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-funct ion approach. The disordered solids consist of two species of atoms (t he 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 calc ulation gives exactly the phonon self-energy to first order of the def ect density. We show that for small defect density the present calcula tion only modifies the previous calculation slightly, but for large de fect density the present calculation differs appreciably from the prev ious calculation. Our numerical calculations are done in the Debye mod el. 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.