Analysis of thermodynamic properties of molybdenum and tungsten at high temperatures

Using recent and accurate experimental information on various thermodynamic quantities up to the melting temperature ${\mathit{T}}_{\mathit{f}}$ of molybdenum and tungsten, we make a detailed study of some of their high-temperature properties. In particular, we consider the entropy, reduced to a fixed crystal volume, and interpret the result in terms of an electronic part and a temperature-dependent entropy Debye temperature. The analysis reveals large explicit anharmonic effects. When plotted versus the reduced temperature T/${\mathit{T}}_{\mathit{f}}$, various quantities of Mo and W related to anharmonicity show a striking similarity. For instance, the heat capacity ${\mathit{C}}_{\mathit{P}}$ is the same for Mo and W, to better than 1%, for T/${\mathit{T}}_{\mathit{f}}$>0.2. We also make a detailed study of the temperature dependence of the Grüneisen parameter at constant pressure and at constant volume.