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Role of stacking disorder in ice nucleation

Abstract

The freezing of water affects the processes that determine Earth’s climate. Therefore, accurate weather and climate forecasts hinge on good predictions of ice nucleation rates1. Such rate predictions are based on extrapolations using classical nucleation theory1,2, which assumes that the structure of nanometre-sized ice crystallites corresponds to that of hexagonal ice, the thermodynamically stable form of bulk ice. However, simulations with various water models find that ice nucleated and grown under atmospheric temperatures is at all sizes stacking-disordered, consisting of random sequences of cubic and hexagonal ice layers3,4,5,6,7,8. This implies that stacking-disordered ice crystallites either are more stable than hexagonal ice crystallites or form because of non-equilibrium dynamical effects. Both scenarios challenge central tenets of classical nucleation theory. Here we use rare-event sampling9,10,11 and free energy calculations12 with the mW water model13 to show that the entropy of mixing cubic and hexagonal layers makes stacking-disordered ice the stable phase for crystallites up to a size of at least 100,000 molecules. We find that stacking-disordered critical crystallites at 230 kelvin are about 14 kilojoules per mole of crystallite more stable than hexagonal crystallites, making their ice nucleation rates more than three orders of magnitude higher than predicted by classical nucleation theory. This effect on nucleation rates is temperature dependent, being the most pronounced at the warmest conditions, and should affect the modelling of cloud formation and ice particle numbers, which are very sensitive to the temperature dependence of ice nucleation rates1. We conclude that classical nucleation theory needs to be corrected to include the dependence of the crystallization driving force on the size of the ice crystallite when interpreting and extrapolating ice nucleation rates from experimental laboratory conditions to the temperatures that occur in clouds.

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Figure 1: Reaction coordinate and free energy landscape for ice nucleation at 230 K.
Figure 2: Randomly selected critical ice nuclei with cubicity and size corresponding to the saddle point of the free energy landscape (white circle in Fig. 1c).
Figure 3: Stability and cubicity of ice crystallites along the pathway of nucleation and growth.

References

  1. 1

    Herbert, R. J., Murray, B. J., Dobbie, S. J. & Koop, T. Sensitivity of liquid clouds to homogenous freezing parameterizations. Geophys. Res. Lett. 42, 1599–1605 (2015)

    ADS  PubMed  PubMed Central  Google Scholar 

  2. 2

    Murray, B. J. et al. Kinetics of the homogeneous freezing of water. Phys. Chem. Chem. Phys. 12, 10380–10387 (2010)

    CAS  PubMed  Google Scholar 

  3. 3

    Li, T., Donadio, D., Russo, G. & Galli, G. Homogeneous ice nucleation from supercooled water. Phys. Chem. Chem. Phys. 13, 19807–19813 (2011)

    CAS  PubMed  Google Scholar 

  4. 4

    Moore, E. B. & Molinero, V. Is it cubic? Ice crystallization from deeply supercooled water. Phys. Chem. Chem. Phys. 13, 20008–20016 (2011)

    CAS  PubMed  Google Scholar 

  5. 5

    Malkin, T. L. et al. Stacking disorder in ice I. Phys. Chem. Chem. Phys. 17, 60–76 (2015)

    CAS  PubMed  Google Scholar 

  6. 6

    Haji-Akbari, A. & Debenedetti, P. G. Direct calculation of ice homogeneous nucleation rate for a molecular model of water. Proc. Natl Acad. Sci. USA 112, 10582–10588 (2015)

    ADS  CAS  PubMed  Google Scholar 

  7. 7

    Reinhardt, A. & Doye, J. P. K. Free energy landscapes for homogeneous nucleation of ice for a monatomic water model. J. Chem. Phys. 136, 054501 (2012)

    ADS  PubMed  Google Scholar 

  8. 8

    Morishige, K. & Uematsu, H. The proper structure of cubic ice confined in mesopores. J. Chem. Phys. 122, 044711 (2005)

    ADS  Google Scholar 

  9. 9

    Peters, B. & Trout, B. Obtaining reaction coordinates by likelihood maximization. J. Chem. Phys. 125, 054108 (2006)

