Microstructures provide key insights into understanding the mechanical behavior of ice. Crystallographic preferred orientation (CPO) develops during plastic deformation as ice deforms dominantly by dislocation glide on the basal plane, modified and often intensified by dynamic recrystallization. CPO patterns in fine-grained ice have been relatively well characterized and understood in experiments and nature, whereas CPO patterns in “warm” (
Ice sheets and glaciers play crucial roles in Earth's climate system, and understanding their dynamic behavior is essential for a variety of predictive purposes, including making projections of glacier and ice sheet discharge and sea level rise (e.g., Bindschadler et al., 2013; Faria et al., 2014b; Dutton et al., 2015; Golledge et al., 2015; Bamber et al., 2019). In addition, glacial ice is a monomineralic rock that deforms at high homologous temperatures as ice flows, and glaciers represent natural tectonic systems that undergo the equivalent of regional high-grade metamorphism under known driving forces (Hambrey and Milnes, 1977; Van der Veen and Whillans, 1994). Similar to rocks in active orogens, flowing glacial ice develops both structures and crystallographic fabrics or crystallographic preferred orientations (CPOs) that reflect the conditions and kinematics of deformation. Studying the internal structure of glaciers on the crystal scale provides key insights into ice mechanics and aids in the understanding of tectonic processes (Hambrey and Milnes, 1977; Hooke and Hudleston, 1978; Faria et al., 2014b; Wilson et al., 2014; Hudleston 2015).
Quantifying flow behavior of ice under natural conditions is essential for the accurate incorporation of glacier flow into climate models and for using ice as an analog for high-temperature deformation of crustal and mantle rocks (Hambrey, 1997; Wilson, 1981; Faria et al., 2014b; Wilson et al., 2014). Glaciers move by two gravity-driven processes: (1) frictional sliding (including deformation of underlying sediments) of the ice mass over the underlying rock surface (e.g., Flowers, 2010, and references therein) and (2) slow, continuous creep (flow) within the ice mass itself (e.g., Glen, 1955; Alley, 1992; Budd and Jacka, 1989; Cuffey and Paterson, 2010). Creep is governed by thermally dependent, micro-scale deformation processes and therefore participates in important thermo-mechanical feedbacks in the Earth's cryosphere, atmosphere and oceans. This is especially important because of the highly non-linear dependence of strain rate on stress (Glen, 1955; Budd and Jacka, 1989; Bons et al., 2018).
Terrestrial glaciers, ice sheets and ice shelves comprise crystals of hexagonal ice (Ih; Fig. 1a; Pauling, 1935; Faria et al., 2014b). As ice deforms plastically during flow, anisotropy in the form of a CPO develops due to a dominance of intracrystalline glide on the basal plane, and this is modified by recrystallization (Weertman, 1983; Duval et al., 1983; Faria et al., 2014b). Similarly to other crystalline materials, such as rocks (e.g., Wenk and Christie, 1991), CPO development modifies the internal flow strength (e.g., Steinemann, 1958; Lile, 1978; Pimienta and Duval, 1987; Alley, 1988, 1992; Azuma and Azuma, 1996; Gagliardini, 2009), and thus documenting natural ice CPOs provides insight into the large-scale flow rates of glaciers and ice sheets (e.g., Azuma, 1995; Azuma and Azuma, 1996; Faria et al., 2014b; Montagnat et al., 2014; Llorens et al., 2016a; Vaughan et al., 2017). The CPO of ice is commonly represented by the preferred orientation of
Schematic image showing
Coarse-grained (highly variable but typically
We aim to (1) better quantify the CPO patterns (
Much of the preexisting research on CPO development in natural ice has been done on ice cores from Antarctica and Greenland, and this has been nicely summarized by Faria et al. (2014a). Schytt (1958) produced the first microstructural study of deep polar ice from the ice core extracted from the Norwegian–British–Swedish Antarctic Expedition of 1949–1952. Many studies of ice cores have been subsequently undertaken, in both Antarctica (Gow and Williamson, 1976; Lipenkov et al., 1989; EPICA community members, 2004; Seddik et al., 2008; Durand et al., 2009; Weikusat et al., 2009b, 2017; Azuma et al., 1999, 2000) and Greenland (Herron and Langway, 1982; Herron et al., 1985; Langway et al., 1988; Thorsteinsson, 1997; Gow et al., 1997; Wang et al., 2002; Svensson et al., 2003b; Montagnat et al., 2014). Studying microstructures in ice sheets offers the advantages of examining an extensive record of ice deforming under relatively simple kinematic conditions. As a result, CPOs in ice caps have been well defined and interpreted from ice cores, except perhaps at the base of ice sheets.
