Anharmonic nuclear motion and the relative stability of hexagonal and cubic ice

Physical Review X

Volumn 5, Issue 2, 2015, Pages

  Engel, Edgar A ^a   Monserrat, Bartomeu ^a   Needs, Richard J ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

CALCULATIONS; QUANTUM THEORY; VIBRATIONS (MECHANICAL);

ANHARMONICITIES; FIRST PRINCIPLES; HEXAGONAL ICE; NUCLEAR MOTIONS; QUANTUM-MECHANICAL CALCULATION; RELATIVE STABILITIES; VIBRATIONAL ENERGIES; VIBRATIONAL MODES;

ICE;

EID: 84937677942     PISSN: None     EISSN: 21603308     Source Type: Journal    
DOI: 10.1103/PhysRevX.5.021033     Document Type: Article

References (65)

1. T. Bartels-Rausch, V. Bergeron, J. H. E. Cartwright, R. Escribano, J. L. Finney, H. Grothe, P. J. Gutiérrez, J. Haapala, W. F. Kuhs, J. B. C. Pettersson, S. D. Price, C. I. Sainz-Díaz, D. J. Stokes, G. Strazzulla, E. S. Thomson, H. Trinks, and N. Uras-Aytemiz, Ice structures, patterns, and processes: A view across the ice-fields, Rev. Mod. Phys. 84, 885 (2012).
2. M. B. Baker and T. Peter, Small-scale cloud processes and climate, Nature (London) 451, 299 (2008).
3. K. C. Young, Microphysical Processes in Clouds (Oxford University Press, New York, 1993).
4. B. J. Murray, D. A. Knopf, and A. K. Bertram, The formation of cubic ice under conditions relevant to the earth's atmosphere, Nature (London) 434, 202 (2005).
5. J. E. Shilling, M. A. Tolbert, O. B. Toon, E. J. Jensen, B. J. Murray, and A. K. Bertram, Measurements of the vapor pressure of cubic ice and their implications for atmospheric ice clouds, Geophys. Res. Lett. 33, L17801 (2006).
6. T. H. G. Carr, J. J. Shephard, and C. G. Salzmann, Spectroscopic signature of stacking disorder in ice I, J. Phys. Chem. Lett. 5, 2469 (2014).
7. K. Thürmer and S. Nie, Formation of hexagonal and cubic ice during low-temperature growth, Proc. Natl. Acad. Sci. U.S.A. 110, 11757 (2013).
8. O. Yamamuro, M. Oguni, T. Matsuo, and H. Suga, Heat capacity and glass structure of pure and doped cubic ices, J. Phys. Chem. Solids 48, 935 (1987).
9. Y. P. Handa, D. D. Klug, and E. Whalley, Difference in energy between cubic and hexagonal ice, J. Chem. Phys. 84, 7009 (1986).
10. E. Mayer and A. Hallbrucker, Cubic ice from liquid water, Nature (London) 325, 601 (1987).
11. J. A. McMillan and S. C. Los, Vitreous ice: irreversible transformations during warm-up, Nature (London) 206, 806 (1965).
12. M. Sugisaki, H. Suga, and S. Seki, Calorimetric study of the glassy state IV: Heat capacities of glassy water and cubic ice, Bull. Chem. Soc. Jpn. 41, 2591 (1968).
13. W. F. Kuhs, C. Sippel, A. Falenty, and T. C. Hansen, Extent and Relevance of Stacking Disorder in "Ice Ic", Proc. Natl. Acad. Sci. U.S.A. 109, 21259 (2012).
14. B. J. Murray, S. L. Broadley, T.W. Wilson, S. J. Bull, R. H. Wills, H. K. Christenson, and E. J. Murray, Kinetics of the homogeneous freezing of water, Phys. Chem. Chem. Phys. 12, 10380 (2010).
15. D. C. Steytler, J. C. Dore, and C. J. Wright, Neutron diffraction study of cubic ice nucleation in a porous silica network, J. Phys. Chem. 87, 2458 (1983).
16. H. König, A cubic modification of ice, Z. Kristallogr. 105, 279 (1944).
17. F. Izumi and K. Momma, Three-dimensional visualization in powder diffraction, Solid State Phenom. 130, 15 (2007).
18. Z. Raza, D. Alfè, C. G. Salzmann, J. Klimeš, A. Michaelides, and B. Slater, Proton ordering in cubic ice and hexagonal ice; a potential new ice phase-XIc, Phys. Chem. Chem. Phys. 13, 19788 (2011).
19. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevX.5.021033 for more information on the choice of proton ordered structures, the convergence of the free energies with respect to the simulation cell size, the rms vibrational displacements of the nuclei, the choice of the exchange-correlation functional, and the effects of quantum zero-point and thermal expansion.
