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Grain growth inhibited during grain size-sensitive creep in polycrystalline ice: an energy dissipation-rate perspective

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Abstract

Experiments in which two identical polycrystalline ice Ih specimens are simultaneously subjected to the same time–temperature history while one of the specimens is actively deformed via grain size-sensitive (GSS) creep demonstrate distinctly different microstructural evolution: for particular ranges of starting grain size and differential stress, grains do not grow in the deforming specimen. Ice Ih specimens having initial, uniform grain sizes in the range d = 6–63 μm were tested in pairs that were subjected to identical time–temperature conditions (durations t = 4–12 days; T = 240 K) but of which only one was subjected to differential stress (σ1 = 0.25–1.85 MPa; σ3 = 0). Comparing specimens within a pair, for those with coarser initial grain size, the deformed specimens exhibit suppressed or no grain growth. Our results are interpreted from the perspective of nonequilibrium thermodynamics, specifically comparing the energy dissipation rates associated with both grain growth and plastic flow: if the rate of energy dissipation associated with flow exceeds that of grain growth, the grains will not grow. An examination of the limited database on GSS flow and grain growth in silicates conforms to our analysis. The results are applied to the question of the mechanical evolution of terrestrial glaciers and to the ice-rich shells of the outer satellites.

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References

  • Alley RB, Joughin I (2012) Modeling ice-sheet flow. Science 336:551–552. https://doi.org/10.1126/science.1220530

    Article  Google Scholar 

  • Alley RB, Gow AJ, Meese DA (1995) Mapping c-axis fabrics to study physical processes in ice. J Glaciol 41(137):197–203

    Article  Google Scholar 

  • Arena L, Nasello OB, Levi L (1997) Effect of bubbles on grain growth in ice. J Phys Chem B 101(32):6109–6112. https://doi.org/10.1021/jp9632394

    Article  Google Scholar 

  • Ashby MF, Verrall RA (1973) Diffusion-accommodated flow and superplasticity. Acta Metall 21:149–163

    Article  Google Scholar 

  • Austin NJ, Evans B (2007) Paleowattmeters: a scaling relation for dynamically recrystallized grain size. Geology 35:343–346

    Article  Google Scholar 

  • Azuma N, Miyakoshi T, Yokoyama S, Takata M (2012) Impeding effect of air bubbles on normal grain growth of ice. J Struct Geol 42:184–193

    Article  Google Scholar 

  • Barr AC, McKinnon WB (2007) Convection in ice I shells and mantles with self-consistent grain size. J Geophys Res-Planets 112:E02012. https://doi.org/10.1029/2006JE002781

    Article  Google Scholar 

  • Barr AC, Pappalardo RT (2005) Onset of convection in the icy Galilean satellites: influence of rheology. J Geophys Res-Planets 110:E12005. https://doi.org/10.1029/2004JE002371

    Article  Google Scholar 

  • Barr AC, Showman AP (2009) Heat transfer in Europa’s icy shell. In: Pappalardo RT, McKinnon WB, Khurana K (eds) Europa. University of Arizona Press, Tucson, AZ, USA, pp 405–430

    Google Scholar 

  • Bauer M, Elsaesser MS, Winkel K, Mayer E, Loerting T (2008) Compression-rate dependence of the phase transition from hexagonal ice to ice II and/or ice III. Phys Rev B 77:220105. https://doi.org/10.1103/PhysRevB.77.220105

    Article  Google Scholar 

  • Baum WA, Kreidl T, Westphal JA, Danielson GE, Seidelmann PK, Pascu D, Currie DG (1981) Saturn’s E ring: I. CCD observations of March 1980. Icarus 47(1):84–96

    Article  Google Scholar 

  • Behn MD, Goldsby DL, Hirth G (2021) The role of grain-size evolution on the rheology of ice: implications for reconciling laboratory creep data and the Glen flow law. Cryosphere 15:4589–4605. https://doi.org/10.5194/tc-15-4589-2021

    Article  Google Scholar 

  • Bennett K, Wenk HR, Durham WB, Stern LA, Kirby SH (1997) Preferred crystallographic orientation in the ice I ➔ II transformation and the flow of ice II. Philos Mag A 76(2):413–435. https://doi.org/10.1080/01418619708209983

