Effect of grain sizes and shapes on phonon thermal conductivity of bulk thermoelectric materials

This paper presents a phonon transport model for bulk thermoelectric materials to investigate the effect of the grain sizes and grain shapes on phonon thermal conductivity. An analytical solution for the effective thermal conductivity contributing from the grains and grain boundaries of the bulk thermoelectric material is obtained, and the impact of the grain geometric characteristics on the thermal conductivity is analyzed. The theoretical model exhibits quite a well description on the often experimentally observed grain size-dependent thermal conductivity. Meanwhile it is demonstrated that the grain shapes significantly influence the thermal conductivity, especially for small grain sizes (with dimensionless values ξ a < 10 ). An optimal grain shape is achieved that leads to a minimum value of thermal conductivity of the bulk thermoelectric material.