Journal of Glaciology, Vol. 57, No. 201, 2011
Instruments and Methods
Complete determination of ice crystal orientation using Laue X-ray
diffraction method
Institute of Low Temperature Science, Hokkaido University, Sapporo 060-0819, Japan
E-mail: miyamoto@lowtem.hokudai.ac.jp
Alfred Wegener Institute for Polar and Marine Research, Columbusstrasse, D-27568 Bremerhaven, Germany
ABSTRACT. Ice crystal orientation fabric data from ice cores contain important information concerning
the internal structure and the flow behaviour of ice sheets. When ice cores are recovered from the
Antarctic and Greenland ice sheets, crystal orientation measurements are performed immediately to
obtain fundamental physical property information. In the past, we have measured the c-axis orientation
of ice crystals by a manual optical method using a universal stage. This method is very time-consuming,
involving tedious work in a cold laboratory. Recently, automated systems have been developed that
enable measurement of c-axis orientation, grain size and other microstructures. However, in order to
detect the full crystal orientation of an ice crystal, we also need information on its a-axis orientation. A
variety of other crystal orientation measurement methods have previously been discussed, but some
shortcomings for ice-core studies cannot be neglected. We have developed a crystal-orientation
analysing device using the Laue X-ray diffraction method. As this device can measure the orientations of
all crystal axes with high accuracy, it is possible to obtain new microstructure information on natural ice
crystals. For the first time, we are able to quantify very low subgrain misorientation angles in polar icecore samples, allowing us to investigate micro-deformation features of individual crystals. Here we
discuss the analysis process, which is customized to measure standard ice thin sections, and show
preliminary results.
Ice masses in polar regions show various deformation
characteristics depending on stress, temperature, hydrostatic
pressure and other parameters (Budd and Jacka, 1989).
Deformation of ice in glaciers and ice sheets is controlled
mainly by dislocation activity in ice crystals (Schulson and
Duval, 2009). Thus, the formation, accumulation and
recovery of dislocations determine the strength of the
material. Accumulated in subgrain boundaries as arrays,
dislocations cause lattice misorientations (Weertman and
Weertman, 1992; Hull and Bacon, 2001). Characteristics of
the probable dislocation types involved in this misorientation
can be determined if full crystal orientation measurements
are available (Prior and others, 2002). Since different
subgrain boundary types, classified by shape and c-axis
orientations, have been observed as major microstructure
features during creep tests on polar and artificial ice (Hamann
and others, 2007; Weikusat, 2009), we can improve our
knowledge of dislocation activity using high-accuracy, full
crystal orientation analysis on the subgrain scale. To determine microstructural features of natural ice-core samples, the
measurement device must be suitable for ice crystals of a few
millimetres to several centimetres in diameter.
Three predominant techniques are employed to measure
orientation of ice crystals: optical observation, etch-pit
observation and electron backscatter diffraction.
The most traditional course is an optical approach using a
Rigsby stage, a universal stage with four rotation axes. This
method utilizes the birefringence and extinction of the
optically uniaxial ice crystal between crossed polarizers
(Rigsby, 1951; Langway, 1958; Kamb, 1962). Because a
typical ice crystal is hexagonal, with only one optical axis,
the only measurable orientation is the c-axis. Although this
method requires elaborate and time-consuming measurement procedures, it has a major advantage: abundant
previous studies are available for data comparison using this
method (e.g. Rigsby, 1951; Gow and Williamson, 1976;
Herron and Langway, 1982; Azuma and Higashi, 1985; Alley
and others, 1995). Thus fabric patterns (e.g. single-maximums or girdles) exhibited by different ice-core samples are
comparable even if measurement methods are different.
Automated devices also using the principles of the optical
extinction method have become available since the late
1990s (Wang and Azuma, 1999; Wilen and others, 2003;
Wilson and others, 2007) and are now commonly used in
ice-core studies. The chief merits of these analysers are
automation and speed: each thin-section sample takes just a
few tens of minutes to process. However, automated
techniques have a low angular resolution (58), and we
know empirically that large artefact errors occur, possibly
due to illumination problems (M. Montagnat and others,
unpublished information). Furthermore, the measured angles deviate from the true angles due to the large differences
between the refractive indices of air and ice if c-axes are
aligned with high angles with respect to the thin section
(Langway, 1958).
