Grain-Growth-Assisted Percolation Model for Thermal Conductivity of Y₂O₃-Doped AlN

Abstract

A theoretical model is proposed for explaining the increase in thermal conductivity experimentally found upon annealing in an AlN polycrystal doped with ≈3vol%Y₂O₃. The model foresees the concurrent effect of the growth of AlN-matrix grains and of the collapse of grain boundaries filled by the low thermal conductivity Y₂O₃ phase. Such depleted grain boundaries form directly bonded two-grain junctions. Grain growth produces a reduction of scattering of phonons at grain boundaries, and the increase of the number of directly bonded grain boundaries increases the average size of the thermally conductive AlN clusters. Thus, both the phenomena accompanying the microstructural evolution can lead to an increase of thermal conductivity in the polycrystal. The mathematical formulations of phonon scattering at grain boundaries and the percolation model are revisited and rearranged to give a comprehensive model of grain-growth-assisted percolation, which links the microstructural evolution of the polycrystal to the experimentally observed increase in its thermal conductivity.