SELF-CONSISTENT CALCULATION OF THE PHONON SELF-ENERGY AND THERMAL-CONDUCTIVITY FOR DISORDERED SOLIDS

We present a self-consistent calculation of the phonon self-energy as a function of frequency for disordered solids by using a Green's-function approach. The disordered solids consist of two species of atoms (the host lattice and defect atoms), which are arranged randomly in the three-dimensional lattice sites. The present calculation contains the contributions to second order of the defect density. The previous calculation gives exactly the phonon self-energy to first order of the defect density. We show that for small defect density the present calculation only modifies the previous calculation slightly, but for large defect density the present calculation differs appreciably from the previous calculation. Our numerical calculations are done in the Debye model. We calculate the thermal conductivity as a function of temperature. We find that the present calculation is able to explain the observed T2 behavior of the thermal conductivity for disordered solids at low temperatures.