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 ( $C_{12}{=C}_{44}$) 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.