    Article  Google Scholar 

  • Bestmann M, Pennacchioni G, Nielsen S, Göken M, de Wall H (2012) Deformation and ultrafine dynamic recrystallization of quartz in pseudotachylyte-bearing brittle faults: a matter of a few seconds. J Struct Geol 38:21–38. https://doi.org/10.1016/j.jsg.2011.10.001

    Article  Google Scholar 

  • Billings SE, Kattenhorn SA (2005) The great thickness debate: Ice shell thickness models for Europa and comparisons with estimates based on flexure at ridges. Icarus 177(2):397–412. https://doi.org/10.1016/j.icarus.2005.03.013

    Article  Google Scholar 

  • Bindschadler RA, Scambos TA (1991) Satellite-image-derived velocity field of an Antarctic ice stream. Science 252(5003):242–246

    Article  Google Scholar 

  • Caswell TE, Cooper RF, Goldsby DL (2015) The constant-hardness creep compliance of polycrystalline ice. Geophys Res Lett 42(15):6261–6268. https://doi.org/10.1002/2015GL064666

    Article  Google Scholar 

  • Clark RN (1981) Water frost and ice: the near-infrared spectral reflectance 0.65–2.5 µm. J Geophys Res-Solid Earth 86(B4):3087–3096

    Article  Google Scholar 

  • Clark RN, Fanale FP, Zent AP (1983) Frost grain size metamorphism: implications for remote sensing of planetary surfaces. Icarus 56:233–245

    Article  Google Scholar 

  • Coble RL (1963) A model for boundary diffusion controlled creep in polycrystalline materials. J Appl Phys 34(6):1679–1682

    Article  Google Scholar 

  • Collins GC, McKinnon WB, Moore JM, Nimmo F, Pappalardo RT, Prockter LM, Schenk PM (2009) Tectonics of the outer planet satellites. In: Watters TR, Schultz RA (eds) Planetary tectonics. Cambridge University Press, Cambridge, pp 264–350. https://doi.org/10.1017/CBO9780511691645.008

    Chapter  Google Scholar 

  • Cooper RF, Kohlstedt DL (1982) Interfacial energies in the olivine basalt system. Adv Earth Planetary Sci 12:217–228

    Google Scholar 

  • Cooper RF, Yoon WY, Perepezko JH (1991) Internal nucleation of highly undercooled magnesium metasilicate melts. J Am Ceram Soc 74(6):1312–1319. https://doi.org/10.1111/j.1151-2916.1991.tb04104.x

    Article  Google Scholar 

  • Courtney TH (1990) Mechanical behavior of materials. McGraw-Hill, New York, USA

    Google Scholar 

  • Cuffey KM, Thorsteinsson T, Waddington ED (2000) A renewed argument for crystal size control of ice sheet strain rates. J Geophys Res-Solid Earth 105(B12):27889–27894

    Article  Google Scholar 

  • De Bresser JHP, Ter Heege JH, Spiers CJ (2001) Grain size reduction by dynamic recrystallization: can it result in major rheological weakening? Int J Earth Sci 90(1):28–45. https://doi.org/10.1007/s005310000149

    Article  Google Scholar 

  • Deblonde G, Peltier WR (1991) Simulations of continental ice sheet growth over the last glacial-interglacial cycle: experiments with a one-level seasonal energy balance model including realistic geography. J Geophys Res-Atmos 96(D5):9189–9215. https://doi.org/10.1029/90JD02606

    Article  Google Scholar 

  • Druetta E, Nasello OB, Di Prinzio CLD (2014) Experimental determination of ⟨10-10⟩/Ψ tilt grain boundary energies in ice. J Mater Sci Res 3(1):69–76. https://doi.org/10.5539/jmsr.v3n1p69

    Article  Google Scholar 

  • Durham WB, Stern LA, Kirby SH (2001) Rheology of ice I at low stress and elevated confining pressure. J Geophys Res 106(6):11031–11042

    Article  Google Scholar 

  • Echelmeyer KA, Harrison WD, Larsen C, Mitchell JE (1994) The role of the margins in the dynamics of an active ice stream. J Glaciol 40(136):527–538. https://doi.org/10.1017/S0022143000012417

