Subgrain boundaries in Antarctic ice quantified by X-ray Laue
diffraction
Ilka WEIKUSAT,1 Atsushi MIYAMOTO,2 Se´rgio H. FARIA,3 Sepp KIPFSTUHL,1
Nobuhiko AZUMA,4 Takeo HONDOH2
1Alfred Wegener Institute for Polar and Marine Research, Columbusstrasse, D-27568 Bremerhaven, Germany
E-mail: ilka.weikusat@awi.de
2Institute of Low Temperature Science, Hokkaido University, Sapporo 060-0819, Japan
3GZG, Section of Crystallography, University of Go¨ttingen, Goldschmidtstrasse 1, D-37077 Go¨ttingen, Germany
4Department of Mechanical Engineering, Nagaoka University of Technology, 1603-1 Kamitomioka,
Nagaoka 940-2188, Japan
ABSTRACT. Ice in polar ice sheets undergoes deformation during its flow towards the coast.
Deformation and recrystallization microstructures such as subgrain boundaries can be observed and
recorded using high-resolution light microscopy of sublimation-edged sample surfaces (microstructure
mapping). Subgrain boundaries observed by microstructure mapping reveal characteristic shapes and
arrangements. As these arrangements are related to the basal plane orientation, full crystallographic
orientation measurements are needed for further characterization and interpretation of the subgrain
boundary types. X-ray Laue diffraction measurements validate the sensitivity of different boundary types
with sublimation used by microstructure mapping for the classification. X-ray Laue diffraction provides
misorientation values of all four crystal axes. Line scans across a subgrain boundary pre-located by
microstructure mapping can determine the rotation axis and angle. Together with the orientation of the
subgrain boundary this yields information on the dislocation types. Tilt and twist boundaries composed
of dislocations lying in the basal plane, and tilt boundaries composed of nonbasal dislocations were
found. A statistical analysis shows that nonbasal dislocations play a significant role in the formation of
all subgrain boundaries.
INTRODUCTION
Changes in the flow of the huge Antarctic ice sheet can
significantly influence sea-level rise and are a major cause of
uncertainty in the prediction of sea-level evolution (Solomon
and others, 2007). The basis of ice-sheet flow models is
Glen’s flow law (e.g. Huybrechts, 2007), a power law typical
for dislocation-creep controlled deformation describing ice
deformation on a macroscopic scale, but the actual physical
deformation or strain-rate controlling processes are not
reflected in this law (Alley and others, 2005). Rather, it is
extrapolated from creep experiments in the secondary creep
stage, although the stage at which the polar ice deforms is
not known.
The creep deformation of natural ice is governed by
dislocation dynamics, which is highly anisotropic at the
crystal scale. In the hexagonal ice Ih, the most common
dislocations are those gliding on the basal plane. Two more
glide-plane sets theoretically permitted by the hexagonal
symmetry are nonbasal planes providing glide on the
prismatic and pyramidal plane, but the peculiar behaviour
of dislocations (Hondoh, 2000) leads to the well-known
high anisotropy of the plasticity of ice: nonbasal deformation
of ice single crystals requires stresses at least 60 times larger
than those activating the basal slip (Duval and others, 1983).
Nonetheless, during extensive deformation by dislocation
creep of polycrystalline ice, four independent slip systems
are locally required (Hutchinson, 1977) in order to achieve
deformation compatibility at grain boundaries (GBs). Basal
glide only provides two independent slip systems, so
nonbasal glide has sometimes to be activated, at least
locally. This is accepted as the rate-limiting process under
high-stress conditions leading to a stress exponent n3 in
Glen’s flow law, but during the low-stress deformation of
polar ice sheets these processes are not yet clear (Montagnat
and Duval, 2004).
Although individual dislocations and their distribution
and dynamics have frequently been observed (e.g. Higashi
and others, 1988; Baker, 2003), slip system activity can only
be observed if dislocations (of the same type) occur
frequently enough to exert deformation. Well-developed
dislocation walls (subGBs) are easy to observe with optical
methods such as polarization methods (Durand and others,
2008) or microstructure mapping (Kipfstuhl and others,
2006). SubGB grooves have been proven to be typical
deformation-induced structures (Hamann and others, 2007)
and to occur frequently in a polar ice core (EDML; Weikusat
and others, 2009b). Remarkably, subGBs observed in such
high spatial resolution as provided by microstructure map-
ping reveal distinct characteristics in shape and arrangement
with respect to the c-axes orientations of the individual
crystals (Hamann and others, 2007; Weikusat and others,
2009): straight subGBs occur parallel to the basal plane
trace (intersection line of basal plane with the sectioned
observation plane), whereas zigzag-shaped substructures are
observed, typically in their main direction, showing high
angles to the basal plane and parallel to the basal plane in
their shorter segments (Fig. 1).
