A New Closed-Form Model for Solid-State Sintering Kinetics
Résumé
The aim of this work was to revisit the two-sphere model of solid-state sintering kinetics to make it consistent with the morphological evolution of the particle contacts during most of the sintering process. Mass transport equations for solid-state sintering are written in a closed-form. The usual simplifications of tangent or secant spheres are avoided and the true evolution of the neck geometry is taken into account, depending on the relative weight of densifying / nondensifying mechanisms. Finite difference methods are used to compute the evolution of geometrical parameters and of the shrinkage rate as a function of time and temperature. The model combines the usual mechanisms of volume, surface, and grain-boundary diffusion as well as vapor transport. The ratio of concave to convex surfaces is deduced from neck growth and from the packing coordination number. A smooth transition from the classical first stage to the intermediate stage of sintering, where curvature gradients have vanished at the particle surface, is obtained. The same model can then be applied to describe sintering kinetics until pore closure. This model providing a realistic evolution of the contact morphology makes it possible to analyze the competition between densifying and nondensifying mechanisms throughout the early and intermediate stages of sintering. The competition between lattice diffusion and vapor transport or surface diffusion is thus analyzed.