fe-C alloys with the purpose to develop an objective method to characterize the change in
the microstructure with the carbon content.
The second challenge addressed in this work is the prediction of the martensite start temperature
(Ms) as a function of alloying content, which has gained a lot of attention over the past century. It is
quite understandable since it is a key measure for alloy design. Often a pure empirical approach has
been used to model the alloy effect on Ms, although other approaches have been attempted as well
such as neural network models. The problem with both these approaches is that the predictability
may not be sufficient when the full composition range is considered. Therefore several researchers
have attempted a more fundamental approach, based on thermodynamics, for predicting Ms. With a
thermodynamic approach the idea is to model the transformation barrier and how it depends on
alloying content and other parameters, such as prior austenite grain size (PAGS) or prior
deformation. Such transformation barrier model would then be coupled to a reliable thermodynamic
database to calculate the Gibbs free energy of austenite and martensite as a function of alloying
content and temperature. It is this approach that has been attempted in the present work.
Finally, a minor part of this work is devoted to the formation of inverse bainite in high-carbon alloys.
This is a subject that has not received so much attention as it might have deserved in the literature.
Here the decomposition of high-carbon austenite into inverse bainite is characterized and classified
by optical microscopy (OM) and by SEM. The results from the experimental study are discussed in
relation to formation of ordinary bainite, with the main purpose to strengthen the evidence for
bainite being a diffusion controlled transformation.
2 Low temperature austenite decomposition
Low temperature austenite decomposition in carbon steels may be better described by the word
commonly used for the process, which also explains its purpose: hardening or quench hardening.
The sole purpose of this process is to produce a microstructure that provides strength and hardness
to the final product. In principle the processing may seem trivial: rapid quenching from the austenitic
regime to complete transformation into martensite or bainite. Nevertheless, when studied in more
detail several technological and scientific challenges arise, of which many can be attributed to the fine
microstructure. However, before discussing these challenges in more detail a few words on the
subject hardening should be addressed.
Iron began to replace bronze as the most common metallic material for tools and weapons some
3000 years ago [7]. To craft iron into a hatchet or a sword that could hold an edge and withstand
long wear was not common knowledge, instead it was an art of craftsmanship. The ability to hold an
edge is of course a direct consequence of the quench hardening process, which has to be carried out
with accuracy. At this time there was for obvious reasons no method to study the process in more
detail. So even though hardening had been applied for a few millennia it was not until the
introduction of modern steelmaking and later the birth of metallography that the hardening process
could be studied more in-depth. The hardened microstructure of steels was first described by
Osmond and he named it after another pioneer metallographer: Adolf Martens [8]. Thus, the hard
phase of steels was named martensite.
Ferrous martensite may be produced from austenite by providing sufficient cooling so all diffusional
transformations are omitted, such as formation of ferrite or perlite. It may be convenient to
introduce the concept of hardenability which is defined as the “susceptibility to hardening by rapid
cooling” or as “the property, in ferrous alloys, that determines the depth and distribution of hardness
produced by quenching” [9]. In general, an increase in alloying content permits a decrease in
quenching rate, i.e. increases the hardenability.
2.1 Martensite
The martensitic microstructure has a high level of complexity and to resolve its true nature is a
challenge. It is also known that the microstructure varies with composition and especially the carbon
content has a strong influence. A common practice is to distinguish between two major types of
ferrous martensite, namely, lath- and plate martensite [14], [15]. This is a general classification and
several researchers recognize morphologies such as surface martensite [16], butterfly martensite [17],
[18], thin-plate martensite [19], [20], and lenticular martensite [21], [22].
A martensitic transformation is defined by the following characteristics: (a) displacive; (b)
diffusionless; and (c) kinetics and morphology are dominated by the strain energy arising from the
shear-like displacements [23], [24]. Martensitic transformations can occur in many types of metallic
and nonmetallic crystals, minerals, and compounds [25]. A displacive phase transformation is a
structural change in the solid state which occurs by coordinated shifts of atoms [23]. This
coordinated movement of atoms is sometimes referred to as a military phase transformations, which
is in contrast to civilian diffusion-based phase changes that occur by uncorrelated jumps of individual
atoms across an essentially incoherent interface [25]. A characteristic feature of the martensitic
transformation is the shape change that may produce a surface relief if the transformation occurs
near a free surface. In 1924, Bain [26] discussed the nature of the martensitic transformation in steels.
He recognized that a contraction of about 20 percent along one of the austenite <001> axes and an
expansion of about 12 percent along two of the <011> axes perpendicular to the chosen <001> axis
transformed the austenite lattice into a ferrite bcc lattice. Hence, the fcc lattice of austenite could as
well be viewed as a bct lattice with the axial ratio 1.414. This lattice correspondence has been named
as the Bain correspondence and may be illustrated by Figure 2.1, which is reproduced from [27]. The
Bain correspondence demonstrates that the bcc lattice could be generated from the fcc lattice
through a homogeneous distortion. Nevertheless, it lacks some of the fundamental features of a
martensitic transformation, for instance it does not produce an invariant plane. This plane is the
interface between the martensite and the parent phase and should be undistorted and unrotated, and
hence becomes the martensite habit plane. The Bain strain alone does not fulfill the criteria to
produce such a plane, and therefore is not an invariant plane strain [28].
Figure 2.1: Bain correspondence in the transformation of (a) austenite into (b) martensite. Annotation: ○, Fe atom;
x, positions available for carbon. Reproduced from Guo et al. [29].
Some 30 years after Bain proposed his theory, works by Wechsler et al. [30] and by Bowles and
Mackenzie [31], [32] established a more solid understanding of martensite formation. These works
applied the principles of matrix algebra to martensitic transformations and established what is now
known as the phenomenological theory of martensite crystallography (PTMC) [33]. The PTMC was
the first martensite theory that could predict experimentally observed habit planes, orientation
relationships, and macroscopic distortions from knowledge only of the crystal structures of the
parent and product phases. The PTMC thus introduced a mathematical and logical route between
experimental observation and theoretical considerations [27].
2.1.1 Lattice orientation relationship
A characteristic feature of the martensitic transformation is the lattice orientation relationship (OR)
between the parent and product phases [27]. Pioneers Kurdjumov and Sachs [34] studied a carbon
steel with 1.4C* by X-ray pole figure analysis and suggested the well-known K-S OR:
(111)γ//(011)α and [-101]γ//[-1-11]α.
The K-S OR states that the closed packed planes (CPP) along with the closed packed directions
(CPD) of martensite (product phase) and austenite (parent phase) are parallel. Other commonly
quoted OR are the Nishiyama-Wasserman (N-W OR) [35], [36] and the Greninger-Troiano (G-T
OR) [37]. These were both determined from studies on high-nickel ferrous alloys containing large
amount of retained austenite using X-ray diffraction techniques. More recently, Kelly et al. [38] and
Compositions are given in mass% if not stated otherwise
Zhang and Kelly [39] have studied martensite formed in low carbon steels by TEM and measured
orientation of thin layers of austenite retained between laths using convergent beam Kikuchi line
diffraction patterns (CBKLDP) to determine the OR, they report:
(111)γ // (101)α and [1-10]γ 2.5°±2° from [1-1-1]α.
Zhang and Kelly [39] pointed out that CBKLDP has an accuracy of ±0.5° and can thereby very
accurately determine the local OR between parent and product phase, given that sufficient amounts
of retained austenite are present. Therefore this method cannot be applied to low-carbon martensite
containing low amounts of retained austenite.
2.1.2 The habit planes
In the early 1940s Greninger and Troiano [40] studied the orientation habit of martensite formed in
plain carbon and nickel steels. They concluded that lenticular martensite did not form along any lowindices plane of austenite. Instead they reported that the orientation habit of martensite abruptly
changed from a {4 4 10}γ to a {4 10 18}γ habit at roughly 1.4C. Later Greninger and Troiano [37],
[41] extended their analysis of the orientation relationships and were the first to suggest a double
shear mechanism, that later developed into the PTMC [30–32]. In carbon steels the martensite
morphology changes with carbon content and so does the observed habit plane. For lath martensite
it is close to {111}γ or {557}γ, but changes to {225}γ or {259}γ for plate martensite [27].
2.1.3 Martensite – A hierarchic structure
The K-S OR predicts that 24 unique crystallographic martensite variants may develop from a single
parent austenite grain, when annealing twins are disregarded. For lath martensite, these 24 variants
may in turn be divided into four groups, each consisting of six variants with a common habit plane.
These four groups have been named as “packets” [42–44]. By adopting the nomenclature used by
Morito et al. [42] the four packets are made up by the following variant groups: V1-V6, V7-V12,
V13-V18, and V19-V24. The packet may be further subdivided into three “blocks”, which each
consists of two martensite variants with a low degree of misorientation. For instance, the three
blocks of packet V1-V6 are: V1/V4, V2/V5, and V3/V6 [42]. The unique variants, for example V1,
have been named as sub-blocks and are in fact the martensite unit that contains the individual laths.
The lath has been described as a needle-like martensite unit, a few microns long and less than a
micron in diameter [45]. The substructure of the laths consists of dislocations arranged in a typical
cellstructure, which are a result of accommodation deformation due to the large shape strain [46].
Adjacent laths may have a misorientation of a few degrees, but are in principal of the same
crystallographic martensite variant. With the lath as the smallest building block, lath martensite may
be regarded as hierarchic structure, which becomes: parent grain – packet – block – sub-block –
individual lath.
For plate martensite, which is found in high-carbon and high-alloyed grades with low martensite start
temperature, it is not at all evident if it exists a hierarchic structure comparable to what has been
shown for lath martensite. When studied by optical microscopy (OM) plate martensite appears as
individual units of various sizes. The unit size is limited by the parent grain size and by preceding
martensite plates, which inhibits growth of a fresh unit. Some characteristic features of plate
martensite are: (1) the midrib, (2) transformation twins, (3) deformation twins, (4) dislocation arrays,
and (5) transverse micro-cracks [47], [48]. Characterization work done on plate martensite have
commonly addressed the irrational habit planes [40] and remarkably few studies have been made on
variant selection. One of the few studies were made by Okamoto et al. [19] who characterized
martensite formed in a Fe-30.70Ni-0.28C alloy. By following Okamoto et al. [19] it may be
concluded that a nucleation event in ferrous alloys with a low Ms temperature will result in the
growth of a “plate group”, which consists of four unique crystallographic martensite variants. The
principle plate group, which is referred to variant V1, becomes: V1, V16, V17, and V6 (again by
adopting the nomenclature used in [42]). In total six unique plate groups may form from a single
parent austenite grain.
The regime between these two extreme morphologies of martensite, i.e. lath- and plate martensite, is
often referred to as a mixed regime with a gradual transition from the former to the later. This
morphological transition has been schematically represented in Figure 2.2. However, this is more or
less a crude simplification since it has been shown that the morphological transition is gradual over
the entire composition range [49], [50]. In a recent review on the martensite morphology by Maki
[51] he pointed out that the factors that determine the morphology and substructure of martensite
remain poorly defined.
Figure 2.2: Schematic representation of the transition from lath to plate martensite with increasing carbon content.
As the carbon content is increased the Ms decreases and the martensite morphology changes from lath to plate
martensite. In between these two extremes it is said to be a “mixed” regime.
2.2 Bainite and inverse bainite
The decomposition of austenite into ferrite and cementite in the temperature range below that for
pearlite results in a microstructure that has been named as bainite [52]. Bainite, like pearlite, is a
eutectoid transformation product and may be further subdivided into upper- and lower bainite. Both
these transformation structures are acicular and ferrite is the leading phase in the main growth
direction during the transformation. In bainite, the ferrite has a tendency to form as plate-like units
and grow with an orientation relationship with the austenite [25]. In the case of upper bainite, carbon
will diffuse away from the growing ferrite into the austenite and eventually the carbon content
reaches such a level that cementite nucleates and grows. The shape of the cementite is usually as a
broken lamella in between the ferrite units. At temperatures where lower bainite forms the diffusion
of carbon is slow, which makes the carbides to precipitate in more close relationship with the ferrite.
The resulting carbide dispersed ferrite becomes very fine and may in fact be hard to tell apart from
tempered martensite. Another feature that bainite share with martensite is that it produces a surface
relief effect [53]. This is probably one of the reasons for the uncertainty regarding the mechanism by
which bainite grows: If it forms by a rapid, diffusionless shear mechanism or if it is controlled by
carbon diffusion. However, the surface relief should not be taken as a proof of a diffusionless nature,
since it has been shown that Widmanstätten ferrite [54] as well as Widmanstätten cementite [55]
gives a surface relief. Both these transformations are without a doubt diffusion controlled to their
nature. The diffusionless hypothesis was initially proposed by Zener [56] and suggests that a bainite
unit or a sheaf grows by short consecutive steps [57]. Each of them so rapid that there is not enough
time for carbon to diffuse. The carbides are then formed in a subsequent step from the
supersaturated bainitic ferrite, which involves carbon diffusion. The final product, here lower bainite,
may be seen from Figure 2.3. Macroscopically the growth rate of bainite is rather slow and could as
well be controlled by carbon diffusion. This hypothesis, that the nature of bainite growth is diffusion
controlled, has long been supported by Hillert, who in 1957 [58] proposed that there should be a
symmetry among the eutectoid transformation products of austenite in the Fe-C system. He
suggested that pearlite would form if ferrite and cementite behaves as equal partners as the eutectoid
transformation progresses. Bainite forms when ferrite is the leading phase, and the ferrite constituent
is identical to Widmanstätten ferrite. Hillert also introduced, for symmetry reasons, a third
transformation product that would have cementite as the leading phase and he named it as inverse
bainite. Also for inverse bainite the cementite, as the leading phase, should be identical to
Widmanstätten cementite.
