The structures of the divalent simple metals

Abstract

An expression is derived for the structure-dependent part of the total energy of a simple metal, which differs from previous formulations in that it incorporates corrections arising from k and E dependence of diagonal elements of the pseudopotential. This is applied to the study of the divalent simple metals using the model potential of Heine and Abarenkov, and calculations are presented which support and augment the qualitative discussion of these structures by Heine and Weaire. The variation of c/a ratio in the hexagonal metals Be, Mg, Zn, Cd is reproduced quite well. In particular, the large values of c/a for Zn and Cd are seen to result from an effect closely related to the occurrence of the rhombohedral structure for α-Hg. The peculiar variation of c/a with composition in disordered Cd-Mg alloys is also accounted for by this model. Calculations of the variation of energy of Hg with distortion of the face-centred cubic structure show it to be unstable with respect to rhombohedral distortion and metastable with respect to tetragonal distortion, as suggested by Heine and Weaire to account for the distorted α- and β-Hg structures. The calculated magnitude of distortion is in both cases much too large. The general conclusion is that the model provides a good qualitative description of the structures of these metals, although detailed agreement with experiment is at present not achievable.