A NEW THERMODYNAMIC APPROACH FOR HIGH-PRESSURE PHYSICS

In the last decade, advances in theoretical first principles calculations and experiments in high-pressure physics have been remarkable, and we are on the threshold of determining many physical properties at extreme pressure, P, and temperature, T, conditions. Another method of finding physical properties at extreme conditions is properly called a thermodynamic route. Many thermodynamic identities are related to appropriate derivatives of the Helmholtz energy, F. These identities are recast into differential equations, the solution of which is the variation of a physical property vs. volume along isotherms. The integrating constants of the differential equation are found from the boundary conditions, e.g. the value of the physical property along the P = 0 axis as a function of T. This method emphasizes experiments done at high T and P = 0 rather than high P. We show the source of differential equations for alpha, alpha K-T, C-V, gamma, and the cross derivative, partial derivative(2)K(T)/partial derivative P partial derivative T, and find the solutions at extreme conditions of V and T. For example, we find alpha, the thermal expansivity, from the appropriate differential equation, and we compare the predicted alpha at high P and T for MgO and perovskite with shock wave measurements of alpha. In the past, the authors have applied the general principles described above to various problems in which the focus was on producing results on physical properties to compare with experiments. In this paper, the focus is on the method of producing the differential equations themselves, and we have found some new and interesting results. For example, we show that the differential equation for alpha(V) arises from the fundamental theorem of calculus regarding second partial derivatives. We also show that the bulk modulus measured at P = 0 can be used to determine the variation of alpha K-T, with V within a small zone of pressure around the T-axis. In general, we demonstrate that good estimates of physical properties for conditions at high pressure and high temperature can be made even when the pressure data are sparse, provided only that there is good high-temperature data at P = 0.