There are two typical end-member
Under simple shear conditions, the basal planes of ice crystals dominantly align with the shear plane, and the
An enigmatic CPO pattern can develop in valley glaciers and deep in ice sheets in coarser-grained ice that has undergone significant recrystallization. This pattern is always associated with warmer (
Previous studies of coarse-grained ice in valley glaciers done by Rigsby (1951) on Emmons Glacier, Kamb (1959) on Blue Glacier and Jonsson (1970) on Isfallsglaciären used light optical measurements to delineate a CPO characterized by a multimaxima pattern of the type described above but were limited to measuring
Possible analogs to the multimaxima CPOs found in nature have been produced in experiments by Steinemann (1958) and Duval (1981), in both cases at temperatures near the melting point and under torsion–compression conditions. The maxima developed at high angles to the shear plane. It should be noted, however, that the grain size in the experiments is much smaller than in natural ice with these CPOs.
Ice with the multimaxima CPO in valley glaciers (Rigsby, 1951; Meier et al., 1954; Kamb, 1959; Higashi, 1967; Jonsson, 1970; Fabre, 1973; Vallon et al., 1976; Tison and Hubbard, 2000; Hellmann et al., in review) and deep in ice sheets (Gow and Williamson, 1976; Matsuda and Wakahama, 1978; Russell-Head and Budd, 1979; Gow et al., 1997; Diprinzio et al., 2005; Gow and Meese, 2007; Montagnat, 2014; Fitzpatrick et al., 2017; Li et al., 2017) consists of large, branched crystals that lack undulose extinction and have irregular, lobate grain boundaries (Figs. 2a and 3). Individual grains are so large that even with the maximum-size thin section (using any method of analysis), the exact shape and extent of individual grains remain unknown. Additionally, the branching nature of these crystals may result in sectioning artifacts that lead to apparent “island grains” – branches of the same grain appearing multiple times throughout one 2D thin section (Fig. 3; e.g., as illustrated in glacial ice by Bader (1951) and Rigsby (1968), in sea ice by Dempsey and Langhorne (2012), and in quartz by Stipp et al. (2010)). Without a complete crystal orientation – one that includes ice
A number of interpretations have been proposed for the multimaxima CPOs, though it is clear that there is no single explanation that can be applied to all cases. Earlier studies made efforts to quantify an angular relationship between clusters of
A number of previous studies have proposed that recrystallization dominated by grain boundary migration results in the multimaxima CPOs (Rigsby, 1955; Gow and Williamson, 1976; Gow et al., 1997; Duval, 2000; Diprinzio et al., 2005; Gow and Meese, 2007; Montagnat et al., 2014). While dynamic recrystallization likely plays an important role, these studies do not provide an interpretation as to why recrystallization results in the geometrically spaced clustering of
We argue that previously employed methods have most probably not been able to clearly determine a representative CPO for glacial ice consisting of coarse, branching crystals. Optical studies using the Rigsby stage, such as those illustrated in Fig. 2, which accommodates
Three methods – etching (Matsuda, 1979; Matsuda and Wakahama, 1978), semi-automated Laue diffraction (Miyamoto et al., 2011; Weikusat et al., 2011) and EBSD (Dingley, 1984; Prior et al., 1999) – enable the measurement of full crystallographic orientations in ice (Obbard et al., 2006; Obbard and Baker, 2007; Weikusat et al., 2017; Kim et al., 2020). Etching is time-intensive, and the results are of low angular resolution. The other two methods produce results of high angular resolution. Laue X-ray diffraction has been applied as a spot-based method, while EBSD provides the orientation of every pixel measured.
