neck growth
Where two particles touch, they meet at a point, and if you looked very closely at that junction just after firing began you would see a tiny waist forming — a rounded bridge of material spanning the gap, like the pinched middle of an hourglass or the wet bridge that forms when two water droplets kiss. That bridge is the neck, and its widening over time is neck growth. It is the single most-studied event in all of sintering, because it is where the abstract driving force becomes visible motion, and because its rate reveals which mechanism is carrying the matter.
The neck grows because of its shape. Along the axis between the two particles the neck surface curves outward like the outside of a ball, but around the waist it is sharply hollowed inward — a saddle. That concave hollow, with radius of curvature far smaller than the particles, is a place of very low chemical potential: by delta-mu = gamma times Vm times (1/r1 + 1/r2), atoms are drawn there from the higher-potential convex surfaces of the particles. As atoms pile in, the neck radius x grows toward the particle radius r. Careful models give a power law, (x/r)^n = B(T) times t / r^m, where B carries the diffusion coefficient and temperature, and the exponents n and m fingerprint the path: n near 7 and m near 4 for surface diffusion, n near 6 for grain-boundary diffusion, n near 5 for lattice diffusion, near 3 for evaporation-condensation, near 2 for the viscous flow of a glass. The high exponents mean the neck grows fast at first and then crawls, which is why the initial stage passes quickly and the final stage drags.
The deep lesson of neck growth is the fork between two futures that look identical at the neck but differ utterly for the part. If the atoms filling the neck are scavenged from the particle surfaces — by surface diffusion or evaporation-condensation — the neck fattens but the particle centres stay exactly as far apart as before: strong bond, zero shrinkage, pure coarsening. If instead the atoms come out of the grain boundary that forms in the plane of the neck, or from the lattice beneath it, then material is removed from between the centres and the particles slide closer: that is densification. Every real sinter is a race between these two, decided at the neck.
The classic two-sphere experiment: sinter two spheres of the same ceramic side by side, then measure the neck diameter as it grows with time. Plot log(x/r) against log(t); the slope hands you 1/n, and n tells you at a glance whether surface, boundary, or lattice diffusion is running the show.
A neck is the welded bridge between two particles; how fast it grows fingerprints the transport mechanism.
A fat, strong-looking neck can be a warning sign, not a success: if it grew by surface diffusion, the body coarsened without densifying, and the pores are now larger and harder to remove than before.