Nature of the Volume Isotope Effect in Ice.

The substitution of hydrogen (H) by deuterium (D) in ice Ih and in its H-ordered version, ice XI, produces an anomalous form of volume isotope effect (VIE), i.e., volume expansion. This VIE contrasts with the normal VIE (volume contraction) predicted in ice-VIII and in its H-disordered form, ice VII. Here we investigate the VIE in ice XI and in ice VIII using first principles quasiharmonic calculations. We conclude that normal and anomalous VIEs can be produced in ice VIII and ice XI in sequence by application of pressure (ice XI starting at negative pressures) followed by a third type-anomalous VIE with zero-point volume contraction. The latter should also contribute to the isotope effect in the ice VII → ice X transition. The predicted change between normal and anomalous VIE in ice VIII at 14.3 GPa and 300 K is well reproduced experimentally in ice VII using x-ray diffraction measurements. The present discussion of the VIE is general, and conclusions should be applicable to other solid phases of H(2)O, possibly to liquid water under pressure, and to other H-bonded materials.

[1]  Andrzej Falenty,et al.  Formation and properties of ice XVI obtained by emptying a type sII clathrate hydrate , 2014, Nature.

[2]  A. M. Saitta,et al.  Quantum-driven phase transition in ice described via an efficient Langevin approach , 2014 .

[3]  G. Galli,et al.  Dispersion interactions and vibrational effects in ice as a function of pressure: a first principles study. , 2012, Physical review letters.

[4]  C P Herrero,et al.  Anomalous nuclear quantum effects in ice. , 2011, Physical review letters.

[5]  Stefano de Gironcoli,et al.  Order―disorder phase boundary between ice VII and VIII obtained by first principles , 2010 .

[6]  Emilio Artacho,et al.  Density, structure, and dynamics of water: the effect of van der Waals interactions. , 2010, The Journal of chemical physics.

[7]  Kyuho Lee,et al.  Higher-accuracy van der Waals density functional , 2010, 1003.5255.

[8]  J. Finney,et al.  Ice XV: a new thermodynamically stable phase of ice. , 2009, Physical review letters.

[9]  Stefano de Gironcoli,et al.  QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials , 2009, Journal of physics. Condensed matter : an Institute of Physics journal.

[10]  Joseph A Morrone,et al.  Tunneling and delocalization effects in hydrogen bonded systems: a study in position and momentum space. , 2009, The Journal of chemical physics.

[11]  T. Iitaka,et al.  Compression of H 2 O ice to 126 GPa and implications for hydrogen-bond symmetrization: Synchrotron x-ray diffraction measurements and density-functional calculations , 2008 .

[12]  H. Mao,et al.  In situ high-pressure x-ray diffraction study of H2O ice VII. , 2008, The Journal of chemical physics.

[13]  Maoshuang Song,et al.  Ultrasonic measurements of single-crystal gold under hydrostatic pressures up to 8 GPa in a Kawai-type multi-anvil apparatus , 2007 .

[14]  G. Shen,et al.  Toward an internally consistent pressure scale , 2007, Proceedings of the National Academy of Sciences.

[15]  J. Finney,et al.  The Preparation and Structures of Hydrogen Ordered Phases of Ice , 2006, Science.

[16]  R. Wentzcovitch,et al.  Theoretical study of the isostructural transformation in ice VIII , 2005 .

[17]  Nicola Marzari,et al.  First-principles determination of the structural, vibrational and thermodynamic properties of diamond, graphite, and derivatives , 2004, cond-mat/0412643.

[18]  A. M. Saitta,et al.  Phonon dispersion of ice under pressure. , 2004, Physical review letters.

[19]  R. Wentzcovitch,et al.  Amorphization in quenched ice VIII: A first-principles study , 2004 .

[20]  Stefano de Gironcoli,et al.  Anomalous pressure-induced transition(s) in ice XI. , 2004, Physical review letters.

[21]  M. Dion,et al.  van der Waals density functional for general geometries. , 2004, Physical review letters.

[22]  B. Karki,et al.  Vibrational and quasiharmonic thermal properties of CaO under pressure , 2003 .

[23]  R. Wentzcovitch,et al.  Low ↔ high density transformations in ice , 2003 .

[24]  K. Aoki,et al.  Infrared investigation on ice VIII and the phase diagram of dense ices , 2003 .

[25]  Stefano de Gironcoli,et al.  Phonons and related crystal properties from density-functional perturbation theory , 2000, cond-mat/0012092.

[26]  Stefano de Gironcoli,et al.  High-pressure thermal expansion, bulk modulus, and phonon structure of diamond , 1999 .

[27]  H. Mao,et al.  Raman Spectroscopy of Dense H2O and the Transition to Symmetric Hydrogen Bonds , 1999 .

[28]  Hideki Tanaka.  Thermodynamic stability and negative thermal expansion of hexagonal and cubic ices , 1998 .

[29]  H. Mao,et al.  Recent Progress in High-Pressure Brillouin Scattering: Olivine and Ice , 1998 .

[30]  M. Parrinello,et al.  Tunnelling and zero-point motion in high-pressure ice , 1998, Nature.

[31]  Yingkai Zhang,et al.  Comment on “Generalized Gradient Approximation Made Simple” , 1998 .

[32]  J. Finney,et al.  The structure of a new phase of ice , 1998, Nature.

[33]  M. Hanfland,et al.  Raman Scattering and X-ray Diffraction of Ice in the Megabar Range. Occurrence of a Symmetric Disordered Solid above 62 GPa , 1997 .

[34]  D. R. Hamann,et al.  H 2 O hydrogen bonding in density-functional theory , 1997 .

[35]  Burke,et al.  Generalized Gradient Approximation Made Simple. , 1996, Physical review letters.

[36]  Hamel,et al.  Variation of interatomic distances in ice VIII to 10 GPa. , 1994, Physical review. B, Condensed matter.

[37]  Price,et al.  Ab initio molecular dynamics with variable cell shape: Application to MgSiO3. , 1993, Physical review letters.

[38]  Wang,et al.  Accurate and simple analytic representation of the electron-gas correlation energy. , 1992, Physical review. B, Condensed matter.

[39]  R. Wentzcovitch,et al.  Invariant molecular-dynamics approach to structural phase transitions. , 1991, Physical review. B, Condensed matter.

[40]  Stefano de Gironcoli,et al.  Ab initio calculation of phonon dispersions in semiconductors. , 1991, Physical review. B, Condensed matter.

[41]  Chan,et al.  Theory of the thermal expansion of Si and diamond. , 1991, Physical review. B, Condensed matter.

[42]  Martins,et al.  Efficient pseudopotentials for plane-wave calculations. , 1991, Physical review. B, Condensed matter.

[43]  R. Whitworth,et al.  A determination of the crystal structure of ice XI , 1989 .

[44]  J. Finney,et al.  Structure and hydrogen ordering in ices VI, VII, and VIII by neutron powder diffraction , 1984 .

[45]  Y. Tajima,et al.  Phase transition in KOH-doped hexagonal ice , 1982, Nature.

[46]  W. Holzapfel.  On the Symmetry of the Hydrogen Bonds in Ice VII , 1972 .

[47]  L. Pauling.  The Structure and Entropy of Ice and of Other Crystals with Some Randomness of Atomic Arrangement , 1935 .

[48]  K. Umemoto.  Computer Simulations on Phase Transitions in Ice , 2010 .

[49]  Richard C. Ward,et al.  The equilibrium low‐temperature structure of ice , 1985 .