The second major method of crystal orientation measurement is by observation, under a microscope, of etch pits,
which are generated by the application of a polyvinyl
formal solution (Higuchi, 1958; Matsuda, 1979). As the
etch pits form shapes of a section cut from a hexagonal
column, the full crystal orientation can be determined. This
Miyamoto and others: Instruments and methods
Table 1. Comparison of crystal orientation measurement methods for ice samples
(for example)
Manual optical
Universal stage
Many comparable datasets
with good statistics
Langway (1958)
optical method
Commercial analyser
or developed their
own equipment
grain size
Automated procedure
1. Tedious and
time-consuming work
2. Low angular resolution
1. Low angular resolution
2. Artefact error
c- and a-axes
a-axis is measurable
SEM with EBSD and
cold chamber or
Every crystal
orientation with
area mapping
Laue X-ray
X-ray source, camera
and pulse motor
Every crystal
orientation at
measured points
1. Area mapping of crystal
2. High angular resolution
3. Automated procedure
4. All crystal axis orientation
is measurable
See text
Etch pits
method also involves laborious, time-consuming work in a
cold laboratory. Furthermore, the results depend on the skill
of the operator, and only low angle resolutions (>58) can be
obtained. In addition, a reliable method to generate a
measurable etch pit on the ice surface is difficult to
establish because the density of the polyvinyl formal
solution, sublimation time, temperature and other factors
strongly influence the quality of etch-pit shape. Additionally, the shape of the etch pits changes every moment
(personal communication from N. Azuma, 2010). The
advantage of the etch-pit method is that we can measure
c- and a-axes orientations with high spatial resolution
(several tenths of a micrometre), strongly depending on the
visibility of the etch pit and thus the operator’s skill.
The third method for crystal orientation measurements is
electron backscatter diffraction (EBSD) used as an add-on
package with a scanning electron microscope (SEM; Randle
and Engler, 2000). This is a long-established method in
metallurgy, material science and geology (Humphreys,
2001; Pennock and Drury, 2005) but is rarely used for ice.
EBSD enables area mapping of crystal orientation with high
spatial resolution, but the measurable area for mapping is
normally small (a few mm2) due to the small sample size of a
few cm2 (Iliescu and others, 2004; Obbard and others, 2006;
Piazolo and others, 2008). This small sample size is
problematic for the localization of relevant structures since
natural polar ice-core samples contain large grains and a
heterogeneous distribution of microstructure features. Moreover, an expensive and complex measurement set-up is
required to measure ice-core samples, including an SEM
equipped with an EBSD detector and cryogenic thermostat
chamber or stage. The measurement conditions (e.g. the
complicated sublimation and condensation dynamics in a
vacuum) must also be controlled (Iliescu and others, 2004;
Weikusat and others, in press). Advantages of this method
are full automation and the possibility of detecting all crystal
axis orientations with high accuracy.
All three methods described above have recently been
used in ice-core studies. Currently, the most common
1. Tedious and
time-consuming work
2. Low angular resolution
3. Complicated procedure
1. Small measurement area
(a few mm2)
2. Cold chamber or stage
is necessary
See text
Wang and Azuma
(1999); Wilson and
others (2007)
Matsuda (1979)
Iliescu and others
(2004); Obbard and
others (2006)
Miyamoto and others
(2005); this study
technique is the automated optical method because no
special skills are required to measure crystal orientation, and
advanced commercial devices are available.
X-ray diffraction was used by M. von Laue in 1912–13 to
prove the periodic lattice structure of crystals and the
electromagnetic character of X-radiation (Ewald, 1962). This
method, named after Laue, is now primarily used to measure
single crystal orientations and is traditional for crystal
orientation measurements; the approach is still common in
material sciences. In our study, we adapt this method, for the
first time, to polycrystalline samples from an ice sheet.