    Article  Google Scholar 

  • Evans B, Renner J, Hirth G (2001) A few remarks on the kinetics of static grain growth in rocks. Int J Earth Sci 90:88–103. https://doi.org/10.1007/s005310000150

    Article  Google Scholar 

  • Exner HE (1972) Analysis of grain- and particle-size distributions in metallic materials. Int Metall Rev 17:25–42

    Article  Google Scholar 

  • Fan S, Prior DJ, Cross AJ, Goldsby DL, Hager TF, Negrini M, Qi C (2021) Using grain boundary irregularity to quantify dynamic recrystallization in ice. Acta Mater 209:116810

    Article  Google Scholar 

  • Feltham P (1957) Grain growth in metals. Acta Metall 5(2):97–105

    Article  Google Scholar 

  • Ford HA, Fischer KM, Lekic V (2014) Localized shear in the deep lithosphere beneath the San Andreas fault system. Geology 42(4):295–298. https://doi.org/10.1130/G35128.1

    Article  Google Scholar 

  • Gasson E, DeConto RM, Pollard D, Levy RH (2016) Dynamic Antarctic ice sheet during the early to mid-Miocene. Proc Natl Acad Sci USA 113(13):3459–3464. https://doi.org/10.1073/pnas.1516130113

    Article  Google Scholar 

  • Goldsby DL, Kohlstedt DL (1997) Grain boundary sliding in fine-grained ice I. Scripta Mater 37(9):1399–1406

    Article  Google Scholar 

  • Goldsby DL, Kohlstedt DL (2001) Superplastic deformation of ice: experimental observations. J Geophys Res-Solid Earth 106(B6):11017–11030

    Article  Google Scholar 

  • Gow AJ (1969) On the rates of growth of grains and crystals in south polar firn. J Glaciol 8(53):241–252

    Article  Google Scholar 

  • Herring C (1950) Diffusional viscosity of a polycrystalline solid. J Appl Phys 21:437–445

    Article  Google Scholar 

  • Hillert M (1965) On the theory of normal and abnormal grain growth. Acta Metall 13(3):227–238

    Article  Google Scholar 

  • Hillert M, Ågren J (2006) Extremum principles for irreversible processes. Acta Mater 54:2063–2066

    Article  Google Scholar 

  • Hondoh T, Higashi A (1978) X-Ray diffraction topographic observations of the large-angle grain boundary in ice under deformation. J Glaciol 21(85):629–638

    Article  Google Scholar 

  • Hoppa G, Greenberg R, Tufts BR, Geissler P, Phillips C, Milazzo M (2000) Distribution of strike-slip faults on Europa. J Geophys Res-Planets 105(E9):22617–22627

    Article  Google Scholar 

  • Joughin I, Tulaczyk S, Bindschadler R, Price SF (2002) Changes in West Antarctic ice stream velocities: observation and analysis. J Geophys Res-Solid Earth 107(B11):2289. https://doi.org/10.1029/2001JB001029

    Article  Google Scholar 

  • Joughin I, MacAyeal D, Tulaczyk S (2004) Basal shear stress of the Ross ice streams from control method inversions. J Geophys Res-Solid Earth 109:B09405

    Article  Google Scholar 

  • Kamb B (2001) Basal zone of the West Antarctic ice streams and its role in lubrication of their rapid motion. In: Alley RB, Bindschadler RA (eds) The West Antarctic Ice Sheet: Behavior and Environment (Antarctic Research Series Volume 77). American Geophysical Union, Washington, DC, USA, pp 157–200

    Google Scholar 

  • Karato S (1989) Grain growth kinetics in olivine aggregates. Tectonophysics 168:255–273

    Article  Google Scholar 

  • Karato S (2008) Deformation of earth materials: an introduction to the rheology of solid earth. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Karato S, Wu P (1993) Rheology of the upper mantle: a synthesis. Science 260:771–778

    Article  Google Scholar 

  • Karato S, Paterson MS, Fitz Gerald JD (1986) Rheology of synthetic olivine aggregates: influence of grain size and water. J Geophys Res 91(B8):8151–8176

    Article  Google Scholar 

  • Kattenhorn SA, Prockter LM (2014) Evidence for subduction in the ice shell of Europa. Nat Geosci 7(10):762–767. https://doi.org/10.1038/ngeo2245

