We have computed phonon scattering rates and density of states in silicon germanium alloys using Green's function calculations and density functional theory. This method contrasts with the virtual crystal approximation (VCA) used in conjunction with Fermi's golden rule, which cannot capture resonance states occurring through the interaction of substitutional impurities with the host lattice. These resonances are demonstrated by density of states and scattering rate calculations in the dilute limit and show broadening as the concentration increases. Although these deviations become significant from the VCA at high frequencies, the relaxation times obtained for these phonon modes are small in both the full scattering theory and the VCA, resulting in their negligible contribution to thermal transport.United States. Dept. of Energy. Office of Science (Solid-State Solar-Thermal Energy Conversion Center Award DE-SC0001299/DE-FG02-09ER46577
