Lattice dynamics of a mixed diatomic lattice

A pseudo-unit-cell model is utilized to calculate some lattice-dynamical properties of a mixed diatomic lattice of the form $A{B}_{1-x}{C}_x$, where $0\le x\le 1$. The pseudo unit cell is formed by $A$, $\mathrm{}(1-x)B$, and $\mathrm{xC}$ ions and the resulting mixed crystal lattice is a repetition of such cells. The lattice dynamics of both a linear and a three-dimensional mixed zinc-blende lattice have been studied. The lattice-dynamical model consists of central and noncentral short- and long-range interactions among ions of appropriate effective ionic charge. The model parameters are deduced from physical observables such as the elastic constants and the long-wavelength optical and impurity mode frequencies of the end systems when $x\to 0$ and $x\to 1$. Explicit calculations for the phonon dispersion and frequency distribution function have been performed for the linear mixed diatomic lattice and for $\mathrm{Zn}{\mathrm{S}}_{1-x}{\mathrm{Se}}_x$ and $\mathrm{Ga}{\mathrm{P}}_{1-x}{\mathrm{As}}_x$.