    ADS  PubMed  Google Scholar 

  10. 10

    Peters, B., Beckham, G. T. & Trout, B. L. Extensions to the likelihood maximization approach for finding reaction coordinates. J. Chem. Phys. 127, 034109 (2007)

    ADS  PubMed  Google Scholar 

  11. 11

    Mullen, R. G., Shea, J.-E. & Peters, B. Transmission coefficients, committors, and solvent coordinates in ion-pair dissociation. J. Chem. Theory Comput. 10, 659–667 (2014)

    CAS  PubMed  Google Scholar 

  12. 12

    Peters, B., Zimmermann, N. E. R., Beckham, G. T., Tester, J. W. & Trout, B. L. Path sampling calculation of methane diffusivity in natural gas hydrates from a water-vacancy assisted mechanism. J. Am. Chem. Soc. 130, 17342–17350 (2008)

    CAS  PubMed  Google Scholar 

  13. 13

    Molinero, V. & Moore, E. B. Water modeled as an intermediate element between carbon and silicon. J. Phys. Chem. B 113, 4008–4016 (2009)

    CAS  PubMed  Google Scholar 

  14. 14

    Hansen, T., Koza, M. & Kuhs, W. Formation and annealing of cubic ice: I. Modelling of stacking faults. J. Phys. Condens. Matter 20, 285104 (2008)

    Google Scholar 

  15. 15

    Kuhs, W. F., Sippel, C., Falenty, A. & Hansen, T. C. Extent and relevance of stacking disorder in “ice Ic”. Proc. Natl Acad. Sci. USA 109, 21259–21264 (2012)

    ADS  CAS  PubMed  Google Scholar 

  16. 16

    Malkin, T. L., Murray, B. J., Brukhno, A. V., Anwar, J. & Salzmann, C. G. Structure of ice crystallized from supercooled water. Proc. Natl Acad. Sci. USA 109, 1041–1045 (2012)

    ADS  CAS  PubMed  Google Scholar 

  17. 17

    Hondoh, T., Itoh, T., Amakai, S., Goto, K. & Higashi, A. Formation and annihilation of stacking faults in pure ice. J. Phys. Chem. 87, 4040–4044 (1983)

    CAS  Google Scholar 

  18. 18

    Hudait, A., Lupi, S. Q. L. & Molinero, V. Free energy contributions and structural characterization of stacking disordered ices. Phys. Chem. Chem. Phys. 18, 9544–9553 (2016)

    CAS  PubMed  Google Scholar 

  19. 19

    Hondoh, T. Dislocation mechanism for transformation between cubic ice Ic and hexagonal ice Ih. Phil. Mag. 95, 3590–3620 (2015)

    ADS  CAS  Google Scholar 

  20. 20

    Quigley, D. Thermodynamics of stacking disorder in ice nuclei. J. Chem. Phys. 141, 121101 (2014)

    ADS  CAS  PubMed  Google Scholar 

  21. 21

    Bolhuis, P. G., Chandler, D., Dellago, C. & Geissler, P. L. Transition path sampling: throwing ropes over rough mountain passes, in the dark. Annu. Rev. Phys. Chem. 53, 291–318 (2002)

    ADS  CAS  PubMed  Google Scholar 

  22. 22

    Rein ten Wolde, P., Ruiz-Montero, M. J. & Frenkel, D. Numerical calculation of the rate of crystal nucleation in a Lennard-Jones system at moderate undercooling. J. Chem. Phys. 104, 9932–9947 (1996)

    ADS  Google Scholar 

  23. 23

    Nguyen, A. H. & Molinero, V. Identification of clathrate hydrates, hexagonal ice, cubic ice, and liquid water in simulations: the CHILL+ algorithm. J. Phys. Chem. B 119, 9369–9376 (2015)

    CAS  PubMed  Google Scholar 

  24. 24

    Pronk, S. & Frenkel, D. Can stacking faults in hard-sphere crystals anneal out spontaneously? J. Chem. Phys. 110, 4589 (1999)

    ADS  CAS  Google Scholar 

  25. 25

    Herrero, C. P. & Ramirez, R. Configurational entropy of hydrogen-disordered ice polymorphs. J. Chem. Phys. 140, 234502 (2014)

