Lattice Thermal Resistivity due to Point Defects
Scattering of phonons by point defects can be studied in the long-wave limit by measuring the thermal conductivity of dielectric solids at low temperatures where it first departs from the Casimir T3 dependence, and by measuring the first departure of the lattice thermal conductivity of metallic alloys from Makinson’s T2 dependence. At high temperatures the long wavelength limit is still a fair approximation provided the defect concentration is high. Scattering of phonons by point defects can be expressed in terms of a local change in the phonon velocity at the defect. The scattering cross-section as function of frequency is proportional to the density of states. In the absence of dispersion this results in a fourth-power dependence. Strong dispersion can simulate resonance effects. The case of the vacancy is considered. The vacancy has no low-lying resonances; apparent resonances due to vacancies in KCℓ are traced to a strongly dispersed TA branch. A simple model of the vacancy yields scattering cross-sections in rough agreement with experiments for KCℓ, for SnTe and for ZnC.
KeywordsPoint Defect Lattice Thermal Conductivity Lithium Isotope Dielectric Solid Rough Agreement
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