The role of kink boundaries in the deformation and recrystallisation of polycrystalline ice

Journal Pre-proof The role of kink boundaries in the deformation and recrystallisation of polycrystalline ice Meike Seidemann, David J. Prior, Narayana Golding, William B. Durham, Kat Lilly, Matthew J. Vaughan PII:

S0191-8141(18)30308-0

DOI:

https://doi.org/10.1016/j.jsg.2020.104010

Reference:

SG 104010

To appear in:

Journal of Structural Geology

Received Date: 4 October 2017 Revised Date:

25 January 2020

Accepted Date: 3 February 2020

Please cite this article as: Seidemann, M., Prior, D.J., Golding, N., Durham, W.B., Lilly, K., Vaughan, M.J., The role of kink boundaries in the deformation and recrystallisation of polycrystalline ice, Journal of Structural Geology (2020), doi: https://doi.org/10.1016/j.jsg.2020.104010. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier Ltd.

CRediT author statement Meike Seidemann: Conceptualization, Methodology, Investigation, Project administration, Funding acquisition, Writing-Original Draft preparation, WritingReview & Editing. David J. Prior.: Conceptualization, Methodology, Funding acquisition, Supervision, Writing-Original Draft preparation, Writing- Review & Editing. Narayana Golding: Investigation, Supervision. W.B. Durham: Methodology, Supervision, Writing- Review & Editing. Kat Lilly: Data curation. Matthew Vaughan: Resources.

250 µm

Inverse pole figure

<11‐20> a‐axes <21‐30>

<10‐10> m‐axes

re m

cr ys

ta

lli se

d

gr ai ns

EBSD data

na nt gr ain s

re

Polycrystalline ice

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The role of kink boundaries in the deformation and recrystallisation of polycrystalline ice

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Meike Seidemann a,∗, David J. Priora , Narayana Goldingb , William B. Durhamb , Kat Lillya ,

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Matthew J. Vaughana

6 a

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Department of Geology, University of Otago, 360 Leith Walk, Dunedin 9016, New Zealand

b

Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, 77 Massachusetts Avenue, MA 02139, USA

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Keywords: Deformation, Ice, Kinking, Recrystallization, Basal slip, Ripplocations

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*Corresponding author. Tel.: +49 15252060519

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Email addresses: [email protected] (Meike Seidemann),

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[email protected] (David J. Prior), [email protected] (Narayana

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Golding), [email protected] (William B. Durham), [email protected] (Kat

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Lilly), [email protected] (Matthew J. Vaughan)

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Preprint submitted to Journal of Structural Geology 1

31 July 2019

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Abstract

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Kinking is a common process in materials with a strong visco-plastic anisotropy but its impact on the

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plastic deformation and recrystallisation of crystal aggregates is still poorly constrained. Here, kinking

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is studied via constant stress experiments on polycrystalline ice under relatively low temperature (240

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K) and high differential stress (13.3 MPa and 2.7 MPa, with 50 MPa confining pressure). EBSD data

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analysis shows that samples comprise large and small grains, interpreted as remnant and

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recrystallised. Boundary trace analyses and misorientation data of kinked remnant grains reveal that

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kink boundaries are best characterised with rotation axes within the basal plane of the ice crystal.

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Inferred slip directions within the basal plane are variable and include <11-20>, <10-10> and

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intermediate directions. Shorter grain boundaries with rotation axes outside the basal plane surround

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kink boundaries and indicate that non-basal dislocations or ripplocations play a role in

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accommodating local kink deformation. More kink boundaries per gain and a larger boundary

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misorientation are generally found in remnant grains in the high-stress sample. At an aggregate level,

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kinking as a key facilitator for the dynamic recrystallisation process is represented by many relatively

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straight grain boundaries with basal rotation axes in the remnant and recrystallised grain population.

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The statistically preferred slip direction within the basal plane is <21-30>, consistent with coupled slip

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on two crystallographic a-axes with uneven contributions.

46 47 48 49 50 51

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1. Introduction

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Kinking is an important process in metals and rocks, including polycrystalline ice. However, the

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mechanisms responsible for kinking and the impact of local kink formation on the deformation and

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recrystallisation of the aggregate are not fully understood. Rock deformation studies are often

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associated with relatively small samples as high stresses and temperatures are required and high

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confining pressures are needed to prevent sample cracking. Deformation experiments on

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polycrystalline ice at comparable homologous temperatures require significantly lower stresses and

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confining pressures, and thus provide the opportunity to study the microstructural and mechanical

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behaviour in rocks at a larger scale. High-homologous temperatures in ice experiments do not entail

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the significant engineering problems associated with deformation at high-homologous temperatures

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for most other rocks. The deformation of polycrystalline ice is in many cases an analogue to the

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deformation of quartz (i.e. Wilson et al., 2014). At high-homologous temperature, both ice and

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quartz show a similar recrystallisation behaviour with a tendency to accommodate strain primarily by

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subgrain rotation recrystallisation and grain boundary migration recrystallisation with new grain

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nucleation (i.e. Stipp et al., 2001; Schulson, 2002; Faria et al., 2014). What is more, ice and quartz

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share a similar crystal symmetry and slip at a single crystal level occurs mostly in the basal plane,

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although combinations of basal and prismatic slip have been reported at high-homologous

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temperature for both materials (Hirth and Tullis, 1992; Wei and Dempsey, 1994). Ice and quartz both

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exhibit the ability to form localised zones with equant-shaped grains and a drastically reduced grain

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size from the starting material (i.e. Schulson, 2002; Vernooij et al., 2006). For simplicity and as a

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continuation of the nomenclature used in most previous literature, we will refer to these localised

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zones as ‘shear zones‘ in this introduction. Sample-scale shear zones resulting from fully ductile

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failure (so termed plastic faulting or P-faulting) of polycrystalline ice have been associated with high

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confinement conditions (confining pressure>> axial stress) and shear heating as a major softening

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mechanism (Golding et al., 2010, 2012). On the other hand, shear localisation in high-temperature 3

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plane strain studies on polycrystalline ice with inclusions has been found to coincide with kinking

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(Mansuy et al., 2000, 2002). The spatial link between ice shear zones (or localisation bands) and

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kinking has also been inferred from modelling results (Lebensohn et al., 2009; Montagnat et al.,

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2011; Grennerat et al., 2012). Mansuy et al. (2000) propose that stable kink bands occurring parallel

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to the basal plane can lead to the development of shear zones.

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Kinking is a process that leads to the creation of new high-angle grain boundaries within existing

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grains by buckling of the crystal planes (Fig. 1). The primary identifying feature of kinking is the kink

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bands. These are the domains between two kink boundaries. The parent grain is often cross- cut by

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kink bands with alternating crystal orientations. Kinking is commonly observed in materials with a

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strong viscoplastic anisotropy, especially in layered silicates such as micas (Meike, 1989; Bell and

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Wilson, 1981) but also in graphite (Kelly, 1981), ionic ceramics (Basu et al., 2006) and layered,

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hexagonal carbides and nitrides (MAX-phases) (Barsoum, 2013). The allegedly paramount

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importance of the kinking process to plastic deformation in sheet silicates, graphite, ionic ceramics

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and MAX-phases is reflected in the definition of a whole new class of materials, the so-called kinking

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non-linear elastic solids (KNE) (Barsoum et al., 2004).

