Third-Order Elastic Constants of Magnesium. II. Theoretical

Abstract

A theoretical model has been developed to predict the elastic constants of magnesium. The energy density of the metal consisted of a volume-dependent term, an electrostatic term, and a band-structure term which was derived from pseudopotential theory. The pseudopotential used was the local one proposed by Ashcroft and used by Suzuki et al. in calculating the elastic constants of the alkali metals. There were two adjustable parameters. One is the core radius ${r}_{c}$ and the other is a shear-independent term adjusted to give equilibrium at the observed atomic volume. The calculations were carried out for five different core radii in order to determine the ${r}_{c}$ which gives the best agreement between theory and experiment. Both the Hartree dielectric function and a modified dielectric function were used. The results were found to be rather insensitive to whichever dielectric function is used. From a comparison of the calculated elastic constants with experiment, it was found that the best agreement was obtained for ${r}_{c}=1.358{a}_{0}$ (and the modified dielectric function). There was only a slight preference, however, over ${r}_{c}=1.38{a}_{0}$ (and the Hartree dielectric function). The core radius determined from elastic-constant calculations was found to be in good agreement with the values obtained by other investigators from a comparison of theory with experiment for electronic properties, such as the resistivity of liquid magnesium. Thus the same pseudopotential predicts both mechanical and electronic properties of magnesium. Because magnesium exists in the nonprimitive hcp structure, a macroscopic strain gives rise to interlattice displacements, i.e., internal strains. The internal-strain parameter has been calculated by requiring the energy density of the strained state to be a minimum. It was seen that internal-strain contributions to the Brugger elastic constants, although small, did improve the over-all agreement between theory and experiment.