Thermal expansion and Grüneisen parameters for anisotropic solids

An improved definition of Grüneisen parameters ${\hat{\gamma }}_{\mu }$ for anisotropic solids leads to a clearer relationship with the measured thermal expansivities ${\alpha }_{\mu }$. The corresponding definition of mode Grüneisen parameters ${\hat{\gamma }}_{\mu }^i$ expresses the contribution of mode $i$ to ${\alpha }_{\mu }$, and these are related to the cubic coefficients in the potential-energy function. A phenomenological two-component model due to Grüneisen is then revived in a simplified form and is shown to yield insight into the temperature dependence of ${\alpha }_{\mu }$. The data on tellurium are analyzed as an example.