Simulation of elastic-network relaxation: TheSi1−xGexrandom alloy

A method for relaxing a tetrahedral elastic network with length mismatch is developed. Systematic study of simulations finds close agreement with the predictions of analytic theory for mean values of nearest-neighbor bond lengths and reveals unexpected details in the full distributions in the limits x→0,1. Application of the method to the problem of strain relaxation in bulk crystalline ${\mathrm{Si}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Ge}}_{\mathit{x}}$ predicts trends in local structure that could be tested by experiment.