Structure of Di- and Trivalent Metals

Abstract

The structures of the di- and trivalent metals Be to Hg and Al to Tl are discussed qualitatively in terms of pseudopotentials and second-order perturbation theory. Attention is concentrated on the effect of the valence $z$, and of the position $q_0$ of the first zero of the pseudopotential. The $q_0$ in turn can be related to atomic properties such as the radius of the ion core and the $\mathrm{sp}$ promotion energy. When $q_0$ falls near a set of reciprocal lattice vectors, distortions from a simple structure are likely to occur. The variation of $q_0$ through the periodic table suggests a qualitative explanation of the variation of the $\frac{c}{a}$ ratio from Be to Cd, the occurrence of distorted structures in Hg, Ga, and In, and the behavior of the InPb and InSn solid-solution alloys, as well as features of the molten metals and some other elements. A few detailed calculations support the qualitative arguments, but the pseudopotentials have to be known much more precisely than they are at present before quantitative agreement with experiment can be expected.