Merits, shortcomings and sources are summarized in Table 1.
The experimental arrangement for our full crystal orientation
fabric analyser is shown in Figure 1a and b. The specially
designed X-Yaxes pulse motor stages, manufactured by Chuo
Precision Industrial Co., Ltd (positioning accuracy 50 mm;
unidirectional repeatability 5 mm), the charge-coupled
device (CCD) camera, the light-emitting diode (LED) light
source and the X-ray camera (Rad-icon Shad-o-Box 1024)
with X-ray source device (Rigaku SLX-2000, 60 kV and
250 mA) were assembled to detect each crystal orientation
within thin-section samples. Since all devices were installed
in a cold laboratory at –158C, a cold chamber or cryo-stage
was not required. For ice-core studies, we prepared standard
thin sections of 100 mm 100 mm with a thickness of
<0.5 mm for crystallographic analyses. Sections this large are
necessary to observe a few hundred grains because of the
large grain sizes, typically a few millimetres to a few
centimetres in natural polar ice. Crystal orientations of
>200 grains are required for sufficient fabric determination.
Development of a semi-automated Laue X-ray
diffraction method
Using an earlier version of this device (Miyamoto and
others, 2005), we had already succeeded in obtaining
Miyamoto and others: Instruments and methods
Fig. 1. (a) Photograph of entire experimental arrangement in cold laboratory. (b) Schematic of X-Y stages, collimator, sample holder and
X-ray camera.
accurate c- and a-axis orientation measurements, providing
complete ice-core thin-section crystal orientation of fabrics.
In our study, however, longer analysis times were required
for a single grain, so it was not suitable for many measurements. In order to reduce measurement time and apply the
method to microstructure studies, we aimed to automate the
analysis of Laue X-ray diffraction, which is traditionally used
only in single crystal analysis.
The Laue pattern digitizing and analysis software was
developed in collaboration with Norm Co., Ltd, a Japanese
software company that develops various X-ray analyses.
However, this software is designed to analyse the orientation
of single crystals and is unsuitable for the study of
polycrystals. Thus, we ‘customized’ the software to the
requirements of ice-core analysis. Specifically, the following
changes were made so as to analyse many measurement
points in a reasonable time:
1. We prepare a thin section using an X-ray transparent
object slide that consists of a 2 mm thick clear acrylic
resin plate. The maximum size of the thin section is
100 mm 100 mm, and the thickness is <0.5 mm
depending on grain size. The ice-sample thin section is
covered with silicone oil and polyester film to avoid
sublimation during measurement. The sample is inserted
into the sample holder of the X-ray device (Fig. 2). This is
the only step that had to be performed in a cold
2. We decide upon a measurement position through the
CCD camera with a polarizer using a stage controller.
We recognize each grain on the monitor according to the
1. The objective orientations (c-axis and three a-axes) were
inputted in advance.
2. After each individual analysis, the c-axis and three a-axes
orientations were sent to a text file.
3. Many minor changes, such as the Laue pattern simulation
algorithm for finding a matching pattern (the solution) and
the procedure cycle (opening the Laue figure, digitizing
Laue spots, finding a matching pattern, displaying the
result and saving the result), were implemented to reduce
analysis time. With the previous software we required a
long calculation time and several operator interactions
when proceeding to the next operation.
The present program version is 5.1.1.
The steps in our crystal-orientation analysis are as
Fig. 2. Photograph of sample holder with ice core, thin-section
Miyamoto and others: Instruments and methods
Fig. 3. Schematic diagram of measured four axes (c, a1, a2 and a3) of
hexagonal ice crystal.
grey-value differences. We fix measurement points by
operating the X-Y stage using a joystick manipulator. The
X-ray collimator axis and fixed point on the monitor are
already linked. The measurement positions are saved as a
series of X-Y coordinates in a text file. When we want to
make equally spaced measurement points or grid
measurement points for microstructure study or other
purposes, we edit a test file that represents such
coordinates or we move the X-Y stage equidistant to
the stage controller. The minimum detectable grain size
is 0.5 mm, which is larger than the collimator size;
smaller grains were difficult to recognize through the
CCD camera.
