SCATTERING OF PHONONS BY SPHERICAL DEFECT AGGREGATES

The phonon relaxation time due to defect aggregates in solids is studied by the perturbation method. The defect aggregates are assumed to have spherical shape and to be formed by the clustering of a large number of atoms that differ from the host crystal atoms in mass alone. The relaxation time τ obtained is found to be of the Rayleigh type with a frequency dependence of ω−4 type for wavelengths λ large compared with the diameter d of the defects, ω being the phonon frequency. However, its dependence on ω is observed to be approximately of ω−2 type for λ smaller than, and yet comparable in order of magnitude with d. This result is at variance with the geometrical scattering that is generally taken to be valid for shorter‐wavelength phonons. The transition of τ from ω−4 to ω−2 is found to be rather smooth. Copyright © 1979 WILEY‐VCH Verlag GmbH & Co. KGaA