The Wulff shape of alumina: II. Experimental measurements of pore shape evolution rates

The rate at which a facetted tetragonal cavity of nonequilibrium shape appr oaches a cubic equilibrium (Wulff) shape via surface diffusion was modeled. The shape relaxation rate of a facetted "stretched cylinder" was also mode led, For the first geometry, only an approximate solution based on lineariz ing the mean potential difference between the source and sink facets was ob tained. For the stretched cylinder, both an approximate and an exact soluti on can be obtained; the approximate solution underestimates the evolution r ate by a factor of approximate to 2, To assess the applicability of the mod els, nonequilibrium shape pores of identical initial geometry (approximate to 20 mu m x 20 mu m x 0.5 mu m) were introduced into (0001), {10 (1) over bar 2}, {11 (2) over bar 0}, and {10 (1) over bar 0} surfaces of sapphire s ingle crystals using microfabrication techniques, ion-beam etching, and hot pressing. The large (approximate to 20 pm x 20 mu m) faces of the pore are low-index surfaces whose nature is dictated by the wafer orientation. A se ries of anneals was performed at 1900 degrees C, and the approach of the po re shape to an equilibrium shape was monitored, The kinetics of shape evolu tion are highly sensitive to the crystallographic orientation and stability of the low-index surface that dominates the initial pore shape. The measur ed 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. Howev er, surface-attachment-limited kinetics (SALK) appears to play a major role in determining the pore shape evolution rate in cases where the initial bo unding surfaces have orientations that are part of the Wulff shape.