Thermodynamics and densification kinetics in solid-state sintering of ceramics

Based on the stability analysis of the closed pores in two dimensions which was determined mathematically with their particle coordination number and dihedral angle, the stability of those in three dimensions was determined with a spherical pore model. The model is set up by first excluding the effect of interface tension, so the pore was supposed to be spherical, and then the tensile stress arisen from the interface tension was supposed to act on this hypothesized spherical pore. On the basis of the spherical pore model, microstructure models based on pores, not grains, for the real powder compacts were first established. Densification kinetics were then determined from the models by the densification rate equations, which were derived by relating density to pore size to grain size ratio, for the intermediate and final stages of sintering. The criteria for pore shrinkage were discussed quantitatively. The derived equations can be used to simulate the relation between densification rate and density during heating with a constant rate and for the explanation of the effects of pore size distribution, agglomerates, and green density on sintering.