A five-parameter temperature-corrected Murnaghan equation for P-V-T surfaces
We have derived an explicit, empirical V(T,P) equation based on an exponential temperature correction of the isothermal Murnaghan equation. The equation is symmetrical with respect to the first‐ and second‐order derivatives of volume and is consistent with the thermodynamic relationship between (∂KT/∂T)P and (∂αP/∂P)T. The only input data required are the five room temperature, room pressure parameters: Koo, K'oo, αoo, α′oo, and (∂KT/∂T)oo. We have successfully tested our equation against literature pressure‐volume‐temperature (P‐V‐T) data for two materials which exhibit quite different isochore behavior: NaCl and SiO2 (α quartz). For NaCl our equation predicts isochores which are very nearly straight and parallel, reflecting the fact that the product αPKT is approximately constant for this substance. For SiO2 our equation reproduces the strong negative curvature [(∂2T/∂P2)V ≪ 0] of the experimentally determined isochores. These results suggest that our five‐parameter equation can be used to accurately predict the P‐V‐T behavior of a wide variety of solids, including those for which isochore curvature is pronounced.
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Plymate, Thomas G., and James H. Stout. "A five‐parameter temperature‐corrected Murnaghan equation for P‐V‐T surfaces." Journal of Geophysical Research: Solid Earth 94, no. B7 (1989): 9477-9483.
Journal of Geophysical Research: Solid Earth