Stationary disorder in anharmonic crystals

The effect of stationary point defects on the self-consistent phonon spectrum of anharmonic crystals is examined. The proposed approach, which generates an effective harmonic Hamiltonian from the system Hamiltonian, is amenable to a classical average $t$-matrix approximation or ultimately a coherent-potential approximation when an appropriate separable kernel scheme is used. As is typical of these approximations, especially in the treatment of nondiagonal disorder, only the dilute defect limit is exact. It is shown how this approach can be used in a thermal equilibrium situation when the number of vacancies or interstitials is not fixed.