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 ($\alpha$) and bending ($\beta$) 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 $\frac{\beta }{\alpha }\propto (1-f_i)$, which confirms the interpretation of $\beta$, since bond-bending forces should vanish in the ionic limit $f_i\to 1$. 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%.