Cauchy Relation in DenseH2O Ice VII

Abstract

By high-pressure Brillouin spectroscopy, sound velocities for all directions and three elastic constants of cubic ice VII have been determined up to 8 GPa at room temperature, with in situ identification of the orientation of the ice VII single crystal grown in a diamond-anvil cell. We have found the unusual result that the Cauchy relation (C» = C44) holds at every pressure for ice VII. This result suggests that the interactions between the atoms can be described by central forces. By a force-constant analysis of elastic constants, we show that the self-clathrate structure of two diamond-type sublattices can induce effectively central forces, and discuss their broad stability fields in the ice VII phase. PACS numbers: 78.35.+ c, 62.50.+ p, 62.65. +k, 64.70.KbThe behavior of H20 ice at high pressure is of fundamental importance in condensed matter and planetary science. An interesting variety of ice polymorphism exists under different conditions of pressure and temperature [1]. At room temperature, compression of liquid water leads to a tetragonal ice VI phase at pressures above 1.05 GPa and further to a cubic ice VII phase above 2. 1 GPa. However, above this pressure the phase diagram simplifies down to only two VII and VIII phases. In these higher-pressure phases, high density is achieved by forming "self-clathrate" structures [1 -4]. The structure of ice VII can be built up, as shown in Fig. 1, from two interpenetrated but unconnected diamond-type (ice I,) sublattices of oxygen atoms, where the oxygen atoms form a body-centered cubic (bcc) lattice and the protons are disordered within Pauling s ice rules (ice VIII is the protonordered form of ice VII). A further feature of ice VII that is related to the unconnected sublattices is that only four of the eight nearest-neighbor oxygen atoms are hydrogen bonded to the central oxygen atom.For pressure-induced H20 ice at pressures above 1.05 GPa and 300 K, Polian and Grimsditch [5,6] measured the Brillouin spectra only at a scattering geometry of 180 and observed the pressure dependence of nv in ices VI and VII up to 67 GPa without identification of the crystal orientation, where nv is the product of the refractive index and the sound velocity, respectively [see Eq. (3)]. From the pressure dependence of nv, they observed the VI VII phase transition at about P = 2. 1 GPa, and moreover claimed the possible existence of a symmetric ice X phase above 44 GPa. Around this region, however, Pruzan, Chervin, and Canny [7] have found no evidence of ice X in the Raman spectra, and Hemley et al. [8] have indicated from a synchrotronx-ray diffraction investigation that the bcc oxygen sublattice of ice VII persists to 128 GPa. Therefore, ice VII has a broad stability field at room temperature.Elastic properties determined by high-pressure Brillouin scattering [9] shed new light on the characteristic behavior of polymorphic varieties of ice, and provide some insight into the forces of interaction. The sound velocity for the probed acoustic phonon, which can be determined from the me...

Recent Progress in High-Pressure Brillouin Scattering: Olivine and Ice.

“…Ruby fluorescence was used for pressure calibration. From the elasticity data of single-crystal ice VII obtained by Shimizu et al [4] in the lower pressure range, we can derive the upper and lower bounds from the corresponding combinations of elastic constants by assuming the relations will not change. This is a reasonable assumption as there is no known phase transition occurring within the experimental pressure range.…”

“…Significant recent progress has been made in the coupling of Brillouin scattering and diamond anvil techniques for characterizing physical properties of materials under elevated pressures [1][2][3][4][5][6]. In some ways parallel to ultrasonic methods for measuring sound velocity and elasticity, high-pressure Brillouin scattering techniques, however, provide greater feasibility for measuring the entire set of elastic moduli for single crystals to moderate pressures.…”

Thermal conductivity of compressedH2O to 22 GPa: A test of the Leibfried-Schlömann equation

“…At room temperature, cubic ice VII (space group P n3m) is stable between 2.1 and ≈60 GPa. 13,14 With its extrapolated zero pressure bulk modulus K 0 = 21.1 ± 0.5 GPa and the pressure derivative K 0 = 4.4 ± 0.1, 15 ice VII is compressed by more than 30% at 22 GPa.Symmetric DACs with 600-μm-culet diamonds and steel gasket were used to compress distilled H 2 O to 22 GPa. Pressure was determined from ruby fluorescence.…”

“…At room temperature, cubic ice VII (space group P n3m) is stable between 2.1 and ≈60 GPa. 13,14 With its extrapolated zero pressure bulk modulus K 0 = 21.1 ± 0.5 GPa and the pressure derivative K 0 = 4.4 ± 0.1, 15 ice VII is compressed by more than 30% at 22 GPa.…”

Sound speed and thermal property measurements of inert materials: Laser spectroscopy and the diamond-anvil cell

“…The recent availability of elastic moduli on hydrogen (EOS up to 24 GPa) [18,19], methane (up to 5 GPa) [20], nitrous oxide and carbon dioxide (up to 4.5 GPa) [21], water (ice VII) (2.2 -7.4 GPa) [22], and~02 (6-9.5 GPa) [23]; including the pressure dependence of n and a in N20 and C02; will improve our grasp of the compositional stratifications, oscillations and evolutional history of the Jovian planets and their moons. The acoustic velocities, refractive index and elastic constants of two sulfides (hydrogen and deuteritsm) have been determined (up to 5 GPa) [24].…”