Figure 2.3: Lower bainite formed at 618 K (345 °C) in alloyed steel with 0.69C. 10,000 times magnification.
Reproduced from Oblak and Hehemann [57].
3 Characterization techniques
The science discipline of examining and determining the constitution and structure of metals has
been named metallography. The father of metallography is Henry Clifton Sorby who was the first
person to examine correctly polished and chemically etched metal samples under the microscope in
the 1860s. Today the discipline covers the examination of metals over a wide range of length scales,
from millimeter scale down to the atomic scale [52].
3.1 Optical microscopy
The classical metallographic tool is the optical microscope (OM), which allows for accurate
metallographic examinations of metallic materials of various shapes and sizes. Before the OM
investigation, specimens are usually mechanical polished and chemical etched [52]. This will produce
a proper surface and thus allow for examination of microstructural features which may arise from
solidification or solid state transformations. Features that might be studied are for instance:
Grains (size and shape) and grain boundaries
Phases and phase interfaces
Annealing twins
Composition gradients that affect the microstructure
Inclusions (distribution, size and shape)
Precipitates (distribution, size and shape)
Imperfections (cracks and notches)
Surface structures (Corrosion attacks, fracture surfaces, and cracks)
Figure 3.1 displays an OM micrograph on transformation structures in a high-carbon alloy. This
figure well illustrates the capabilities of accurate metallography using OM. From the figure three
different features can quite easily be distinguished, those are: spiky nodules, plate-like units formed in
zig-zag patterns, and a matrix phase. Since the heat treatment process and alloy composition is
known in this case, these three features may be recognized as inverse bainite, plate martensite, and
retained austenite, respectively. However, there are limitations of the OM technique; those are first
and foremost the limited depth of field and the spatial resolution, which is of the same order of
magnitude as the wavelength of light, i.e. features smaller than a few tens of a micron cannot be
observed. Moreover, the limited depth of field at high magnification makes it difficult to picture
features which are non-planar [52]. The limited depth of field might not be critical for studying
martensite and inverse bainite on a polished surface, as seen from Figure 3.1, but to resolve the fine
microstructural features in more detail is beyond the resolution of OM.
Figure 3.1: Microstructure of a 1.67C carbon steel isothermally heat treated at 400 °C for 1 minute after a 10
minutes austenitization at 1100 °C. The dark etching spiky nodules are inverse bainite formed during the isothermal
hold. Apart from inverse bainite the figure shows plate martensite (dark gray) formed during the final quenching to
room temperature. The matrix is retained austenite. The specimen was prepared by mechanical polishing followed by
etching in Nital.
3.2 Electron microscopy
Even though the OM is a versatile characterization tool, its limited spatial resolution makes it
insufficient to study the nanostructure of materials. Therefore, it becomes necessary to apply electron
microscopy techniques to resolve such details of the materials structure. By using modern SEM and
TEM it is possible to achieve a resolution better than 1 nm and thus resolve the very fine structural
features. In addition, it is possible to determine the local crystallography as well as the local chemical
composition using electron microscopes, which will add substantial information to the
characterization work.
3.2.1 Scanning electron microscopy
The SEM is primarily used to study the surface, or near surface, structure of bulk specimens.
Electrons are generated from a source and then focused on to the surface by condenser lenses. The
electron source has usually been of the tungsten filament thermionic emission type, although field
emission gun (FEG) sources are growing in popularity since they may achieve higher resolutions and
higher probe currents [59]. The electrons generated from the source will generate various secondary
emissions after interaction with the specimen surface. These emissions and corresponding contrast
mechanisms have been listed in Table 3.1:
Table 3.1: Overview of contrast mechanisms, detectors, and typical lateral and depth resolution [52].
Detected signal
Type of detector
Secondary electrons
Backscattered electrons
Specimen current
Solid-state detector or
No external detector
Depth of
5–100 nm
5–50 nm
50–1000 nm
30–1000 nm
Complementary contrast to
Same as
Same as
backscattered plus secondary
electron signal
500–2000 nm
100–1000 nm
Surface topography,
compositional contrast
Compositional contrast,
surface topography, crystal
orientation, magnetic domains
Semiconductor detector
Characteristic X-rays
(energy-dispersive) or
Element composition, element
(primary fluorescence)
crystal/proportional counter
Detection of nonmetallic and
semiconductive phases
All the detectable signals listed in Table 3.1 may be used for materials characterization. For instance,
secondary electrons excel in detecting the surface topography and are more or less insensitive to
atomic number. Instead the contrast depends strongly on the angle between the incident beam and
the specimen surface. By applying a suitable etchant, chemical or electrolytic, interesting features may
be revealed and could then easily be viewed using the SEM in secondary electron mode. Figure 3.2
gives an example on such image, here carbide precipitations as a result of martensite tempering are
Backscattered electrons (BSE) are electrons that escape the specimen due to elastic scattering. These
electrons are more energetic than the secondary electrons and their yield have a strong correlation to
the average atomic number. Hence, the backscattered electrons carry information on the local
composition and their signal may be used to produce an image with compositional contrast. In
addition, backscattered electrons carry crystallographic information since the yield also is dependent
on the orientation of a crystal with respect to the incident beam [59]. This effect, known as electron
channeling, is usually much weaker when compared to the atomic number contrast. Figure 3.3
displays a martensitic steel where the microstructure has been revealed by channeling contrast in the
Figure 3.2: Plate martensite formed in a high-carbon steel quenched to 200 °C after austenitization at 1000 °C for
10 minutes. Carbide precipitation is clearly visible inside the large martensite unit. These carbides precipitated during a
1 minute tempering at the quenching temperature. The figure is a SE image using an in-lens detector and acquired
using the following setup: 5.0 kV, WD 5 mm, x10,000. The specimen was prepared by mechanical polishing followed
by electrolytic etching.
Figure 3.3: Displays plate martensite formed in a high-carbon steel. The figure is a BSE image acquired using the
following setup: 10.0 kV, WD 2.7 mm, x1000. The specimen was prepared by mechanical polishing.
A SEM technique that is rapidly developing is the electron backscattered diffraction technique
(EBSD). It is a fully automated quantitative material characterization technique based on mapping
the crystallography of the investigated specimen. EBSD relies on the detection of Kikuchi patterns,
which arise from subsequent elastic scattering of inelastically scattered electrons [59]. To obtain an
increased amount of electrons, adding to the Kikuchi pattern, the incident beam should be tilted
about 70° relative to the analyzed surface. To be successful the surface should have a mirror finish
and be essentially free from deformation, for instance by using a vibration-assisted final polishing.
The electron beam is scanned across the specimen while the position (x- and y-coordinates) and
Kikuchi patterns are recorded simultaneously. The next step in the EBSD analysis is to index the
collected Kikuchi patterns; this is commonly done using a Hough transform [11]. For every mappedpoint the best possible solution, i.e. phase and crystallographic orientation, is calculated from the
recorded Kikuchi data. Recent EBSD systems may even select the appropriate phases automatically,
given that a reliable database including the current phases is available. The resulting dataset will
contain crystallographic data for every successfully analyzed point within the mapped area of the
analyzed 2-D cross-section. Commercial EBSD software includes numerous post-processing
possibilities, for example the collected dataset can be viewed as a phase colored map or an inverse
pole figure (IPF) colored map as seen in Figures 3.4a and 3.4b respectively. The reader who wants
further insight in the SEM and EBSD techniques are recommended to the excellent monographs by
Goldstein et al. [60] and by Schwartz et al. [11], respectively.
Figure 3.4: (a) Phase colored EBSD map of a high-carbon steel where martensite is colored in red and retained
austenite is colored in blue. (b) An inverse pole figure colored EBSD map of martensite that corresponds to (a), the
retained austenite is here colored in gray. The EBSD dataset is 45 by 35 microns and acquired using an OXFORD
system and a 50nm step size.
Besides generating characteristic electrons the beam specimen interaction also gives rise to X-rays.
Among these there are the characteristic X-rays, which are a result of ionization of the atoms in the
material. An electron of the primary beam may knock an electron out from an inner shell and thus
leave an electron vacancy. This vacancy will immediately be replaced by an electron from an outer
shell. As this other shell electron transfers to the new lower energy level it releases some excess
energy. This energy can be lost as an X-ray photon which in turn is characteristic for every element.
Therefore, these X-rays may be used to analyze the local or average chemical composition. However,
there are some overlaps in the X-ray energy spectra which may be difficult to overcome.
3.2.2 Transmission electron microscopy
The transmission electron microscope builds on the same principle as the scanning electron
microscope; that is interaction between the generated electron beam and the specimen. The central
part of the TEM is the vertical vacuum chamber. At its top the electron gun is located, which
accelerates electrons to a voltage of about 40-400 kV. Below the electron gun are two or more
condenser lenses with an aperture present in between. The lenses together with the aperture are used
to change the character of the incident beam, which may be defocused to a parallel beam or focused
to a convergent beam. It all depends on the desired analyzing conditions. Below the lenses lies the
specimen chamber. As the TEM relies on interaction of transmitted electrons the specimen chamber
and holder are a crucial part of the equipment. The holder should allow the operator to move the
specimen as well as to tilt it to rather large angles. The electrons that have interacted with the
specimen should also be able to leave the specimen chamber. In addition, X-rays that may have been
generated should be permitted to leave as well. After the specimen the objective lens and the
projector lenses are located. These lenses are used to produce the image. There are several types of
images that may be produced in the TEM, these include: bright field (BF) images, dark field (DF)
images, high angle annular dark field (HAADF) images, selected area electron diffraction (SAED)
images, and convergent beam electron diffraction (CBED) images [59]. It is the objective aperture
that is used to select either the undeflected (bright field) or the diffracted (dark field) beam for the
imaging. The magnified image is often recorded using a charge-coupled device (CCD) array camera.
An example of a BF image is given in Figure 3.5, which displays plate martensite in a high-carbon
A technique that has many similarities with SEM-EBSD is the automatic phase and orientation
mapping for TEM (ASTAR) [12], [13]. Instead of determining the phase and crystal orientation from
collected Kikuchi patterns, ASTAR is based on template matching of electron diffraction spot
patterns acquired in the TEM. The templates, i.e. theoretical diffraction patterns, are calculated with
the crystal structure as input parameter. The commercial ASTAR technique also contains quality
indicators such as “reliability”, which is comparable to confidence index found in the TSL-EBSD
system. ASTAR is explained in more detail in Rauch and Dupuy [12] and Rauch et al. [13].
Figure 3.5: Displays plate martensite formed in a high-carbon steel. The figure is a BF image acquired using an
acceleration voltage of 300 kV and x6000 magnification. The specimen was prepared by electrolytic polishing.
4 Thermodynamics
Today computational thermodynamics are a fundamental engineering tool for materials design.
Coordinated international research using CALPHAD (CALculation of PHAse Diagrams) techniques
has provided the engineering society with reliable databases of important alloying systems, such as
carbon steels. Computational thermodynamics rely on accurate descriptions of the Gibbs energies
for the pure elements and relevant compounds of the material of interest. From these modeled
Gibbs energies, the equilibrium state of the system, i.e. steel grade, may be calculated for a certain
alloy content, temperature and pressure. Moreover, it is possible to study the relative difference in
Gibbs energy of stable and metastable phases as a function of temperature. Regarding martensite
formation in carbon steels, it is of interest to know the T0 temperature [56], the temperature where
the Gibbs energies of austenite and ferrite phases with the same composition are equal, i.e.
. At temperatures above T0, austenite is more stable than ferrite, with the same composition, and
below T0 the vice versa is true. Evidently, the total energy of the system would decrease if austenite
would transform into ferrite of the same composition below T0. Hence, there is a positive driving
force for ferrite formation, which may be defined as:
[Eq. 4.1]
In practice, when using computational thermodynamics, martensite may be treated as supersaturated
ferrite and Equation 4.1 thus becomes relevant for martensite formation as well. Ordinary ferrite
forms in a diffusional manner with a different composition than the parent austenite even above T0
but still inside the austenite-ferrite two-phase field of the phase diagram. The compositions of
austenite and ferrite, locally at the migrating phase-interface, are close to those of the equilibrium tie
line in the phase diagram, i.e. not much driving force is needed for the interface to migrate. Most of
the driving force is used to change the composition by diffusion. However, when regarding the
experimental Ms temperature for pure iron, reported as 818 K (545 °C) [61], the calculated available
driving force is considerable. Figure 4.1 displays how the available driving force increases with
decreasing temperature and reaches 1250 J/mol at the experimental Ms. It should be remembered
though that only the chemical part of the change in Gibbs energy is considered in this calculation. In
general, the Gibbs energy of a martensitic phase is higher than that of ferrite, since coherency strain
energy, surface energy, and defect energies needs to be accounted for [62], [63]. These effects may be
difficult to quantify and therefore it may be more useful to define the requirement of chemical
driving force to start the martensitic transformation. This may be thought of as a transformation
barrier, which will hereafter be denoted
. The barrier is essentially different from
which is the available chemical driving force at a given temperature. The available driving force is a
thermodynamic property, defined in Equation 4.1, which depends on the temperature and alloy
composition. The barrier, on the other hand, depends on the details of the transformation
mechanisms, and will thus account for the elastic and plastic energies stored in the material after the
martensitic transformation. For each steel, the available driving force varies with temperature, and MS
is reached when the available driving force is equal to
Commercial multicomponent steel databases, such as TCFE6 [64], do not contain a metastable
martensitic phase. Instead, the user may treat martensite as supersaturated ferrite when extracting
thermodynamic data from the database. This may lead to some concerns, for instance how to treat
the ordering of carbon atoms [56]. The ordering occurs as a consequence of the very rapid
martensitic reaction giving no time for carbon atoms to perform diffusive jumps. In the ferrite
structure there are three times more interstitial sites than in austenite but only one-third of them
corresponds to the interstitial sites where carbon may be located in the austenite. Thus the carbon
atoms are not randomly distributed in the fresh martensite, since the positions are inherited from the
austenite. The ordering of carbon atoms was first discussed by Zener [56] and is therefore sometimes
referred to as Zener ordering. Ordering of carbon atoms has a very small effect on the
thermodynamic properties of the martensite at low carbon contents. On the other hand, it will have
a dramatic impact at high carbon contents. Therefore, this effect should be taken into account when
evaluating the driving force for martensitic transformations in high-carbon alloys. For example, this
has been done in an evaluation by Fisher [65].