    Article  Google Scholar 

  • Kempf S, Beckmann U, Schmidt J (2010) How the Enceladus dust plume feeds Saturn’s E ring. Icarus 206(2):446–457. https://doi.org/10.1016/j.icarus.2009.09.016

    Article  Google Scholar 

  • Ketcham WM, Hobbs PV (1969) An experimental determination of the surface energies of ice. Phil Mag 19:1161–1173

    Article  Google Scholar 

  • Kim J-W, Ree J-H, Han R, Shimamoto T (2010) Experimental evidence for the simultaneous formation of pseudotachylyte and mylonite in the brittle regime. Geology 38(12):1143–1146

    Article  Google Scholar 

  • Kingery WD, Bowen HK, Uhlmann DR (1976) Introduction to ceramics, 2nd edn. Wiley, New York, USA

    Google Scholar 

  • Kondepudi D, Prigogine I (1998) Modern thermodynamics: from heat engines to dissipative structures. Wiley, Chichester, England, UK

    Google Scholar 

  • Langdon T (1991) The physics of superplastic deformation. Mater Sci Eng, A A137:1–11

    Article  Google Scholar 

  • Liu F, Baker I, Dudley M (1993) Dynamic observations of dislocation generation at grain boundaries in ice. Philos Mag A 67(5):1261–1276. https://doi.org/10.1080/01418619308224770

    Article  Google Scholar 

  • McCarthy C, Cooper RF (2016) Tidal dissipation in creeping ice and the thermal evolution of Europa. Earth Planet Sci Lett 443:185–194. https://doi.org/10.1016/j.epsl.2016.03.006

    Article  Google Scholar 

  • Montagnat M, Duval P (2000) Rate controlling processes in the creep of polar ice, influence of grain boundary migration associated with recrystallization. Earth Planet Sci Lett 183(1):179–186

    Article  Google Scholar 

  • Mukherjee AK, Bird JE, Dorn JE (1969) Experimental correlations for high-temperature creep. Trans Am Soc Metals 62:155–179

    Google Scholar 

  • Nabarro FRN (1948) Deformation of crystals by the motion of single ions. In: Nooky G (ed) Report of a conference on the strength of solids. Physical Society of London, London, England, UK, pp 75–90

    Google Scholar 

  • Nakamura T, Matsumoto M, Yagasaki T, Tanaka H (2016) Thermodynamic stability of ice II and its hydrogen-disordered counterpart: Role of zero-point energy. J Phys Chem B 120:1843–1848. https://doi.org/10.1021/acs.jpcb.5b09544

    Article  Google Scholar 

  • Newman J, Chatzaras V, Tikoff B, Wijbrans JR, Lamb WM, Drury MR (2021) Strain localization at constant strain rate and changing stress conditions: implications for plate boundary processes in the upper mantle. Minerals 11:1351. https://doi.org/10.3390/min11121351

    Article  Google Scholar 

  • Nimmo F, Gaidos E (2002) Strike-slip motion and double ridge formation on Europa. J Geophys Res-Planets 107(E4):5021. https://doi.org/10.1029/2000JE001476

    Article  Google Scholar 

  • Nimmo F, Giese B, Pappalardo RT (2003) Estimates of Europa’s ice shell thickness from elastically-supported topography. Geophys Res Lett 30(5):1233

    Article  Google Scholar 

  • Odum HT, Pinkerton RC (1955) Time’s speed regulator: The optimum efficiency for maximum power output in physical and biological systems. Am Sci 43(2):331–343

    Google Scholar 

  • Ojakangas GW, Stevenson DJ (1989) Thermal state of an ice shell on Europa. Icarus 81(2):220–241. https://doi.org/10.1016/0019-1035(89)90052-3

    Article  Google Scholar 

  • Onsager L (1931) Reciprocal relations in irreversible processes. I. Phys Rev 37:405–426

    Article  Google Scholar 

  • Pappalardo RT, Head JW III, Greeley R, Sullivan RJ, Pilcher C, Schubert G, Moore WB, Carr MH, Moore JM, Belton MJS, Goldsby DL (1998) Geological evidence for solid-state convection in Europa’s ice shell. Nature 391:365–367

