The Piezoelectric Constant of Zinc-Sulfide

The piezoelectric constant of zinc-sulfide has been calculated in two ways. First, by regarding it as a purely ionic crystal and considering that all of the atoms are equally effective in producing the moment, and second, by regarding it as a purely covalent crystal and considering only the nearest neighbors. In the former case, the result agrees completely with that obtained by Born and Bormann.The moment produced in an homogeneous elastic deformation is considered to be $\mathrm{ze}\ensuremath{\Delta}r$, where $\ensuremath{\Delta}r$ is the variation of the distance between the sulfur and zinc atoms on deformation and $\mathrm{ze}$ is the charge on the ions. We first find the moments due to all the sulfur atoms at a given distance from a zinc atom in the crystal. Resolving these along the axes and summing, we get the piezoelectric equations of the crystal. Next, the moments due to various sets of sulfur atoms are summed so as to obtain a quickly converging result, and from this the piezoelectric constant can be obtained. The piezoelectric constant for a purely covalent crystal (formal charge on Zn atom 2-, and on S atom 2+) is found to be 5.4\ifmmode\times\else\texttimes\fi{}${10}^{4}$ and that for a purely ionic crystal (formal charge on Zn 2+ and on S atom 2-) -15.8\ifmmode\times\else\texttimes\fi{}${10}^{4}$. Since the observed value of the piezoelectric constant (-4.20\ifmmode\times\else\texttimes\fi{}${10}^{4}$) lies between these two extremes, it is seen that the crystal has 67 percent ionic character and a formal charge of 0.68 unit on zinc and -0.68 unit on sulfur.