Analysis of pressure derivatives of bulk modulus for materials at high compressions

Abstract

Pressure derivatives of bulk modulus play a central role in describing thermoelastic behaviour and equation of state for materials at high pressures. It is demonstrated here that the relationships between pressure derivative of bulk modulus and volume compression used by earlier workers are not consistent with the thermodynamic constraints based on the second-, and third order pressure derivatives of bulk modulus, and third order Grüneisen parameter in the limit of infinite pressure. It is pointed out that the compatibility of Keane’s equation and the Stacey reciprocal equation of state as considered by Sinha et al. does not hold at high pressures. The Keane equation does not satisfy the thermodynamic constraint according to which the third order Grüneisen parameter must be less than the pressure derivative of bulk modulus at extreme compression. Values of second-, and third order pressure derivatives of bulk modulus for the Earth lower mantle and outer core determined using the K-primed equations reported by Sinha et al. are found to deviate significantly from the results based on the seismic data at finite pressures obtained by fitting the Stacey reciprocal K-primed EOS.