Effect of Local Order on Energy Bands in Binary Alloys

Abstract

Equations are developed giving the dependence of the energy band shape on the state of local and long-range order in an alloy. The approximation used is the "empty-lattice virtual crystal" model, in which a free electron gas is perturbed by a fluctuating potential of zero average value. The energy correction is expressed in terms of the nearest-neighbor order parameter $\ensuremath{\alpha}$ and long-range parameter $\ensuremath{\lambda}$; this is done with the aid of a qualitative formula giving nonnearest-neighbor parameters as functions of $\ensuremath{\alpha}$. The result is evaluated numerically, and it is shown how the band bottom gets squeezed out into a long tail as $\ensuremath{\alpha}$ proceeds from the perfect short-range order \ensuremath{\rightarrow} random \ensuremath{\rightarrow} clustered cases. The effect of long-range order is discussed and the conclusions are compared with those of a previous tight-binding calculation.