Temperature dependence of elastic moduli for non-cubic solids: application to cadmium, magnesium and zinc

Abstract

The fourth-order anharmonic finite strain theory leads to a model for the temperature and pressure dependences of effective elastic moduli, for non-cubic crystals, involving the elastic constants up to the fourth-order. These relationships are used to give an estimation of some combinations of fourth-order elastic constants, using a mean deformation in the fourth-order term and fitting the experimental data at low temperatures. The fourth-order variations of the effective adiabatic elastic moduli with temperature at zero pressure can then be determined. A comparative study of the results with experimental data is given for three hexagonal metals-cadmium, magnesium and zinc-which shows a good agreement between theory and experiment over a large range of temperatures. This development uses both the Lagrangian and Eulerian strain measures previously introduced.