    ADS  PubMed  Google Scholar 

  26. 26

    Morishige, K., Yasunaga, H. & Uematsu, H. Stability of cubic ice in mesopores. J. Phys. Chem. C 113, 3056–3061 (2009)

    CAS  Google Scholar 

  27. 27

    Murray, B. J. & Bertram, A. K. Formation and stability of cubic ice in water droplets. Phys. Chem. Chem. Phys. 8, 186 (2006)

    CAS  PubMed  Google Scholar 

  28. 28

    Engel, E. A., Monserrat, B. & Needs, R. J. Anharmonic nuclear motion and the relative stability of hexagonal and cubic ice. Phys. Rev. X 5, 021033 (2015)

    Google Scholar 

  29. 29

    Amaya, A. J. et al. How cubic can ice be? J. Phys. Chem. Lett. 8, 3216–3222 (2017)

    CAS  PubMed  Google Scholar 

  30. 30

    Zaragoza, A. et al. Competition between ices Ih and Ic in homogeneous water freezing. J. Chem. Phys. 143, 134504 (2015)

    ADS  PubMed  Google Scholar 

  31. 31

    Plimpton, S. J. Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117, 1–19 (1995)

    ADS  CAS  MATH  Google Scholar 

  32. 32

    Steinhardt, P. J., Nelson, D. R. & Ronchetti, M. Bond-orientational order in liquids and glasses. Phys. Rev. B 28, 784–805 (1983)

    ADS  CAS  Google Scholar 

  33. 33

    Peters, B. Using the histogram test to quantify reaction coordinate error. J. Chem. Phys. 125, 241101 (2006)

    ADS  PubMed  Google Scholar 

  34. 34

    Röttger, K., Endriss, A., Ihringer, J., Doyle, S. & Kuhs, W. F. Lattice constants and thermal expansion of H2O and D2O ice Ih between 10 and 265 K. Acta Crystallogr. B 68, 91 (2012)

    PubMed  Google Scholar 

  35. 35

    Oguro, M. & Hondoh, T. Stacking faults in ice crystals. In Lattice defects in ice crystals (ed. Higashi, A. ) 49–67 (Hokkaido University Press, Sapporo, 1988)

  36. 36

    Smallenburg, F., Poole, P. H. & Sciortino, F. Phase diagram of the ST2 model of water. Mol. Phys. 113, 2791–2798 (2015)

    ADS  CAS  Google Scholar 

  37. 37

    Koop, T., Luo, B. P., Tsias, A. & Peter, T. Water activity as the determinant for homogeneous ice nucleation in aqueous solutions. Nature 406, 611–614 (2000)

    ADS  CAS  PubMed  Google Scholar 

  38. 38

    Gillan, M. J., Alfè, D. & Michaelides, A. How good is DFT for water? J. Chem. Phys. 144, 130901 (2016)

    ADS  PubMed  Google Scholar 

  39. 39

    Yamamuro, O., Oguni, M., Matsuo, T. & Suga, H. Heat capacity and glass transition of pure and doped cubic ices. J. Phys. Chem. Solids 48, 935–942 (1987)

    ADS  CAS  Google Scholar 

  40. 40

    Sugisaki, M., Suga, H. & Seki, S. Calorimetric study of the glassy state. IV. Heat capacities of glassy water and cubic ice. Bull. Chem. Soc. Jpn. 41, 2591–2599 (1968)

    CAS  Google Scholar 

  41. 41

    Salzmann, C. G., Mayer, E. & Hallbrucker, A. Thermal properties of metastable ices IV and XII: comparison, isotope effects and relative stabilities. Phys. Chem. Chem. Phys. 6, 1269–1276 (2004)

    CAS  Google Scholar 

  42. 42

    Kohl, I., Mayer, E. & Hallbrucker, A. The glassy water–cubic ice system: a comparative study by X-ray diffraction and differential scanning calorimetry. Phys. Chem. Chem. Phys. 2, 1579–1586 (2000)

    CAS  Google Scholar 

  43. 43

    Johari, G. P. On the coexistence of cubic and hexagonal ice between 160 and 240 K. Phil. Mag. B 78, 375–383 (1998)

    ADS  CAS  Google Scholar 

  44. 44

    Handa, Y. P., Klug, D. D. & Whalley, E. Difference in energy between cubic and hexagonal ice. J. Chem. Phys. 84, 7009–7010 (1986)

