GRUNEISEN RATIOS OF MGO FROM THE CALCULATION OF ENTROPY

A simple method is introduced for estimating the Gruneisen ratio, gamma, of MgO as a function of volume and temperature from the adiabatic lapse rate relating gamma and the entropy, S. The analysis is based upon thermodynamic identities, experimental values of physical properties at ambient pressure, and results of theoretical calculations for elevated pressures. First, the entropy of MgO is computed by integrating the product of the thermal expansion coefficient and the isothermal bulk modulus, alpha K-T, as a function of relative volume, eta = V/V-0, along isotherms using values of K-T'(eta) and delta(T)(eta) = -(alpha K-T)(-1)(partial derivative K-T/partial derivative T)(V). The computed gamma's are expressed in temperature-volume space along adiabats whose slopes yield values for gamma. A small correction to the approach of Anderson and Zou (Phys. Chem. Miner. 1989, 16, 642-648) was necessary because of their simplifying assumptions. Our estimates of the Gruneisen ratios are similar to estimates made by Anderson, Oda, Chopelas, and Issak (Phys. Chem. Miner. 1993, 19, 369-380) from other thermodynamic bases. Geophysical implications of these estimates for the lower mantle are discussed.