Force constant and mass disorder in vibrational systems in the coherent-potential approximation

The coherent-potential approximation (CPA) for vibrational systems is extended to include force-constant changes as well as mass defects in alloys for which the force constants superimpose linearly. Such a model is correct at both the low- and high-concentration limits, and may be reasonable for broad concentration ranges in some real systems, for example, in diatomic alloys like mixed alkali halides. Results for one-dimensional systems with nearest-neighbor force constant and mass disorder have the same over-all agreement with exact results as was previously found for CPA calculations for mass defects only. Applications in three dimensions appear to be computationally feasible.