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(Figure 1 here)

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In polycrystalline ice, kinking has been repeatedly detected during high-temperature (>-15°C) creep

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(Wilson et al., 1986; Manley and Schulson, 1997; Mansuy et al., 2000, 2002; Montagnat et al., 2011,

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2015; Piazolo et al., 2015). The observation that kink boundaries in ice develop semi-perpendicular to

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the basal plane (Wilson et al., 1986; Mansuy et al., 2000) presumes movement, and by association a

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dislocation in the basal (0001) plane (Mansuy et al., 2002). Recent rotation axes and weighted

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Burgers vector analyses of high-resolution EBSD data of single kink boundaries suggest that kinking is

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the manifestation of a basal edge dislocation, or alternatively expressed, a tilt boundary within the

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basal plane (Montagnat et al., 2011; Piazolo et al., 2015). However, observations of kinking are so far

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limited to experimentally deformed ice at high temperatures, where kinking coincides and may be 4

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partially overprinted by extensive dynamic recrystallisation (i.e. Wilson et al., 1986; Montagnat et al.,

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2011) or, to prevent dynamic recrystallisation, limited to low strains of 1-2 % (i.e. Piazolo et al.,

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2015). In addition to that, trace analyses of kink boundaries allowing for a deduction of prominent

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slip systems have been limited to mostly low strains and low-angle (<10°) misorientations.

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In this contribution, we focus the role of kinking in polycrystalline ice deformed at relatively low-

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homologous temperature (T=240 K). High confining pressures (50 MPa) are employed to prevent

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cracking and sample failure at the high stresses required to drive useful strain rates at this

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temperature.

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2. Method

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2.1. Sample preparation

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Cylinders of polycrystalline ‘Standard ice’ were fabricated by placing 180-250 µm sieved ice particles

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(made from deionized water) into 25.4 mm (1 inch) diameter moulds, packing to 40 % porosity,

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flooding with degassed, deionized water and freezing the mixtures uniaxially from the bottom (Stern

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et al., 1997). Samples are transparent with no porosity, once a small bubbly section at the top is

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removed. The microstructure is homogeneous, with polygonal grains and a random CPO (Fig. 2a,b).

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The arithmetic mean grain size and standard deviation are 250 ± 112 µm at a step size of 10 µm (Fig.

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2c). Neighbour-pair and random-pair misorientation angle distributions show only minimal deviations

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(<0.003 %) from the idealized ‘random’ curve for ice 1h (Fig. 2d). The samples’ lengths and cross-

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sectional areas were measured post-deformation with a pre-chilled Vernier calliper with an accuracy

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of ±0.02 mm in a ∼243 K environment. The samples were sealed into thin-walled indium jackets,

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flanked by a steel end cap at the bottom and a ZrO2 spacer and force gauge (here referred to as

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internal force gauge) on top of the sample (Durham et al., 1983; Stern et al., 1997). Special care was

5

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taken to avoid abrupt temperature differences during the measurements and welding of the indium

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jackets to avoid fracturing due to thermal shock.

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(Figure 2 here)

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2.2. Experimental procedure

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Deformation tests were conducted in a conventional rock mechanics triaxial apparatus equipped

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with a cooling alcohol bath for ice deformation experiments (Durham et al., 1983; Heard et al., 1990).

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Nitrogen gas was employed as the confining medium, while a screw-loading mechanism applied

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uniaxial compression from the bottom. The experimental procedure and uncertainties related to

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piston alignment and force gauge readings are given in Durham et al. (1983). Tests were run at a

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constant temperature of 240 K and 50 MPa confining pressure. The sample assembly (sample, indium

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jacket, spacer and internal force gauge) was introduced into the pre-chilled pressure cell and left to

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equilibrate for 15-45 minutes before the confining pressure was slowly built up. Once the internal

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force gauge had stabilised (45-90 minutes), the samples were loaded with uniaxial forces equivalent

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to 2.7 MPa (ice 774) and 13.3 MPa (ice 769), respectively. We attempted to maintain a constant

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stress during the experiments by dynamically adjusting the axial load to the changes in sample length

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and cross-sectional area (Stern et al., 1997; Durham et al., 2001). Experiments were terminated once

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the target strain value (15 % engineering strain for sample 769 and 12.5 % for ice 774) was reached

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by retracting the piston and removing the confining pressure. The sample assemblies remained in the

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rig for 45 minutes before they were extracted from the pressure cell and slowly immersed into

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nitrogen mist above liquid nitrogen. Subsequently, the samples were removed from the indium

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jackets with a razor blade and wrapped in pre-chilled aluminium foil for long-term storage in a liquid

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nitrogen dewar.

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2.3. EBSD imaging and data processing

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Cryo-EBSD data were collected using methods for fine-grained polycrystalline ice outlined by Prior et

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al. (2015). Samples were cut along their long axis, parallel to the shortening direction using a scroll 6

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saw. Sample 769 was prone to breaking at the top and was hence manually cut with a scroll saw

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blade at a slower rate. Mounting on 30 mm by 40 mm SEM ingots was performed with a piece of wet

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tissue (water temperature of 0°C). Ingot and sample temperatures before mounting were at

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approximately +2 and <-130°C, respectively. Grinding plates, pre-chilled to a temperature of -40° to -

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70°C were employed to obtain a flat surface.

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The data were gathered on a Zeiss FEG SEM using 6-8 Pa of nitrogen pressure to avoid charging. EBSD

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patterns were collected with a Nordlys camera and Oxford Instruments AZTEC software with an

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acceleration voltage of 30 kV and a beam current of 50 to 90 nA. Due to the large, 30 mm by 34 mm

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sample size, a long working distance between 28 and 31 mm was chosen. An Emitech K1250 cryo-

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stage kept the samples at a constant stage temperature of -95 to -100°C during imaging. A single

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sublimation by pressure cycle (Prior et al., 2015) with a minimum stage temperature of -75°C was

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employed to remove surface frost prior to imaging.

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EBSD data were processed with Oxford Instruments Channel 5 software by Oxford Instruments.

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Orientation maps were generated using an inverse pole figure colour-code with respect to the

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shortening direction (see Nolze and Hielscher 2016 for more details on this method of display),

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except where explicitly denoted (Fig.2). A minimum misorientation value of 10° was chosen as a

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threshold to distinguish subgrains (flanked by low-angle grain boundaries) from grains surrounded by

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high-angle grain boundaries. Non-indexed pixels were removed and filled with neighbouring values

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using a ‘wild spikes’ extrapolation and a neighbour-pair interpolation in the noise reduction tab in

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Channel 5’s map module Tango. Misorientation profiles and single grain subsets were also defined in

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Tango. Pole figures showing individual obtained points were plotted in the Mambo module.

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Contoured pole figures, texture indices, grain size histograms and internal misorientation maps were

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calculated and plotted in the MTEX 4.0.12 texture analysis toolbox within a Matlab 2013a

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environment (Bachmann et al., 2010). For the MTEX processing, zero solutions were removed and

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grains were calculated from indexed pixels using the same minimum misorientation angle of 10° for

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grain definition as employed for the processing of the data in Channel 5. Grains with less than 10 7

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indexed pixels were removed to clean the data. For the processing of the gKAM map in Fig. 4e, grain

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boundaries were smoothed using the ‘grains=smooth(grains, 5)’ command. The ‘grain size’ was

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computed using the area equivalent grain diameter. The relative frequency in the grain size

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histograms is given as a number percentage.

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(Table 1 here)

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3. Results

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3.1. Microstructures and Crystallographic Preferred Orientations (CPOs)

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EBSD maps were collected as partial vertical cross-sections at the transition from a narrow to wide

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sample diameter in both samples (Fig. 3). These transitions from narrow to wide sample diameters

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are found in the vertical centres of the samples and represent areas of intermediate strain compared

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to the tops and bottoms of the samples (see Fig. 3 legends below maps).

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Grains in the microstructure of sample 769 are mostly small grains (2107 in total) with grain sizes

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<200 µm and equant or elongated grain shapes (Fig. 3a). These grains have grain sizes smaller than

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the grain size of the starting material. Areas with many small grains in contact with each other mean

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that most of the small grains cannot be explained as 2D sections through the tip of a larger grain.