Figure 4.1: Displays the driving force for martensite formation as a function of temperature for pure iron. The
experimental Ms temperature is taken from Morozov et al. [61] and the Gibbs energies for martensite (ferrite) and
austenite was calculated in the Thermo-Calc system [9], [64].
4.1 Measuring the martensite start temperature
Several methods have been proposed to predict the martensite start temperature for commercial
steels. These include empirical-, neural network-, and thermodynamic methods. They have in
common that they rely on experimental Ms temperatures in some sense. It is interesting to notice that
there is no standard method to evaluate the experimental Ms temperature. Instead several methods
have been used, for example metallography [66–68], dilatometry [69–72], magnetometer [72–74], and
thermal arrest measurements [61], [75–78]. Often the experimental uncertainty of the method used
for determining Ms has not been evaluated. In addition, there are uncertainties related to the effect of
the PAGS, which seems to affect Ms significantly [79–81]. Therefore it is reasonable to believe that
the uncertainty for experimental Ms data is rather large. In a paper by Ghosh and Olson [82] they
suggested it to be ±40 K. On the other hand, Mirzayev et al. [83] claim that the accuracy of their
measurements is not worse than ±15 K.
4.2 Predicting the martensite start temperature
Many modern engineering steels rely on the hard phase of martensite, for example: transformation
induced plasticity (TRIP)-assisted steels [84], quenched and partitioned steels [85], and maraging
steels [86]. Therefore, it is no surprise that the prediction of Ms and especially its dependence of
alloying content has gained a lot of attention over the years. An early attempt to rationalize
information on Ms in commercial steels was made by Payson and Savage in 1944 [87] who proposed
an empirical expression that could be used for predicting the Ms temperature of new steels:
[K], [Eq. 4.2]
with alloying content given in mass percent [mass%]. The original equation gave Ms in Farenheit but
has here been recast to give Ms in K. A large number of similar empirical expressions have later been
proposed [67], [88–90] and they have been reviewed a number of times, for instance by Wang et al.
[91], by Skrotzki and Hornbogen [92], and by Sourmail and Garcia-Mateo [93]. These empirical
expressions may have a very practical usage, although they are limited to a certain composition range.
Figure 4.2: Variation of driving force with Ms temperature in binary iron alloys. Reproduced from Raghavan and
Antia [94].
A more fundamental approach is to apply a thermodynamic method to model Ms. This can be done
by evaluating the barrier for the diffusionless austenite to martensite transformation at the measured
Ms temperatures and study how it varies with composition. Raghavan and Antia [94] attempted such
analysis. However, they did not use experimentally determined Ms values in their analysis, instead
they accepted the improved Andrews’ [90] equation evaluated by Kung and Rayment [95]. Raghavan
and Antia [94] calculated the driving force at Ms for some binary and ternary systems, within the
composition range covered by the equation, as a function of composition. Their results are presented
in Figure 4.2 and illustrate how they represented the variation of driving force at Ms in binary alloys
with straight lines. In their analysis they concluded that for multicomponent alloys it did not appear
feasible to develop a simple equation for the required driving force at Ms as a function of
composition. However, they suggested that a more useful result would be to derive a correlation
between the required driving force and Ms by statistical fitting. By calculating the driving force at Ms
for a total of 1152 arbitrarily selected low alloy steels within a given composition range they obtained
a dataset for their statistical analysis. A least-squares fit of all 1152 compositions yielded the
following linear equation:
( )
[Eq. 4.3]
Another example of a thermodynamic approach is the expression proposed by Hsu and Chang [96],
obtained by studying information from Fe-C alloys:
( )) [J/mol],
[Eq. 4.4]
where xc denotes mole fraction of carbon. This expression was intended for use only above xc =
0.02. The last term was supposed to give the temperature dependence of the effect of shear and the
second term was supposed to account for the solution hardening of carbon. The expression could
just as well be written as:
( )
[Eq. 4.5]
Wang et al. [97] have also derived an expression for the required driving force as function of
temperature. They selected 104 engineering steel compositions and calculated the driving force
thermodynamically at estimated Ms temperatures, which were obtained from a trained neural
network [98]. They fitted a straight line to the calculated driving forces and obtained:
( ) [J/mol],
[Eq. 4.6]
When taking the carbon ordering energy into account they obtained a slightly different expression:
( ) [J/mol],
[Eq. 4.7]
It should be noted that Wang et al. [97] did not find it necessary to include the effect of alloying
elements explicitly in their expressions.
A very extensive study was made by Ghosh and Olson in 1994 [99], [100]. They plotted the driving
force, evaluated at the experimental Ms for various alloying contents, xi, as function of that content.
Assuming that the effect of an alloying element on the required driving force should be similar to the
effect on solution hardening they fitted the data with a parabolic curve,
[Eq. 4.8]
where K1, which should hold for pure Fe, was treated as independent of temperature. The second
, was evaluated for a large number of alloying elements and assuming that the effects
were additive they could then predict the Ms values for a large number of steels and obtained
reasonable agreement with experimental values.
Ghosh and Olson [82], [101] later refined their method by introducing a new multicomponent
database, specially evaluated for martensitic transformations, together with a complex method for
representing the critical driving force for starting the martensitic transformation. In their paper they
concluded that the accuracy of Ms predictions, in ternary and multicomponent systems, was
satisfactory if an experimental uncertainty of ±40 K was accepted.
So, even though a lot of work has been invested in predicting Ms there is still no general method
readily available, that one can apply easily. However, it seems like a semi-physical approach that
combines state-of-the-art thermodynamics with key experiments might be the best option to
establish a more general method of predicting Ms.
5 Martensite characterization in carbon steels
It is well-known that the microstructure of ferrous martensite is affected by the alloying content [15],
[27], [102]. Even though the morphological change may seem obvious, it is still very challenging to
make a qualitative as well as quantitative classification of the observed microstructure. Often
microstructure characterization relies on the experience of the operator, i.e. the metallographer. It
may seem unfair to thus suggest that microstructure characterization is to some extent subjective,
since there are quantitative indicators as well. Those are for instance hardness, strength, and other
measurable material properties, although they all would be indirect measurements.
As discussed in Chapter 2 the martensite morphology changes from lath-like to plate-like as the
alloying content is increased. This progressive change in martensite morphology can be represented
by the Figures 5.1a-5.1e, which display specimens with an increasing carbon content. The figures also
illustrate the complexity of the martensitic microstructure, which consists of individual martensite
units forming together in hierarchic structures. Many of the microstructural features are beyond the
magnification range of the OM and therefore only a qualitative understanding of the microstructural
transition is realistic from this series of OM micrographs.
Figure 5.1: Martensite formation in steels with increasing carbon content, all specimens were mechanical polished and
etched with 3% Nital. (a) Interstitial free steel (Fe-1.48Mn-0.0024C), (b) Fe-0.35C, (c) Fe-0.75C, (d) Fe-1.05C,
and (e) Fe-1.80C. The figure is reproduced from [5].
A very useful metallographic technique, which has not been used so extensively in the past decade, is
to study the microstructural change in a specimen with a composition gradient. For instance,
Borgenstam et al. [103] successfully applied the gradient technique to study the critical growth
temperature for martensite and how it was related to Ms. More recently Stormvinter et al. [1] applied
this technique to a carbon steel to qualitatively study the microstructural transition from lath to plate
martensite with increasing carbon content. The steel composition is listed in Table 5.1. After
decarburization using hydrogen, a carbon gradient was obtained close to the surface, as seen from
the wavelength dispersive X-ray spectroscopy (WDS) measurement displayed in Figure 5.2a. They
also measured the hardness versus carbon content and concluded that it agreed well with previously
reported hardness numbers [45], [74], [104], [105], as seen from Figure 5.2b.
Table 5.1: Composition of the carbon steel studied in [1], alloying content is given in mass%.
0.20 – 1.67
Figure 5.2: (a) Carbon profile close to the surface, ~0.01-5 mm, after decarburization measured with WDS and
simulated with DICTRA using the actual conditions. (b) Hardness vs. carbon content [1], [45], [74], [104], [105].
The figure is reproduced from [1].
Stormvinter et al. [1] used a quenching and tempering procedure when characterizing the martensitic
microstructure in the carbon gradient specimens. This procedure made it possible to separate the
first martensite units that formed, close to the Ms temperature, from units formed during the final
quenching to room temperature (RT). Moreover, any position in a heat-treated specimen could be
related to the local carbon content by using the information in Figure 5.2a and hence it was possible
to see how the martensite formation close to Ms was affected by the carbon content.
Figures 5.3a-5.3c are from carbon gradient experiments [1] and show typical transformation
structures found in carbon steels: lath martensite (Figure 5.3a), plate martensite (Figure 5.3c), and
martensite formation in the transition regime between these two extremes (Figure 5.3b). The
tempered martensite appears dark while the martensite formed during quenching to RT appears
bright. Close to the eutectoid composition the martensite microstructure displays characteristic
features for both lath and plate martensite. For instance, in Figure 5.3b a large martensite plate is
visible to the right that has grown to a considerable size. Moreover, it can be seen how new
martensite units have been autocatalyzed on this primary unit. The autocatalysis of new martensite
units on a primary plate is better seen in Figure 5.4, taken from a Fe-1.80C binary alloy (the same
alloy as seen in Figure 5.1e). Apart from these plate-like martensite units, Figure 5.3b shows small
martensite units without typical features of plate martensite and could as well be lath martensite.
The gradual morphologic transition of martensite in the composition range 0.6 to 1.1C can be seen
in Figures 5.5a-5.5f. It is realized that the individual martensite units become more defined and
midribs, characteristic for plate martensite, are visible in Figures 5.5e and 5.5f. It should further be
noted that the change in hardness also appears to be continuous over this composition range, as seen
from Figure 5.2b.
Figure 5.3: OM micrographs of the two main types of martensite and the transition region in between; (a) Quenched
and tempered at 623 K, 100-300 µm, ~0.32C. (b) Quenched and tempered at 473K, 1000-1100 µm ~0.81C. (c)
Quenched to 298 K, >5000 µm, ~1.67C. The figure is reproduced from [1] and the micrometer range refers to the
distance from the surface.
Figure 5.4: Tendency for autocatalysis of new martensite units on a primary martensite unit in a Fe-1.80C binary
Stormvinter et al. [1] performed SEM-BSE imaging of the carbon gradient specimens, which are
shown in Figures 5.6a and 5.6b. In these BSE images the martensite units become visible through
crystallographic contrast, and hence a change in lattice orientation will be reflected in the images.
Figure 5.6b is centered on a martensite unit, which is also indicated with a white arrow in Figure 5.6a,
and it is clearly seen that this unit contains two lattice orientations. This is most probably due to the
internal transformation twinning that occurs when plate martensite grows from the austenite,
although the twin-relation cannot be confirmed in this imaging mode.
The morphological transition observed in specimens with a carbon gradient by Stormvinter et al. [1]
agrees well with the commonly accepted view of martensite, i.e. lath martensite forms in the
composition range 0 to 0.6C and above 1.0C acicular plate martensite is the dominant morphology
[47]. The transition between these two morphologies is usually observed within the composition
range 0.6 to 1.0C [14], [47], [106]. Maki [51] has emphasized that the substructure and crystallography
of martensite units, which forms in this composition range, is fairly complicated. Moreover, Maki et
al. [107] have shown that the morphology of lath martensite changes with the carbon content and
Greninger and Troiano [40] have observed a change in the morphological appearance of plate
martensite in Fe-C alloys. For 1.5 to 1.8C, they found plate-type martensite with clearly visible
midribs, which form in zig-zag patterns. Below this composition range they reported a sudden
change in morphological appearance of the plate martensite, since two plate-like units seemed to be
emanating from a point and grow with an obtuse angle with much less prominent midribs. This latter
morphology has later been described as butterfly martensite [17], [49] and the former as lenticular
martensite [49].
