Effect of local excitations on phonon transport properties

At low temperatures, the thermal conductivity is limited by boundary scattering. As the temperature is increased the conductivity goes through a maximum and then gradually declines. The mechanisms responsible for the increase in resistivity are reviewed: (i) Three-phonon U-processes yield an exponential dependence at low and intermediate temperatures and a T1 dependence at temperatures near the Debye temperature. (ii) Strong point defects modify the high temperature dependence to T/sup 1/2/. (iii) Platelets generally lead to a slower than T1 dependence. Four-phonon processes are considered as a special case of general multi-phonon interaction theory. An inverse relaxation time as a function of the first two Grueneisen parameters is derived. The thermal expansion is considered as a mechanism contributing a T2 component to the resistivity. The thermal conductivity of an expanded crystal is expressed in powers of the dilatation where the leading term is the conductivity of the unexpanded crystal. The conductivity for a number of simple nonmetallic crystals (KCl, Al2O3, BeO, MgO) at constant volume was calculated. Thermal expansion is an important mechanism in high temperature thermal conductivity. At temperatures intermediate to the low temperature exponential region and the high temperature T-1 region for three-phonon U-processes there is no analytic solution. A form for the conductivity containing elements of both the high and low temperature forms is proposed for practical calculations at intermediate temperatures. Low-temperature (1K - 5K) thermal conductivity results for fluorapatite are presented. An estimate of the value and the temperature of the conductivity peak is made