Full three-dimensional (3-D) crystal-orientation changes
across such typical subGBs were determined using X-ray
Laue diffraction (Miyamoto and others, 2011) in order to:
validate and specify the microstructure mapping images
and
Journal of Glaciology, Vol. 57, No. 201, 2011 111
further characterize the different types of grain substruc-
tures with respect to the high mechanic anisotropy of the
hexagonal ice crystal.
Here we present misorientation data and observations on
subgrain boundaries in natural polar ice.
METHODS AND MATERIAL
Samples were obtained from the EPICA (European Project for
Ice Coring in Antarctica) deep ice core from Dronning Maud
Land (EDML) and from one shallow core (B37), drilled
between 2003 and 2006 at Kohnen station (758000 S, 08400 E;
2892ma.s.l.), East Antarctica. The EDML drill site is located
on a flank 5 km from an ice divide with a horizontal flow
velocity at the surface of 0.76ma–1 (Wesche and others,
2007). Samples were stored at –308C after transportation at
–258C from Antarctica to Bremerhaven, Germany. Thin
sections from vertically cut samples (50100mm) were
prepared in a –258C cold laboratory in Bremerhaven using a
microtome according to standard procedures, but using
X-ray transparent plastic plates instead of glass plates.
Microstructure mapping (Kipfstuhl and others, 2006) was
performed in order to obtain an overview of the present
features under an optical microscope. This method uses
sublimation as an etching technique to visualize GBs as
grooves at a very high spatial resolution (one-pixel edge
3.3 mm). A distinction between high-angle GBs and small-
angle subGBs is associated with a discontinuity in the
boundaries’ properties (e.g. Gottstein and others, 1999), so
here the different sublimation behaviour (Saylor and Rohrer,
1999) can be used to distinguish between deep grooves, i.e.
dark GBs, and shallower grooves, i.e. grey subGBs (Kipfstuhl
and others, 2006; Hamann and others, 2007; Weikusat and
others, 2009b). Typical examples of such structures were
selected, and crystal orientations were measured by means
of X-ray Laue diffraction (Miyamoto and others, 2005, 2011).
In total, 83 grains in samples from 15 different depths
(115–2702m) from Holocene ice to marine isotope stage 6
(MIS6) or even MIS7? ice (Ruth and others, 2007) were
measured and 240 individual subGBs were characterized.
RESULTS
Validation of microstructure mapping
Microstructure mapping reveals grooves along lattice mis-
orientation boundaries, which were qualitatively validated
using crossed polarizers additionally to the sublimation
technique (e.g. fig. 4 in Wang and others, 2003; fig. 6 in
Kipfstuhl and others, 2006). However, a high-resolution
crystallographic technique can quantitatively verify the
misorientations. Misorientation angles, , across GBs have
Fig. 1. Schematic description of subGB types described by Hamann
and others (2007) and Weikusat and others (2009a,b). Modified
after figure 7a in Weikusat and others (2009b). Note: as the crystal
orientation data are taken as line scans (1-D track), the z-type
subGB is classified either as normal or as parallel, depending on the
very local subGB segment, where the X-ray Laue line scan crosses
the subGB.
Fig. 2. Misorientation data across GBs (2365.8m depth). (a) Microstructure mapping image with track of orientation measurements (white
circles). Dark thick black lines: GBs. Thin lines: subGBs. GB grooves from the lower surface of the thin section are visible as unfocused lines,
indicating inclination of GBs in three dimensions. (b) Misorientations between neighbouring points calculated from X-ray Laue
measurements. (b) is placed according to (a), i.e. y=0mm is equal with lowest white circle in (a). Insert shows detail of (b) with different
scale of misorientations axis. (c) Stereographic projection of c-axes (box symbols) and a-axes (circle symbols) to illustrate the general
orientation of the centre grain. The basal plane is the great circle formed by the three a-axes.