    Article  Google Scholar 

  • Perol T, Rice JR (2015) Shear heating and weakening of the margins of West Antarctic ice streams. Geophys Res Lett 42(9):3406–3413. https://doi.org/10.1002/2015GL063638

    Article  Google Scholar 

  • Pettit EC, Waddington ED, Harrison WD, Thorsteinsson T, Elsberg D, Morack J, Zumberge MA (2011) The crossover stress, anisotropy and the ice flow law at Siple Dome, West Antarctica. J Glaciol 57:39–52

    Article  Google Scholar 

  • Poirier J-P (1985) Creep of crystals. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Pollard D, DeConto RM (2009) Modeling West Antarctic ice sheet growth and collapse through the past five million years. Nature 458:329–332. https://doi.org/10.1038/nature07809

    Article  Google Scholar 

  • Porco CC, Helfenstein P, Thomas PC, Ingersoll AP, Wisdom J, West R, Neukum G, Denk T, Wagner R, Roatsch T, Kieffer S, Turtle E, McEwen A, Johnson TV, Rathbun J, Veverka J, Wilson D, Perry J, Spitale J et al (2006) Cassini observes the active south pole of Enceladus. Science 311:1393–1401

    Article  Google Scholar 

  • Porco C, DiNino D, Nimmo F (2014) How the geysers, tidal stresses, and thermal emission across the south polar terrain of Enceladus are related. Astron J 148(3):45. https://doi.org/10.1088/0004-6256/148/3/45

    Article  Google Scholar 

  • Prigogine I (1997) The end of certainty: time, chaos, and the new laws of nature. The Free Press, New York, USA

    Google Scholar 

  • Prior DJ, Lilly K, Seidemann M, Vaughan M, Becroft L, Easingwood R, Diebold S, Obbard R, Daghlian C, Baker I, Caswell T, Golding N, Goldsby D, Durham WB, Piazolo S, Wilson CJL (2015) Making EBSD on water ice routine. J Microsc 259(3):237–256. https://doi.org/10.1111/jmi.12258

    Article  Google Scholar 

  • Raj R (1975) Transient behavior of diffusion-induced creep and creep rupture. Metall Trans A 6A:1499–1590

    Article  Google Scholar 

  • Raj R (1981) Morphology and stability of the glass phase in glass-ceramic systems. J Am Ceram Soc 64(5):245–248

    Article  Google Scholar 

  • Raj R, Ashby MF (1971) On grain boundary sliding and diffusional creep. Metall Trans 2:1113–1127

    Article  Google Scholar 

  • Ranganathan M, Minchew B, Meyer CR, Peč M (2021) Recrystallization of ice enhances the creep and vulnerability to fracture of ice shelves. Earth Planet Sci Lett 576:11721. https://doi.org/10.1016/j.epsl.2021.117219

    Article  Google Scholar 

  • Rozel A, Ricard Y, Bercovici D (2011) A thermodynamically self-consistent damage equation for grain size evolution during dynamic recrystallization. Geophys J Int 184:719–728. https://doi.org/10.1111/j.1365-246X.2010.04875.x

    Article  Google Scholar 

  • Rutter EH, Brodie KH (1988) The role of tectonic grain size reduction in the rheological stratification of the lithosphere. Int J Earth Sci 77(1):295–307

    Google Scholar 

  • Schmalzried H (1995) Chemical kinetics of solids. VCH Publishers, Weinheim, FRG

    Book  Google Scholar 

  • Schoof C (2010) Ice-sheet acceleration driven by melt supply variability. Nature 468:803–806. https://doi.org/10.1038/nature09618

    Article  Google Scholar 

  • Sejrup HP, Clark CD, Hjelstuen BO (2016) Rapid ice sheet retreat triggered by ice stream debuttressing: evidence from the North Sea. Geology 44(5):355–358. https://doi.org/10.1130/G37652.1

    Article  Google Scholar 

  • Shimizu I (1998) Stress and temperature dependence of recrystallized grain size: a subgrain misorientation model. Geophys Res Lett 25(22):4237–4240

    Article  Google Scholar 

  • Smith SAF, Di Toro G, Kim S, Ree J-H, Nielsen S, Billi A, Spiess R (2013) Coseismic recrystallization during shallow earthquake slip. Geology 41(1):63–66. https://doi.org/10.1130/G33588.1