3. The actual Laue measurements, i.e. positioning on the
measurement point, irradiation of X-ray and imaging of
the Laue figure by the X-ray camera, are fully automated
in our system.
4. After obtaining all Laue figures, we prepare the Laue
pattern digitizer and analysis program. The objective four
orientations, (001) as c-axis and (210), (110) and (120) as
a-axes (Fig. 3), are inputted to the software.
5. A few Laue spots from different crystal zones are
digitized manually, and solution candidates for the Laue
diagram are calculated by the software. If a candidate is
provided, we confirm the simulated Laue pattern of the
solution (Fig. 4) to reduce analysis error. The calculated
orientations are sent to a result file.
The described improvements and modifications of the
system make the X-ray analyser very suitable for ice-core
studies. Using this semi-automated system, we were able to
analyse 200 measurement points every day.
Spatial resolution
As previously mentioned, we need large thin sections due to
the comparatively large grain size of natural polar ice-core
Fig. 4. Displayed Laue figure on Laue pattern digitization and
analysis program. The black dots indicate original Laue pattern from
X-ray camera. The four numbered red dots show digitized points just
on the acquired Laue spots. The open blue circles indicate simulated
Laue pattern. The comparison of simulated and measured spots
enables high accuracy and accelerated measurements.
samples, typically greater than a few millimetres. However,
since grain substructure characterization is essential to
understand the dislocation dynamics, the spatial resolution
is important. The diameter of the X-ray beam we set up was
0.2 mm, determined by the collimator size, which is suitable
for adjusting a correlation between the X-ray power and the
quality of the Laue spots figure – the sensitivity of the X-ray
camera – in this setting. With the collimator size set to the
smallest diameter of 0.1 mm, the diffracted X-ray power was
very low in order to obtain a satisfactory Laue figure. This
beam size defined the minimum spatial resolution. The
positioning accuracy of the X-Y stage was one order smaller
than this resolution.
For fabric determination, we chose a measuring point
near the centre of each crystal and provided data as shown
by Miyamoto and others (2005). Small crystal-orientation
changes on subgrain boundaries or continuous lattice
bending was observed when we moved the pulse motor
stage in >0.2 mm steps within an individual grain. Even with
small crystal displacement, slight changes of spot position
were detected in each Laue diagram. Such small orientation
changes represent new and important microstructure information for ice-core study, especially those concerning
distinct subgrain boundaries.
Angular precision and accuracy
Due to the grain boundary energies (Suzuki, 1970), subgrain
misorientations are expected to be <108 as in metals
(Humphreys and Hatherly, 2004) or even <58 as in most
rock-forming minerals (Passchier and Trouw, 1996). Hence,
when using Laue X-ray diffraction, the angular precision is
of particular importance. The process of digitizing Laue
spots is a primary factor for error generation because a slight
deviation of digitizing position leads to low angle precision.
For this reason, the precision was determined from repeated
Miyamoto and others: Instruments and methods
Fig. 5. Example of thin section prepared from the Greenland Icecore Project (GRIP) ice-core sample at 2702 m depth (left). This photograph
was taken between crossed polarizers. The minimum scale on the left side shows 1 mm. The black dots (right-hand graphs) show
measurement points within grains A and B.
analyses of the same Laue figure. The standard deviation of
each orientation was <0.58. To estimate the accuracy of
orientation determination, we compare it with the result of
X-ray diffract meter measurement. For orientations determined by the Laue method, the desired ice-lattice plane
orientations were searched using rocking curve measurements. This allowed us to seek the absolute orientation if the
grain showed a perfect crystal without any disturbance such
as polygonization or lattice bending. Both results showed
good agreement, with some angle differences less than the
standard deviation determined by the Laue measurements.
