A thermodynamic theory of the Grüneisen ratio at extreme conditions: MgO as an example

The Gruneisen ratio, γ, is defined as γy=αKTV/Cv. The volume dependence of γ(V) is solved for a wide range in temperature. The volume dependence of αKT is solved from the identity (∂ ln(αKT)/∂ ln V)T ≡ δT-K′. α is the thermal expansivity; KT is the bulk modulus; CV is specific heat; and δTand K′ are dimensionless thermoelastic constants. The approach is to find values of δT and K′, each as functions of T and V. We also solve for q=(∂ ln γ/∂ ln V) where q=δT-K′+ 1-(∂ ln CV/∂ ln V)T. Calculations are taken down to a compression of 0.6, thus covering all possible values pertaining to the earth's mantle, q=∂ ln γ/∂ ln V; δT=∂ ln α/∂ ln V; and K′= (∂KT/∂P)T. New experimental information related to the volume dependence of δT, q, K′ and CV was used. For MgO, as the compression, η=V/V0, drops from 1.0 to 0.7 at 2000 K, the results show that q drops from 1.2 to about 0.8; δT drops from 5.0 to 3.2; δT becomes slightly less than K′; ∂ ln CV/∂ In V→0; and γ drops from 1.5 to about 1. These observations are all in accord with recent laboratory data, seismic observations, and theoretical results.