Kinetic formula for estimating resistive phonon lifetimes

An improved kinetic formula which can be used to estimate the average phonon resistive lifetime [tau][sub [ital R]] from thermal conductivity data is presented. The relation is [kappa]=[ital Cc][sub 2][sup 2][tau][sub [ital R]], where [kappa] is the thermal conductivity, [ital C] is the specific heat, and [ital c][sub 2] is the second sound velocity. At very low temperatures [ital c][sub 2][approx][ital c][sub [ital D]]/ [radical]3 , where [ital c][sub [ital D]] is the Debye velocity, and the result reduces to the standard kinetic formula. However, above about 0.02[ital FTHETA][sub [ital D]] [ital c][sub 2] undergoes a rapid decrease. As a consequence, phonon lifetimes estimated by the modified formula are considerably longer than those obtained from the standard kinetic formula.