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Given that there are more grains per area in the deformed state than the original sample and most

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small grains are likely small grains in 3D, we interpret the small grains as recrystallised grains (Table

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1). Forty- nine large grains (>200 µm) with equant grain shapes and at least one straight grain or

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subgrain boundary are scattered within the recrystallised grains. The size and shape indicate that the

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large grains are likely to be remnant grains (Table 1) preserved from the original microstructure of

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the starting material.

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(Figure 3 here)

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Large grains (>200 µm) show a strong (max=4.1, J-index=3.1) c-axis CPO with asymmetric maxima at

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40° (top) and 20° to bulk shortening at the bottom. The strength of the CPO is probably related to the 8

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small number of grains (49) in the dataset. The maxima are asymmetrical, which indicates a

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component of dextral shear. Conversely, the c-axis CPO of the small grains is almost random

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(max=1.8, entropy close to 0, as expected for a random distribution, Mainprice et al., 2015) with only

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a slight preference of c-axis orientations clustering around the maxima of the large grain

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orientations.

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The microstructure of sample 774 also shows a mixture of large and small grains (Fig. 3b).

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Approximately a quarter of the grains in the microstructure (216 out of 1108 grains) are large (>200

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µm) grains with a mixture of straight and serrated grain boundaries. These grains are mainly free of

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internal distortion, except for one orientation (blue-violet colours, approximately <20-23> direction,

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see also Fig. 6d for orientation within a sample reference frame), where irregular, curved low-angle

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boundaries are observed. Some of the large grains are intersected by bands of smaller (<200 µm)

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grains. The bands are homogeneously distributed over the entire map area. Bands are usually 1-2

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grains wide and up to 10 times as long. Their long-axis is usually oriented at a 60° angle to the bulk

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shortening direction.

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The c-axis CPO of the large grains is a moderate (max=3.66, J-index=1.3) single cone with maxima at

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an angle of 40° to bulk shortening. Small grains show a slightly weaker c-axis CPO (max= 2.56, J-

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index=1.1) with a slight orientation preference to where maxima in the large grain CPO are found.

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(Figure 4 here)

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One band of small grains in ice 774 was manually outlined, based on the criteria for recrystallised

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grains summarised in Table 1. The band is oriented at an approximate angle of 60° to the bulk

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shortening orientation (Fig. 4). The definition of the rims of the band and the cut-off value (200 µm)

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between recrystallised and remnant grains is flexible, as no recrystallised grain piezometer is

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available for polycrystalline ice. We have chosen a cut-off value below the average gain size of the

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starting material (Fig. 2). Nevertheless, some large grains situated on the smaller side of the average

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grain size of 250±112 µm may be mislabelled as recrystallised grains. 9

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Grains within the band show no obvious preferred orientation, although there are several examples

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of neighbouring grains with similar orientations (Fig. 4a). One example is a red grain (denoted with

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"R" in the map) and its surroundings. The maximum misorientation between the R grain and its

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lower neighbour (R2) amounts to 12ᵒ. There are also 4 additional reddish neighbours (r), whose

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misorientation to the R grain is below 28ᵒ. Another blue grain within the band (B) has an adjacent

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grain with the same orientation (B1) and 3 other neighbours with a maximum misorientation of 15ᵒ

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to the firstly mentioned blue grain. Grain boundaries within the band have high-angle

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misorientations of 10-80° and are remarkably straight (Fig. 4a,b). The misorientation patterns along

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and across the band are similar, with high-angle grain boundaries between 10 and 80° misorientation

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(Fig. 4a). Misorientations of below 5° are only found in the misorientation profile parallel to the

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band.

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Schmid factors for ice’s most prominent (0001) <11-20> slip system are homogeneously distributed

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throughout the map (Fig. 4c). The entire range of Schmid factors from 0-0.5 can be detected both

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inside and outside the band of recrystallised grains. Average Schmid factors inside and outside of the

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band are statistically the same.

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Intragranular misorientation maps highlight differences between small grains inside and large grains

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outside the band (Fig. 4d,e). We have chosen two complementary approaches to intragranular

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misorientations; the internal misorientation angle (MTEX property: mis2mean) and the grain

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averaged kernel misorientation (MTEX property: GAM). The internal misorientation angle shows

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lattice bending and high misorientations, indicative of high-angle grain boundaries. On the downside,

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internal misorientation angles are strongly grain size-dependent (i.e. large grains will have higher

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internal misorientation values). The gKAM is regarded as fairly grain size –insensitive and is not

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influenced by high-angle grain boundaries. On the other hand, the gKAM is more susceptible to EBSD

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indexing noise and cannot show lattice bending (Heilbronner & Kilian 2017).

10

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In a map depicting the internal misorientation angle with respect to the average within each grain

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(mis2mean), only two small grains within the band show misorientations >10°. The curved shape of

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these transitions suggests that the misorientation was caused by lattice bending (Fig. 4d). Two

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potentially kinked grains inside the band exhibit straight low-angle grain boundaries at angles oblique

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to bulk shortening. In the upper grain, two of these boundaries are parallel to each other. Peak

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internal misorientation values of up to 18° are found in large grains imminently adjacent to the band

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of recrystallised grains. These grains often show straight, parallel low-angle and high-angle

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boundaries, with a possible kink geometry. Similar straight or semi-straight lines of elevated

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intragranular average misorientation angles (as calculated via the gKAM) are observed in the same

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large grains outside the band. Many of these lines coincide with areas of high misorientation

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gradients (>6ᵒ) shown in the map in Fig. 4d, albeit some of the lines appear less straight in the gKAM

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map. The two grains inside the band with straight low angle boundaries (Fig. 4d) also show

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corresponding lines of elevated gKAM values in 4 out of 5 cases (Fig. 4e). Similar gKAM magnitudes of

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0.4ᵒ are detected for all grains with only some local spots amounting to magnitudes of above 0.4ᵒ.

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Twenty-two grains outside the band show lines of elevated gKAM misorientations of ~0.4ᵒ oriented

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oblique to bulk shortening, as opposed to three grains within the band.

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(Figure 5 here)

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3.2. The kinking mechanism in single grains

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A combination of rotation (or misorientation) axes distributions in inverse pole figures for single

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kinked grains and trace analyses for selected grain boundaries were employed to constrain the slip

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systems responsible for kinking on a grain-scale. Rotation axes distributions in inverse pole figures

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alone can be ambiguous, as more than one slip system can generate the same rotation axis (Fig. 5).

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’Trace analyses’ provide additional information on the crystal distortion to better constrain slip

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systems (i.e. Prior et al., 2002; Piazolo et al., 2008; Hildyard et al., 2009). Grain boundaries with

274

differing misorientations were selected for the trace analyses (Fig. 6e,f,g,7e,f,g). For the rotation axes 11

275

distributions displayed in inverse pole figures, this enabled the rotation axes for values below 5°with

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larger errors (Prior, 1999) to be verified based on the higher misorientation values (5-10°) for the

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low-angle range (<10°) (Table 1).

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Kink boundaries, per definition, are ideally identified by straight grain boundaries and a rotation axis

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in the basal plane (Table 1). However, kink boundaries can also appear curved with bends of up to

280

20ᵒ when modified by subsequent deformation (section 4.2.1). We differentiate between low-angle

281

kink boundaries (<10°misorientation) and high-angle kink boundaries (>10°). Additionally, we

282

investigate high-angle kink boundaries in a misorientation range (50-70°, Fig. 6a,b,g), that appears

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characteristic in sample 769.