Weikusat and others: Subgrain boundaries in Antarctic ice112
been measured (Fig. 2) and, as expected, show c-axes
misorientations ranging from a few degrees to almost 908.
Whether all structures are revealed by microstructure
mapping can be demonstrated by observing the orientations
within ‘clean’ grains without any sublimation substructures
visible with the optical microscope (Fig. 3). Such undis-
turbed grains or grain parts reveal only some noise below
0.58, which can thus be regarded as the angular resolution of
the misorientation measurements.
Subgrain boundaries
SubGBs appear as shallow grooves (thin grey lines) in the
microstructure mapping image due to the sublimation
behaviour depending on its misorientation angle (Saylor
and Rohrer, 1999). Indeed, X-ray Laue orientation measure-
ments reveal higher misorientations at deep sublimation
grooves (GBs) compared to shallow sublimation grooves
(subGBs) (Fig. 2b and insert). Frequencies of misorientations
measured across such thin sublimation features are given in
Table 1. It is remarkable that a high fraction (42%) of subGBs
cannot be detected by their c-axis misorientations (c<0.58)
and that only a few subGBs have misorientations >38.
A correlation of subGB misorientation angles with grain
microstructure data (grain size, grain aspect ratio, grain
irregularity, grain elongation direction) cannot be observed.
The orientation of c-axes (angle between the vertical core
axis as overall main compression direction and the c-axes)
cannot be correlated with misorientation angles.
Another important observation regarding subGBs is their
preferred occurrence close to GBs, and especially close to
peculiar shapes of GBs: for example, subGBs typically show
up at the outside of smoothly curved GBs (Weikusat and
others, 2009b), but they are frequently also directly attached
to edges or necking GBs.
Subgrain boundary types
For 70% of all subGBs, misorientation in c- or a-axes was
high enough to be detected. Examining the misorientations
of c- and a-axes separately (e.g. c and a in Figs 2b and 3b)
enables an immediate recognition of the misorientation
rotation axis. Observed configurations of misorientations,
shown schematically in Figure 4, are:
Arbitrary misorientation rotation axis: The rotation axis is
not (close to) a crystallographic axis, so none of the four
calculated misorientations of the crystallographic axes is
particularly low (Fig. 4a; for an example see Fig. 5). This
is the case for 23% of all subGBs with a detectable
misorientation
c-axis is (close to) misorientation rotation axis: The
misorientation of the c-axis is significantly lower (i.e. 0
within measurement accuracy) than those of the a-axes
(Fig. 4b; for an example see Fig. 6) in 8% of the
subGBs.
One a-axis is (close to) misorientation rotation axis: The
majority (70%) of all subGBs with misorientation >0.58
show misorientation of one a-axis significantly lower (i.e.
0 within measurement accuracy) than those of the other
three crystal axes (Fig. 4c; for an example see Figs 7
and 8).
Characteristic subGB types discovered with microstructure
mapping (Hamann and others, 2007; Weikusat and others,
2009a,b) can be summarized by their basic arrangement
(Fig. 1):
normal to the basal plane: either of long and straight
shape (n-type; Fig. 1) like the classical conception of a
grain undergoing polygonization (Nakaya, 1958; Alley
and others, 1995, fig. 2) or rather short as segment of
irregularly zigzag or step-like shaped subGB (z-type;
Fig. 1).
parallel to the basal plane: straight shallow sublimation
grooves (p-type; Fig. 1), typically occurring in peculiar
swarms of multiple subGBs parallel to each other.
(Although some segments of irregularly zigzag-shaped
subGB can also be parallel to the basal plane (z-type;
Fig. 1), the normal segments are typically the dominant
features.)
Fig. 3. Misorientation data within a sublimation feature-free grain
(454.8m depth). (a–c) as in Figure 2. Misorientations among
neighbouring points within the centre grain are less than 0.58, the
angular resolution.
Table 1. Frequencies of misorientations across shallow sublimation
grooves (total number of subGBs measured: n 240)
Misorientation Frequency
c-axes a-axes
8 % %
<0.5 42 36
0.5–1 28 32
1–2 17 22
2–3 8 6
3–4 4 4
4–5 1 1
Weikusat and others: Subgrain boundaries in Antarctic ice 113
no particular arrangement with the basal plane: typically
bowed smooth shapes resembling GBs (Fig. 1), but as
shallow sublimation grooves.
