Lattice diffusion from the grain boundary in the sintering of metal powders

Although sintering maps have been in use since 1974, there is no explicit solution for the diffusion of atoms from the grain boundary to the neck by lattice diffusion. The approximate solutions in the literature are considered and their weaknesses examined. Two new solutions are presented, an upper limit solution with surface curvature at a maximum all along the neck, and a more accurate solution in which the form of the surface curvature at the neck can be varied as appropriate. The applicability of the solutions in regions of lattice diffusion dominance is considered vis a vis the coupled solution for lattice and boundary solution. Finally the effect of the new solution is shown for sintering maps.