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 alpha over a wide range of compression (eta = V/V0, 0.6 less-than-or-equal-to eta less-than-or-equal-to 1.0) and temperature (300 K less-than-or-equal-to T less-than-or-equal-to 2500 K). Three methods are combined to find alpha. 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 alpha to eta along isochores and suggest values of alpha 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 alpha varies from about 1.40alpha(a) to 0.40alpha(a). along a geotherm through the upper and lower mantle, where alpha(a) is alpha at ambient conditions.