Recasting the Callaway and von Baeyer thermal conductivity model on defective oxide materials: the ZnO–In2O3 system as an example

Abstract

Point defects and nanoscale interfaces effectively scatter short and mid-to-long wavelength phonons, respectively, thereby considerably reducing the thermal conductivity. In this paper, a classical physical model of phonon transport and scattering, the Callaway and von Bayer method, is recast with the introduction of the phonon mean free path cut-off, or equivalently, the minimum phonon relaxation time. To illustrate the method, we compute the thermal conductivity for the ZnO–In₂O₃ binary system in which the compositionally dependent structure is available, including solid solutions consisting of point defects and natural superlattices. The calculated thermal conductivity is in good agreement with the experimental measurements, and suggests a threshold value of about 50 nm for the interface spacing, above which the thermal conductivity becomes less sensitive to the interfaces with increasing temperature. A useful design clue is implied for the nanostructural engineering of high temperature thermoelectrics and thermal barrier coatings.