The observation of these characteristic arrangements with
respect to the crystallography of the crystal is in accordance
with observations from X-ray diffraction topography on
laboratory-grown ice single crystals shown as an example in
Figure 9: higher dislocation densities accumulated in planes
normal to the basal plane (Fig. 9a), and higher-dislocation-
density regions developed parallel to the basal plane
(Fig. 9a–c). Figure 9e reveals complex interaction of such
planes in basal and in prismatic orientation leading to a
zigzag arrangement (Fig. 9d). The similarity in arrangement
of subGB and higher-dislocation-density regions with
respect to the crystallography of ice suggests that the
formation processes are related or rely on similar mechan-
isms. The regions of possible subGB formation may be pre-
established by the observed variations in dislocation density.
Among the regions of high dislocation density, only some
develop further by accumulating more dislocations and only
those with highest energy are revealed by sublimation,
leading to the peculiar step-shaped subGB groove. Details
on X-ray diffraction topography method and further images
of local variations in dislocation density are provided by
Higashi and others (1988).
Combining the information on misorientation rotation
axes and arrangement with respect to the basal plane gives
additional information to characterize subGBs (Table 2).
Boundaries arranged normal to the trace of the basal plane
are not further distinguished here into n-type and z-type,
because X-ray Laue measurements are collected as one-
dimensional (1-D) line scans, so misorientation measure-
ments cross the z-type boundaries at the typically longer part
which is normal to the basal plane trace. All basal-plane
normal subGBs, where a misorientation axis close to the
crystal axes could be determined, originate from rotations
around one a-axis (Table 2; example in Fig. 7), whereas basal-
plane-trace parallel subGBs with a rotation axis close to the
crystallographic directions can be divided into two types:
(1) originating from a rotation around one a-axis (example in
Fig. 8) and (2) originating from a rotation around the c-axis
(example in Fig. 6). Approximately one-third of all subGBs
cannot be classified easily either by their arrangement or by
their rotation axis. Remarkably, no boundary normal to the
basal plane and rotated around an a-axis was observed.
Fig. 4. Rotation axes generating different configurations of misorientation. (a) Schematic of two crystals rotated around an arbitrary axis with
respect to each other (left) and the two corresponding systems of crystal axes showing all misorientation angles (right). (b) Schematic of two
crystals oriented to each other by rotation around the c-axis (left) and the two corresponding systems of crystal axes, with c being normal to
the image plane, showing all misorientation angles (right). (c) Schematic of two crystals misoriented by rotation around one a-axis (left) and
the two corresponding systems of crystal axes, with a1 being normal to the image plane, showing all misorientation angles (right). (d) Crystal
axes with schematic crystal.
Table 2. Absolute number frequencies of all subGBs with detectable
misorientations (>0.58; n=165)
SubGB arrangement Misorientation rotation axis
c-axis a-axis Arbitrary
Basal-plane normal (n- and z-type) 0 65* 14
Basal-plane parallel (p-type) 11{ 45{ 14
No particular arrangement to basal plane 1 7 8
*Tilt boundary with dislocations in the basal plane (Fig. 7).
{Twist boundary with dislocations in the basal plane (Fig. 6).
{Tilt boundary with dislocations in a nonbasal plane (Fig. 8).
Weikusat and others: Subgrain boundaries in Antarctic ice114
DISCUSSION
Observations of the expected high misorientations across
GBs, low misorientations across subGBs and the very low
fluctuations within undeformed grains free of sublimation
features verify that all subGBs are revealed by sublimation
used for microstructure mapping. The observation that
shallowest sublimation grooves can be observed reliably
with microstructure mapping, but have very small misor-
ientations (<0.58), proves microstructure mapping is an
extremely sensitive method to visualize very small lattice
misorientations.
Implications on energies of subgrain boundaries
An easy correlation of groove depth, i.e. grey value in the
microstructure mapping images, could not be found,
however, probably because of other factors influencing the
sublimation, such as the angle between boundary plane and
section surface: the optimal thermal grooving (Mullins,
1957) can be obtained if the boundary is perpendicular to
the surface, whereas an oblique intersection of boundary
and surface produces oblique grooves which do not achieve
the maximum possible depth. Furthermore, GB thickness
generally varies with impurities (e.g. Barnes, 2003) which
are not considered in this study. Nevertheless, the definite
difference in groove depth between GBs and subGBs
indicates an abrupt transition in the sublimation behaviour
due to GB energy.
