Correlation of temperature dependences of thermal expansion and the heat capacity of refractory metal up to the melting point: Tungsten

In continuing the series of publications started by the article about molybdenum, a detailed study of the correlation between the volume thermal expansion coefficient, $\text{o}(T)$, and the heat capacity, $C(T)$, of another refractory metal, tungsten, is carried out. It is shown that a distinct correlation of $\text{o}(C)$ takes place not only at low temperatures, where it is linear and is known as the Grüneisen law, but also within a much wider temperature region, up to the melting point of the metal. A significant deviation from the low-temperature behavior of the linear dependence of $\text{o}(C)$ occurs when the heat capacity reaches its classical Dulong and Petit limit, $3R$. The concept of the temperature dependence of the differential Grüneisen parameter, $\gamma ' \sim (\partial\text{o}/\partial C)$ is introduced, and its evaluation is proposed.