Role of phonon dispersion in studying phonon mean free paths in skutterudites

Abstract

Experimental thermal conductivity of bulk materials are often modeled using Debye approximation together with functional forms of relaxation time with fitting parameters. While such models can fit the temperature dependence of thermal conductivity of bulk materials, the Debye approximation leads to large error in the actual phonon mean free path, and consequently, the predictions of the thermal conductivity of the nanostructured materials using the same relaxation time are not correct even after considering additional size effect on the mean free path. We investigate phonon mean free path distribution inside fully unfilled (Co4Sb12) and fully filled (LaFe4Sb12) bulk skutterudites by fitting their thermal conductivity to analytical models which employ different phonon dispersions. We show that theoretical thermal conductivity predictions of the nanostructured samples are in agreement with the experimental data obtained for samples of different grain sizes only when the full phonon dispersion is considered.