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(Figure 6 here)

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3.2.1. Ice 769

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The grain selected for the detailed analysis from sample 769 (Fig. 6a-e) has three distinctive (blue)

287

kink bands and represents kinking under higher axial stress conditions. The kinked grain was

288

extracted from a detailed EBSD map (2 µm step size), slightly above the overview map (Fig. 3a).

289

Most distinctive within this grain are two alternate kink orientations, separated by straight, high-

290

angle (50-65°) kink band boundaries (Fig. 6a, Profile A). Distances between the high-angle kink

291

boundaries (referred to as “spacing” from here on) are 0-108 µm. The orientations of the kink band

292

boundaries are perpendicular or semi-perpendicular to the bulk shortening orientation. Along the

293

kink bands, a gradual change in orientation can be observed (Fig. 6a, Profile B). The misorientation

294

angle distribution shows peaks in the neighbour-pair over the random-pair distribution and

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theoretical curve (black line) for misorientation angles between <10° and 50-65° (Fig. 6b). The peaks

296

in the neighbour-pair misorientation distribution correspond to low-angle boundaries along the kink

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bands and high-angle kink boundaries, respectively (Fig. 6b,c). Short (~30 µm) low-angle kink

298

boundaries, oriented parallel and semi-parallel (0-15ᵒ) to bulk shortening, coincide with lattice

299

bending across the long axis of the kink segments (Fig. 6a Profile B,6c). Kink bands are surrounded by 12

300

high-angle kink boundaries (>10°), the majority of them in the domain specific to sample 769 (50-70°)

301

(Fig. 6c). The high-angle kink boundaries with 50-70° misorientation have preferred <21-30> and <11-

302

20> rotation axes.

303

The two main c-axes orientations corresponding to the kink bands and non-kinked areas cluster

304

approximately 80° and 135° to the bulk shortening directions (Fig. 6d). The pole figures also reveal

305

possible rotation axes that can lead to a boundary model for kink boundaries. Dispersion around the

306

m-axes <10-10> and a-axes <11-20> can be traced to a single <21-30> rotation axis in the top of the

307

m- and a-axes pole figure. A trace analysis was performed to constrain the boundary type (i.e. Prior

308

et al., 2002; Piazolo et al., 2008, Fig. 6e). A tilt wall boundary can be reconstructed (black great circle)

309

for a short straight segment of high-angle kink boundary (yellow rectangle in Fig. 6a,c). The Burgers

310

or slip vector for a tilt solution is found in the plane perpendicular to the rotation axis (i.e. Prior et al.,

311

2002 Fig. 9b), yielding a potential Burgers vector of <10-10> for the pink grain areas and <11-20> for

312

the blue kink bands. We call this solution ’potential’ because it implies two assumptions: 1) that the

313

Burgers vector is perpendicular to the rotation axis, meaning that subsequent deformation has not

314

modified this angle and 2) that the Burgers vector has to lie within the “easy-slip” basal plane of

315

polycrystalline ice. A twist solution is unlikely as the plane perpendicular to the rotation axis (green

316

great circle) does not align with the boundary trace (Fig. 6e, Tochigi et al., 2018 Fig. 1b).

317

Slip systems and boundary misorientations were constrained for two additional grains in sample 769

318

(Fig. 6f,g). A blue grain shows three high-angle kink boundaries with an inclination of 62ᵒ to bulk

319

shortening (Fig. 6f). The spacing between the high-angle kink boundaries is 17-33 µm. A trace

320

analysis for a selected kink boundary (yellow rectangle in orientation map) with a 15-20°

321

misorientation gives a <10-10> rotation axis and a potential <11-20> Burgers vector for a tilt solution.

322

A violet grain with three kink bands has 5 high-angle kink boundaries inclined approx. 70ᵒ to bulk

323

shortening. The spacing between the boundaries is 14-35 µm. One of the high-angle (50-60°) kink

324

boundaries (yellow rectangle) has a rotation axis in the basal plane (<11-20>) and a potential Burgers

325

vector in the basal plane, 90° from the rotation axis (<10-10>) (Fig. 6g). 13

326

(Figure 7 here)

327 328

3.2.2. Ice 774

329

Grains with clear stripes of alternating orientations are absent in sample 774. However, many grains

330

have remarkably straight boundaries, which are inclined with respect to bulk shortening and may

331

represent kinking under low axial stress conditions (Fig. 7a,c,f). In contrast to the 3-6 high-angle grain

332

boundaries per grain detected in sample 769, merely 1-3 high-angle kink boundaries per grain are

333

observed in sample 774. A detailed analysis of a single grain from sample 774 showed several

334

straight, inclined (37-60ᵒ to bulk shortening) grain boundaries with misorientations between 2-15°

335

and approximately 52° (Fig. 7a). The spacing between the high-angle kink boundaries is 20-104 µm. In

336

the misorientation angles distributions, the neighbour-pair distribution displays matching peaks for

337

misorientations of 2-15° and 45-50ᵒ (grey bars). Both peaks exceed the random-pair (black bars) and

338

the random distribution (black curve) for ice 1h, respectively (Fig. 7b). Rotation axes for all grain

339

boundaries show clusters in the basal plane (Fig. 7c, inverse pole figures) which identifies the grain

340

boundaries as kink boundaries (Table 1). There is no profound difference in orientation to bulk

341

shortening between low-angle and high-angle kink boundaries (Fig. 7c). However, low-angle kink

342

boundaries have a preference towards <11-20> and <21-30> rotation axes, whereas high-angle kink

343

boundaries also have <10-10> rotation axes. For one high-angle kink boundary with a <10-10>

344

rotation axis (yellow rectangle), a trace analysis was performed. A potential Burgers vector for a tilt

345

solution is <11-20> (Fig. 7d,e).

346

Grain boundaries in two additional grains within sample 774 also qualify as kink boundaries (Fig.

347

7f,g). The trace analysis of a low-angle (<10°) kink boundary (Fig. 7f) with a 49ᵒ angle of inclination to

348

bulk shortening yielded a <10-10> rotation axis and a potential <11-20> Burgers vector for a tilt

349

solution. Because the boundary trace approximately aligns with the plane perpendicular to the

350

rotation axis (green great circle) a twist solution is also possible, but geometrically unlikely due to the 14

351

combination of a very straight boundary and low misorientation. The second additional grain

352

contains 2 high-angle boundaries with a spacing of 43-55 µm. One of the high-angle kink boundaries

353

(25-30° misorientation), oriented at an angle of 90° to bulk shortening, has a <10-10> rotation axis

354

and a potential <11-20> Burgers vector for a tilt solution (Fig. 7g).

355 356

3.3. Kink boundary and boundary analysis for large-scale maps

357

Boundary maps highlighting respective rotation axes and inverse pole figures showing the rotation

358

axis distributions for a given misorientation margin are employed to investigate how kinking may

359

impact the deformation and recrystallisation of the ice samples at an aggregate level (Fig. 8c,d,9c,d).

360

We use the same classification system as for single kinked grains consisting of low-angle (<10°), high-

361

angle (>10°) and sample 769-specific kink boundaries (50-70°, Table 1). As for the single kinked

362

grains, potentially erroneous low-angle rotation axis distributions below 5° were compared with the

363

respective distributions at 5-10° misorientation (section 3.2) to check that the higher errors on the

364

low-angle misorientations are not generating misleading data.

365

(Figure 8 here)

366

3.3.1. Ice 769

367

The misorientation angle distribution of sample 769 shows a peak (>0.005 %) in the neighbour-pair

368

over random-pair and random distributions (black curve) for misorientations from 2-35° (Fig. 8b). A

369

minor elevation (<=0.005 %) in the neighbour-pair over random-pair and random distributions is

370

present for misorientation angles of 40-50°. Low-angle kinking in sample 769 is described by a

371

homogeneous distribution of rotation axes within the basal plane (Fig. 8c, inverse pole figure).

