Compression and bonding of ice VII and an empirical linear expression for the isothermal compression of solids

Abstract

The volume of ice VII was measured between 3.0 and 8.0 GPa at 298 K using a high−pressure x−ray diffraction technique. The specific volume (0.708, +0.023, −0.012 cm³/g), the isothermal bulk modulus (12.54±0.27 GPa), and the modulus’ pressure derivative (5.56±0.14) for ice VII at 298 K and zero pressure were determined using an empirical equation for isothermal compression. That equation is [P V₀²/(V₀ − V)]^1/2 = C_T + S_T [P (V₀ − V)]^1/2, where CT and S_T are constants, V₀ is the ambient volume, and V is the volume at pressure P. This linear relation, which describes the state of nonporous materials along their Hugoniots, is shown to characterize the isothermal compression of solids as well as does the Murnaghan equation. The zero pressure, 298 K oxygen−oxygen distance in ice VII extrapolated from the present data and a simple bonding model for the hydrogen−bonded oxygen atoms strongly support Kamb’s description of the ice VII structure as two interpenetrating ice Ic frameworks.