    ADS  CAS  Google Scholar 

  45. 45

    Ghormley, J. A. Enthalpy changes and heat-capacity changes in the transformations from high-surface-area amorphous ice to stable hexagonal ice. J. Chem. Phys. 48, 503 (1968)

    ADS  CAS  Google Scholar 

  46. 46

    Mayer, E. & Hallbrucker, A. Cubic ice from liquid water. Nature 325, 601–602 (1987)

    ADS  CAS  Google Scholar 

  47. 47

    Shilling, J. E. et al. Measurements of the vapor pressure of cubic ice and their implications for atmospheric ice clouds. Geophys. Res. Lett. 33, L17801 (2006)

    ADS  Google Scholar 

  48. 48

    McMillan, J. A. & Los, S. C. Vitreous Ice: Irreversible transformations during warm-up. Nature 206, 806–807 (1965)

    ADS  CAS  Google Scholar 

  49. 49

    Baragiola, R. A. Water ice on outer solar system surfaces: basic properties and radiation effects. Planet. Space Sci. 51, 953–961 (2003)

    ADS  CAS  Google Scholar 

  50. 50

    Stevenson, K., Kimmel, G., Dohnálek, Z., Smith, R. & Kay, B. Controlling the morphology of amorphous solid water. Science 283, 1505–1507 (1999)

    ADS  CAS  PubMed  Google Scholar 

  51. 51

    Morishige, K. & Iwasaki, H. X-ray study of freezing and melting of water confined within SBA-15. Langmuir 19, 2808–2811 (2003)

    CAS  Google Scholar 

  52. 52

    Morishige, K. & Nobuoka, K. X-ray diffraction studies of freezing and melting of water confined in a mesoporous adsorbent (MCM-41). J. Chem. Phys. 107, 6965 (1997)

    ADS  CAS  Google Scholar 

  53. 53

    Jelassi, J. et al. Studies of water and ice in hydrophilic and hydrophobic mesoporous silicas: pore characterisation and phase transformations. Phys. Chem. Chem. Phys. 12, 2838–2849 (2010)

    CAS  PubMed  Google Scholar 

  54. 54

    Domin, K., Chan, K. Y., Yung, H. & Gubbins, K. E. Structure of ice in confinement: water in mesoporous carbons. J. Chem. Eng. Data 61, 4252–4260 (2016)

    CAS  Google Scholar 

  55. 55

    Dore, J. Structural studies of water in confined geometry by neutron diffraction. Chem. Phys. 258, 327–347 (2000)

    CAS  Google Scholar 

  56. 56

    Findenegg, G. H., Jähnert, S., Akcakayiran, D. & Schreiber, A. Freezing and melting of water confined in silica nanopores. ChemPhysChem 9, 2651–2659 (2008)

    CAS  PubMed  Google Scholar 

  57. 57

    González Solveyra, E., De La Llave, E., Scherlis, D. A. & Molinero, V. Melting and crystallization of ice in partially filled nanopores. J. Phys. Chem. B 115, 14196–14204 (2011)

    Google Scholar 

  58. 58

    Moore, E. B., de la Llave, E., Welke, K., Scherlis, D. A. & Molinero, V. Freezing, melting and structure of ice in a hydrophilic nanopore. Phys. Chem. Chem. Phys. 12, 4124–4134 (2010)

    CAS  PubMed  Google Scholar 

  59. 59

    Moore, E. B., Allen, J. T. & Molinero, V. Liquid-ice coexistence below the melting temperature for water confined in hydrophilic and hydrophobic nanopores. J. Phys. Chem. C 116, 7507–7514 (2012)

    CAS  Google Scholar 

  60. 60

    Jähnert, S. et al. Melting and freezing of water in cylindrical silica nanopores. Phys. Chem. Chem. Phys. 10, 6039–6051 (2008)

    PubMed  Google Scholar 

  61. 61

    Murphy, D. Dehydration in cold clouds is enhanced by a transition from cubic to hexagonal ice. Geophys. Res. Lett. 30, 2230 (2003)