372

Boundary shapes (straight and curved) were disregarded for the definition of kink boundaries in

373

sample 769 (Fig. 8). A comparatively low indexing rate of ~60% in Fig. 6 and 8 (compared to Fig. 7, 9)

374

demanded a higher degree of post-processing, namely more interpolation of missing data from 15

375

neighbouring pixels. As a result, the shape of an a straight boundary can appear skewed or distorted

376

in the post-processed maps (see Fig. 6a).

377

Many large grains show one or more low-angle kink boundaries (light blue) with lengths of 50-310

378

µm and every possible orientation to bulk shortening (Fig.8c). Low-angle kink-boundaries are absent

379

in many of the equant shaped recrystallised grains but are observed in recrystallised grains with

380

elongated grain shapes and their similarly shaped neighbours (green rectangles). Shorter (straight

381

segments amounting to lengths of 20-40 µm, in rare cases up to 80 µm) grain boundaries with

382

rotation axes outside the basal plane (yellow) are detected in high frequencies around low-angle kink

383

boundaries and sometimes act as bridging segments between the kink boundaries (see pink and blue

384

rectangles). The rotation axes of the non-basal grain boundaries include all orientations with

385

misorientations <=18ᵒ to the basal plane (inverse pole figure).

386

High-angle kink boundaries with misorientations of 50-70° are also defined only by a rotation axis

387

within the basal plane for this sample (Fig. 8d). These high-angle kink boundaries (blue, green, red)

388

are homogeneously distributed over the map, creating high-angle boundaries for large grains and

389

small grains (Fig. 8d). In some cases, up to 4 parallel and semi-parallel high-angle kink boundaries

390

with misorientation of 50-70ᵒ are found within the same grain (i.e. light blue rectangles and lowest

391

pink rectangle). The semi-parallel kink boundaries are oriented at an angle of 65-90ᵒ to bulk

392

shortening and have <11-20> and <21-30> rotation axes. Grain boundaries with non-basal rotation

393

axes (yellow) are located in the same grain or a neighbouring grain containing one or more high-

394

angle kink boundaries with misorientations of 50-70°. Straight segments of these non-basal grain

395

boundaries are mostly shorter than the proximally located high-angle kink boundaries. For the high-

396

angle kink boundaries in a misorientation range characteristic in sample 769 (50-70°), <11-20> (blue)

397

and <21-30> (green) rotation axes are statistically preferred (inverse pole figure). The misorientation

398

axis cluster outside of the basal plane matches the inverse pole figure signature of tilt boundaries

399

created by pyramidal slip (Fig. 5d).

16

400

(Figure 9 here)

401 402

3.3.2. Ice 774

403

The selected map for sample 774 shows large grains with a mixture of serrated and straight grain

404

boundaries intersected by bands of small grains (Fig. 9a). In contrast to Fig. 3b, there is an uneven

405

distribution of the bands of small grains throughout the map. Clusters of small grains are mainly

406

found in the top half of Fig. 9a, whereas only two bands of small grains are detected the bottom half

407

of the map. The misorientation angle distribution shows a peak in the neighbour- pair over random-

408

pair and theoretical curve for misorientation angles of 2-20° (Fig. 9b).

409

Kink boundaries with low misorientation angles (light blue) are characterised by 70-280 µm long

410

straight boundaries with oblique to perpendicular orientations to bulk shortening (Fig. 9c).

411

Sometimes low-angle kink boundaries found in large grains also transect into small grains (blue

412

rectangles). Within the population of large grains, kinks can cut through one grain and continue their

413

path in a very similar (<5° different) orientation in an adjacent grain (pink rectangles). The rotation

414

axes of these low-angle kink boundaries are homogeneously distributed within the basal plane

415

(inverse pole figure).

416

Low-angle kink boundaries correlate spatially with the presence of small grains. In the top of the

417

map, where about 40% of the map consists of bands of small grains, low-angle kink boundaries are

418

detected in all large grains. At the bottom, fewer bands of small grains are found. Here, a grid of

419

several low-angle kink boundaries can often be found in large grains (green rectangles) adjacent to

420

the bands of small (recrystallised) grains. Contrastingly, kink boundaries can be absent in large grains

421

1-2 grain diameters away from small grains (black rectangles). Boundaries with rotation axes outside

422

(5ᵒ-14ᵒ) of the basal plane (yellow) are observed in areas of high kink densities (more than one low-

423

angle kink boundaries in one grain, green and red rectangles). These grain boundaries are short (20-

424

90 µm) and can prolong and connect low-angle kink boundaries (i.e. red rectangle). 17

425

Straight high-angle kink boundaries with misorientations >10° have lengths of 70-370 µm and are

426

oriented at angles of 20-90ᵒ to bulk shortening (Fig. 9d). Like their low- angle equivalent, high-angle

427

kink boundaries can transect into neighbouring large grains (lowest of the pink rectangles). Sample

428

769-specific high-angle kink boundaries (50-70°) are dominated by <10-10> rotation axes (lower

429

inverse pole figure), although also <21-30> and <11-20> rotation axis high-angle kink boundaries are

430

detected within the map.

431

High-angle grain boundaries with non-basal rotation axes are frequently found in the same grain as

432

high-angle kink boundaries (green rectangles). These grain boundaries are short (40-125 µm)

433

compared to some longer (>300 µm) grain boundaries with rotation axes outside the basal plane

434

detected in non-kinked grains (blue rectangles). The non-basal rotation axes of all these high-angle

435

grain boundaries do not exceed a maximum angle of 32ᵒ relative to the basal plane (Fig. 9d inverse

436

pole figure). For a misorientation range of 50-70ᵒ, the non-basal rotation axes show a cluster (Fig, 9d,

437

lower inverse pole figure) consistent with tilt boundaries generated by pyramidal slip (Fig. 5d).

438 439

4. Discussion

440

We suggest that the bands of recrystallised grains, with a reduced grain size from the starting

441

material, straight grain boundaries and similar crystallographic orientations to bulk shortening result

442

from kinking. We propose that kinking could provide a mechanism, under fully ductile conditions,

443

with the ability to create new grain boundaries with misorientations of 2-80° (Fig. 4). We

444

demonstrate that straight and curved (<20ᵒ) boundaries with misorientations of 2-70ᵒ are consistent

445

with kinking. The new grain boundaries have misorientation axes in the basal plane (Fig.

446

6c,7c,8c,d,9c,d) and define recrystallised grains with a reduced grain size from the starting material.

447

The microstructural features of the recrystallised grains that we observe differ from cracking and

448

subsequent recrystallisation previously observed in the high-temperature (-7 to -10°C), unconfined

449

deformation of polycrystalline ice (Golding et al., 2010; Chauve et al., 2017a). In these studies, cracks 18

450

are indicated by gaps in the microstructure (loss of cohesion). Such cracks normally thin out towards

451

the crack tips, possibly have wing-shaped endings and may cross-cut several grains. Recrystallised

452

grains within the cracks have round, irregular or serrated grain shapes and only selectively share the

453

straight grain boundaries almost exclusively observed in the recrystallised grains in this study.

454

Moreover, the microstructures of our deformed samples do not show a loss of cohesion and are

455

therefore more consistent with fully ductile deformation (Table 1).