Cryo-EBSD as a technique was first applied to ice in 2004 (Iliescu et al., 2004), and modern cryo-EBSD methods enable routine work on water ice (Prior et al., 2015). CPOs derived from EBSD datasets include
Storglaciären is a small polythermal valley glacier located in the Tarfala Valley in northern Sweden (Fig. 4). The glacier is 3.2 km long, extending in an E–W direction, with a total surface area of 3.1
Simplified map of Storglaciären highlighting the traces of structural elements and orientations of foliation and bedding for the north margin, south margin and center of the glacier in the ablation zone. Locations of samples SG6-B, SG23, SG27 and SG28 are labeled. The orientation diagrams of planar fabric elements (stratification and foliation) are in geographic coordinates. The sample reference frame for the remainder of the paper is represented, where
Primary stratification is easily identified above the equilibrium line on the glacier as gently undulating layers roughly parallel to the ice surface. The ice in Storglaciären undergoes horizontal compression and shortening as it enters the valley from the accumulation cirques, and this amplifies the slight undulations in primary stratification, causing upright, similar folds (Ramsay, 1967) near the margins of the valley (walls) where shearing, which combines with shortening, is most intense. Folds range from a centimeter to meter amplitude and generally have axial surfaces that are vertical near the margins and contain the flow direction. They are associated with an axial planar foliation and have hinges that plunge gently west, away from the flow direction. Foliation develops from preexisting stratification, veins and fracture traces where shear is most intense (e.g., Hambrey, 1975; Roberson, 2008; Jennings et al., 2014) and is defined by variations in crystal size, shape, and bubble concentration and distribution (e.g., Allen et al., 1960; Hambrey, 1975; Hambrey and Milnes, 1977; Hooke and Hudleston, 1978). Foliation tends to become perpendicular to the maximum shortening direction and thus rotates with progressive shear towards parallelism with the flow direction along the glacier margins (Fig. 4; Ragan, 1969), reflecting cumulative strain (Hambrey and Milnes, 1977; Hooke and Hudleston, 1978; Hambrey et al., 1980; Hudleston, 2015).
Detailed mapping in 2016 and 2018 on the surface of the glacier provides the structural framework for this study. Data collection was focused on multiple transects across the glacier in the ablation zone. Relevant data, presented in Fig. 4, highlight the relationship of the structures to one another and the known kinematics.
We collected samples from eight areas of intense deformation in the ablation zone during the 2018 field season. For the purposes of this paper, we are focusing on three samples from the intensely sheared southern margin (SG23, SG27 and SG28) (Fig. 4) because they are from a small area with well-defined kinematics. The other samples collected in 2018 were spread out across the glacier in various and more complex local settings and were not clustered in such a way that data could be combined for a strong interpretation, and thus they do not contribute to the arguments we present here. We excavated 100–200
We prepared samples for EBSD mapping and microstructural analysis in a cold room (
The sample preparation procedure is highlighted in Fig. 5. We initially cut each sample block into three 50
We note that there are associated errors of misorientation with each step. We consider the process in several stages. Each sample is first squared into a rectangular prism, with one side vertical and another parallel to foliation, using guides to ensure perpendicularity. Guides are then used for each of steps 1–4 (Fig. 5), cutting the sample progressively into slabs, rods, cubes and slices. The errors involved in each stage of this process are estimated to be less than 0.5
Whole sections of certain areas of the original blocks were prepared for examination, to mitigate loss of information on internal structure due to the small slices for the composite sections. Slabs cut perpendicularly to foliation (first step in composite preparation) were polished using progressively finer sandpaper, allowed to sublimate overnight and then illuminated using low-angle light, which revealed grains intersecting the surface. Areas of interest in these slabs were targeted for whole section analysis. At least two whole sections were taken from each sample.
