Role of Three-Phonon Normal Processes in the Phonon Conductivity of an Insulator

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In the present work the role of three-phonon normal processes is studied in the framework of Callaway's theory of Phonon conductivity of an insulator under the conditions τ N -1 >τ R -1 , τ N -1 <τ R -1 and τ N -1 ≪τ R -1 where τ R -1 =τ B -1 +τ pt -1 +τ U -1 . Use also made of a parameter `a', which is a measure of the relative strengths of normal and Umklapp processes and is equal to τ N -1 /τ U -1 in Callaway's model. It is shown that for τ N -1 ≪τ R -1 and `a' approaching 10 -3 Callaway's model gives good description of phonon conductivity of Ge in the temperature range 2 to 100 K. For τ N -1 ≫τ R -1 Callaway's theory gives not only the smaller values of phonon conductivity but also leads to wrong temperature dependence in the range 20–100 K.