Elastic Properties of ZnS Structure Semiconductors

A simple phenomenological theory of the elastic constants of sphalerite structure crystals is presented and shown to apply within reasonable errors to the known experimental constants. The theory utilizes a form for bond-stretching ($\ensuremath{\alpha}$) and bending ($\ensuremath{\beta}$) forces first used by Keating, to which are added effective point-ion Coulombic forces. Also it is pointed out that regularities in the experimental elastic constants of these crystals are readily explained in terms of the ionicity ${f}_{i}$ defined by Phillips and Van Vechten. Of particular note are the shear constants which decrease markedly with ionicity. It is found that this decrease is described quantitatively by $\frac{\ensuremath{\beta}}{\ensuremath{\alpha}}\ensuremath{\propto}(1\ensuremath{-}{f}_{i})$, which confirms the interpretation of $\ensuremath{\beta}$, since bond-bending forces should vanish in the ionic limit ${f}_{i}\ensuremath{\rightarrow}1$. Other equally simple formulas for the forces in terms of only the bond length and ${f}_{i}$ are shown to predict all the constants with a rms accuracy of 10%.