Simple model for structural properties and crystal stability of sp-bonded solids.

Abstract

A simple, universal model for structural properties of sp-bonded semiconductors and insulators is presented. The model elucidates the physical mechanisms determining the chemical trends and predicts semiquantitatively the stable crystal structures, bond lengths, bulk moduli, transition pressures of structural phase transformations, long-wavelength transverse optical phonons, and band structures for binary nonmetals in the rocksalt, cesium chloride, and zinc-blende phases. The theory explains the puzzling strong cation and weak anion dependence of the observed structural transition pressures. It predicts, as a function of pressure, a universal sequence of structural phase transformations among the cubic phases of binary solids. A drastic softening of the transverse optical phonons across the pressure-induced phase transition from the zinc-blende to the rocksalt structure in II-VI compounds is also predicted. The physical origin of this softening is shown to be closely related to ferroelectricity. It is shown that the chemical trends in the structural properties of semiconductors and insulators are governed by a counterbalance of attractive and repulsive short-range interactions, whereas long-range interactions play only a minor role, in contrast to the classical point-charge models of ionic crystals. The theory is based on the semiempirical tight-binding method and includes charge transfer and nonorthogonality effects. Only properties of the neutral atoms are used as input for a given crystal. The total energy is explicitly minimized as a function of volume in order to find the static and dynamic equilibrium crystal properties.