Phonon-phonon interactions give rise to hypersonic losses whose estimation is possible using theories proposed by Akhieser and Mason. These estimations involve the nonlinearity parameter $D$ which is a function of second- and third-order elastic moduli. In the present work, the temperature dependence of the nonlinearity parameter of copper has been evaluated in the temperature range 50-300 K, for longitudinal as well as shear wave propagation along the $〈100〉$ axis, making use of the experimental results on the temperature variation of second- and third-order moduli. The nonlinearity parameter $D_{\mathrm{long}}$ for longitudinal waves is found to increase with temperature, while an opposite effect has been obtained for shear waves. Our estimations of ultrasonic attenuation in Cu at 150 MHz using the temperature variation of $D_{\mathrm{long}}$ are in good agreement with experimental results. The agreement is remarkably good at very low temperatures where the calculations of previous workers depart considerably from experiment.

• Received 20 May 1977

DOI:https://doi.org/10.1103/PhysRevB.18.5410