Anderson-Grüneisen parameterδof some hexagonal metals and MgO from third-order elastic-constant data

A simple procedure is described to calculate the Anderson-Grüneisen parameter $\delta$ from the third-order elastic constants of a crystal and is used to evaluate the same for nine hexagonal metals and for the cubic magnesium oxide (MgO). In all the crystals, with the exception of beryllium, the relation $\delta =2\mathrm{}\gamma$ is very nearly satisfied. The relevance of these calculations to the anharmonicity in these crystals is discussed. Anderson's theory has been used to explain the temperature dependence of the bulk modulus of the hexagonal metals magnesium, zinc, cadmium, and beryllium and the results are compared with experimental values.