Diffusion of nondecaying TA-phonons

Decay cascades of acoustic phonons in calcium fluoride

“…The peaks in the uppermost frequency interval of transverse phonons result from scattering processes of the monochromatic source of longitudinal phonons. Slow-transverse phonons decay indirectly via mode conversion [7,8]. At low frequencies the distribution function is governed by scattering, while at high frequencies decay dominates, in accordance with the qualitative discussion in § 3 .…”

“…We now confine ourselves to the isotropic case, where only the longitudinal phonons decay directly. To derive an effective equation for the occupation numbers of the transverse phonons, nT, we retain only terms up to second order in nT and eliminate the longitudinal occupation numbers in the same way as has been done in references [7] and [8]. This finally leads to an equation of the form…”

“…Apart from certain restricted areas of solid angle for the propagation directions, the spontaneous decay of the slow-transverse modes is negligible. On a timescale larger than that on which the fast cascades proceed, they will be downconverted by indirect processes, either via mode conversion due to elasticscattering [7,8] or via up-conversion into longitudinal or fast-transverse modes, which may subsequently decay into phonons of lower frequency (see appendix 2). Because of the anisotropy of the rates in (2.2), even an initially isotropic phonon distribution will develop into an anisotropic distribution, i.e.…”

“…In the high-frequency regime, where the impurity scattering rate is much smaller than the damping rate due to spontaneous decay, the longitudinal and fast-transverse components of the decay cascade move rapidly to lower frequencies generating also slowtransverse phonons in the decay processes, which cannot decay directly via three-phonon interaction. It has been pointed out by Guseinov and Levinson [7,8] that these phonons can decay indirectly on a longer timescale via mode conversion due to impurity scattering into directly decaying phonons. An effective equation for the temporal evolution of the occupation numbers of the non-decaying modes and a scaling law for their dependence on time and frequency have been derived by these authors.…”

Structure and Ordering of Mixed Aluminates Y1−xErxAlO3 by NMR, Acoustic, and Heat Pulse Techniques

“…In the heat pulse method the main role in the formation of the maximum of the signal recorded by the bolometer is played by fast transverse phonons in a certain range of frequencies [18, 191, whereas the attenuation of ultrasound due to the Akhiezer mechanism represents the total effect of phonon scattering by local inhomogeneities in the solid solution. Then, in the case of the heat pulse method the relation between the wavelength of lattice vibrations and the cluster sizes, which determines the scattering efficiency, and phonon dispersion features [20] are more important. Hence, the maximum normalized time t,/L2, corresponding to the minimum time of phonon relaxation, could be observed at some concentration x which defers from the value x corresponding to the minimum in sound attenuation.…”