Spontaneous decay rates of LA phonons in quasi-isotropic solids

The spontaneous decay rates of LA phonons are calculated in terms of the second- and third-order elastic constants in the isotropic model. It is shown that the dominant decay channel is LA→TA+TA but not LA→LA+TA and total decay rates at 1-THz frequency range from ${10}^5$ to ${10}^6$ ${\sec }^{\mathrm{-}1}$ for Si, Ge, GaAs, LiF, NaF, and fused silica. These results indicate that the rates of frequency down conversion of the LA phonons assumed currently in the study of the transport properties of high-frequency phonons are incorrect in both their magnitudes and branching ratios.