    ADS  Google Scholar 

  62. 62

    Hansen, T. C., Koza, M. M., Lindner, P. & Kuhs, W. F. Formation and annealing of cubic ice: II. Kinetic study. J. Phys. Condens. Matter 20, 285105 (2008)

    Google Scholar 

  63. 63

    Limmer, D. T. & Chandler, D. Phase diagram of supercooled water confined to hydrophilic nanopores. J. Chem. Phys. 137, 044509 (2012)

    ADS  PubMed  Google Scholar 

  64. 64

    Turnbull, D. Formation of crystal nuclei in liquid metals. J. Appl. Phys. 21, 1022 (1950)

    ADS  CAS  Google Scholar 

  65. 65

    Haynes, W. M. CRC Handbook of Chemistry and Physics: A Ready-Reference Book of Chemical and Physical Data (CRC Press, 2009)

  66. 66

    Jacobson, L. C., Hujo, W. & Molinero, V. Thermodynamic stability and growth of guest-free clathrate hydrates: a low-density crystal phase of water. J. Phys. Chem. B 113, 10298–10307 (2009)

    CAS  PubMed  Google Scholar 

  67. 67

    Limmer, D.T. & Chandler, D. Premelting, fluctuations, and coarse-graining of water-ice interfaces. J. Chem. Phys. 141, 18C505 (2014)

    PubMed  Google Scholar 

  68. 68

    Espinosa, J. R., Vega, C. & Sanz, E. Ice–water interfacial free energy for the TIP4P, TIP4P/2005, TIP4P/Ice, and mW models as obtained from the mold integration technique. J. Phys. Chem. C 120, 8068–8075 (2016)

    CAS  Google Scholar 

  69. 69

    Espinosa, J. R., Vega, C. & Valeriani, C. Seeding approach to crystal nucleation. J. Chem. Phys. 144, 034501 (2016)

    ADS  PubMed  Google Scholar 

  70. 70

    Ketcham, W. M. & Hobbs, P. V. An experimental determination of the surface energies of ice. Phil. Mag. 19, 1161–1173 (1969)

    ADS  CAS  Google Scholar 

  71. 71

    Hardy, S. C. A grain boundary groove measurement of the surface tension between ice and water. Phil. Mag. 35, 471–484 (1977)

    ADS  CAS  Google Scholar 

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Acknowledgements

We thank A. Haji-Akbari for discussions and for sharing configurations from nucleation trajectories of the TIP4P/ice model reported in ref. 6. This work was supported by the National Science Foundation through the Center of Chemical Innovation award CHE-1305427 “Center for Aerosol Impacts on Climate and the Environment” and the Environmental Chemical Sciences award CHE-1309601. We thank the Center for High Performance Computing at the University of Utah for an award of computing time and technical support.

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Contributions

V.M. and L.L. conceived the work. L.L. performed and analysed all molecular simulations and calculations with the 1D stacking model. M.G. contributed the 2D lattice model and analysis. A.H. computed thermodynamic parameters for the stacking models. R.G.M. provided codes for maximum likelihood optimization. A.H.N. provided codes for clustering analysis. L.L., B.P., M.G., A.H. and V.M. interpreted the results. L.L. and V.M. wrote the paper with input from B.P. and M.G.

Corresponding author

Correspondence to Valeria Molinero.

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Extended data figures and tables

Extended Data Figure 1 Evolution of the cubicity of crystallites along the 28,510 shooting points sampled with aimless shooting.

Different colours correspond to distinct sets of shooting points obtained through aimless shooting starting from different seeds (Methods section ‘Aimless shooting’). The first four sets from the left are seeded with configurations from two spontaneous crystallization trajectories at 205 K, in which ice crystallites are stacking-disordered. The last eight sets originate from two configurations of liquid water seeded with a sphere of hexagonal ice of critical size at 230 K. Configurations containing critical-sized crystallites (highlighted with small circles) span all values of cubicities. We note that all critical-sized crystallites are considered in the committor analysis, irrespective of their cubicity. In the last eight sets, ice crystallites in the seeded configurations start with C = 0 (hexagonal crystallites) and evolve through the aimless shooting procedure towards stacking-disordered crystallites. These results are consistent with the existence of a thermodynamic driving force towards stacking-disordered ice crystallites.