Measurements of GB energies for ice are available for
larger misorientation boundaries (Suzuki, 1970). However,
our observations allow some discussion of GB energies for
small-angle boundaries, because the thermal-etching groove
depth, i.e. surface dihedral angle of the groove,  S, depends
on the ratio of GB energy, , and surface energy, S (Saylor
and Rohrer, 1999),

s
¼ 2 cos  s
2
, ð1Þ
assuming that the surface energy is isotropic. The GB energy,
, of a small-angle grain boundary is in turn correlated to the
misorientation angle,  (Read and Shockley, 1950; Hirth and
Lothe, 1982):
 ¼ 0ðA ln Þ, ð2Þ
with 0 and A depending on the character and orientation of
the boundary and the form of the dislocation arrangement
(shear modulus, Burgers vector and Poisson ratio; core
parameters of dislocation sets). We observed that very low 
(<0.58) produces thermal grooves, requiring that  has a very
steep slope in the  –  space in this range, i.e. GB energy is
low only for tiny misorientations (<0.18) and reaches a
certain critical-threshold GB energy, C, to produce grooves
at low misorientations. It can thus be predicted that a very
fast increase in GB energy should occur in the lower
misorientation range, which is consistent with the estimated
development for smallest values of  by Suzuki (1970).
Using the dislocation spacing, D, derived by Frank’s
formula (Humphreys, 2004),
b
D

  2 sin 2
 
, ð3Þ
with b being the Burgers vector of the dislocation (4.52 A˚ for
basal dislocations and 7.36 or 8.63 A˚ for nonbasal disloca-
tions), and the energy of single dislocations
d  G b
2
2
ð4Þ
with G being the shear modulus (4 109Nm–2), an upper
bound of the energy of a subGB can be estimated:
  d
D
: ð5Þ
For the measured typical misorientations (0.5–38) for bound-
aries with dislocations in the basal plane, the estimated
values for  range from 8 to 47mJm–2. This is about 8–50%
of the energy usually assumed for high-angle grain bound-
aries in ice (65mJm–2 (Hobbs, 1974, p. 440) and 60–
100mJm–2 (Suzuki, 1970)). Highest misorientations of 58
were observed across shallow sublimation grooves showing
the classical tilt geometry with edge dislocations in the basal
plane. These boundaries have energies, , of 79mJm–2
which is well within the range of high-angle grain bound-
aries. Misorientations for boundaries with dislocations on
nonbasal planes range from 0.58 to 48, but their energy has
to be estimated significantly higher (3–90mJm–2) due to the
larger Burgers vector of c or c+ a dislocations. This finding is
Fig. 5. Misorientation data across two subGBs highlighted in white
(1855.9m depth). (a–c) as in Figure 2. Left subGB has misorien-
tation below the detection limit. Right subGB has no particularly
low misorientation in the c- or one a-axis. (d) Misorientation with
respect to the leftmost measurement point in a at x=0mm shows a
gradient in misorientation and a significantly low value in one axis
despite the arbitrary rotation axis close to the subGB.
Weikusat and others: Subgrain boundaries in Antarctic ice 115
supported by subGB energy estimates using Equation (2): as
well as larger Burgers vectors, the angle of the boundary
with the basal plane is included in this estimation (Read and
Shockley, 1950), causing higher  values for boundaries with
dislocations on nonbasal planes (10–20%) than for other
subGB types. The GB–subGB geometry in Figure 8 indeed
seems to indicate a higher energy than expected for a
subGB: the dihedral angles appear almost equilibrated for
boundaries of similar energy. This finding is common with
the strongest parallel subGB grooves with rotation around
one a-axis. From the boundary energy estimates and the
observations on groove depth, we can expect that the
subGB–GB threshold angle is 4–58 for boundaries with basal
dislocations, but close to 38 for boundaries with nonbasal
dislocations. Note that the estimations using Equations (2)
and (5) give upper bounds of GB energies considering stable
states of dislocation walls. However, most cases observed
during this study probably represent unstable states with
even higher energies than those estimated here.
