The Gibbs energy formulation of the α, β, and γ forms of Mg₂SiO₄ using Grover, Getting and Kennedy's empirical relation between volume and bulk modulus

Abstract

 The empirical linear relation between volume and logarithm of bulk modulus of a material, discovered by Grover, Getting and Kennedy is taken as the basis for our equation of state. Using the latest experimental information on the adiabatic bulk modulus, the equation of state is applied to the three polymorphs of Mg₂SiO₄ to develop a consistent dataset of their thermodynamic properties in the temperature range of 200–2273 K and a pressure range of 0.1 MPa–30 GPa. The results imply that the bulk sound velocity contrast (v ^β−v ^α)/v ^α increases with temperature along the α–β phase boundary and reaches the value 8.9% at 13.5 GPa, a pressure equivalent to 410 km depth in the Earth. The bulk sound velocity contrast (v ^γ−v ^β)/v ^β decreases with temperature along the β–γ phase boundary and becomes less than 0.7% at temperatures and pressures equivalent to those associated with the 520-km seismic discontinuity in the Earth.