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A quadratic equation for the Graneisen coefficient γ was derived using a method in which the Walsh-Christian and Mie-Graneisen equations were combined. It was assumed that the constant-volume specific heat is a linear equation for temperature and that γ depends on specific volume. The Hugoniot pressures and the quasi-static pressures at an ambient temperature included in the solution of the quadratic equation γ were obtained from the existing experimental data for Fe. The Hugoniot temperatures were available from the existing theoretical Hugoniots for Fe. The validity of the assumption for the constant-volume specific heat was shown.

Thermal Properties of Close-Packed Fe at High Pressures (1st Report, Derivation of Classical Thermodynamic Relations)