The sudden transition in the sublimation behaviour of
GBs and subGBs is due to different boundary structures of
GB and subGB: subGBs are strictly periodic crystal
dislocation arrangements which minimize the GB energy.
In GBs dislocation cores tend to overlap and to lose their
identity as individual lattice defects (Gottstein and
Shvindlerman, 1999). The observation of strong, regular
and deep etch grooves from misorientation 4–908
indicates a similar structure for all grain boundaries,
whereas the appearance variability of subGBs may be due
to a multitude of boundary types (e.g. tilt boundaries and
twist boundaries) which are expected to have different
energies, apart from misorientation differences. For instance,
Equation (2) is strictly valid only for one-dislocation set tilt
boundaries with small misorientation angles.
Implications on dislocation types
Although the actual characteristic structures of dislocations in
ice are very peculiar and rather complicated (Hondoh, 2000),
Fig. 6. Misorientation data across several subGBs parallel to the basal plane trace (1855.9m depth). (a–c) as in Figure 2. Multiple subGBs at
x<2mm cannot be resolved due to the spatial resolution. The misorientation across subGB at x=10mm shows that the c-axis has a
significantly lower value than the three a-axes. (d) Schematic illustration of the configuration of a rotation around the c-axis assuming a
dislocation wall composed of screw dislocations lying in the basal plane. This configuration describes a twist boundary comprising two sets
of screw dislocations in the basal plane with Burgers vectors b ¼ a.
Weikusat and others: Subgrain boundaries in Antarctic ice116
the combined information on misorientation rotation axes
and arrangement with respect to the basal plane allow basic
inferences regarding the activity of different dislocation types.
Basal tilt boundary: A dislocation wall accumulating
dislocations normal to the basal plane and a resulting
rotation around one a-axis can be produced by an array
of basal edge dislocations with Burgers vector b= a
(Fig. 7d). The vast majority of all measured subGBs
perpendicular to the basal plane are indeed mainly
composed of basal edge dislocations, and thus are basal
tilt boundaries (Table 2).
Fig. 7. Misorientation data of a subGB normal to the basal plane trace (655.9m depth). (a–c) as in Figure 2. One a-axis has a significantly
lower misorientation value than the other three axes across the subGB (x =2.25mm). (d) Schematic illustration of the configuration of a
dislocation wall composed of edge dislocations perpendicular to the basal plane indicated by ‘T’ and the rotation axis, a1. This configuration
describes a tilt boundary comprising edge dislocations in the basal plane with Burgers vector b ¼ a.
Fig. 8. Misorientation data of a subGB parallel to the basal plane trace (1204.1m depth). (a–c) as in Figure 2. One a-axis has a significantly
lower value than the other three axes across the subGB (x=1.75mm). (d) Schematic illustration of the configuration of a dislocation wall
composed of edge dislocations parallel to the basal plane indicated by ‘T’ and the rotation axis, a1. This configuration describes a tilt
boundary comprising dislocations in a nonbasal plane with Burgers vector b ¼ c or b ¼ c þ a.
Weikusat and others: Subgrain boundaries in Antarctic ice 117
Basal twist boundary: A dislocation wall parallel to the
basal plane and a resulting rotation around the c-axis can
be produced by two sets of basal screw dislocations with
Burgers vectors b= a (Fig. 6d). Only 16% of all
measured parallel subGBs are basal twist boundaries
(Table 2).
Nonbasal tilt boundary: A dislocation wall accumulating
dislocations parallel to the basal plane and a resulting
rotation around one a-axis can be produced by an array
of nonbasal edge dislocations with Burgers vector b= c
or b= c+ a (Fig. 8d). X-ray diffraction topographs using
different diffraction vectors ([0110] and [0002]) confirm
the occurrence of walls mainly consisting of dislocations
with the Burgers vector b= c (Fig. 9b and c). More than
half of all measured parallel subGBs are nonbasal tilt
boundaries (Table 2).
The observations of this study and the interpretation given
above led to the theoretical considerations by Hondoh
(2009).
One-third of all subGBs measured here cannot be
specified regarding a dominant activity of dislocation types,
and thus are probably mixed boundaries composed of mixed
dislocations, which is usually considered to be the typical
appearance of dislocations (e.g. Hull and Bacon, 1984;
Weertman andWeertman, 1992). However, as only a limited
amount of subGBs could be measured with the semi-
Fig. 9. X-ray diffraction topographs (for method description see Higashi and others, 1988) from laboratory-grown ice single crystals. Grey-
value contrasts indicate variations in dislocation density and in configuration of dislocations and in direction of the diffraction vector, g.