    Article  Google Scholar 

  • Spahn F, Schmidt J, Albers N, Hörning M, Makuch M, Seiß M, Kempf S, Srama R, Dikarev V, Helfert S, Moragas-Klostermeyer G, Krivov AV, Sremčević M, Tuzzolino AJ, Economou T, Grün E (2006) Cassini dust measurements at Enceladus and implications for the origin of the E ring. Science 311:1416–1418

    Article  Google Scholar 

  • Speciale PA, Behr WM, Hirth G, Tokle L (2020) Rates of olivine grain growth during dynamic recrystallization and postdeformation annealing. J Geophys Res-Solid Earth 125:e2020JB020415. https://doi.org/10.1029/2020JB020415

    Article  Google Scholar 

  • Stern LA, Durham WB, Kirby SH (1997) Grain-size-induced weakening of H2O ices I and II and associated anisotropic recrystallization. J Geophys Res-Solid Earth 102(B3):5313–5325. https://doi.org/10.1029/96JB03894

    Article  Google Scholar 

  • Suckale J, Platt JD, Perol T, Rice JR (2014) Deformation-induced melting in the margins of the West Antarctic ice streams. J Geophys Res-Earth Surf 119(5):1004–1025. https://doi.org/10.1002/2013JF003008

    Article  Google Scholar 

  • Sutton AP, Balluffi RW (1995) Interfaces in crystalline materials. Clarendon Press, Oxford

    Google Scholar 

  • Tobie G, Choblet G, Sotin C (2003) Tidally heated convection: constraints on Europa’s ice shell thickness. J Geophys Res-Planets 108(E11):5124. https://doi.org/10.1029/2003JE002099

    Article  Google Scholar 

  • Tufts BR, Greenberg R, Hoppa G, Geissler P (1999) Astypalaea Linea: a large-scale strike-slip fault on Europa. Icarus 141:53–64

    Article  Google Scholar 

  • Tulaczyk S, Kamb B, Engelhardt HF (2001) Estimates of effective stress beneath a modern West Antarctic ice stream from till preconsolidation and void ratio. Boreas 30(2):101–114

    Article  Google Scholar 

  • Twiss RJ (1977) Theory and applicability of a recrystallized grain size paleopiezometer. Pure Appl Geophys 115:227–244

    Article  Google Scholar 

  • Verberne BA, Plümper O, de Winter DM, Spiers CJ (2014) Superplastic nanofibrous slip zones control seismogenic fault friction. Science 346(6215):1342–1344

    Article  Google Scholar 

  • Walpole RE, Myers RH (1972) Probability and statistics for engineers and scientists. Macmillan Co, New York

    Google Scholar 

  • Warren JM, Hirth G (2006) Grain size sensitive deformation mechanisms in naturally deformed peridotites. Earth Planet Sci Lett 248:438–450

    Article  Google Scholar 

  • Whillans IM, van der Veen CJ (1997) The role of lateral drag in the dynamics of Ice Stream B, Antarctica. J Glaciol 43(144):231–237

    Article  Google Scholar 

  • Willis JK, Church JA (2012) Regional sea-level projection. Science 336:550–551

    Article  Google Scholar 

  • Ziegler H (1958) An attempt to generalize Onsager’s principle, and its significance for rheological problems. Z Angew Math Phys 9b:748–763

    Article  Google Scholar 

  • Ziegler H, Wehrli C (1987) The derivation of constitutive relations from the free energy and the dissipation function. Adv Appl Mech 25:183–238

    Article  Google Scholar 

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Acknowledgements

Greg Hirth, David Goldsby and Christine McCarthy are thanked for numerous, spirited discussions concerning many aspects of the theory explored here. The perceptive comments of Mark Behn and an anonymous reviewer improved the manuscript significantly. This research was supported financially, in part, by a grant from the Solar Systems Workings Program of the Science Mission Directorate of NASA (Grant NNX16AQ14G to R.F.C.) and by the National Science Foundation through a Graduate Research Fellowship (to T.E.C.).

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Caswell, T.E., Cooper, R.F. Grain growth inhibited during grain size-sensitive creep in polycrystalline ice: an energy dissipation-rate perspective. Phys Chem Minerals 49, 28 (2022). https://doi.org/10.1007/s00269-022-01202-9

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