Wulff shape of alumina: II, Experimental measurements of pore shape evolution rates

The rate at which a facetted tetragonal cavity of nonequilibrium shape approaches a cubic equilibrium (Wulff) shape via surface diffusion was modeled. The shape relaxation rate of a facetted `stretched cylinder' was also modeled. For the first geometry, only an approximate solution based on linearizing the mean potential difference between the source and sink facets was obtained. For the stretched cylinder, both an approximate and an exact solution can be obtained; the approximate solution underestimates the evolution rate by a factor of ≈2. To assess the applicability of the models, nonequilibrium shape pores of identical initial geometry (≈20 μm×20 μm×0.5 μm) were introduced into (0001), {101̄2}, {112̄0}, and {101̄0} surfaces of sapphire single crystals using microfabrication techniques, ion-beam etching, and hot pressing. The large (≈20 μm×20 μm) faces of the pore are low-index surfaces whose nature is dictated by the wafer orientation. A series of anneals was performed at 1900 °C, and the approach of the pore shape to an equilibrium shape was monitored. The kinetics of shape evolution are highly sensitive to the crystallographic orientation and stability of the low-index surface that dominates the initial pore shape. The measured variations of the pore aspect ratio were compared to those predicted by the kinetic model. The observations suggest that when the initial bounding surface is unstable, shape relaxation may be controlled by diffusion. However, surface-attachment-limited kinetics (SALK) appears to play a major role in determining the pore shape evolution rate in cases where the initial bounding surfaces have orientations that are part of the Wulff shape.