evaporation-condensation

Some materials, when hot, do not just sit there — a few of their atoms take off into the vapour above the surface, like the faint mist that rises from a snowbank on a sunny day even though it never melts. Evaporation-condensation is the sintering path that uses this: atoms evaporate from one part of the powder, cross the gap as vapour, and condense back down on another part. Matter is transported through the air (or furnace atmosphere) rather than through the solid, and where it lands is decided by a subtle rule about surface shape.

The rule is the Kelvin equation: the vapour pressure just above a surface depends on how that surface is curved. Over a convex bump — the outside of a particle — the pressure is slightly raised; over a concave hollow — the neck between two particles — it is slightly lowered, by p/p0 = exp(gamma times Vm / (r times R times T)) with the sign of the curvature radius r flipping between the two. So there is always a gentle pressure difference driving vapour from the convex particle surfaces (high pressure, easy to evaporate) toward the concave necks (low pressure, easy to condense). Atoms quietly ferry across the pore and build up the neck. This is the same physics that makes small water droplets in a cloud evaporate and feed the big ones, and that ripens the ice crystals in old ice cream into coarse, gritty grains.

Here is the essential point, and the reason evaporation-condensation is usually a nuisance rather than a help: it fattens the neck and rounds the pores, but it moves no material out from between the particle centres, so the centres stay exactly as far apart — there is zero shrinkage and zero densification. It is a pure coarsening path. It matters most for volatile ceramics — think of PbO escaping from lead-based electroceramics, or the sublimation of Si3N4 and SiC at high temperature — where vapour transport can noticeably coarsen the microstructure and enlarge pores, spending the driving force uselessly. Sometimes it is deliberately exploited (to round sharp particles, or in vapour-based coarsening studies), but for a maker chasing full density it is a leak to be plugged, often by firing under a controlled atmosphere or a powder bed that suppresses evaporation.