Thermodynamics of Densification: II, Grain Growth in Porous Compacts and Relation to Densification

It is shown that grain‐boundary motion in a sintering array of particles can be limited by the geometry of the sintered particle network. Despite its curvature, the grain boundary can encounter an energy barrier when it attempts to move through smaller grains toward its center of curvature. This energy barrier decreases to zero when the radius ratio ( R ) between adjacent grains approaches a critical value, R → R c =− [cos (Ψ e )] −1 , where Ψ e is the dihedral angle relating surface and grain‐boundary energies. The change in radius ratio ( R → R c ) can occur by interparticle mass transport, viz., coarsening. This result suggests grain growth kinetics within a sintering array can be controlled by coarsening kinetics, making it distinctly different from grain growth in the fully dense material which occurs by boundary motion. More significantly, it is shown that when a grain disappears from between larger grains by coarsening, the driving force for sintering between the newly joined grains is reinitiated. That is, grain growth via coarsening can continually drive sintering and array shrinkage. It is shown that coarsening by itself does not lead to significant array shrinkage, but can promote significant shrinkage when sintering is reinitiated. Densification is therefore expected to be predictably related to grain growth, and thus coarsening kinetics. It is shown that the relative density of a ring of spheres that undergoes cyclic coarsening and sintering is nearly linearly related to grain size. Conceptual relations between density and grain growth for real powder compacts are discussed and related to the function that describes the compact's distribution of pore coordination numbers. Finally, since coarsening can be the rate‐limiting step for densification, it is suggested that theory and related experiments associated with densification kinetics should be reevaluated.