Anharmonic properties of the hexagonal metals, magnesium, zinc and beryllium - I. Lattice dynamics and third order elastic constants

Abstract

The lattice dynamics and the anharmonic properties of the hexagonal metals magnesium, zinc and beryllium have been worked out utilising the approach of Keating. In Magnesium, the dispersion curves are fitted using ten second order parameters and the six second order elastic constants are evaluated. The ten third order elastic constants are calculated using three third order parameters. The experimental measurements on the pressure derivatives of the second order elastic constants in magnesium are in good agreement with the calculated values. The dispersion relations and the second order elastic constants in zinc are fitted using twelve second order parameters. The third order elastic constants of zinc evaluated with the use of three anharmonic parameters are in good agreement with experiment. The dispersion curves and the second order elastic constants of beryllium are obtained using twelve second order parameters. The three third order parameters are obtained from the measured pressure derivatives of three of the second order elastic constants and the third order elastic constants of this metal are computed. The anisotropic thermal expansion of these metals on the present model will be discussed in Section 2 of this paper.