The Grüneisen parameter and its higher order derivatives for the Earth lower mantle and core

Expressions have been obtained for the higher order derivatives of the Grüneisen parameter in the limit of infinite pressure. The usefulness of these expressions has been demonstrated by considering a relationship between reciprocal Grüneisen parameter and the pressure-bulk modulus ratio at finite pressures. It has been found that the relationship under study satisfies the boundary conditions at infinite pressure for the higher order Grüneisen parameters. In order to investigate the applicability of the present formulation at finite pressures, we have calculated the Grüneisen parameter and its higher order derivatives for the Earth lower mantle and core using the input data from Stacey and Davis (2004).