Equation of state of cubic solids; some generalizations

Abstract

The equations of state (pressure-volume-temperature relationships) for a number of cubic solids can be approximated at high temperature ( T > θ D ) by a temperature-independent isothermal bulk modulus B T which varies linearly with the applied pressure. This is demonstrated by an analysis of both piston-displacement and ultrasonic data, as well as by an elementary calculation based on the Mie-Grüneisen equation of state. These generalizations also should be valid for B T at low temperatures to within one or two percent except for the inert gas solids. The high temperature equation of state which follows from this analysis contains the following features: (a) the Grüneisen constant γ is a temperature-independent linear function of volume, (b) B T is a linear function of temperature at constant pressure, (c) (∂( B S − B T )/∂ T) V = β B T γ and (∂( B S − B T )/∂ P) T = −βγ T, where β is the volume thermal expansion coefficient. These relationships should hold as a first approximation for most cubic solids.