the intermediate stage of sintering
Once the necks between particles have grown fat enough to touch their neighbours, the porous body stops looking like a heap of beads and starts looking like a sponge riddled with connected tunnels. The intermediate stage of sintering is this long middle chapter, in which the pore space is a continuous, branching network of channels running along the edges where grains meet, and that network slowly narrows and drains as the body shrinks. It is the workhorse stage: most of the densification of the whole firing happens here.
A useful mental picture, due to Coble, is to treat the microstructure as tidy polyhedral grains packed like foam, with the pores sitting as long cylindrical channels along the three-grain edges. Atoms diffuse from the grain boundaries (which act as sources) into these cylindrical pores' surfaces, or equivalently vacancies flow from the pores to the boundaries and are annihilated; either way the channels shrink in radius and the body densifies. Over this stage relative density typically climbs from roughly 65 percent to about 90 percent, and the linear shrinkage mounts up to most of its final 15 to 20 percent. Crucially, grain growth switches on in earnest during the intermediate stage: as boundaries sweep and grains coarsen, the pore channels both narrow (good, densifying) and get swept along or pinched (which sets the stage for the trouble to come).
The intermediate stage is where a firing schedule earns its keep, and where the densification-versus-coarsening contest is decided in practice. As long as the pore channels stay pinned to the grain edges, they keep a fast diffusion short-circuit to the boundary and can be emptied efficiently. But if grains grow too fast, the channels can be left behind, and the still-open network starts breaking up into the isolated closed pores of the final stage while there is still porosity to remove. The art is to run this stage so that densification stays ahead of grain growth — often by holding at a temperature high enough to move matter but not so high that boundaries outrun their pores, sometimes helped by a grain-growth-inhibiting dopant.
Slice a partly fired alumina at about 80 percent density and its pore space looks like a fine sponge: long channels threading along the grain edges, all still connected to the outside, so the piece will still soak up dye — the hallmark of the intermediate stage's open, interconnected porosity.
Intermediate stage: pores form connected channels along grain edges that steadily shrink as the body densifies.
The intermediate stage delivers most of the shrinkage, so a warp or crack usually traces to a density gradient present before firing. Uneven green density means uneven shrinkage here, and the part distorts even if it reaches full density.