The precision and accuracy with which an orientation can
be absolutely determined is 0.58 and is affected by the
digitizing of Laue spots and the crystal quality. However, the
relative orientations between neighbouring measurement
points are the crucial parameter when detecting and
characterizing subgrain boundaries. Pre-mapping of samples using sublimation etching by microstructure mapping
(Kipfstuhl and others, 2006) gives a first impression of the
crystal quality by revealing subgrain boundaries as grooves.
Thus, this method enables the identification of undisturbed
grains. Subsequent Laue X-ray diffraction measurements
within these undisturbed grains and misorientation calculation of adjacent points reveal some noise below 0.58.
Possible continuous lattice bending, which does not evoke
sublimation etch grooves in the undisturbed grains, can be
ruled out by spatially referenced examination of misorientation data. Thus, the 0.58 data noise can be regarded as the
relative angular precision. In this study, we calculated the
misorientation angle of the c- and a-axes separately
between neighbouring measurement points. For the a-axis
measurements, we calculated the misorientation angle
between each a1 axis of neighbouring measurement points.
The other two axes, a2 and a3, were also calculated in this
way, but, since the ice crystal has six rotational symmetries
about the c-axis, we had to find the a-axes combinations to
minimize each of its misorientation angles.
Subgrain structure measurement
We adapted our Laue X-ray method to analyse subgrain
structures within ice crystals. We performed measurements
on a grid in individual ice crystals in a thin-section sample
(Fig. 5). The numbers of measurement points in grains A and
B, which have diameters of 4 mm, are 230 and 257,
respectively. When grains were near-perfect crystals, Laue
spots of each measurement point appeared at the same
position in the Laue diagram. On the other hand, when a
grain had some subgrain structures, we observed spots out of
position compared with adjacent points in each Laue figure.
Figure 6 shows a result of multilayered, superposed Laue
figures of all measurement positions in grains A and B. The
Laue spots of grain A exhibit the original shape of the X-ray
beam, i.e. Laue spots appear at the same position in all Laue
figures. There is a lack of crystal orientation changes within
this grain. Only some noise below 0.58 is observed (see
above). On the other hand, the Laue spots in grain B do not
retain the original shape of the X-ray beam. The spot position
in each Laue figure shifts slightly due to small changes in
crystal orientation, indicating subgrain structures such as a
subgrain boundary or continuous lattice bending.
Figure 7 shows an example of a misorientation angle
across a discrete subgrain boundary in a Dome Fuji
Miyamoto and others: Instruments and methods
Fig. 6. Multilayered Laue figures from grains A and B. The Laue images of the 230 measurements for grain A and the 257 measurements for
grain B are superposed. The stretching spots on Laue figure of grain B are evidence of Laue spots changing position with each measurement.
In fact, if we observe all Laue figures of grain B as an animation movie, we readily understand the movement of the spots as the crystal lattice
changes from point to point.
(Antarctica) ice-core sample, which was pre-localized using
an optical microscope and microstructure mapping technique (Kipfstuhl and others, 2006). This method provides a
qualitative possibility to distinguish between a distinct
subgrain boundary and continuous lattice bending. We can
observe subgrain boundaries as shallow sublimation
grooves compared with deep, high-angle grain boundary
grooves using the sublimation-etch method. The misorientation angle of the subgrain boundary in Figure 7 was
determined from the analysis along a line crossing the
subgrain boundary. The results indicate that the c-axis
orientation hardly changes, whereas the a-axes show a
misorientation angle. This crystal orientation relation across
the subgrain boundary shows 38 of rotation around the
c-axis. This novel result for natural polar ice can be
produced from the complete determination of several ice
crystal orientation measurements in reasonable time by our
semi-automated Laue X-ray diffraction method.
