Kinetic formula for estimating resistive phonon lifetimes

An improved kinetic formula which can be used to estimate the average phonon resistive lifetime τR from thermal conductivity data is presented. The relation is {κ}=Cc₂²{{{τ}}}R, where κ is the thermal conductivity, C is the specific heat, and{c}₂$ is the second sound velocity. At very low temperatures ${c}₂{c}D/ 3 , where{c}D$ is the Debye velocity, and the result reduces to the standard kinetic formula. However, above about 0.02${FTHETA}D$ ${c}₂$ 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.