Theory of correlations and scattering of lattice vibrations by defects using double-time Green's functions

The correlations between the displacements and momenta of atoms in a crystal near a point defect are calculated using the method of double-time thermal Green's functions. As a simple example, the mean square displacement and momentum of an atom of different mass in a cubic crystal are found to confirm earlier derivations by different techniques. The scattering of lattice waves by impurities is also calculated by the same technique in a simple case. Resonant scattering is found under certain conditions, and this may have a marked effect on the thermal conductivity of insulating crystals. A comparison is made with experimental results on KCl containing iodine impurities. The effect of Sn impurities on the thermal conductivity of Si is predicted.