Figure 5.5: Martensite morphology of a sample cooled to RT without tempering, observed in OM: (A) 900-1000
µm, ~0.76C; (B) 1100-1200 µm, ~0.83C; (C) 1300-1400 µm, ~0.92C; (D) 1500-1600 µm, ~0.97C; (E)
1700-1800 µm, ~1.09C; (F) 1900-2000 µm, ~1.11C. The figure is reproduced from [1] and the micrometer range
refers to the distance from the surface.
Figure 5.6: (a) Martensite morphology observed in SEM-BSE, 800-1000 µm ~0.75C; (b) High magnification of
the area marked by the arrow in (a). The figure is reproduced from [1].
5.1 High-carbon martensite investigated by TEM and ASTAR
Classic TEM has been used to study martensite since the early 1960s, and it was clear already from
the pioneering works on medium- and high-carbon ferrous martensite that the microstructure and
substructure of plate martensite is complex [45], [108]. Characteristic features that has been reported
are for instance: (a) twins, (b) planar defects, (c) dislocation arrays, (d) midrib region, and (e) microcracks [47], [48]. Pioneers Kelly and Nutting [45] were the first to make examinations of ferrous
martensite using thin-foils in the TEM when they studied martensite in two high-carbon low alloy
steels with 1.0 and 1.4C respectively. They reported that both steels displayed plate-like martensite
units, a few microns long and less than a micron thick. Within these units they observed nano-sized
twinning, which had a 15 to 100 Å interspacing, and reported the twin-plane to be {112}α.
Furthermore, they found some retained austenite in the 1.4C steel and concluded that the {112}α
twins were produced from {110}γ planes. Later, Oka and Wayman [48] studied two high-carbon low
alloy steels with 1.28 and 1.82C. The martensite units found in both these steels also contained
{112}α transformation twins, but in the 1.82C steel {101}α planar defects were observed. They
suggested that the {101}α planar defects were accommodation distortion imposed by the growing
There have in fact been surprisingly few studies following the works by Kelly and Nutting [45] and
by Oka and Wayman [48] on plate martensite in high-carbon low alloy steels. On the contrary, when
regarding martensite formation in general a vast number of TEM studies have been reported. In
recent years there has been a significant development of characterization capability, for instance
automated crystallographic techniques as TEM-ASTAR. Therefore, Stormvinter et al. [3] selected
two high-carbon low alloyed steels with the ambition to combine ASTAR with classical TEM to
provide a comprehensive basis for discussing the development of plate martensite in these alloys.
The alloys chosen by Stormvinter et al. [3] for TEM observations contained 1.20 and 1.67C
respectively. Figure 5.7a is from the 1.67C alloy and shows a large plate-like martensite unit on the
right-hand side with a distinct midrib in the vertical direction. On the left-hand side of this large
martensite unit, it can be seen that smaller martensite units have developed in characteristic zig-zag
patterns, which are surrounded by heavily dislocated retained austenite. Stormvinter et al. [3]
confirmed by SAED (Figure 5.7c) that the large martensite unit to the right was internally twinned.
The twins were of {112}α-type and can be seen from Figures 5.7b and 5.7d, which are DF
micrographs. The extension of these twins appears limited by a discrete crystallographic plane, as can
be seen from the figures. This limiting plane was determined as {101}α and may in fact be
accommodation distortion of either fault- or twin-type.
Figure 5.7: TEM micrographs of the 1.67C steel. (a) On the right hand side in the BF micrograph a large plate
martensite unit is seen with a midrib in the vertical direction. On the left hand side, areas of retained austenite are
present, which seem to contain a high amount of dislocations. (b) DF micrograph centered on the midrib of the large
plate martensite unit on the right-hand side in Figure 5.7a. There is strong diffraction close to the midrib. (c) SAED
from the midrib area with the 200α-twin spot used for DF indicated. (d) High magnification DF micrograph
corresponding to the central part of Figure 5.7b. It is seen that the strong diffraction is due to nano-sized
transformation twinning along the midrib. The figure is reproduced from [3].
Another example of plate martensite in the 1.67C alloy, with transformation twinning on the midrib,
is shown in Figures 5.8a and 5.8b. In addition to classic TEM, Stormvinter et al. [3] attempted
ASTAR on these martensite units. The result of the ASTAR is displayed in Figure 5.9 as an IPF
colored map. When comparing the ASTAR results to the TEM imaging it is realized that the nanosize transformation twinning was not resolved by ASTAR, since only a small area (Indicated by (1))
shows a crystal orientation that deviates from the primary orientation of unit A. This can easily be
understood from the fact that the size of the twins was in the order of the probe-size (20nm).
However, by decreasing the probe-size to 10nm and analyze only a small fraction, close to the
midrib, of martensite unit A the transformation twinning could be better reproduced by ASTAR.
This result is seen from the insert in Figure 5.9. Stormvinter et al. [3] used a conventional electron
source when conducting the ASTAR; however, by using a FEG source the probe-size could be
further decreased and it is thus likely that the spatial resolution would be good enough to accurately
resolve the transformation twinning. Nevertheless, it will still be very challenging to simultaneously
resolve transformation twinning in multiple martensite units, since only twins aligned parallel to the
electron beam may be accurately analyzed using ASTAR. The reason is simply that for nonparallel
twins the incident electron beam will pass through multiple twins and thus give rise to double
diffraction. This will make the recognition of the diffraction pattern impossible since it does not
correspond to an actual crystal orientation. Still ASTAR can be a very useful technique for studying
martensite formation, since it allows for orientation and phase mapping in materials with large
deformations: i.e. martensitic steels. For example, the martensite-martensite orientation relationships
may be calculated from the ASTAR data. In the study by Stormvinter et al. [3] this was done for the
martensite units annotated A, B and C in Figure 5.9.
Figure 5.8: TEM micrographs of the 1.67C steel. (a) BF micrograph of martensite units surrounded by retained
austenite. The midrib of the central unit has been indicated by an arrow. In addition, two kink couplings with adjacent
units have been indicated by arrows. (b) High-magnification DF micrograph on the midrib of the martensite unit
indicated by the arrow in a. The figure is reproduced from [3].
Figure 5.9: IPF colored map of martensite obtained by ASTAR. The area corresponds to the Figure 5.8a where it
is shown in BF. The insert displays an IPF colored map on the midrib of the martensite unit indicated by the arrow in
Figure 5.9a. The figure is reproduced from [3].
Based on the microstructural observations in 1.20 and 1.67C steels Stormvinter et al. [3] presented a
schematic on the development of martensite in high-carbon low alloy steels, as seen from Figure
5.10. They concluded that development of plate martensite seems to occur as follows: (A) In the first
stage of the transformation, the growth occurs by formation of {112}α twins. (B) As the martensite
unit continues to grow there is a build-up of elastic stresses, which are represented by the dark-blue
area in the surrounding matrix. These elastic stresses may be partly relieved and become more
uniform by various accommodation components. The accommodation may occur by dislocation
motion, in the martensite unit or in the surrounding austenite. The area of the martensite units,
which are mainly affected by these accommodations, is colored light-green in Figure 5.10. If the
transformation temperature is low, and as found in the 1.67C steel, accommodation may occur
through {101}α twinning/faults, which have been illustrated with black lines. (C) The martensite
transformation progresses by autocatalytic nucleation of new martensite units, which may have a
different shape strain and orientation relationship to the parent phase. Commonly these new units
belong to the same plate group and make a well-defined coupling to the preceding unit, which may
be of kink- or wedge-type. The martensite units from the same plate group in Figure 5.10 “(C)” may
be viewed as a “cluster”. Hence, it may be the result of a single nucleation event with successive
autocatalysis of new martensite units.
It is realized that the formation temperature and alloying content is important to consider when
discussing the development of plate martensite. This may be illustrated by the variety of plate
martensitic microstructures found in the literature, i.e.: butterfly- [17], [18], lenticular- [21], [22], and
thin-plate martensite [19], [109]. On the other hand, when the development of plate martensite is
seen from a more general perspective some common principles may be distinguished: (1) Initial
growth of a midrib, which has a completely twinned substructure. (2) Transverse thickening of the
midrib, given that plastic accommodation can occur by either deformation twinning or dislocation
formation. (3) Subsequent autocatalytic nucleation of other martensite units from the same plate
group. The variety of observed microstructures may be explained by the conditions for these steps to
occur, which most likely are governed by temperature and alloying content.
Figure 5.10: Schematic on the development of martensite in high-carbon low alloy steels. (A) Represents the first
stage of transformation, the growth occurs by formation of {112}α twins. (B) As the martensite unit continues to grow
there is a build-up in the elastic stresses, which are represented by the dark-blue area in the surrounding matrix. The
light-green area belongs to the martensite crystal and has been affected by accommodations. However, if the
transformation temperature is low, accommodation may occur through {101}α twinning/faults, which have been
illustrated with black lines. (C) The martensite transformation progresses by nucleation of new martensite units, which
have a different orientation relationship to the parent phase. These new units may form a kink coupling or a zig-zag
pattern with the preceding unit. The figure is reproduced from [3].
5.2 EBSD – Variant pairing tendency of martensite in Fe-C alloys
In the previous sections the emphasis has been on qualitative martensite characterization of the
transition from lath to plate martensite [1] and the development of plate martensite in high-carbon
steels [3]. In this final section on martensite characterization the emphasis is on quantitative
martensite characterization by EBSD. The discussion is based on two of the appended supplements;
of which one introduces the methodology and the feasibility for studying tetragonal bct-martensite
[4] and the second presents the effect of carbon content on the variant pairing tendency of
martensite in binary Fe-C alloys [5].
As discussed in Chapter 3 (Section 3.2.1) EBSD is an analysis technique that relies on detection of
the local crystallography of a specimen. The collected data can be used to determine the phase as
well as the crystal orientation. Recently, Miyamoto et al. [110] developed a novel method to
accurately determine the OR between austenite and martensite that is based only on the martensite
crystal orientations acquired by EBSD [110]. Stormvinter et al. [4] extended this methodology to
study martensite formation with large tetragonality formed in Fe-C alloys. For this purpose they
selected high-purity binary alloys having the nominal compositions of 0.35, 0.75, 1.05, 1.80C and an
interstitial free (IF) steel. The chemical compositions of the alloys together with the Ms temperature,
calculated according to Stormvinter et al. [2], are listed in Table 5.2.
Figure 5.11a displays IPF colored martensite units in the 1.80C alloy, which all belong to a single
parent austenite grain with no annealing twins. To interpret the martensite microstructure solely
based on IPF colored maps is rather difficult. However, these martensite units display a very
characteristic pole figure (PF) pattern as seen from Figure 5.11b. The figure displays a standard
<001>α-BCC stereographic projection of experimental data points, which have been superimposed by
the calculated nodes obtained by numerical fitting [110]. This pattern can be compared to the wellknown K-S OR [34]. In agreement with the K-S OR, Figure 5.11b displays 24 unique martensite
orientations, which may be seen from the clustering of 8 martensite variants around every <001>γ.
This circle pattern around every <001>γ is called a Bain circle [111].
Moreover, Stormvinter et al. [4] discussed how the tetragonality of high-carbon martensite would
influence the EBSD data analysis, since in general martensite is treated as bcc rather than bct when
conducting EBSD analysis. They first attempted indexing of martensite as tetragonal bct on the
1.80C alloy, since it has the highest c/a ratio. Figures 5.11c and 5.11d from the 1.80C alloy display
[001]α-BCT and [010]α-BCT/[100]α-BCT pole figures of the martensite units displayed in Figure 5.11a when
indexed as tetragonal bct instead of cubic bcc. As can be seen from Figure 5.11c, the [001]α-BCT crystal
direction could be separated from the [010]α-BCT and [100]α-BCT crystal directions. Figure 5.11d on the
other hand contains data belonging to both [100]α-BCT and [010]α-BCT since they are indistinguishable.
Taking Bain correspondence ([1-10]γ // [100]α-BCT, [110]γ // [010]α-BCT, [001]γ // [001]α-BCT) into
account, it can be understood that only [001]α-BCT should be contained in the Bain circle. Stormvinter
et al. [4] attempted bct indexing on the 0.35, 0.75 and 1.05C alloy as well, and the success rate of bct
indexing, can be seen in Figure 5.11e. The success rate is defined as a ratio between the number of
data points, whose [001]α-BCT is contained in the Bain circle, and the total number of data points. It is
clearly seen that the success rate decreases with decreasing tetragonality and reaches 1/3 at 0.35C,
which would be expected from mathematical statistics for the random case. Thus, it could be
concluded that accurate indexing of martensite as tetragonal bct was only feasible for the 1.80C alloy
of the five alloys studied. In addition, Stormvinter et al. [4] showed that bct indexing of the EBSD
data has a minor effect on the OR analysis and thus the simplified bcc indexing is feasible for all
carbon contents.
Table 5.2: Chemical composition, calculated Ms and PAGS for the studied alloys.
Calc. Ms
Figure 5.11: (a) Displays an IPF colored map of martensite units from one single parent austenite grain, in the
1.80C alloy. Only data points with a confidence index higher than 0.2 are displayed. (b) <001> α-BCC PF of
martensite units visible in (a). Experimental data-points have been superimposed by calculated nodes for <001>α-BCC
and <001>γ, which were obtained by fitting to the former. Hence, white circles and black crosses are for martensite
and austenite, respectively. (c) PF [001]α-BCT and (d) PF [010]α-BCT/[100]α-BCT of martensite units visible in (a)
when indexed as tetragonal bct. (e) Variation of success rate of bct indexing as a function of carbon content and
tetragonality. The figure is reproduced from [4].
