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 elas­ tic constants in the isotropic model. It is shown that the dominant decay channel is LA -+ T A + T A but not LA ...... LA+TA and total decay rates at I-THz frequency range from 105 to 106 sec-I for Si, Ge, GaAs, LiF, NaP, 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. Recently there have been considerable activities in theoretical investigations of high-frequency phonon trans­ port in the presence of elastic scattering and frequency down conversion.l -4 At low temperatures, or equivalently in the regime Ii w > > kB T (w being the angular frequency of a pho­ non and T the ambient temperature) the down conversion of a phonon is predominantly caused by the splitting into a pair of low-frequency phonons. In the isotropic model em­ ployed currently degenerate T A phonons are prohibited to decay through this splitting process owing to the energy and momentum conservation condition, leading to an anomalously long anharmonic lifetime of high-frequency T A phonons.5 In contrast, LA phonons can really decay spontaneously via three-phonon processes exhibiting the de­ cay rate proportional to w 5 in the context of the continuum elasticity theory,5,6 which has recently been verified experi­ mentally.7 However, there seem to be still some problems on the magnitude and on the dominant decay channel of the LA phonons. Orbach and Vredevoe5 found that the dom­ inant channel is