20. R. Ramírez and C. P. Herrero, Quantum path integral simulation of isotope effects in the melting temperature of ice Ih, J. Chem. Phys. 133, 144511 (2010).
21. C. P. Herrero and R. Ramírez, Isotope effects in ice Ih: A path-integral simulation, J. Chem. Phys. 134, 094510 (2011).
22. L. Hernández de la Peña, M. S. Gulam Razul, and P. G. Kusalik, Quantum effects in ice Ih, J. Chem. Phys. 123, 144506 (2005).
23. S. Habershon, T. E. Markland, and D. E. Manolopoulos, Competing quantum effects in the dynamics of a flexible water model, J. Chem. Phys. 131, 024501 (2009).
24. A. Zeidler, P. S. Salmon, H. E. Fischer, J. C. Neuefeind, J. M. Simonson, and T. E. Markland, Isotope effects in water as investigated by neutron diffraction and path integral molecular dynamics, J. Phys. Condens. Matter 24, 284126 (2012).
25. C. P. Herrero and R. Ramírez, High-density amorphous ice: A path-integral simulation, J. Chem. Phys. 137, 104505 (2012).
26. B. Pamuk, J. M. Soler, R. Ramírez, C. P. Herrero, P.W. Stephens, P. B. Allen, and M. V. Fernandez-Serra, Anomalous Nuclear Quantum Effects in Ice, Phys. Rev. Lett. 108, 193003 (2012).
27. C. Vega, M. M. Conde, C. McBride, J. L. F. Abascal, E. G. Noya, R. Ramírez, and L. M. Sesé, Heat capacity of water: A signature of nuclear quantum effects, J. Chem. Phys. 132, 046101 (2010).
28. H. Tanaka and I. Okabe, Thermodynamic stability of hexagonal and cubic ices, Chem. Phys. Lett. 259, 593 (1996).
29. D. Quigley, Communication: Thermodynamics of stacking disorder in ice nuclei, J. Chem. Phys. 141, 121101 (2014).
30. R. Ramírez, N. Neuerburg, and C. P. Herrero, The phase diagram of ice: A quasi-harmonic study based on a flexible water model, J. Chem. Phys. 139, 084503 (2013).
31. S. J. Singer and C. Knight, in Advances in chemical physics, edited by S. A. Rice and A. R. Dinner (Wiley, Hoboken, NJ, 2011), Vol. 147.
32. J. D. Bernal and R. H. Fowler, A Theory of water and ionic solution, with particular reference to hydrogen and hydroxyl ions, J. Chem. Phys. 1, 515 (1933).
33. T. L. Malkin, B. J. Murray, C. G. Salzmann, V. Molinero, S. J. Pickering, and T. F. Whale, Stacking disorder in ice I, Phys. Chem. Chem. Phys. 17, 60 (2015).
34. T. C. Hansen, M. M. Koza, and W. F. Kuhs, Formation and annealing of cubic ice: I. Modelling of stacking faults, J. Phys. Condens. Matter 20, 285104 (2008).
35. T. C. Hansen, M. M. Koza, P. Lindner, and W. F. Kuhs, Formation and annealing of cubic ice: II. kinetic study, J. Phys. Condens. Matter 20, 285105 (2008).
36. J. Hallett, W. P. Arnott, M. P. Bailey, and J. T. Hallett, in Cirrus, edited by K. D. Lynch, K. Sassen, D. O'C. Starr, and G. Stephens (Oxford University Press, Oxford, 2002).
37. E. B. Moore, E. de la Llave, K. Welke, D. A. Scherlis, and V. Molinero, Freezing, melting and structures of ice in a hydrophilic nanopore, Phys. Chem. Chem. Phys. 12, 4124 (2010).
38. D. L. Silva, Jr. and M. de Koning, Structure and energetics of extended defects in ice Ih, Phys. Rev. B 85, 024119 (2012).
39. L. Hernández de la Peña and P. G. Kusalik, Quantum effects in liquid water and ice: Model dependence, J. Chem. Phys. 125, 054512 (2006).
40. L. Pauling, The structure and entropy of ice and of other crystals with some randomness of atomic arrangement, J. Am. Chem. Soc. 57, 2680 (1935).
41. Y. Tajima, T. Matsuo, and H. Suga, Phase transition in KOH-Doped hexagonal ice, Nature (London) 299, 810 (1982).
42. S. M. Jackson and R.W. Whitworth, Thermally-stimulated depolarization studies of the ice XI-Ice Ih phase transition, J. Phys. Chem. B 101, 6177 (1997).