Figure 5.12: The observed change in orientation relationship between parent and product phase with increasing
carbon content expressed as deviation angle between austenite and martensite CPP and CPD. The figure is reproduced
from [4].
However, when calculating the deviation angle between CPP and CPD of martensite and austenite
they found it necessary to consider the martensite tetragonality. This may be understood from the
fact that the CPP and CPD will rotate when going from a cubic to a tetragonal lattice, unlike the
principal cube axes that will stay parallel. Comparing the deviation angle between CPP and CPD of
the parent and product phase is a common way to express the OR. In Figure 5.12 the effect of
carbon content on the OR, as reported by Stormvinter et al. [4], is displayed and it is seen how the
OR shift from close to G-T OR towards K-S OR as the carbon content increases. Moreover, these
results were found consistent with previously reported OR on low-carbon [110] and high-carbon
steels [34].
There may be several factors affecting the OR, such as lattice parameters of martensite and austenite,
austenite strength for accommodation of shape strain and substructure in martensite arising from
lattice invariant shear (LIS) mode. Oka and Okamoto [112] made theoretical predictions of the OR
for an 1.8C alloy by using phenomenological theory of martensitic crystallography (PTMC) with the
assumption of two different LIS systems (112)[-1-11]α and (101)[10-1]α, which correspond to the
ORs shown as A and B in Figure 5.12, respectively. (112)[-1-11]α is the ordinary LIS for (112)α twin
and it appears in most of plate martensite in ferrous alloys while (101)[10-1]α corresponds to the
(101)α twin reported only in high carbon martensite [13]. The prediction by Oka and Okamoto [112],
A and B in Figure 5.12, illustrate the significant effect of LIS on OR. It is interesting that the
measured ORs for high carbon alloys agree with the OR B whereas ORs for lower carbon martensite
are rather close to OR A. Stormvinter et al. [4] did however not investigate the mechanism for the
observed change in OR in more detail.
Instead, Stormvinter et al. [5] used the experimentally determined OR to investigate the effect of
carbon content on the variant pairing tendency of martensite formed in these five alloys. Variant
pairing tendency implies quantification of the nearest neighboring of martensite units. In most cases
the number of crystallographically unique martensite-martensite neighbors is limited to 24. The
misorientation, and thus boundary character, of such neighbors may be calculated from the
experimentally determined OR. An EBSD dataset, for example as seen from Figure 5.13, may
contain several thousands of martensite-martensite boundaries and is therefore ideal for variant
pairing determination. Stormvinter et al. [5] showed how the quantified variant pairing can be
interpreted and transposed into knowledge of the martensite microstructure.
Figure 5.13: IPF colored EBSD map taken from the IF steel. The figure is reproduced from [5].
Figure 5.14: Variant pairing frequency diagrams which display the length fractions of inter-variant boundaries for
(a) IF steel, (b) 0.35C alloy, (c) 0.75C alloy, (d) 1.05C alloy, and (e) 1.80C alloy. The error bars represent the
standard deviation of three measurements, each acquired from an area of 800x265µm. Reproduced from [5].
The results from the analysis [5] of martensite-martensite boundaries are presented in Figures 5.14a5.14e, and show the length fraction of variant boundaries in relation to variant 1. As seen from the
figures there is a clear dominance of intra close-packed plane group (CP group) variant pairing at
lower carbon contents. Moreover, there is a shift from V1/V4 dominance towards V1/V2
dominance as the carbon content is increased. However, the variant pairing tendency of martensite
formed in the 1.80C alloy is in strong contrast, as seen from Figure 5.14e, to that of the other alloys.
For this high-carbon alloy, pairing of V1 with variants V2, V6, V16 and V17 seems to be more
frequent, with a dominance of V1/V16 pairing. This tendency for V1/V16 pairing is also observed
in the 0.75 and 1.05C alloys, although not as pronounced as in the 1.80C alloy.
Figure 5.15: IPF colored EBSD map taken from the IF steel. The map shows an area with a dominant martensite
packet and blocks and sub-blocks have been labeled with its corresponding martensite variants. EBSD data from the
region enclosed by the yellow box was used for the analysis by standard stereographic projection. Misorientation
boundaries are colored as follows: (White) 4°-13° and (Black) > 19°. The figure is reproduced from [5].
As seen from Figure 5.14a, martensite formed in the IF steel is dominated by V1/V4 pairing. This
particular variant pair, V1/V4, has previously been associated with sub-block boundaries of low
misorientation [42], [113], [114]. The packet and block martensite microstructure is rather obvious in
the IF steel, as seen from Figure 5.1a. Another noticeable feature of the IF steel is seen from Figure
5.15; the block boundaries are few when compared to the sub-block boundaries. In fact, the large
block-size of the IF steel may be seen from Figures 5.1a and 5.13 as well. Hence, as the sub-block
boundaries, as seen from Figure 5.15, dominates the microstructure it is realized that the V1/V4
boundary also is the most frequently observed, as seen from Figure 5.14a. The smaller blocksize/sub-block-size ratio for the 0.35C explains why the V1/V4 variant pairing is not found to be as
dominant as for the IF steel, although it displays martensite formed in packets and blocks as seen
from Figure 5.1b. In the 0.35C alloy all martensite units that belong to the CP group shows up in the
variant pair frequency analysis. Nevertheless, the sub-block boundaries, V1/V4, are the most
The 0.75C alloy, with the close to eutectoid composition, does not display a typical lath martensitic
microstructure, since packets and blocks cannot be easily identified as seen from Figure 5.1c.
However, when the EBSD data is used to color martensite units according to their CP group
association the packets become more evident, as seen from Figure 5.16a. Moreover, the martensite
units, a few microns in size, seem to be separated primarily by high-angle boundaries in this alloy.
Figure 5.16b displays an IPF colored map of a limited number of such martensite units, taken from a
single CP group (CP1 in Figure 5.16a). These martensite units have been labeled with their
corresponding martensite variant, V1 through V6, and boundaries are colored as follows: Yellow –
Twin (V1/V2; V3/V4; V5/V6), White – Low angle (V1/V4; V2/V5; V3/V6), and Black – High
angle (All other combinations). High angle boundaries, preferably twin boundaries (yellow), seem to
dominate in this alloy, although there are a considerable fraction of low angle (white) boundaries as
well. This is also seen from the variant pairing analysis, displayed in Figure 5.14c. The results for the
0.75C alloy may be compared with the results for a 0.61C alloy by Morito et al. [42]. Both results
display variant pairing of martensite units that belong to the same CP group. However, no tendency
for block or sub-block formation is observed in either of the alloys. These similarities indicate that an
increase in carbon content from 0.61 to 0.75C does not affect the structure significantly. The
observed strong peak of the V1/V2 variant pairing in Figure 5.14c is an important observation. If
the martensite in the 0.75C alloy may be classified as lath martensite, it indicates that a lower
formation temperature would promote V1/V2 variant pairing. This temperature dependence of
variant pairing has recently been observed by Takayama et al. [114] in low-carbon bainite. They
found that a lowered formation temperature promotes V1/V2 pairing. This variant pairing is unique
since it is the only pairing that is twin-related. In addition, a recent EBSD work [115] by Naraghi et
al. on athermal martensite formed in stainless steels also supports this observation of twin-related
variant pairing at low transformation temperatures.
Figure 5.16: Displays EBSD data from the 0.75C (a) Martensite units from a single prior austenite grain colored
according to CP group belonging. (b) IPF coloring of martensite units from a single CP group. The martensite units
have been labeled with their corresponding crystallographic variant. The boundaries are colored as follows: Yellow –
Twin (V1/V2; V3/V4; V5/V6), White – Low angle (V1/V4; V2/V5; V3/V6), and Black – High angle
(All other combinations). The figure is reproduced from [5].
In the 1.80C alloy the variants V1, V6, V16 and V17, which all belong to the same plate group, tend
to be paired more frequently, as seen from Figure 5.14e. The dominance of plate group variant
pairing is supported by the previous studies on variant selection of plate martensite [19], [116], [117].
The strong coupling between the plate group martensite variants may also be seen from Figure 5.17.
Here the EBSD-data from the 1.80C alloy is displayed as an IPF colored map, where the martensite
variants are colored as follows: V1 – Orange, V6 – Dark blue, V16 – Pink, and V17 – Light blue.
According to Okamoto et al. [19], variant pairs V1/V6, V1/V16 and V1/V17 correspond to wedge-,
kink-, spear-type respectively. They reported that wedge and spear variant pairs are favored due to
self-accommodation, while kink type is not. Therefore, Stormvinter et al. [5] supposed that the
observed dominance of V1/V16 pairing (kink type) could be due to the autocatalytic plate
The results from the variant pairing analysis [5] of 1.05C displayed in Figure 5.14d may be
interpreted as a transition between CP group pairing and plate group pairing. This conclusion agrees
well with the observed microstructure obtained using OM, as seen from Figure 5.1d. In the figure it
can be seen that large plate-like martensite units, with transverse micro-cracks, are embedded in a
matrix of smaller martensite units.
Figure 5.17: IPF colored EBSD map taken from the 1.80C alloy. EBSD data from the region enclosed by the
yellow box was used for the analysis by standard stereographic projection. Martensite variants are IPF colored as
follows: V1 – Orange, V6 – Dark blue, V16 – Pink, and V17 – Light blue and the white regions correspond to
retained austenite. It should be noted how the transverse thickening of the primary plates seems to occur by autocatalytic
nucleation of new martensite units on the former. The figure is reproduced from [5].
Based on their results, Stormvinter et al. [5] presented three schematics to illustrate the observed
change of martensite morphology with increasing carbon content. These schematics are presented in
Figures 5.18a-5.18c. Martensite formation in the IF steel is represented by Figure 5.18a, where a
prior austenite grain has transformed into a martensitic packet and block structure. In this figure one
CP group has been highlighted and it contains three blocks, which are colored according to their
corresponding Bain group association. The blocks contain sub-blocks, which are separated by
boundaries colored in light gray. Figure 5.18b displays formation of CP groups in the Fe-0.75C alloy.
The microstructure within every CP group would be very similar to Figure 5.16b, i.e. preferably
V1/V2 twin-type boundaries between the individual martensite variants. The absence of blocks and
sub-blocks seems to be the characteristic feature of this type of medium carbon lath martensitic
microstructure. The well-known characteristic hierarchy of lath martensite is in strong contrast to the
plate martensite formed in the Fe-1.80C alloy displayed in Figure 5.18c. Here the development of
martensite into plate groups is illustrated. This occurs by subsequent autocatalysis of variants which
belong to the same plate group. Every plate group contains four martensite variants and in total there
may be six plate groups present in one prior austenite grain (when disregarding annealing twins).
However, to make the microstructural interpretation easier, only one out of the six plate groups are
displayed here. This also seems reasonable since it is not clear from the present analysis how the
individual plate groups will be distributed within the prior austenite grain.
Figure 5.18: Schematics of martensite formation in (a) IF steel, (b) Fe-0.75C alloy and (c) Fe-1.80C alloy. The
region composed by variants belonging to the same Bain group is represented by the same color. The figure is reproduced
from [5].
5.3 Transition between lath and plate martensite
In the present thesis it has been demonstrated how different analyzing tools may provide
information to get a more fundamental understanding of the martensite microstructure. This
includes: (1) OM and classic SEM to analyze apparent morphology of the martensite units. (2)
Classic TEM to get detailed information on the substructure as well as the possibility to do more
detailed crystallographic analysis. (3) Automated crystallographic techniques, such as EBSD and
ASTAR, to analyze orientation relationships as well as martensite-martensite boundary
characteristics, i.e. variant pairing tendency. When interpreting the combined knowledge gathered [1],
[3–5] it seems clear that the complexity of the martensite morphology has to be resolved in multilength scale approach, where all these techniques are combined. Moreover it also seems rather clear
that the transition from lath martensite towards plate martensite is gradual and that the two
morphologies makes good reference points for interpreting a material in the mixed regime. In
addition, the recently developed variant pairing analysis may prove a good compliment to traditional
metallography, since it allows for quantification of boundary character, and thus martensite character.
This is well illustrated in Figure 5.19 that shows how the variant pairing tendency changes with the
carbon content. This EBSD technique has a clear advantage over ASTAR, since it can be applied to
an area large enough to be representative for the whole specimen. On the other hand, ASTAR has its
advantages since it can very well reproduce the local microstructure and allows for on-line
interchanging to classic TEM. In conclusion, by combining the strengths from various
characterization techniques it is possible to get a good understanding of the morphological transition
in ferrous martensite with increasing carbon content, although it may still prove very challenging and
time-consuming to perform the characterization.
Figure 5.19: Variant pairing tendency given as length fraction of variant boundary versus carbon content and based
on the experimental results from the present work. The figure is reproduced from [5].
6 Discussion on inverse bainite
As mentioned in Chapter 2 (Section 2.2), there has been a long debate concerning the nature of the
bainite formation and whether it can be regarded as diffusionless or diffusion controlled. The
conflict has been on-going since the 1940s when Zener [56] presented a comprehensive review of
the mechanisms involved in the austenite decomposition. The experimental results by Ko and
Cottrell [53], that bainite grows with a surface relief, were taken as a strong indication of a
diffusionless nature. However, as pointed out by Hillert [118] the surface relief is an indication of the
displace nature of the transformation, i.e. the fcc lattice is transformed into the bcc lattice in a
military fashion. It does not imply that such transformation omits diffusion of carbon, especially for
a transformation with slow growth rate as for instance the bainite transformation.