Orientation of c-axes is identical in all five images (vertical). The direction of the diffraction vector g is given. (a) Stable walls of higher
dislocation density normal to the basal plane (upper rim of plane indicated by dotted line and white arrows) and stable walls of higher
dislocation density parallel to basal plane (black arrow indicates a strong example of many more horizontal dislocation walls). (b) Stable
dislocation wall parallel to basal plane exhibited as a horizontal dark band indicated by arrows (diffraction vector is [0110]). (c) X-ray
topograph of the same crystal as (b), but with diffraction vector [0002]. The same dislocation wall indicated by the arrows in (b) displays a
strong band here, which shows that this wall consists mainly of dislocations with the Burgers vector b= c. (d) Zigzag structure of regions of
higher dislocation density. (e) Interacting walls parallel to basal (black arrows) and prismatic planes (white arrows).
Weikusat and others: Subgrain boundaries in Antarctic ice118
automatic X-ray Laue diffraction method and the obvious
typical types (normal and parallel) may have been favoured
unintentionally, the subGBs with no particular shape and
arrangement, i.e. mixed boundaries, might be under-repre-
sented in this study. However, the finding that among the
typical subGB types the almost pure nonbasal tilt boundary is
the second frequent boundary type together with the basal tilt
boundary indicates that nonbasal edge dislocations cannot
be neglected concerning the deformation around EDML.
CONCLUSIONS
X-ray Laue diffraction validates and quantifies the occur-
rence of sublimation grooves along GBs and subGBs
observed with microstructure mapping. Misorientation val-
ues of subGB in natural ice range from <0.58 to 48.
A combination of full crystallographic analyses and
geometrical information enables subgrain boundary types
to be identified. Basal tilt boundaries composed of basal
edge dislocations (b= a) have been found as basal-plane
normal features caused by a rotation around one a-axis,
which describes a symmetric bending of the basal plane.
Basal twist boundaries composed of sets of basal screw
dislocations (b= a) could be identified as basal-plane paral-
lel features caused by a rotation around the c-axis, which
describes a rotation of basal planes above each other.
Geometries of subGB as basal-plane parallel features caused
by a rotation around one a-axis, which describes a bending
of pyramidal or prism planes, can be interpreted as nonbasal
tilt boundaries comprising edge dislocations on nonbasal
planes (b= c or c+ a).
Boundary energies estimated using the measured mis-
orientation angles and characteristics of the dislocation
types give values of 8–90mJm–2. Note that the highest
boundary-energy values, which are within the range of high-
angle grain boundaries, are obtained with nonbasal tilt
boundaries. Due to this finding, the threshold angle for GB–
subGB transition can be expected to be less for nonbasal
boundaries (38) than for basal boundaries (4–58).
The combination of X-ray Laue diffraction and micro-
structure mapping shows that nonbasal tilt boundaries and
thus nonbasal edge dislocations are frequent subGBs and
should not be neglected for the deformation under low-stress
deformation of the Antarctic ice sheet in Dronning
Maud Land.
ACKNOWLEDGEMENTS
This project was funded by the German Science Foundation
(DFG HA 5675/1-1 and WE 4695/1-2) and supported by
travel grants in the framework of a cooperation agreement
between the German Science Foundation (DFG) and the
Japanese Society for the Promotion of Science. This work is a
contribution to the European Project for Ice Coring in
Antarctica (EPICA), a joint European Science Foundation/
European Commission scientific programme, funded by the
EU and by national contributions from Belgium, Denmark,
France, Germany, Italy, the Netherlands, Norway, Sweden,
Switzerland and the United Kingdom. The main logistic
support was provided by Institut Polaire Franc¸ais–Emile
Victor (IPEV) and Programma Nazionale di Ricerche in
Antartide (PNRA) (at Dome C) and the Alfred Wegner
Institute (at Dronning Maud Land). This is EPICA publication
No. 273. We thank P. Duval and D. Samyn for helpful
comments and discussion.
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MS received 12 April 2010 and accepted in revised form 31 August 2010
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