Volume derivatives of the Grüneisen parameter in the limit of infinite pressure

Abstract

Expressions have been obtained for the volume derivatives of the Grüneisen parameter, which is directly related to the thermal and elastic properties of materials at high temperatures and high pressures. The higher order Grüneisen parameters are expressed in terms of the volume derivatives, and evaluated in the limit of infinite pressure. The results, that at extreme compression the third-order Grüneisen parameter remains finite and the fourth-order Grüneisen parameter tends to zero, have been used to derive a fundamental theorem according to which the volume derivatives of the Grüneisen parameter of different orders, all become zero in the limit of infinite pressure. However, the ratios of these derivatives remain finite at extreme compression. The formula due to Al’tshuler and used by Dorogokupets and Oganov for interpolating the Grüneisen parameter at intermediate compressions has been found to satisfy the boundary condition at infinite pressure obtained in the present study.