It is important to note that the copper and aluminum ingots on which the samples were mounted were up to
A typical whole section EBSD analysis with
EBSD maps and associated CPOs for composite sections from samples SG23, SG27 and SG28. Data from each pair of composites are combined to give the bulk CPO for each sample.
A Zeiss Sigma variable-pressure field-emission-gun SEM fitted with a Nordlys EBSD camera from Oxford Instruments was used for cryo-EBSD analyses. The instrument is fitted with a custom-built cryo-stage that is continuously cooled by liquid nitrogen from an external dewar via a copper braid connection (Prior et al., 2015). The stage is cooled to below
We collected full cross-sectional-orientation maps of whole sections (e.g., Fig. 6a and b) and composite sections (e.g., Fig. 7a) at a
EBSD data were collected using Aztec Software from Oxford Instruments and exported into Oxford HKL Channel 5. We used EBSDinterp 1.0, a graphic-user-interface-based MATLAB® program developed by Pearce (2015) to reduce noise and interpolate non-indexed EBSD data points using band contrast variations. Noise-reduced data were then processed using MTEX, a texture analysis toolbox for MATLAB® (Bachmann et al., 2010), to determine full crystallographic orientations, intergranular misorientations and grain boundaries and to calculate one-point-per-grain CPO plots (Mainprice et al., 2015). The overall CPO in our samples is best represented using one-point-per-grain plots rather than all-pixel orientation plots due to the area bias introduced by larger grains in a small sample size. We note that representing the data using all-pixel orientations does take into account the issue of parent grains with satellite island grains, but this is only if the sample is large enough to contain a sufficient number of grains to provide a truly representative CPO (Appendix A). If the sample does not contain a representative number of grains, as is often the case with coarse-grained ice, then using one point per grain provides a more representative CPO (Fig. A1). The kinematic reference frame used for plotting CPO is shown in Fig. 4.
Orientation measurements of bedding and foliation are consistent with previous observations on Storglaciären and other valley glaciers. Bedding is difficult to distinguish from foliation at the margins of Storglaciären but is more obviously recognizable in the center of the glacier. Although locally variable due to folding, in the center of the ablation zone, bedding generally dips shallowly west. Along the margins, the foliation is subvertical, dipping steeply inwards towards the center of the glacier (Fig. 4). In the center towards the front of the glacier, the foliation becomes progressively shallower and dips shallowly up the glacier where sheared basal ice is closer to the surface (Fig. 4). The combination of transformed stratification and foliation in the ablation zone forms a series of arcs on the surface reflecting in three dimensions an overall nested-spoon arrangement, opening up-glacier, much in the same way as described by Kamb (1959) for Blue Glacier.
Grains are locally variable in size, ranging from 1 to
The size of an individual whole section is determined by the technique used for the analysis. For U-stage work it is
Misorientation profiles A–A
Several
When composites SG23, SG27 and SG28, which are in the same kinematic reference frame, are individually plotted as one point per grain, and these results are combined on one CPO plot, the multimaxima nature of the pattern diminishes (Fig. 8). The composite pattern has one
Combined data (one point per grain) from SG23, SG27 and SG28 in the same kinematic reference frame. Plots from left to right show
It is important to note that another source of error in creating Fig. 8 results from combining data from the three samples into one pole diagram. The reference frame for this is the foliation plane (
EBSD maps of whole sections confirm that island grains are likely part of the same larger grain based on identical full crystallographic orientations (Fig. 6a and b). Individual grains within a two-dimensional surface that have exactly the same orientation or a slight misorientation are likely branching segments of the same grain, or subgrains of the larger grain in three dimensions (Figs. 3 and 6b and c). Even small (
Whole section analyses also allowed us to better understand the deformation mechanisms. While some subgrains are present in the suite of whole sections analyzed, most crystals show little evidence of significant lattice distortion. Individual grains are relatively strain-free (Fig. 6e). A lack of intragranular distortion, combined with the presence of lobate–cuspate grain boundaries; no visible shape preferred orientation; and evidence of grain boundary drag around bubbles (e.g., Fig. 6a), similar to pinning effects discussed by Evans et al. (2001), suggests that recrystallization in these samples is dominated by grain boundary migration (Urai et al., 1986). These interpretations are consistent with those in microstructural studies of experimentally deformed ice at high temperatures (e.g., Kamb, 1972; Montagnat et al., 2015; Vaughan et al., 2017; Journaux et al., 2019) and natural ice samples deformed at relatively high temperatures (Duval and Castelnau, 1995).