Recently, Borgenstam et al. [6] studied the decomposition of high-carbon austenite with the purpose
to test the symmetry among the diffusional transformation products in the Fe-C alloys. The term
symmetry was here used to define the relation between the eutectoid decomposition products as
follows: “Pearlite is the result of cooperative growth of ferrite and cementite where the two phases
behave as equal partners. It is favored by a close-to-eutectoid composition. Bainite forms with ferrite
as the leading phase in the main growth direction, which is identical to the growth direction of
Widmanstätten ferrite. Bainite is favored by a low carbon content. Inverse bainite forms with
cementite as the leading phase in the main growth direction, which is identical to the growth
direction of Widmanstätten cementite. Inverse bainite is favored by a high carbon content.”. The
concept of inverse bainite was first introduced by Hillert in 1957 [58] but has been discussed only a
few times during the elapsed 50 years, mainly by Aaronson and co-workers [119–121]. Evidently, the
diffusionless mechanism cannot be applied to inverse bainite, since it is not possible to imagine the
growth of a low-carbon cementite plate that later enriches in carbon by the onset of a diffusional
Borgenstam et al. [6] based their study on a large number of micrographs from isothermal treatments
of a high-carbon steel. Below the A1 temperature they observed austenite decomposition into pearlite
in a Fe-1.67C-0.22Mn-0.27Si-0.47Cr. However, below 773 K (500 °C) pearlite was replaced by an
acicular eutectoid with cementite as the leading phase. An example of these “spiky nodules” can be
seen from the micrograph by Modin and Modin [122] presented in Figure 6.1.
Figure 6.1: Spiky nodules of inverse bainite formed after 60 s at 723 K (450 °C) in a steel with 1.65C. OM
micrograph at 600 times magnification. Reproduced from Modin and Modin [122].
Figure 6.2: Acicular eutectoid (inverse bainite) between plates of cementite, formed after 1 s at 823 K (550 °C) in
steel with 1.34C. The arrows mark inverse bainite ahead of the cementite plate. TEM micrograph on plastic replica at
12,000 times magnification. Reproduced from Kinsman and Aaronson [119].
As the transformation temperature was lowered further the “spikes” of the nodules became less
pronounced and the eutectoid structure appeared more “fan-like” or columnar. At even lower
transformation temperatures the eutectoid structure again appeared spiky with protruding tips.
However, Borgenstam et al. [6] could show that this was in fact a gradual shift from cementite being
the leading phase of the hypereutectoid structure towards ferrite as the leading phase. This may be
illustrated by Figure 6.2 that shows how cementite is dominating the growth of inverse bainite in the
upper temperature range. In contrast, Figure 6.3 displays a hypereutectoid structure, transformed at
much lower temperature, where the growth has been dominated by the ferrite. From the figure it can
be seen how the shorter carbide units have been nucleated and grown from a primary ferrite plate.
Hence, the carbides are formed subsequently. This implies that as the isothermal transformation
temperature is lowered the growth of the hypereutectoid transformation structure shifts from a
cementite dominance (Figure 6.2) towards a ferrite dominance (Figure 6.3), i.e. there is a transition
from growth of inverse bainite towards ordinary bainite as the transformation temperature is
lowered. This is not so unlikely when taking the asymmetry of the Fe-C phase diagram into account.
As can be seen from Figure 6.4, the extrapolated A3 and Acm show that the supersaturation with
respect to ferrite increases more rapidly than to the supersaturation with respect to cementite. The
supersaturation may be interpreted as a driving force and hence the nucleation and growth of ferrite
becomes more likely as the temperature decreases.
Figure 6.3: Two thin spikes with a central plate of ferrite (white) and shorter plates of cementite (dark). Formed
after 1 h at 573 K (300 °C) in steel with 1.67C. Etched for carbides. Additional etching in nital was applied in the
insert. Two arrows mark the same platelet of cementite. SEM at 12,000 times magnification. Reproduced from
Borgenstam et al. [6].
Figure 6.4: Extrapolated solubility lines for ferrite and cementite in Fe-C austenitee [9], [64]. The figure is
reproduced from [6].
Most of the changes of microstructure of the eutectoid products in high-carbon steels with
temperature are gradual and may be explained by the asymmetry of supersaturation with respect to
ferrite and cementite at decreasing temperature. Moreover, Borgenstam et al. [6] showed that inverse
bainite, which forms by a diffusion controlled process, has many similarities to ordinary bainite. For
instance, they both form with a shape change that gives rise to a surface relief. However, the bainite
controversy will probably survive until a key experiment accepted by the proponents of both sides
can resolve the true nature of the transformation mechanism.
7 Thermodynamically based prediction of the
martensite start temperature
Some years ago, Borgenstam and Hillert [123] reviewed a comprehensive amount of experimental Ms
temperatures of binary and ternary ferrous alloys and made some noticeable distinctions in their final
assessment: (a) They used experimental Ms values directly and took them mainly from studies using
very rapid cooling; (b) They distinguished between data for two kinds of martensite yielding separate
plateaux in the cooling curves, where plateau III was supposed to belong to lath martensite and
plateau IV to plate martensite; (c) Results for Fe-Co were included which was an important addition
because it expanded the temperature range to above the value for pure Fe. They also proposed the
following expressions graphically for the requirement of driving force to start a martensitic
transformation into either lath or plate martensite:
[Eq. 7.1]
[Eq. 7.2]
The concept of two separate Ms temperatures, one for lath- and one for plate martensite, is
originating from the works by Morozov et al. [61], [75] who studied how the decomposition of
austenite in pure Fe and in Fe with 0.01C was affected by the cooling rate, from moderate to
extremely rapid cooling. They observed four transformation plateaux, as seen in Figure 7.1, where
plateaux III and IV were identified as caused by lath and plate martensite, respectively. According to
that information one should distinguish between the Ms temperatures for lath and plate martensite,
supposedly 818 K (545 °C) [61] and 693 K (420 °C) [75] for pure iron.
Figure 7.1: Beginning of the γ → α transformation in iron as a function of cooling rate, redrawn from Morozov et
al. [75]
In an attempt to construct a sound thermodynamic method to predict Ms of commercial steels,
Stormvinter et al. [2] accepted that the two expressions, Equations 7.1 and 7.2, for the necessary
driving force to form lath and plate martensite by Borgenstam and Hillert [123] holds for pure Fe.
They then referred experimental data on Ms for binary alloys, Fe-X(= C, Cr, Mn, Ni), from rapid
cooling experiments [70], [74], [76], [78], [124–127] to either plateau III or IV. From this information
they calculated the driving force at Ms and the difference from Equations 7.1 and 7.2 was accepted as
an effect of the alloying element and was evaluated as proportional to the content of each alloying
element. A linear superposition law was assumed for the combined effect of alloying elements on the
driving force, yielding the following expressions to be used for predicting the Ms temperature of
commercial steels (compositions given in mole fraction):
, [J/mol]
[Eq. 7.3]
, [J/mol]
[Eq. 7.4]
In the analysis by Stormvinter et al. [2] Zener ordering of carbon atoms was taken into account, since
it will have a dramatic impact on the Gibbs energy of the fresh martensite at high carbon contents.
In order to use Equations 7.3 and 7.4 to predict Ms of a commercial steel, it is necessary to find the
temperature where the available driving force for the alloy composition equals the required driving
force, i.e. the transformation barrier. To validate their proposed thermodynamic method for
prediction of Ms, they applied it to a number of datasets available in the rich martensite literature
[67], [68], [128], [129]. Both Equations 7.3 and 7.4 were used and the highest predicted Ms
temperature was accepted for each steel. For steels where Equation 7.3 (lath) gave the highest
predicted Ms, open symbols were used in the figures, while filled symbols were used when Equation
7.4 (plate) gave the highest predicted Ms. For example, Figure 7.2 displays a comparison of the
predicted Ms by the model and the experimentally determined Ms by Grange and Stewart [67] and by
Steven and Haynes [68].
Figure 7.2: Comparison between experimental Ms by Grange and Stewart [67], and by Steven and Haynes [68]
and predicted Ms temperatures. The figure is reproduced from [2]. Open symbols: lath martensite and filled symbols:
plate martensite.
The thermodynamic model proposed by Stormvinter et al. [2] has been used to develop a simple and
user-friendly software for calculation of Ms. This software is for the moment exclusive for the Herom research center partners and may therefore not be distributed outside Hero-m yet. A screenshot of
the user-interface can be seen in Figure 7.4. It is the belief of the present author that this software
will be developed further, for instance to include the effect by PAGS on Ms.
Figure 7.3: User-interface of the computer program for calculating Ms developed within the Hero-m center.
8 Concluding remarks and future prospects
The martensite transformation in steels has a substantial amount of complexity. In addition, it is also
one of the most important phase transformations to account for in process development and
materials design. Some important aspects of the martensitic transformation have been thoroughly
discussed in the present thesis. Those include: (1) The quantification of the martensite
microstructure and how that may be used to classify martensitic steels. (2) The feasibility of
developing a predictive model for Ms that is based on the current state-of-the-art thermodynamics.
Both these subjects may have a true industrial significance, since it may aid engineers in alloy design.
However, there are still challenges left before the full potential of both these methods can be fully
realized. A number of these challenges will be listed here:
The limited amount of experimental Ms data from binary and ternary alloys that is relevant for
steels. It is evident that additional experimental data would make further improvements of the
thermodynamic model as developed here [2], since it in principle relies on experimental Ms data
from binary and ternary alloys. However, it is important to keep in mind that such data should
contain information of experimental conditions, for instance cooling rate and PAGS. Very often
this kind of additional data is left out when the final experimental data is presented.
Improved thermodynamic databases, which are optimized for low temperatures. It is likely that
the never-ending increase in computational power will further fuel the capabilities of doing
computer based experiments. Ab initio and related techniques have already proved that they can
provide reliable data that may be extremely difficult to obtain through an ordinary experiment.
This new information may be used together with experimental data to optimize thermodynamic
databases to handle low temperature phase transformations, as the martensitic for instance.
Improvement of the commercially available EBSD software. For instance, to include easy-to-use
post-processing software to analyze orientation relationships and variant pairing. It is most
probable that EBSD analysis will become more sophisticated since this is a recent developed
area. Especially if one considers the growing popularity of FEG-SEMs equipped with EBSD
There has been a recent interest in three-dimensional (3D) characterization of materials, for
instance TMS (The Minerals, Metals and Materials Society) hosted an international conference
(3DMS in Seven Springs, Pennsylvania) dedicated to the topic in the past summer (2012). It is
likely that 3D characterization will add substantial information to the structure-property
relationships of materials. 3D characterization includes, among other techniques, 3D EBSD that
allows for detailed analysis of the crystallography of a finite volume. 3D EBSD is already
commercially available and may be applied to study morphology, boundary character, and variant
grouping of martensitic steels.
The growth kinetics of martensite may not yet be categorized as “well-known”. Obviously the
rapid transformation rate has made it difficult to study how the transformation progresses. On
the other hand, synchrotron sources and detector capabilities have improved significantly since
most of the experiments were conducted. It is therefore likely that it would be feasible to study
the growth kinetics using a synchrotron source to gain more insight to this phase transformation.
Steels forming lath martensite would probably be the best candidate to choose, since experiments
indicate that the growth rate can be several orders of magnitude lower when compared to the
growth rate of plate martensite.
9 Acknowledgments
First of all I would like to express my sincere gratitude to my principal supervisor Assoc. Prof.
Annika Borgenstam and co-supervisor Prof. John Ågren for giving me this opportunity to do
research on some very interesting aspects of physical metallurgy. I do much appreciate how you
encourage me to find and develop the researcher within me, although always prepared with guidance
if needed. I would also like to express my deepest gratitude to my second co-supervisor, Dr. Peter
Hedström, for non-depleting enthusiasm as well as professional assessment of my work.
I would like to acknowledge Prof. Yves Brechét and his co-workers at INP-Grenoble for a superb
spring in 2010. Also Prof. Tadashi Furuhara and his co-workers should be sincerely acknowledged
for accepting me into their lab in the summer of 2011. A special thanks to Dr. Goro Miyamoto for
his never-ending patience in my struggles to learn crystallography of martensite.
I would also like to acknowledge my colleagues at KTH for providing a welcoming, professional and
inspiring environment for research. A special thanks to Dr. Lars Höglund for being very helpful with
computer related challenges.
I would also like to thank the VINN Excellence Center Hero-m, VINNOVA, Swedish Steel
Industry, and KTH Royal Institute of Technology for providing finance for performing this work.
As well as Stiftelsen Axel Hultgren fond, Ångpanneföreningens Forskningsstiftelse, Stiftelsen
Bergshögskolans jubileumsfond, Knut och Alice Wallenbergs stiftelse, and Stiftelsen De Geerska
fonden for providing travel grants.
Finally, I would like to express my deepest gratitude to my family for their support and
encouragement. I am also in debt to all my friends for giving me such a wonderful time; you know
who you are (Ingen nämnd – Ingen glömd).
10 Bibliography
A. Stormvinter, P. Hedström, and A. Borgenstam, “Investigation of Lath and Plate Martensite
in a Carbon Steel,” Solid State Phenomena, vol. 172–174, pp. 61–66, Jun. 2011.
