The Wulff Shape of Alumina: I, Modeling the Kinetics of Morphological Evolution

Abstract

The rate at which fully facetted nonequilibrium shaped particles and pores approach their equilibrium (Wulff) shape via surface diffusion was modeled, and calculations relevant to alumina were performed to guide experimental studies. The modeling focuses on 2‐D features, and considers initial particle/pore shape, size, surface energy anisotropy, and temperature (surface diffusivity) as variables. The chemical potential differences driving the shape change are expressed in terms of facet‐to‐facet differences in weighted mean curvature. Two approaches to modeling the surface flux are taken. One linearizes the difference in the mean chemical potential of adjacent facets, and assumes the flux is proportional to this difference. The other approach treats the surface chemical potential as a continuous function of position, and relates the displacement rate of the surface to the divergence of the surface flux. When consistent values for the relevant materials parameters are used, the predictions of these two modeling approaches agree to within a factor of 1.5. As expected, the most important parameters affecting the evolution times are the cross‐sectional area (volume in 3‐D) and the temperature through its effect on the surface diffusivity. Pores of micrometer size are predicted to reach near‐equilibrium shapes in reasonable times at temperatures as low as 1600°C. The detailed geometry of the initial nonequilibrium shape and the Wulff shape appear to have relatively minor effects on the times required to reach a near‐equilibrium shape.