456 457

4.1. Grain size reduction by kinking

458

A local grain size reduction by kinking is likely in these samples. The characteristic microstructural

459

and crystallographic features of a band of recrystallised grains in sample 774 (Fig. 4) can be explained

460

by the generation of boundaries by kinking. Kinking has been documented to create straight

461

boundaries with misorientations between 10-70ᵒ (Fig. 6,7), matching the straight boundaries with

462

misorientations of 10-90ᵒ between recrystallised grains (Fig. 4a). Neighbouring recrystallised grains

463

share the same or a similar CPO, indicative of an origin from the same parent grain. Moreover,

464

results from maps with statistically significant numbers of grains demonstrate that kinking is a

465

sample-wide phenomenon. Large-scale maps with boundaries colour-coded according to their

466

respective rotations axes (Fig. 8c,9c) depict straight low-angle boundaries with orientations oblique

467

to bulk shortening and a homogenous distribution of rotation axes in the basal plane, consistent with

468

low-angle kinking (Fig. 6,7). These low-angle kink boundaries are present in remnant grains in the

469

high-stress and remnant grains adjacent to recrystallised grains in the low-stress sample. Straight or

470

curved grain boundaries with orientations of up to 90ᵒ to bulk shortening and rotation axes in the

471

basal plane suggest that high-angle kink boundaries surround recrystallised and cross-cut remnant

472

grains throughout the samples (Fig, 8d,9d). The orientation of low-and high-angle kink boundaries to

473

bulk shortening in each sample, up to four semi-parallel and parallel high-angle kink boundaries in

474

sample 769 and the frequent spatial co-existence with shorter grain boundaries with non-basal 19

475

rotation axes (Fig.8c,d,9c,d) correspond to the characteristic features of kink boundaries observed in

476

single grains (Fig.6,7).

477

Kinking as a strong strain accommodation mechanism in the absence of dynamic recrystallisation has

478

been inferred from modelling of columnar ice aggregates under high-temperature compression

479

creep (Lebensohn et al., 2009; Grennerat et al., 2012). Only a weak correlation between local strain

480

as measured by a digital image correlation method and favourable grain orientation for basal slip (a

481

high Schmid factor) has been determined (Grennerat et al., 2012). In our deformed samples, kink

482

bands are found in favourably and non-favourably oriented grains for basal slip (high and low Schmid

483

factors) and the Schmid factors inside and outside the band of recrystallised grains are the same (Fig.

484

4c). Kinking as a primary grain size reduction mechanism could also explain why recrystallised grains

485

<100 µm do not exhibit internal kink boundaries (Fig. 4,8c,d,9c,d). Studies on deformation twinning,

486

a process similar to kinking, have shown that twinning in metals and alloys first appears in large

487

grains at a given stress and only affects smaller grain sizes if the overall stress is increased (Christian

488

and Mahajan, 1995; Dobron et al., 2011). Twinning in calcite occurs at lower stresses in larger grains

489

(Rowe and Rutter, 1990).

490

4.2. Deformation in single kinked grains

491

4.2.1. Kinking and c-axis parallel strains

492

Previous analyses of kinking in polycrystalline ice have often focused on the orientation of kink

493

boundaries to the main axis of compression (i.e. Wilson et al., 1986) or crystallographic axes or

494

planes within the kinked crystal (i.e. Piazolo et al., 2015). Kink boundaries investigated within this

495

study (Fig. 6d,f,g,7d,f,g) support earlier observations stating that the trace of kink boundaries is

496

inclined at a high angle (up to sub-perpendicular) to the basal plane (Starkey, 1968; Wilson et al.,

497

1986). In contrast to earlier results reporting bends of up to 5ᵒ in kink boundaries (Wilson et al. 1986;

498

Mansuy et al. 2000; Piazolo et al. 2015), bends of up to 20ᵒ were detected (Fig. 6a,c). A

499

misorientation profile taken adjacent to a kink boundary bent by ~20ᵒ reveals a continuous decrease 20

500

in misorientation to the starting point (Fig. 6a, Profile B). This observation suggests that existing,

501

previously straight kink boundaries can be modified by continuous lattice bending (shortening)

502

parallel to the kink boundaries. Observations of curved kink boundaries in our single-grain analysis

503

were restricted to cases, in which kink boundaries were oriented perpendicular to bulk shortening

504

(Fig.6a,7g).

505

Our analysis based on constraining of the potential slip systems with rotation axes reveals that all

506

kink boundaries within single grains can be explained by tilt boundaries generated by basal slip (Fig.

507

6,7). Our results indicate that kink boundaries are generated by a variety of misorientation axes and

508

Burgers vectors within the basal plane. Following the theory of dislocations moving along certain slip

509

systems, a variety of rotation axes and burgers vectors in the basal plane are only possible if basal

510

dislocations are present and crystal slip occurs on two coupled a-axes (Fig. 5b, 10). Within the low-

511

angle kink boundary range (<10°, Fig. 7f), the determined a-rotation axis (<11-20>), tilt boundary

512

model and interpretation of a possible coupled two a-axis slip match earlier results from trace

513

analyses for low-angle kinking (<10°) for ice deformed at higher temperatures (Piazolo et al., 2008;

514

Montagnat et al., 2015).

515

Kink boundaries within single grains appear to be accompanied by shorter grain boundaries with

516

rotation axes outside the basal plane yielding c-axis parallel strains (Fig. 6c,7c, 8c,d,9c,d). The

517

rotation axes outside the basal plane (Fig. 5) and the short nature of the segments compared to kink

518

boundaries supposedly created by basal dislocations (Shearwood and Worth, 1989; Shearwood and

519

Whitworth, 1991; Hondoh et al., 1990), suggest that these grain boundaries were created by non-

520

basal slip systems. To accommodate locally increased stresses in strain localised regions, non-basal

521

slip systems are often required (Montagnat et al., 2011). The short boundaries with non-basal

522

dislocations appear to prolong or connect existing kink boundaries (Fig. 6c,7c,8c,9c,d). Our

523

observation supports the findings of high-temperature creep studies in polycrystalline ice, indicating

524

that even though kink formation is commenced by slip on the basal plane (Wilson et al., 1986), well-

21

525

defined kink boundaries may be linked to the activation of non-basal slip systems (Piazolo et al.,

526

2008; Montagnat et al., 2011; Piazolo et al., 2015).

527

An alternative theory that challenges the development of kink boundaries due to basal dislocations in

528

anisotropic materials is the material sciences derived ripplocation theory (Barsoum et al., 2004).

529

Ripplocations are atomic-sized ripples recently reported for the first time in a naturally occurring

530

mineral (Aslin et al. 2019) and have been i.a. employed to explain c-axis parallel strains during the

531

formation of kink bands (Gruber et al. 2016, Barsoum & Tucker 2017). In contrast to dislocations,

532

ripplocations are currently thought to possess no Burgers vector (Gruber et al. 2016). Hence,

533

ripplocations in the basal plane can suitably explain both the variety of observed rotation axes in the

534

basal plane associated with kink boundaries and the connecting grain boundaries with rotation axes

535

outside the basal plane (Fig. 6c,7c,8c,d,9c,d). Especially ~300 µm long grain boundaries with rotation

536

axes up to 32ᵒ relative to the basal plane in Fig. 9d may be an indicator of the presence of

537

ripplocations. To our knowledge, studies on ripplocations have so far been limited to materials in

538

which no non-basal dislocations have been observed. Whether ripplocations or dislocations are

539

responsible for kink boundaries and grain boundaries with rotation axes outside the basal plane in

540

polycrystalline ice or even a combination of both micro-mechanisms is possible, will have to be

541

constrained in the future.