Extended Data Figure 2 Free energy difference between stacking-disordered and hexagonal ice computed with the 1D stacking model.

ΔGsd-Ih(N,C) is plotted as a function of cubicity, for a variety of crystal sizes N and their corresponding number of layers in the crystals (see labels on the right side). The zoomed area shows the crossover to stable hexagonal crystallites for crystallites with 22 layers.

Extended Data Figure 3 Probability distributions of radius of gyration for cubic, hexagonal and stacking-disordered ice crystallites.

Radii of gyration evaluated for critical-sized ice crystallites, with N* = 356 ± 5 identified by RC7 = NCHI (that is, accounting only for the cubic, hexagonal and interfacial ice in the ice nucleus). The crystallites were collected from the equilibrium path sampling trajectories used to compute the free energy landscape. The blue line corresponds to hexagonal crystallites (C = 0 to 0.15) sampled over about 900 configurations, the green line corresponds to stacking-disordered crystallites (C = 0.6 ± 0.05) sampled over about 7,000 configurations and the red line corresponds to cubic crystallites (C = 0.9 to 1) sampled over about 400 configurations. The shape of the crystallites is independent of their cubicity, and not far from that of a perfect sphere with 350 water molecules, Rgsphere = 10.6 Å.

Extended Data Figure 4 Probability distribution of cubicity for crystallites with stacking in one or two directions in the 2D lattice model.

The black line shows that the distribution of cubicity in the equilibrium ensemble of crystallites with 33 cells (corresponding to NCH ≈ 200 water molecules) is slightly shifted towards cubic-rich crystallites. The blue line shows the distribution of cubicity for the subset of crystallites that have stacking of cubic and hexagonal layers along one direction only (the blue arrow points to a snapshot of a typical configuration with 1D stacking). The distribution of crystallites with 1D stacking is slightly shifted towards hexagonal-rich crystallites. The red line shows the distribution of cubicity for the subset of crystallites that have stacking of cubic and hexagonal layers along two directions (the red arrow points to a typical configuration with 2D stacking). This subset is defined as crystallites with hexagonal regions of at least four cells that are connected horizontally to a cubic region, and hexagonal regions of at least four cells connected vertically to a cubic region. The distribution of crystallites with 2D stacking is clearly shifted towards large values of cubicity, indicating that the occurrence of crystallites with two stacking directions causes the shift of the distribution of the entire ensemble of crystallites (black line). Stacking-disordered crystallites with an equivalent biasing mechanism towards the cubic polymorph may be expected in other materials that present cubic and hexagonal polymorphs with similar bulk free energies and for which the cubic and hexagonal layers can be seamlessly stacked.

Extended Data Figure 5 Randomly selected crystallites generated with the 2D lattice model.

All crystallites contain 33 lattice cells (equivalent to NCH = 198) as in Extended Data Figure 4 and have cubicity C = 0.60 ± 0.03. Red cells correspond to cubic ice, blue cells to hexagonal ice, and grey cells to liquid. Crystallites in snapshots a, b, d, l, m and o have stacking in two directions, while those in snapshots c, e, f, g, h, i, j, k, n and p display stacking in one direction.

Extended Data Figure 6 Cubicity of ice crystallites predicted with the 2D stacking model as a function of crystal size.

The red line corresponds to ΔGIc-Ih = 627 J mol−1, the difference in stability between cubic and hexagonal ice predicted by recent density functional theory calculations28; the black line corresponds to ΔGIc-Ih = 155 J mol−1, the upper limit47 proposed based on vapour pressures of stacking-disordered ices. Most probable values of cubicity for a given system size, that is, cubicities along the minimum free energy path, are calculated according to Methods section ‘ΔGsd-Ih using a 2D lattice stacking model’.

Extended Data Table 1 Comparison of thermodynamic properties for mW and water
Extended Data Table 2 Maximum likelihood scores for each candidate reaction coordinate RC, and predicted value of the coordinate at the transition state, RC*
Extended Data Table 3 Overlap of the transition state ensembles of four of the top size reaction coordinates of Extended Data Table 2

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Lupi, L., Hudait, A., Peters, B. et al. Role of stacking disorder in ice nucleation. Nature 551, 218–222 (2017). https://doi.org/10.1038/nature24279

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