Volume dependence of Grüneisen ratio for lower mantle and core of the earth

摘要

In this study, we have examined the various formulations for volume dependence of the Grüneisen ratio, γ. The thermodynamic constraints for γ∞, q∞ and λ ∞ have been used to discuss the validity of various relationships. The volume dependence of γ and its derivatives, reported by Stacey and Davis [F. D. Stacey and P. M. Davis, Phys. Earth Planet. Inter. 142 (2004) 137184], are analyzed. The Al'tshuler et al.'s relationship of γ(V), widely used in recent literature, has been found to be inadequate on the variation of λ with compression. The estimates of γ, q and λ are obtained with the combination of generalized free volume theory and reciprocal K-prime equations of state for the Earth's interior.