A. Stormvinter, A. Borgenstam, and J. Ågren, “Thermodynamically Based Prediction of the
Martensite Start Temperature for Commercial Steels,” Metallurgical and Materials Transactions A,
A. Stormvinter, P. Hedström, and A. Borgenstam, “A transmission electron microscopy study
of plate martensite formation in high-carbon low alloy steels,” To be published, 2012.
A. Stormvinter, G. Miyamoto, T. Furuhara, and A. Borgenstam, “Effect of Carbon Content
on the Orientation Relationship between Austenite and bct-Martensite in Fe-C Alloys
resolved by Electron Backscattered Diffraction,” To be published, 2012.
A. Stormvinter, G. Miyamoto, T. Furuhara, P. Hedström, and A. Borgenstam, “Effect of
Carbon Content on Variant Pairing of Martensite in Fe-C alloys,” To be published, 2012.
A. Borgenstam, P. Hedström, M. Hillert, P. Kolmskog, A. Stormvinter, and J. Ågren, “On the
Symmetry Among the Diffusional Transformation Products of Austenite,” Metallurgical and
Materials Transactions A, vol. 42, no. 6, pp. 1558–1574, Nov. 2010.
World Steel Association, “World crude steel output increases by 6.8% in 2011,” 2012.
[Online]. Available: http://www.worldsteel.org/media-centre/press-releases/2012/2011world-crude-steel-production.html. [Accessed: 24-Jan-2012].
G. Krauss, Steels: processing, structure, and performance. Materials park, OH: ASM International,
2005, pp. 1–658.
J.-O. Andersson, T. Helander, L. Höglund, P. Shi, and B. Sundman, “Thermo-Calc &
DICTRA, computational tools for materials science,” Calphad, vol. 26, no. 2, pp. 273–312,
Jun. 2002.
P. Gustafson, “A Thermodynamic Evaluation of the Fe-C System,” Scandinavian Journal of
Metallurgy, vol. 14, no. 5, pp. 259–267, 1985.
A. J. Schwartz, M. Kumar, B. L. Adams, and D. P. Field, Eds., Electron Backscatter Diffraction in
Materials Science, 2nd ed. Boston, MA: Springer US, 2009.
E. F. Rauch and L. Dupuy, “Rapid Spot Diffraction Patterns Identification through Template
Matching,” Archives of Metallurgy and Materials, vol. 50, pp. 87–99, 2005.
E. F. Rauch, J. Portillo, S. Nicolopoulos, D. Bultreys, S. Rouvimov, and P. Moeck,
“Automated nanocrystal orientation and phase mapping in the transmission electron
microscope on the basis of precession electron diffraction,” Zeitschrift für Kristallographie, vol.
225, no. 2–3, pp. 103–109, Mar. 2010.
G. Krauss and A. Marder, “The morphology of martensite in iron alloys,” Metallurgical
Transactions, vol. 2, no. 9, pp. 2343–2357, 1971.
P. G. McDougall and C. M. Wayman, “The Crystallography and Morphology of Ferrous
Martensites,” in Martensite, G. B. Olson and W. S. Owen, Eds. Materials park, OH: ASM
International, 1992, pp. 59–95.
J. A. Klostermann and W. G. Burgers, “Surface martensite in iron-nickel,” Acta Metallurgica,
vol. 12, no. 4, pp. 355–360, Apr. 1964.
M. Umemoto, T. Hyodo, T. Maeda, and I. Tamura, “Electron microscopy studies of butterfly
martensite,” Acta Metallurgica, vol. 32, no. 8, pp. 1191–1203, Aug. 1984.
H. Sato and S. Zaefferer, “A study on the formation mechanisms of butterfly-type martensite
in Fe–30% Ni alloy using EBSD-based orientation microscopy,” Acta Materialia, vol. 57, no. 6,
pp. 1931–1937, Apr. 2009.
H. Okamoto, M. Oka, and I. Tamura, “Couplings of thin-plate martensites in an Fe-Ni-C
alloy,” Transactions JIM, vol. 19, pp. 674–684, 1978.
T. Kakeshita, K. Shimizu, T. Maki, and I. Tamura, “Growth behavior of lenticular and thin
plate martensites in ferrous alloys and steels,” Scripta Metallurgica, vol. 14, no. 10, pp. 1067–
1070, 1980.
M. Umemoto, K. Minoda, and I. Tamura, “Some characteristics of the substructure of
lenticular martensite in Fe-Ni-C alloys,” Metallography, vol. 15, no. 2, pp. 177–191, May 1982.
A. Shibata, S. Morito, T. Furuhara, and T. Maki, “Substructures of lenticular martensites with
different martensite start temperatures in ferrous alloys,” Acta Materialia, vol. 57, no. 2, pp.
483–492, Jan. 2009.
M. Cohen, G. B. Olson, and P. C. Clapp, “On the Classification of Displacive Phase
Transformations,” in Proceedings of the International Conference on Martensitic Transformations
ICOMAT 1979, 1979, pp. 1–11.
C. M. Wayman, “The Growth of Martensite Since E.C. Bain - Some Milestones,” Materials
Science Forum, vol. 56–58, pp. 1–32, 1991.
D. A. Porter, K. E. Easterling, and M. Y. Sherif, Phase Transformations in Metals and Alloys, 3rd
ed. CRC Press, 2009.
E. C. Bain, “The nature of martensite,” Transactions AIME, vol. 70, pp. 25–46, 1924.
Z. Nishiyama, Martensitic Transformation. New York: Academic press, 1978.
J. S. Bowles and C. M. Wayman, “The bain strain, lattice correspondences, and deformations
related to martensitic transformations,” Metallurgical Transactions, vol. 3, no. 5, pp. 1113–1121,
May 1972.
Z. Guo, C. S. Lee, and J. W. Morris, “On coherent transformations in steel,” Acta Materialia,
vol. 52, no. 19, pp. 5511–5518, Nov. 2004.
M. S. Wechsler, D. S. Lieberman, and T. A. Read, “On the Theory of the Formation of
Martensite,” Transactions AIME, vol. 197, pp. 1503–1515, 1953.
J. S. Bowles and J. K. Mackenzie, “The Crystallography Martensite Transformations I,” Acta
Metallurgica, vol. 2, pp. 129–137, 1954.
J. K. Mackenzie and J. S. Bowles, “The crystallography of martensite transformations II,” Acta
Metallurgica, vol. 2, no. 1, pp. 138–147, 1954.
C. M. Wayman, Introduction to the Crystallopgraphy of Martensitic Transformations. New York: The
Macmillan Company, 1964.
G. Kurdjumow and G. Sachs, “Uber den Mechanismus der Stahlhartung,” Zeitschrift fur Physik,
vol. 64, no. 5–6, pp. 325–343, May 1930.
Z. Nishiyama, “No Title,” Sci. Rep. Tohoku Univ., vol. 23, p. 637, 1934.
G. Wassermann, “No Title,” Mitt. K-W-I Eisenforsch., vol. 17, p. 149, 1935.
A. B. Greninger and A. R. Troiano, “The Mechanism of Martensite Formation,” Transactions
AIME, vol. 185, pp. 590–598, 1949.
P. M. Kelly, A. Jostsons, and R. G. Blake, “The orientation relationship between lath
martensite and austenite in low carbon, low alloy steels,” Acta Metallurgica et Materialia, vol. 38,
no. 6, pp. 1075–1081, 1990.
M. X. Zhang and P. M. Kelly, “Accurate orientation relationship between ferrite and austenite
in low carbon martensite and granular bainite,” Scripta Materialia, vol. 47, no. 11, pp. 749–755,
Dec. 2002.
A. B. Greninger and A. R. Troiano, “Crystallography of Austenite Decomposition,”
Transactions AIME, vol. 140, pp. 307–331, 1940.
A. B. Greninger and A. R. Troiano, “Mechanism of Martensite Formation Summary,”
Transactions AIME, vol. 145, pp. 289–291, 1941.
S. Morito, H. Tanaka, R. Konishi, T. Furuhara, and T. Maki, “The morphology and
crystallography of lath martensite in Fe-C alloys,” Acta Materialia, vol. 51, no. 6, pp. 1789–
1799, Apr. 2003.
H. Kitahara, R. Ueji, N. Tsuji, and Y. Minamino, “Crystallographic features of lath martensite
in low-carbon steel,” Acta Materialia, vol. 54, no. 5, pp. 1279–1288, Mar. 2006.
T. Maki, “Recent advance in understanding martensite in steels,” in Proceedings of the
International Symposium on Steel Science IS3-2007, 2007, pp. 1–10.
P. Kelly and J. Nutting, “The Martensite Transformation in Carbon Steels,” Proceedings of the
Royal Society of London Series A, vol. 259, pp. 45–58, 1960.
B. Sandvik and C. Wayman, “Characteristics of lath martensite: Part I. crystallographic and
substructural features,” Metallurgical and Materials Transactions A, vol. 14, no. 4, pp. 809–822,
A. R. Marder and G. Krauss, “The Morphology of Martensite in Iron-Carbon Alloys,”
Transactions ASM, vol. 60, pp. 651–660, 1967.
M. Oka and C. M. Wayman, “Electron metallography of the substructure of martensite in
high-carbon steels,” Transactions AIME, vol. 62, no. 2, pp. 370–379, 1969.
M. Umemoto, E. Yoshitake, and I. Tamura, “The morphology of martensite in Fe-C, Fe-Ni-C
and Fe-Cr-C alloys,” Journal of Materials Science, vol. 18, no. 10, pp. 2893–2904, 1983.
T. Maki, “Microstructure and Mechanical Behaviour of Ferrous Martensite,” Materials Science
Forum, vol. 56–58, pp. 157–168, 1990.
T. Maki, “Morphology and substructure of martensite in steels,” in Phase transformations in steels.
Volume 2: Diffusionless transformations, high strength steels, modelling and advanced analytical techniques,
1st ed., E. Pereloma and D. V. Edmonds, Eds. Cambridge, UK: Woodhead Publishing
Limited, 2012, pp. 34–58.
G. F. Vander Voort, Ed., ASM Handbook, Volume 9, Metallography and Microstructure. Materials
park, OH: ASM International, 2004.
T. Ko and S. A. Cottrell, “The Formation of Bainite,” Journal of The Iron and Steel Institute, vol.
172, pp. 307–313, 1952.
T. Ko, “The Formation of Bainite in an En 21 Steel,” Journal of The Iron and Steel Institute, vol.
175, pp. 16–18, 1953.
G. R. Speich, “Unpublished work, reproduced by H. Warlimont in a report from the Edgar C.
Bain Laboratory for Fundamental Research,” Monroeville, PA, 1961.
C. Zener, “Kinetics of the Decomposition of Austenite,” Transactions AIME, vol. 167, pp.
550–595, 1946.
J. M. Oblak and R. F. Hehemann, “Structure and Growth of Widmanstätten Ferrite and
Bainite,” in Transformation and Hardenability in Steels, Ann Arbor, MI: Climax Molybdenum Co.,
1967, pp. 15–38.
M. Hillert, “The Role of Interfacial Energy During Solid State Phase Transformations,”
Jernkontorets Annaler, vol. 141, pp. 757–789, 1957.
P. J. Goodhew, J. Humphreys, and R. Beanland, Electron Microscopy and Analysis, 3rd ed.
London: Taylor & Francis, 2001, pp. 1–251.
J. Goldstein et al., Scanning Electron Microscopy and X-ray Microanalysis, 3rd ed. New York:
Springer, 2003, pp. 1–586.
O. P. Morozov, D. A. Mirzayev, and M. M. Shteynberg, “The Polymorphous Gamma-Alpha
Transformation in Iron of a High Level of Purity,” Physics of Metals and Metallography, vol. 34,
pp. 114–119, 1972.
J. W. Christian, “Thermodynamics and Kinetics of Martensite,” in Proceedings of the International
Conference on Martensitic Transformations ICOMAT 1979, 1979, pp. 220–234.
J. Ågren, “Martensitic transformations,” in A graduate course in the theory of PHASE
TRANSFORMATIONS, Stockholm: US-AB, 2004, pp. 119–134.
“TCFE6 - TCS Steels/Fe-Alloys Database.” Thermo-Calc Software AB, Stockholm, SE.
J. Fisher, “Free Energy Change Accompanying the Martensite Transformation in Steels,”
Transactions AIME, vol. 185, pp. 688–690, 1949.
A. B. Greninger and A. R. Troiano, “Kinetics of the Austenite to Martensite Transformation
in Steel,” Transactions ASM, vol. 28, pp. 537–574, 1940.
R. Grange and H. Stewart, “The temperature range of martensite formation,” Transactions
AIME, vol. 167, pp. 467–501, 1946.
W. Steven and A. Haynes, “The temperature of formation of martensite and bainite in lowalloy steels,” Journal of the Iron and Steel Institute, vol. 183, no. 8, pp. 349–359, 1956.
S. M. C. van Bohemen, M. Santofimia, and J. Sietsma, “Experimental evidence for bainite
formation below Ms in Fe–0.66C,” Scripta Materialia, vol. 58, no. 6, pp. 488–491, Mar. 2008.
M. Oka and H. Okamoto, “Swing back in kinetics near Ms in hypereutectoid steels,”
Metallurgical and Materials Transactions A, vol. 19, no. 3, pp. 447–452, 1988.
R. B. G. Yeo, “The Effects of Some Alloying Elements on the Transformation of Fe-22.5 Pct
Ni Alloys,” Transactions AIME, vol. 227, pp. 884–890, 1963.
