Model for the metastable system of type (GaAs${)}_{1\mathrm{-}x}$(${\mathrm{Ge}}_2$${)}_{\mathrm{x}}$

A model is presented to explain the observed properties of the metastable alloy system of type (GaAs${)}_{1\mathrm{-}\mathrm{x}}$(${\mathrm{Ge}}_2$ ${)}_{\mathrm{x}}$. It assumes only the observed short-range order and exhibits the critical composition $x_c$ below which long-range order exists. The value of $x_c$ in the model depends on the morphology of the kinetic growth. An analytic approximation is used to show the existence of $x_c$, the critical behavior of the correlation length, and the variation of the long-range order parameter S as a function of x.