Pore-boundary interactions and evolution equations for the porosity and the grain size during sintering

The retardation of grain boundary migration by a pore is analyzed numerically and by an analytical approximation, which becomes exact in the limiting case of small velocities. At high velocities, the numerical solution describes separation of the pore from the boundary. Based on the analysis of a single migrating boundary facet dragging a pore, evolution equations for the grain size and the porosity are suggested for the final stage of sintering. It turns out that three-dimensional pores on two-grain junctions have an only moderate effect on the rate of grain coarsening: pores with a high mobility follow the migrating grain boundary easily, while those with a low mobility detach from the boundary. It is also shown that a two-dimensional pore does not detach and can therefore reduce the coarsening rate to very low values if the pore mobility is low. This strong dependence on the pore configuration suggests that other possible configurations need to be analyzed, before final evolution eq uations can be formulated.