Self-consistent phonons in configurationally disordered quantum crystals. I. Theory

A generalization of the coherent potential approximation (CPA) to strongly anharmonic systems is presented that takes into account the static relaxations in the vicinity of each defect and the changes in the averaged mean lattice constant and in the mean square fluctuations. In the limits of a perturbed classical, harmonic crystal or an ideal, anharmonic crystal the theory reduces to the conventional CPA and the self-consistent phonon results, respectively. For the numerical solution an approximation is used that starts from the renormalized harmonic phonons in ideal crystals. As an example, some characteristic results are discussed for the systems ofoD₂ orpH₂ in Ne.Deceased.