INFLUENCE OF ISOTOPIC DISORDER ON PHONON FREQUENCIES AND PHONON LINEWIDTHS OF AN ANHARMONIC CRYSTAL

Based on a perturbation theory using Matsubara functions and a diagram matic treatment, it is shown that the phonon linewidths of an anharmon ic crystal with isotopic impurities include two different contribution s, a disorder-induced temperature-independent part, caused by harmonic scattering processes of phonons at isotopic impurities, and a disorde r-influenced temperature-dependent part, caused by anharmonic decay pr ocesses. Whereas in case of an anharmonic ideal crystal it is usual to restrict the corresponding self-energy on diagonal elements only, thi s is no longer sufficient in the presence of impurities. For that reas on it is shown that only nondiagonal elements of the effective vertex function of the harmonic phonon propagator contribute to the disorder- induced contribution to the phonon linewidth, whereas the correspondin g harmonic and the anharmonic frequency shifts are determined by diago nal and nondiagonal elements as well. As an application, numerical res ults of the disorder-induced temperature-independent as well as the di sorder-influenced temperature-dependent contribution to the phonon lin ewidths of a diatomic linear chain with a single mass defect are prese nted.