Patterns of
Only two published sets of experiments document both
We provide a more detailed comparison of our CPOs from natural ice to experimentally obtained CPOs from two warm-temperature (
Orientation data from Qi et al. (2019) show well-defined CPO patterns with a two-cluster
Samples PIL91 (
The elongation of the main
The
In an attempt to mimic a possible grain sampling bias similar to that which we propose when dealing with warm coarse-grained ice, we randomly resampled subsets of 50 grains – allowing for random duplicates in the resampling (thus one grain may appear more than once in the resampling) – from the two warm experiments by Qi et al. (2019) at low and high strains, and we compared these to the stacked suite of natural samples in the same kinematic reference frame (Fig. 9). Subsets of the experimental data produce patterns that are more diffuse and patchy than those for the full dataset and are broadly similar to patterns observed in natural coarse-grained ice. Importantly, the Qi et al. (2019) study does not suffer from grain sampling biases common to CPO characterization in warm glacial ice, due to the significantly finer and more consistent grain size (Fig. 9). Compared to the experimental results, the main
We interpret these results to mean that the grain sampling bias issue was not entirely resolved by making and combining composite sections, due to the very large grain size with interlocking shapes that still have not been entirely characterized. However, the overall similarity between the stacked data from composite sections from the three samples in the same kinematic reference (Fig. 8) and the CPO pattern presented by Qi et al. (2019) for fine-grained ice that has undergone low shear strains at a high homologous temperature (Fig. 9, PIL91) suggests that the operative deformation mechanisms are similar.
It is important to note that we do not know the exact deformational history experienced by the ice in our natural samples, but the recent part of that history corresponds most closely to simple shear parallel to the ice margin. An additional similarity between the experiments (Qi et al., 2019) and the conditions of deformation experienced by our samples is that there is a small component of compression, which for our natural samples is perpendicular to the margins of the glacier, associated with the narrowing of the valley in the direction of flow (Fig. 10a). Thus our samples may represent similar kinematics to those in the experiments conducted by Duval (1981) and Budd et al. (2013) that involved simple shear combined with compression normal to the shear plane (Fig. 10b).
Hudleston (2015) calculated the finite shear strain required to rotate fractures towards parallelism with the flow direction along the margins of Storglaciären, and this indicated that the finite shear strain where we collected ice samples for our study is likely much greater than 2. This estimate exceeds the strain of the high-strain experiments done by Qi et al. (2019), and we might therefore expect our data to best match the high-strain experimental data. However, the
By developing a new sample preparation method to create composite sections for each sample collected, we are able for the first time to use cryo-EBSD to obtain complete (
We predict that from our study and from a comparison with experimental results, a fully representative CPO, if enough data from a large-enough volume of ice were sampled, would consist of (1) a
Our new sample preparation method allows for the faster and more accurate collection of complete crystallographic orientation data and microstructural analyses of coarse-grained ice. This opens up a range of opportunities for further analyses to aid in the understanding of micromechanical processes governing rheological properties of such ice. Future work will benefit from the better quantification of 3D grain size and shape to help improve the sample preparation methods in order to minimize any grain sampling bias. Additionally, more work should be done to quantify the effects of dynamic recrystallization in the context of shear strain along the margins of glaciers and should be taken into account when assessing these CPO patterns.
