A model for the computation of thermal expansivity at high compression and high temperatures: MGO as an example

We compute the value of the thermal expansivity α over a wide range of compression (η ≡ V/V0, 0.6 ≤ η ≤ 1.0) and temperature (300 K ≤ T ≤ 2500 K). Three methods are combined to find α. We utilize: 1) the high P,T data base from the PIB ab initio model for MgO, which specifies the Helmholtz energy and the volume and temperature derivatives; 2) the measured thermal expansivity and its various pressure and temperature derivatives; and 3) several thermodynamic identities relating T and V dependence of various physical properties. We present a simple equation relating α to η along isochores and suggest values of α. for MgO over V, P, T conditions, including those of the earth's lower mantle. The parameters in the equation are evaluated by using the ab initio data base. We find that α varies from about 1.40αa to 0.40αa along a geotherm through the upper and lower mantle, where αa is α at ambient conditions.