Acoustic-Optical Phonon Interactions in Solids
We present here a scheme of studying the role of optical phonons in heat transfer and in generating heat resistance via various three-phonon acoustic-optical N and U processes. Using the Debye dispersion law in the reduced zone scheme we write for acoustic modes ω= cq and for optical modes ωo = ωD + ωg + co (qD − q), where ωD is the Debye frequency for the corresponding acoustic polarization mode, qD is the Debye radius, c and co are, respectively, acoustic and optical phonon velocities, and ωg is the frequency gap at the zone boundary. Following Klemens1 we introduce a factor \(r = 2/\sqrt 3 (\alpha - \beta )\,/\,(\alpha + \beta )\) to reduce the cubic anharmonic Hamiltonian for optical phonons. Here α and β are two effective force constants such that at the zone boundary α/β = (ωo/ωD)2.
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