Thermal properties of close-packed Fe up to 400 GPa determined using Hugoniot functions

A quadratic equation for the temperature-independent Gr\"{u}neisen coefficient $\gamma$ was derived by a method in which the Walsh-Christian and Mie-Gr\"{u}neisen equations are combined. Some previously existing \textit{ab initio} temperature Hugoniots for hexagonal closed-packed solid Fe are inaccurate because the constant-volume specific heats on the Hugoniots $C_{VH}$, which are related uniquely to the solutions of the quadratic equation, have values that are too small. A $C_ {VH}$ distribution in the solid phase range was demonstrated to agree approximately with a previous \textit{ab initio} distribution. In contrast, the corresponding $\gamma $ distribution was significantly different from the \textit{ab initio} distribution in the lower pressure region, and the $\gamma $ distribution in the liquid phase range had a considerably larger gradient than the \textit{ab initio} distribution. The causes of these disagreements are clarified. [Ref. Y. Sano and T. Sano, Phys. Rev. B 69, 144201 (2004).]