Further measurements show crystal orientation relations
on subgrain boundaries with rotations of 28 around one
a-axis (Fig. 8). We emphasize that these are the first
measurement results of the misorientation angle across
subgrain boundaries in ice-core samples. They reveal the
characteristics of the orientation relationship across a
discrete subgrain boundary such as the previously mentioned misorientation relationship for rotation around the
c-axis and one a-axis, and the orientation pattern on the
subgrain boundaries can be classified. Each result shows an
example of a twist boundary and a tilt boundary as the
subgrain rotation mechanism. This microstructure could not
be determined without the complete measurement of ice
crystal orientation on the subgrain boundaries. Detailed
analysis and novel statistics on subgrain boundary misorientations in natural Antarctic ice-core samples (EDML
(EPICA Dronning Maud Land) ice core) enabled by this new
Laue X-ray method, along with microstructure mapping, are
described by Weikusat and others (2011).
Our new Laue X-ray diffraction method is customized for
analysis of ice-core thin-section samples. It can measure full
crystal orientations (c-axis and a-axes) accurately. The
important improvements obtained with our new method are:
1. Complete determination of ice-crystal orientation, including a-axis.
2. Highly accurate measurements compared with traditional methods.
3. Application to standard-sized (100 mm 100 mm) thinsection samples to produce sufficient statistical results
and easy combination with standard methods such as
microstructure mapping.
4. Spatial resolution of 0.2 mm, which is less than the
grain-size scale of natural polar ice.
5. Relative angular resolution of 0.58, which is excellent
for grain statistics and below the hypothetical transition
between high-angle grain boundaries and subgrain
boundaries (Suzuki, 1970), relevant for substructure
6. Easy procedure. Each step, other than step 1, is
completely operable outside the cold laboratory.
7. Numerous data points to measure physical properties of
ice throughout the ice core, processed in a relatively
short time through semi-automatic measurements.
The application of this method for grain statistics and
subgrain studies will be a practical and powerful tool for
crystallographic study of ice-core samples. The combination
of our new method with microstructure mapping (Kipfstuhl
and others, 2006) is an important improvement. It is difficult
to observe subgrain boundaries between crossed polarizers
due to the expected low misorientation angles of less than a
Miyamoto and others: Instruments and methods
Fig. 7. Sample from the Dome Fuji ice core at 1975 m depth. The upper photo shows the grain with subgrain boundary, which was taken
using the microstructure mapping technique (Kipfstuhl and others, 2006). The subgrain boundary (sGB) can be observed as the faint black
line compared with the grain boundary. The white dots on the line indicate the measurement points. The lower graph shows the
misorientation angle between each adjacent measurement point. All measured orientations are plotted on the stereo net. The orientation of
the c-axis from each measurement point in the dotted open circle is almost unchanged, although the measurements are taken across the
subgrain boundary. The symbol ‘r’ indicates the rotation axis associated with this subgrain boundary. This is an example of rotation around
the c-axis on a subgrain structure.
few degrees on subgrain boundaries in ice, estimated by
grain-boundary energy measurements (Suzuki, 1970). Our
system will satisfy the demands of ice-core researchers such
as Kipfstuhl and others (2006, 2009), Hamann and others
(2007) and Weikusat and others (2009). Our goal is to make
additional improvements toward a fully automated X-ray
diffraction analysing system that will further facilitate and
accelerate microstructural measurements in ice.
Fig. 8. Sample from the same section as Figure 7. The sample depth is also 1975 m. This is an example of rotation around one a-axis on a
subgrain structure.
Miyamoto and others: Instruments and methods
This work was supported by Creative Scientific Research
(No. 14GS0202) from the Japanese Ministry of Education,
Science, Sports and Culture, by Grant-in-Aid for Scientific
Research (C) (No. 22540426) from Japan Society for the
Promotion of Science and by the German Science Foundation (DGF HA 5675/1-1). We thank S. Nakatsubo and
M. Ohi for technical advice and assistance, including the
design of the X-ray device and the shutter control instrument. We thank S. Horikawa for support on the Laue imagegrabbing program and A. Hori for support on X-ray
diffraction measurement. We express appreciation to all
members of the GRIP (Greenland) and Dome Fuji ice-core
drilling projects. We thank the scientific editor, T. H. Jacka,
and three anonymous reviewers for valuable comments and
suggestions which improved the manuscript.
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MS received 12 April 2010 and accepted in revised form 8 October 2010
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