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 partic
le/pore shape, size, surface energy anisotropy, and temperature (surface di
ffusivity) as variables. The chemical potential differences driving the sha
pe 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 approa
ch treats the surface chemical potential as a continuous function of positi
on, and relates the displacement rate of the surface to the divergence of t
he surface flux. When consistent values for the relevant materials paramete
rs are used, the predictions of these two modeling approaches agree to with
in a factor of 1.5, As expected, the most important parameters affecting th
e evolution times are the cross-sectional area (volume in 3-D) and the temp
erature 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 degrees C. The detailed geometry of the initial
nonequilibrium shape and the Wulff shape appear to have relatively minor e
ffects on the times required to reach a near-equilibrium shape.