542 543

4.2.2. Locking angles of kink boundaries

544

The misorientations of the kink boundaries investigated within this study appear to depend on the

545

stress configuration. Previous work on kinking in multi-layered aggregates suggests that kink bands

546

have a ‘locking angle’, which will not be exceeded for a given differential stress (Reches and

547

Johnson,1976; Johnson, 1977; Collier, 1978). A potential relationship between the maximum

548

misorientation angle for a kink boundary and the differential stress may explain why locking angles

549

often amount up to 70° in sample 769 (Fig. 6a,b,f,g) and mostly below 25° in sample 774 (Fig. 22

550

7a,b,f,g). Another difference between kinking in the two samples investigated in this study is the

551

number of high-angle kink boundaries within a grain. Three to six high-angle kink boundaries were

552

detected in single grains in sample 769 as opposed between two and three kink boundaries in sample

553

774. Nevertheless, the spacing between the kink boundaries in both samples is similar. More

554

measurements are needed to examine a possible relationship between the spacing of kink

555

boundaries and stress conditions, as for instance inferred from modelling of kink bands in naturally

556

deformed quartz (Nishikawa and Takeshita, 1999).

557

(Figure 10 here)

558

4.3. Slip systems, local stresses and kinking at a multiple grain level

559

Our results suggest that kinking is a strong strain accommodation mechanism at a multiple grain-

560

scale (Fig. 8c,d,9c,d). For both low and high misorientations and 2.7 MPa and 13.3 MPa axial stress,

561

the evidence of straight and curved grain boundaries with statistically preferred rotation axes in the

562

basal plane is ample (Fig. 8c,d,9c,d). Various rotation axes within the basal plane can be caused by a

563

ripplocation defect in the basal plane or crystal slip on two coupled a-axes in the basal plane (Fig. 5b).

564

To determine if there is a preferred slip orientation, we calculated Schmid factor distributions for the

565

large-scale kink maps in Fig. 8 and 9. Higher relative frequencies occurred at maximum Schmid

566

factors of 0.495 (critical resolved shear stress accommodated by a specific slip system) were detected

567

for slip on (0001) <21-30> than for (0001) <11-20> and (0001) <10-10> (Fig. 10). The maximum

568

amount of shear stress in both samples is thus accommodated by slip in the <21-30> direction, which

569

is consistent with basal slip on two a-axes with uneven contributions.

570 571

5. Conclusions

572

Observations from EBSD data of two polycrystalline ice samples, deformed at different stresses,

573

suggest that: 23

574

•

Recrystallisation and the grain size reduction from remnant grains to recrystallised grains are

575

driven by kinking, as evidenced by the 1) the creation of new straight boundaries with

576

misorientations of 2-80° and rotation axes in the basal plane, 2) similar crystallographic

577

orientations of neighbouring recrystallised grains and 3) kinked remnant grains adjacent to

578

bands of recrystallised grains.

579

•

Observed rotation axes of kink boundaries lie within the basal (0001) plane of the ice crystal,

580

including <11-20>, <10-10> and intermediate directions. These rotation axes require

581

simultaneous slip on two crystallographic a-axes or ripplocations within the basal plane.

582

•

Rotation axes outside the basal plane constrain a local activity of a strain component parallel

583

to the c-axis of the ice crystal, created by non-basal dislocations or ripplocations. Non-basal

584

dislocations are triggered by locally elevated stresses due to kinking and aid local kink

585

deformation and recrystallisation by prolonging and connecting kink boundaries.

586

Ripplocations do not have a fixed Burgers vector and rotation axis and can also explain

587

boundaries created by a conjunction of rotation axes inside and outside the basal plane.

588

•

Several examples of remnant grains show up to six parallel kink boundaries with locking

589

angles of 70ᵒ in the high-stress sample (13.3 MPa axial load), whereas remnant grains in the

590

low-stress sample (2.7 MPa) exhibit a maximum of three straight kink boundaries with

591

locking angles of 25ᵒ. These observations suggest that the locking angle of kink boundaries

592

depends on the stress configuration.

593

•

Hundreds of grains display straight kink boundaries with rotation axes within the basal plane,

594

consistent with ripplocations or crystal slip on two a-axes in the basal plane. The preferred

595

slip direction for ∼1000 recrystallised and remnant grains in each sample is <21-30>, which

596

can solely be produced by basal dislocations if slip occurs on to a-axes with uneven

597

contributions. These observations suggest that the development and evolution of kink

598

boundaries plays a key role in the recrystallisation process.

599 24

600 601 602 603 604 605 606 607 608 609

Acknowledgements

610

This work was supported by a Marsden Grant UOO1116; NASA grant NNX13AK98G; a travel grant

611

from the Polar Environments Research Theme (PERT), Otago; and University of Otago Doctoral

612

Scholarships (M. Seidemann and M. J. Vaughan). Virginia Toy and Adam Treverrow are thanked for

613

helpful comments on an earlier version of this contribution presented within the framework of Meike

614

Seidemann’s PhD thesis. We also thank Chris Wilson and Ren´ee Heilbronner whose reviews helped

615

improve and clarify this manuscript.

616 617 618 619 620 25

621 622 623 624 625 626 627 628 629 630

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766 767

32

Table 1: Definitions of ambiguous terms.

ductile

Non-brittle deformation, characterised by an absence of micro-cracking.

high-angle grain boundary

Grain boundary with a misorientation of >10°, excluding high-angle kink boundaries.

high-angle kink boundary

Kink boundary with a misorientation of >10°.

769-specific kink boundary

Kink boundary with a misorientation of 50-70°, misorientation range characteristic in sample 769.

kink boundary

Straight grain boundary, sometimes also curved with bends <=20ᵒ due to subsequent deformation, with a rotation axis in the basal (0001) plane. We have exemplarily discriminated between <10-10>, <11-20> and <21-30> rotation axes in our analysis.

kinked grain

Remnant grain intersected by one or more low- or high-angle kink boundary(ies), can contain recrystallised grains when one or more high-angle kink boundary(ies) are present.

locking angle

Maximum misorientation angle for a kink boundary under a given differential stress.

low-angle grain boundary

Grain boundary with a misorientation of <10°, excluding low-angle kink boundaries.

recrystallised grains

Small grains (<200um), below average grain size of starting material of ∼250 µm, with equant or elongated grain shapes.

remnant grains

Grains interpreted to remain from the starting material, identified by polygonal grain shapes and arithmetic mean grain size of ~250 ±100 µm, sometimes with partly serrated grain boundaries due to grain boundary migration.

33

Figures

Figure 1: A schematic diagram illustrating the kinking process and associated nomenclature in a polygonal ice grain. Kink boundaries are defined here as straight grain boundaries with unspecific rotation axes within the basal (0001) plane (i.e. <11-20>, <10-10> and <21-30>, see also Fig. 10 for a directions overview within an ice crystal). Misorientation angles vary from low (close to 0ᵒ) to high (close to 90ᵒ) angles.

1

Figure 2: Microstructure and CPO of the undeformed starting material “Standard ice”. a) EBSD orientation map imaged at a step size of 10 µm. Inverse pole figure colour-coding with respect to the Y-direction was employed to visualise grain orientation. Areas of non-indexing (white) are due to a crack introduced during sample preparation. b) Equal area, upper hemisphere projections showing caxis (<0001>) and m-axis (<10-10>) CPOs. c) Relative Frequency vs. grain size histogram for 1220 grains. The arithmetic mean grain size and standard deviation are given in the top right corner. d) Neighbour-pair distribution (white bars), random-pair distribution (grey bars) and the random distribution for a hexagonal ice 1h crystal (black line) are displayed in a misorientation angle histogram. The histogram was calculated with a bin width of 5ᵒ and a minimum misorientation angle of 2ᵒ. Plots a)-c) were generated with MTEX 4.0.12. The misorientation angles diagram in d) was created in Channel 5.

