Some Properties of Phonon Thermal-Conductivity Resonances

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Abstract
A unified treatment is given of impurity-induced phonon scattering resonances in thermal conductivity. A mean scattering rate may be defined within the relaxation-time approximation which has a nearly common Lorentzian form for all resonances occurring at a given frequency, except that the width may vary. The peak mean scattering rate is nearly independent of everything about the impurity except the resonance frequency and the degeneracy of the resonance mode. Three impurity types are discussed in detail and compared: (a) a substitutional impurity with no internal degrees of freedom, (b) an impurity with an internal harmonic-oscillator degree of freedom, and (c) an impurity with an internal degree of freedom having just two energy levels. The dominant role of resonance widths in determining thermal-conductivity dips is emphasized, and additional line-shape effects are discussed.