the initial stage of sintering

When a pressed powder first reaches temperature, the particles are only kissing — touching at tiny points, like a bag of marbles. The initial stage of sintering is the opening act, in which each of those point contacts grows into a small welded bridge called a neck. It answers the question: what happens first, before any real shrinkage? The particles round off their sharpest features, the contacts widen into necks, and the loose heap begins to behave like a connected body — but it is still very porous and has barely shrunk.

Quantitatively, the initial stage is usually taken to run until the neck radius x reaches roughly 0.2 to 0.3 of the particle radius r, which corresponds to a rise in relative density of only a few percent — say from 55 up to perhaps 65 percent of theoretical. Matter races to the neck because the neck surface is sharply concave: its saddle-shaped hollow is a low-chemical-potential sink that pulls atoms in from the nearby convex particle surfaces. The neck grows as a power law in time, (x/r)^n proportional to t, and the exponent n betrays which transport path is winning — around 7 for surface diffusion, 6 for grain-boundary diffusion, 5 for lattice diffusion, 3 for evaporation-condensation, 2 for viscous flow. Whether the body actually shrinks in this stage depends entirely on where the neck's atoms come from: if they arrive over the surface, the neck fattens but the particle centres stay put, so there is no densification.

The initial stage matters because it quietly sets up everything that follows. Surface diffusion and evaporation-condensation are fast at these lower temperatures and tend to dominate early, rounding particles and blunting the sharp curvatures — which is coarsening, and it spends the driving force without removing any porosity. A powder that coarsens too much in the initial stage arrives at the densifying stages with less driving force and larger, more stubborn pores. This is why good practice often means heating quickly through the low-temperature range, to skip past the non-densifying head start and reach the temperatures where grain-boundary and lattice diffusion can actually pull the body together.