2

3

Figure 3: EBSD orientation maps of samples 769 (a) and 774 (b) at the top were colour-coded according to the shortening direction (Y). Mapping yielded respective indexing values of 62.4 % (a) and 69.3 % (b) at a step size of 10 µm. Area-equivalent grain diameters below 200 µm are shown on pattern quality maps to highlight the distribution of recrystallised grains (bottom). c-axes CPOs for large remnant grains (>200 µm) and small recrystallised grains (<200 µm) are shown on equal-area, upper hemisphere projections below. Contouring was performed in MTEX 4.0.12 with a 10°halfwidth. The maps of both samples were taken from the transition between narrow and wide sample diameters (big red rectangles in sample legends below the maps). Additionally labelled are the locations of the more detailed maps employed for Fig. 4, 7 and 9.

4

5

Figure 4: Microstructural properties of a band of recrystallised grains and surrounding remnant grains in sample 774. a) EBSD orientation map colour-coded with respect to the bulk shortening direction (Y). The location of the map within the sample is indicated in Fig. 3. Misorientation profiles are given below. The band of recrystallised grains is highlighted in grey in the transects. Misorientation is given with respect to the starting point. b) Selected grain boundary misorientations are superimposed on a pattern quality (band contrast) map. c) Schmid factor map showing the amount of critical resolved shear stress (CRSS) on ice’s most prominent (0001) <11-20> slip system per grain. Arithmetic means of the Schmid factors were calculated for small grains (<200 µm) within the band and large grains (>200 µm) outside of the band, respectively and are shown in a box below the map. d) Intragranular misorientation map denoting the misorientation of each pixel respective to the mean orientation of the grain (mis2mean). e) Map showing the grain averaged kernel average misorientation (gKAM) for each grain determined from noise-reduced EBSD data. Kernel average misorientations (KAMs) denoting the intragranular average misorientation angle per pixel were calculated from nearest neighbour pixels (order of 1). The gKAM is the arithmetic mean of all KAM measurements within a grain. Misorientations above 6ᵒ were ignored for the calculation of the KAMs. NaN values with insufficient EBSD indexing are shown as white spots.

6

7

Figure 5: Predictions of slip systems and their respective rotation axes (modified from Vaughan 2016). The slip plane and possible slip directions are shown on the left. The middle shows the slip direction, rotation axis and slip plane in a stereographic projection (upper hemisphere pole figure). Inverse pole figures on the right show whether the respective rotation axis corresponds to a tilt or a twist boundary.

8

9

Figure 6: Kinking in single grains in sample 769. a)-e) Detailed analysis of a kinked grain. a) EBSD orientation map imaged at a step size of 3 µm. The map was colour-coded with respect to the bulk shortening direction (Y). The transects below show misorientation along and perpendicular to kink boundaries with respect to the starting point. b) Misorientation angle distribution for the map shown in (a). c) Band contrast maps with grain boundaries colour-coded according to their rotation axes and inverse pole figures with the number of lines indicating multiples of the uniform distribution (mud). d) Pole figures (equalarea, upper hemisphere projections) display the CPO for the general grain (top) and a selected boundary fragment (see yellow rectangles in a, c, bottom). e) Trace analysis for the boundary fragment denoted with the yellow rectangle. f)-g) Slip systems and misorientation ranges for two additional grains. The maps were imaged at a step size of 10 µm. Orientation maps, pole figures and trace analyses were created as described for (a), (d)and (e), respectively.

10

11

Figure 7: Kinking in single grains in sample 774. a) EBSD orientation map for a selected grain with a step size of 10 µm. Inverse pole figure colour-coding of the grain was performed with respect to the shortening direction (Y). Transects below the map show misorientation parallel (A) and perpendicular to the kink boundaries (B). b) Misorientation angle histogram for the map in (a). c) Kink boundaries are superimposed on pattern quality (band contrast) maps and colourcoded according to their rotation axes (see legend). The pattern quality maps show kink boundaries with misorientations of 2-10ᵒ (top) and 10-90ᵒ (bottom). Zigzag patterns in the lines of the kink boundaries are an artefact of the imaging resolution. Inverse pole figures on the right show the rotation axes of the kink boundaries in a crystal reference frame. The number of lines in the inverse pole figures depict multiples of the uniform distribution (mud). d) CPOs of the selected grain (top) and a boundary fragment (yellow rectangle in (a), bottom) in sample reference frames. Pole figures are equal –area, upper hemisphere projections. e) Trace analysis for a boundary fragment (yellow rectangle in a). f)-g) Investigation of the kink boundaries in two additional grains. See (a), (d) and (e)

for

a

description

of

the

orientation

maps,

12

pole

figures

and

the

trace

analyses.

13

Figure 8: Grain boundary analysis of sample 769. a) Inverse pole figure orientation map colour-coded with respect to the bulk shortening direction (Y). The map was taken at a step size of 10 µm with an indexing rate of 62.5 %. b) Misorientation angle distribution for the map in (a). c) Pattern quality (band contrast) map. Boundaries with basal rotation axes for low-angle misorientations of <10° are shown in light blue and non-basal rotation axes in yellow. Black lines denote all high-angle boundaries with misorientations >10°. d) Boundary map with non-basal rotation axes (yellow) and basal rotation axes (black) for misorientations for >10° on a pattern quality map. Superimposed are 769-specific kink boundaries within a misorientation range of 50-70°, colour-coded according to their rotation axes. Inverse pole figures in the bottom left of the maps are equal-area, upper hemisphere projections with the number of lines indicating multiples of the uniform distribution (mud).

14

15

Figure 9: Boundary analysis of sample 774. a) Orientation map (inverse pole figure colour-code with respect to the shortening direction) showing 219 large grains >200 µm and 724 small grains with an area-equivalent grain diameter <200 µm. The map was imaged at a step size of 10 µm with an indexing rate of 95 %. b) Misorientation angle histogram for the map in (a). c) Pattern quality map with grain and kink boundaries with misorientations < 10ᵒ. Potential low-angle kink boundaries with rotation axes within the basal plane are light blue, grain boundaries with non-basal rotation axes are yellow (see legend). High-angle (>10ᵒ) grain boundaries are additionally given in black. d) Boundaries with non-basal rotation axes (yellow) and basal rotation axes (black) for misorientations >10° are superimposed on a pattern quality map. 769-specific kink boundaries within a misorientation range of 50-70° are highlighted in blue, green and red according to their rotation axes (see legend). Inverse pole figures in the bottom left of the maps are equal-area, upper hemisphere projections with the number of lines indicating multiples of the uniform distribution (mud).

16

Figure 10: The Schmid factor distributions and maximum values for three differing slip directions in the basal plane. The top row shows results for a map of sample 769 with 2156 large and small grains (Fig. 8); the bottom row for a map of sample 774 with 943 large and small grains (Fig. 9). Slip systems employed were the commonly known a- axis slip on the basal plane on (0001) <11-20> (column 1, blue). If slip on two <11-20> axes happened simultaneously with equal amounts of slip being accommodated by either of the axes, the result would be an m-slip direction in (0001) <10-10> (column 2, red). However, slip could also be performed on two <11-20> axes with one a- axis

17

dominating. This scenario was created by assuming slip in a (0001) <21-30> direction (green). Numbers in the top right corner of the plot denote the maximum Schmid factor and corresponding relative frequency of the respective distribution.

18

Highlights • • • •

Kinking produces bands of recrystallised grains with a reduced grain size. Trace analyses and rotation axes distributions are used to constrain slip systems. Kink boundaries are created by basal slip on two a-axes or ripplocations. The <21-30> slip direction is statistically preferred within the basal plane.

Declaration of interests ☐ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☒The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

Funding sources: Marsden Grant; NASA grant; Polar Environments Research Theme (PERT), Otago; and University of Otago Doctoral Scholarships