C. L. Magee and R. G. Davies, “On the volume expansion accompanying the f.c.c. to b.c.c.
transformation in ferrous alloys,” Acta Metallurgica, vol. 20, no. 8, pp. 1031–1043, Aug. 1972.
R. Pradhan and G. S. Ansell, “Kinetics of the martensite transformation in athermal Fe-C-NiCr alloys,” Metallurgical Transactions A, vol. 9, no. 6, pp. 793–801, Jun. 1978.
D. A. Mirzayev, M. M. Shteynberg, T. N. Ponomareva, and V. M. Schastlivtsev, “Influence of
Cooling Rate on the Position of Martensitic Transformation Points. Carbon Steels,” Physics of
Metals and Metallography, vol. 47, no. 1, pp. 102–111, 1980.
O. P. Morozov, D. A. Mirzayev, and M. M. Shteynberg, “Some Regularities of
Transformations in Iron Cooled at High Rates,” Physics of Metals and Metallography, vol. 32, pp.
170–177, 1971.
M. M. Shteynberg, D. A. Mirzayev, and T. N. Ponomareva, “Gamma-Alpha Transformation
of Iron-Manganese Alloys During Cooling,” Physics of Metals and Metallography, vol. 43, pp. 143–
149, 1977.
A. Gilbert and W. S. Owen, “Diffusionless transformation in iron-nickel, iron-chromium and
iron-silicon alloys,” Acta Metallurgica, vol. 10, no. 1, pp. 45–54, 1962.
W. D. Swanson and J. G. Parr, “Transformations in Iron-Nickel Alloys,” Journal of The Iron and
Steel Institute, pp. 104–106, 1964.
P. J. Brofman and G. S. Ansell, “On the effect of fine grain size on the Ms temperature in Fe27Ni-0.025C alloys,” Metallurgical Transactions A, vol. 14, no. 9, pp. 1929–1931, Sep. 1983.
S.-J. Lee and Y.-K. Lee, “Effect of Austenite Grain Size on Martensitic Transformation of a
Low Alloy Steel,” Materials Science Forum, vol. 479, pp. 3169–3172, 2005.
H. Yang and H. Bhadeshia, “Austenite grain size and the martensite-start temperature,” Scripta
Materialia, vol. 60, no. 7, pp. 493–495, Apr. 2009.
G. Ghosh and G. B. Olson, “Computational thermodynamics and the kinetics of martensitic
transformation,” Journal of Phase Equilibria, vol. 22, no. 3, pp. 199–207, 2001.
D. A. Mirzayev, V. M. Schastlivtsev, and S. Y. E. Karzunov, “Martensitic Points of Fe-C
Alloys,” Physics of Metals and Metallography, vol. 63, pp. 129–132, 1987.
P. J. Jacques, “Phase transformations in transformation induced plasticity (TRIP)-assisted
multiphase steels,” in Phase transformations in steels. Volume 2: Diffusionless transformations, high
strength steels, modelling and advanced analytical techniques, 1st ed., E. Pereloma and D. V. Edmonds,
Eds. Cambridge, UK: Woodhead Publishing Limited, 2012, pp. 213–246.
J. G. Speer, “Phase transformations in quenched and partitioned steels,” in Phase transformations
in steels. Volume 2: Diffusionless transformations, high strength steels, modelling and advanced analytical
techniques, 1st ed., E. Pereloma and D. V. Edmonds, Eds. Cambridge, UK: Woodhead
Publishing Limited, 2012, pp. 247–270.
W. Sha, “Phase transformations in maraging steels,” in Phase transformations in steels. Volume 2:
Diffusionless transformations, high strength steels, modelling and advanced analytical techniques, 1st ed., E.
Pereloma and D. V. Edmonds, Eds. Cambridge, UK: Woodhead Publishing Limited, 2012,
pp. 332–362.
P. Payson and C. H. Savage, “Martensite Reactions in Alloy Steels,” Transactions ASM, vol. 33,
pp. 261–275, 1944.
L. A. Carapella, “Computating A’' or Ms (Transformation Temperature on Quenching) from
Analysis,” Metal Progress, vol. 46, no. 108, 1944.
E. S. Rowland and S. R. Lyle, “The Application of Ms Points to Case Depth Measurement,”
Transactions ASM, vol. 37, pp. 27–47, 1946.
K. W. Andrews, “Empirical Formulae for the Calculation of Some Transformation
Temperatures,” Journal of The Iron and Steel Institute, vol. 203, pp. 721–727, 1965.
J. Wang, P. J. van der Wolk, and S. van der Zwaag, “Determination of Martensite Start
Temperature in Engineering Steels Part I. Empirical Relations Describing the Effect of Steel
Chemistry,” Materials transactions JIM, vol. 41, pp. 761–768, 2000.
B. Skrotzki and E. Hornbogen, “Projekt COSMOS -Temperaturen und Verlauf der
martensitischen Umwandlung in Stahlen,” 1991.
T. Sourmail and C. Garcia-Mateo, “Critical assessment of models for predicting the Ms
temperature of steels,” Computational Materials Science, vol. 34, no. 4, pp. 323–334, 2005.
V. Raghavan and D. Antia, “The driving force for martensitic transformations in low alloy
steels,” Metallurgical and Materials Transactions A, vol. 27, no. 4, pp. 1127–1132, 1996.
C. Kung and J. Rayment, “An examination of the validity of existing empirical formulae for
the calculation of Ms temperature,” Metallurgical and Materials Transactions A, vol. 13, no. 2, pp.
328–331, 1982.
T. Y. Hsu and H. Chang, “On calculation of Ms and driving force for martensitic
transformation in Fe-C,” Acta Metallurgica, vol. 32, no. 3, pp. 343–348, Mar. 1984.
J. Wang, P. J. van der Wolk, and S. van der Zwaag, “Determination of Martensite Start
Temperature for Engineering Steels Part II. Correlation between Critical Driving Force and
Ms Temperature,” Materials transactions JIM, vol. 41, pp. 769–776, 2000.
J. Wang, P. J. van der Wolk, and S. van der Zwaag, “Effects of Carbon Concentration and
Cooling Rate on Continuous Cooling Transformations Predicted by Artificial Neural
Network,” ISIJ International, vol. 39, pp. 1038–1046, 1999.
G. Ghosh and G. B. Olson, “Kinetics of F.C.C. → B.C.C. heterogeneous martensitic
nucleation—I. The critical driving force for athermal nucleation,” Acta Metallurgica et
Materialia, vol. 42, no. 10, pp. 3361–3370, Oct. 1994.
[100] G. Ghosh and G. B. Olson, “Kinetics of F.c.c. → b.c.c. heterogeneous martensitic
nucleation—II. Thermal activation,” Acta Metallurgica et Materialia, vol. 42, no. 10, pp. 3371–
3379, Oct. 1994.
[101] G. Ghosh and G. B. Olson, “The isotropic shear modulus of multicomponent Fe-base solid
solutions,” Acta Materialia, vol. 50, no. 10, pp. 2655–2675, Jun. 2002.
[102] G. Krauss, “Martensitic Transformation, Structure and Properties in Hardenable Steels,” in
Hardenability concepts with applications to steel, D. V. Doane and J. S. Kirkaldy, Eds. Metallurgical
Society of AIME, 1978, pp. 229–248.
[103] A. Borgenstam, M. Hillert, and J. Ågren, “Critical temperature for growth of martensite,” Acta
Metallurgica et Materialia, vol. 43, no. 3, pp. 945–954, Mar. 1995.
[104] A. Litwinchuk, F. X. Kayser, H. H. Baker, and A. Henkin, “The Rockwell C hardness of
quenched high-purity iron-carbon alloys containing 0.09 to 1.91% carbon,” Journal of Materials
Science, vol. 11, no. 7, pp. 1200–1206, 1976.
[105] A. Borgenstam, “Unpublished work.” 2006.
[106] G. Krauss, “Martensite in steel: strength and structure,” Materials Science and Engineering A, vol.
273–275, no. 1–2, pp. 40–57, Dec. 1999.
[107] T. Maki, K. Tsuzaki, and I. Tamura, “The morphology of microstructure composed of lath
martensites in steels,” Transactions ISIJ, vol. 20, pp. 207–214, 1980.
[108] G. Thomas, “Electron microscopy investigations of ferrous martensites,” Metallurgical
Transactions, vol. 2, no. 9, pp. 2373–2385, Sep. 1971.
[109] T. Maki, S. Furutani, and I. Tamura, “Shape Memory Effect Related to Thin Plate Martensite
with Large Thermal Hysteresis in Ausaged Fe-Ni-Co-Ti Alloy,” ISIJ International, vol. 29, pp.
438–445, 1989.
[110] G. Miyamoto, N. Takayama, and T. Furuhara, “Accurate measurement of the orientation
relationship of lath martensite and bainite by electron backscatter diffraction analysis,” Scripta
Materialia, vol. 60, no. 12, pp. 1113–1116, Jun. 2009.
[111] G. Nolze, “Irrational orientation relationship derived from rational orientation relationships
using EBSD data,” Crystal Research and Technology, vol. 43, no. 1, pp. 61–73, Jan. 2008.
[112] M. Oka and H. Okamoto, “Roles of {101} twinnings in Martensite Transformation of a 1.80
mass% Carbon Steel,” Materials transactions JIM, vol. 33, no. 3, pp. 229–234, 1992.
[113] S. Morito, X. Huang, T. Furuhara, T. Maki, and N. Hansen, “The morphology and
crystallography of lath martensite in alloy steels,” Acta Materialia, vol. 54, no. 19, pp. 5323–
5331, Nov. 2006.
[114] N. Takayama, G. Miyamoto, and T. Furuhara, “Effects of transformation temperature on
variant pairing of bainitic ferrite in low carbon steel,” Acta Materialia, vol. 60, no. 5, pp. 2387–
2396, Mar. 2012.
[115] R. Naraghi, P. Hedström, and A. Borgenstam, “Spontaneous and Deformation-Induced
Martensite in Austenitic Stainless Steels with Different Stability,” Steel Research International, vol.
82, no. 4, pp. 337–345, Apr. 2011.
[116] J. C. Bokros and E. R. Parker, “The mechanism of the martensite burst transformation in FeNi single crystals,” Acta Metallurgica, vol. 11, no. 12, pp. 1291–1301, 1963.
[117] M. Umemoto and C. Wayman, “Crystallography and morphology studies of Fe-Pt
martensites: Lenticular to thin plate transition and thin plate morphologies,” Acta Metallurgica,
vol. 26, no. 10, pp. 1529–1549, Oct. 1978.
[118] M. Hillert, “Diffusion in growth of bainite,” Metallurgical and Materials Transactions A, vol. 25,
no. 9, pp. 1957–1966, Sep. 1994.
[119] K. R. Kinsman and H. I. Aaronson, “The inverse bainite reaction in hypereutectoid Fe-C
alloys,” Metallurgical Transactions, vol. 1, no. 5, pp. 1485–1488, 1970.
[120] H. J. Lee, G. Spanos, G. J. Shiflet, and H. I. Aaronson, “Mechanisms of the bainite (nonlamellar eutectoid) reaction and a fundamental distinction between the bainite and pearlite
(lamellar eutectoid) reactions,” Acta Metallurgica, vol. 36, no. 4, pp. 1129–1140, Apr. 1988.
[121] G. Spanos, H. S. Fang, D. S. Sarma, and H. I. Aaronson, “Influence of carbon concentration
and reaction temperature upon bainite morphology in Fe-C-2 Pct Mn alloys,” Metallurgical
Transactions A, vol. 21, no. 6, pp. 1391–1411, Jun. 1990.
[122] H. Modin and S. Modin, Microstructures in Three Isothermally Transformed Carbon Steels with HighCarbon Contents. Stockholm, SE: Meritförlaget, 2000.
[123] A. Borgenstam and M. Hillert, “Driving force for f.c.c. --> b.c.c. martensites in Fe---X alloys,”
Acta Materialia, vol. 45, no. 5, pp. 2079–2091, 1997.
[124] D. A. Mirzayev, O. P. Morozov, and M. M. Shteynberg, “The Gamma-Alpha Transformation
in Iron and in its Alloys,” Physics of Metals and Metallography, vol. 36, pp. 99–105, 1973.
[125] D. A. Mirzayev, V. N. Karzunov, V. N. Schastlivtsev, I. I. Yakovleva, and Y. V. Kharitonova,
“The Gamma-Alpha Transformation in Low-Carbon Fe-Cr Alloys,” Physics of Metals and
Metallography, vol. 61, no. 2, pp. 114–122, 1986.
[126] D. A. Mirzayev, S. Y. E. Karzunov, V. M. Schastlivtsev, I. L. Yakovleva, and Y. E. V.
Kharitonova, “Peculiarities of Martensite and Bainite Transformation in Chromium Steels,”
Physics of Metals and Metallography, vol. 62, pp. 100–109, 1986.
[127] E. A. Wilson, “Doctoral Thesis,” University of Liverpool, 1965.
[128] H. Finkler and M. Schirra, “Transformation behaviour of the high temperature martensitic
steels with 8-14% chromium,” Steel research, vol. 67, no. 8, pp. 328–342, 1996.
[129] G. Vander Voort, Ed., Atlas of Time-Temperature Diagrams for Nonferrous Alloys. Materials park,
OH: ASM International, 1991, p. 474.
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