surface diffusion
The very outside skin of a crystal, or the inner walls of a pore, is the most open environment an atom can find: an atom sitting on a surface is missing half its neighbours, held by fewer bonds, and so it is the easiest place of all to move. Surface diffusion is atoms skating across these free surfaces and pore walls, and it is typically the fastest diffusion path of the three — faster than grain boundaries, far faster than the bulk.
Fewer bonds means a lower barrier to jumping, so surface diffusion has the smallest activation energy of the three paths and the largest diffusion coefficient at a given temperature. The ordering, from fastest to slowest, is almost always surface, then grain boundary, then lattice, mirroring how open each environment is. And like the boundary path, its low activation energy makes it relatively more important at lower temperatures, where the high-Q bulk route has frozen out. The limitation is again geometry: surfaces exist only at the outside and at pore walls, so surface diffusion can only move atoms around the surface — it cannot, by itself, carry matter from the interior to fill a pore.
That last point is the crux of why surface diffusion matters in sintering — and why it is a double-edged sword. Surface diffusion readily moves atoms from a particle's convex bumps into the concave neck between two touching particles, welding them together and smoothing the microstructure. But it does this by rearranging matter already at the surface, so it grows the neck and coarsens the powder without pulling the particle centres closer — it does not densify. It can even compete against densification by rounding off the very curvature that drives shrinkage. So a process dominated by surface diffusion may strengthen a body while leaving its pores stubbornly open.
In the early stage of sintering, surface diffusion quickly rounds the sharp contact between two powder particles into a smooth neck; because it only shuffles surface atoms, the particles bond and coarsen but their centres do not approach, so this fast path builds necks without removing porosity.
Surface diffusion: atoms skate across free surfaces and pore walls — the fastest, lowest-barrier path, but one that rearranges surface matter without densifying.
Fastest does not mean most useful. Surface diffusion moves only surface atoms, so in sintering it coarsens the powder and grows necks without shrinking the body — it can even work against densification by consuming the driving curvature.