CPO representations using modern techniques, such as AITA or EBSD, are often plotted as all-pixel orientations. Gagliardini et al. (2004) demonstrated that the weighted-area procedure based on all-pixel orientations is a statistically better representation of the CPO if the volume of ice measured is fully representative, such that results from two samples of that volume are the same. This assumes that the measured area of a grain in cross section is the mean projected area of the grain. All-pixel orientations are especially important for providing estimates of bulk physical properties, such as the polycrystal elasticity tensor, and may take into account the issue of parent grains with satellite island grains, although this will only be true if the sample is large enough to contain a sufficient number of grains to provide a truly representative CPO. In addition, the presence of island grains calls into question the assumption that the measured area of a grain in cross section is the mean projected area of the grain. If there are no repeat grains in a representative sample, one-point-per-grain plots would yield the same CPO patterns (e.g., small circle girdle in Fig. A1), although the eigenvalues of the orientation tensor, if calculated, would generally differ. If the volume of ice measured is not fully representative, one point per pixel will bias CPO patterns towards larger grains and is a sure way to produce a multimaxima CPO.
EBSD map and associated CPO plots for sample PIL36 deformed in uniaxial compression at
This produces unrepresentative grain area biases, as these large grains may not be the largest or close to the largest grain in a representative volume of ice. The one-point-per-grain method will reduce that area bias but could have repeat grains and bias results towards finer grains if the fine grains differ in CPO from the large grains (unlikely in the case of Storglaciären). One-point-per-grain analyses, therefore, represent the CPO pattern better when you have less representative samples (Fig. A1). This is true in our case, in which we have a broad range of grain sizes in 2D and few grains. In addition to better representing the CPO pattern, plotting the one-point-per-grain method allows for direct comparison with the fabrics described in earlier studies when all the data were represented this way.
The issue of statistics is not straightforward for coarse-grained ice with the existence of multimaxima CPOs. Any way of attempting to eliminate the effects of multiple counting of individual grains that appear more than once in a thin section or in multiple sections intersecting a single crystal would be ad hoc. Doing statistical tests while ignoring this phenomenon is of little use. The method of Kamb (1959) of contouring provides a way of establishing the statistical significance of maxima in a fabric, but this is only meaningful if multiple points from the same grain are excluded. We believe that use of eigenvalue methods and associated statistics is inappropriate for multimaxima fabrics.
The EBSD data for this article can be accessed at
MEM, PJH and DJP designed the research. MEM and PJH collected field data, and MEM transported samples from Sweden to New Zealand. MEM, DJP, SF and PJL prepared the samples. MEM, DJP, SF and MN collected the microstructural data using cryo-EBSD. MEM, ZM, PJH and DJP processed and analyzed the data. CQ provided experimental data for comparison. MEM wrote the paper incorporating discussions, suggestions and improvements from all authors, primarily PJH, DJP and ZM.
The authors declare that they have no conflict of interest.
We are grateful to the University of Stockholm and the Tarfala Research Station for making this fieldwork possible and providing us with the tools necessary to access the glacier and collect samples, to Troy Zimmerman for his field assistance, and to Hannah Blatchford for her help transporting samples to New Zealand and aiding in sample preparation. Thoughtful and helpful reviews were provided by Maurine Montagnat and Andrea Tommasi. We also appreciate helpful comments and suggestions by the editor Olivier Gagliardini.
This research was made possible by funding provided by a Grant in Aid of Research administered by Sigma Xi, The Scientific Research Honor Society; a Graduate Student Research Grant administered by the Geological Society of America; and by the Marsden Fund of the Royal Society of New Zealand (grant no. UOO052) awarded to David J. Prior.
This paper was edited by Olivier Gagliardini and reviewed by Maurine Montagnat and Andrea Tommasi.