The Gruneisen ratio for the last 30 years

Abstract

Knopoff and Shapiro (1969) reviewed the status of the Gruneisen ratio, γ = (αK(T)V/C(V)), in particular with regard to its use in geophysics. They presented equations for γ that were commonly used at that time and pointed out that these equations were marred because they apparently did not account for the effect of two important properties, shear displacement and dispersion (frequency versus wavenumber). I review the progress in research on γ for the past 30 years and show what has been done to overcome or bypass these two defects. I also show that the experimental database has increased sufficiently to test a basic assumption in the Mie-Gruneisen equation of state (EoS) derivation, namely that γ is independent of T. The basic assumption should be that γ is independent of T at constant V, and many solids fail this test in that (δγ/δT)(V) is not zero. This weakens the assumption that the Mie-Gruneisen EoS can be used reliably at high T without a careful check. The main progress, made for closely packed solids, is in the determination of γ for the lower mantle and the core. Little progress has been made for loosely packed solids, so the value of γ for the upper mantle and the lithosphere is still an open question.