43. J. F. Nagle, Lattice statistics of hydrogen bonded crystals. The residual entropy of ice, J. Math. Phys. (N.Y.) 7, 1484 (1966).
44. C. P. Herrero and R. Ramírez, Configurational entropy of hydrogen-disordered ice polymorphs, J. Chem. Phys. 140, 234502 (2014).
45. K. Hirsch and L. Ojamäe, Quantum-chemical and force-field investigations of ice Ih: Computation of proton-ordered structures and prediction of their lattice energies, J. Phys. Chem. B 108, 15856 (2004).
46. S. J. Clark, M. D. Segall, C. J. Pickard, P. J. Hasnip, M. I. J. Probert, K. Refson, and M. C. Payne, First principles methods using CASTEP, Z. Kristallogr. 220, 567 (2005).
47. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized Gradient Approximation Made Simple, Phys. Rev. Lett. 77, 3865 (1996).
48. D. Vanderbilt, Soft self-consistent pseudopotentials in a generalized eigenvalue formalism, Phys. Rev. B 41, 7892 (1990).
49. B. Monserrat, N. D. Drummond, and R. J. Needs, Anharmonic vibrational properties in periodic systems: Energy, electron-phonon coupling, and stress, Phys. Rev. B 87, 144302 (2013).
50. B. Monserrat, N. D. Drummond, C. J. Pickard, and R. J. Needs, Electron-Phonon Coupling and the Metallization of Solid Helium at Terapascal Pressures, Phys. Rev. Lett. 112, 055504 (2014).
51. S. Azadi, B. Monserrat, W. M. C. Foulkes, and R. J. Needs, Dissociation of High-Pressure Solid Molecular Hydrogen: A Quantum Monte Carlo and Anharmonic Vibrational Study, Phys. Rev. Lett. 112, 165501 (2014).
52. J. Lekner, Energetics of hydrogen ordering in ice, Physica (Amsterdam) 252B, 149 (1998).
53. S. J. Singer, J. L. Kuo, T. K. Hirsch, C. Knight, L. Ojamäe, and M. L. Klein, Hydrogen-Bond Topology and the Ice VII/VIII and Ice Ih/XI Proton-Ordering Phase Transition, Phys. Rev. Lett. 94, 135701 (2005).
54. D. M. Ceperley and B. J. Alder, Ground State of the Electron Gas by a Stochastic Method, Phys. Rev. Lett. 45, 566 (1980).
55. J. P. Perdew and A. Zunger, Self-interaction correction to density-functional approximations for many-electron systems, Phys. Rev. B 23, 5048 (1981).
56. J. P. Perdew and Y. Wang, Accurate and simple analytic representation of the electron-gas correlation energy, Phys. Rev. B 45, 13244 (1992).
57. A. D. Becke, Density-functional exchange-energy approximation with correct asymptotic behavior, Phys. Rev. A 38, 3098 (1988).
58. C. Lee, W. Yang, and R. G. Parr, Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density, Phys. Rev. B 37, 785 (1988).
59. J. P. Perdew, A. Ruzsinszky, G. I. Csonka, O. A. Vydrov, G. E. Scuseria, L. A. Constantin, X. Zhou, and K. Burke, Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces, Phys. Rev. Lett. 100, 136406 (2008);
60. J. P. Perdew, A. Ruzsinszky, G. I. Csonka, O. A. Vydrov, G. E. Scuseria, L. A. Constantin, X. Zhou, and K. Burke, Erratum: Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces, Phys. Rev. Lett. 102, 039902(E) (2009).
61. A. Tkatchenko and M. Scheffler, Accurate Molecular Van Der Waals Interactions from Ground-State Electron Density and Free-Atom Reference Data, Phys. Rev. Lett. 102, 073005 (2009).
62. S. M. Jackson, V. M. Nield, R.W. Whitworth, M. Oguro, and C. C. Wilson, Single-crystal neutron diffraction studies of the structure of ice XI, J. Phys. Chem. B 101, 6142 (1997).
63. P. Geiger, C. Dellago, M. Macher, C. Franchini, G. Kresse, J. Bernard, J. N. Stern, and T. Loerting, Proton ordering of cubic ice Ic: Spectroscopy and computer simulations, J. Phys. Chem. C 118, 10989 (2014).
64. A. Soper, The radial distribution functions of water and ice from 220 to 673 K and at pressures up to 400 MPa, Chem. Phys. 258, 121 (2000).
65. P. Mehl and P. Boutron, Cryoprotection of red blood cells by 1,3-Butanediol and 2,3-Butanediol, Cryobiology 25, 44 (1988).