A model for the sintering and coarsening of rows of spherical particles

The formation of interparticle contacts and neck growth by grain boundary and surface diffusion during the sintering of rows of spherical particles is modeled. It is shown that rows of identical particles sinter into a metastable equilibrium configuration whereas rows of particles with different sizes evolve continuously by sintering followed by relatively slow coarsening. During coarsening, smaller particles disappear and larger particles grow. The model is based on a variational principle arising from the governing equations of mass transport on the free surface and grain boundaries. Approximate solutions are found through the use of very simple shapes in which the particles are modeled as truncated spheres and neck formation is represented by a circular disc between particles. Free and pressure assisted sintering of rows of identical and different size particles are studied through this numerical treatment. The effect of initial particle sizes, dihedral angles, diffusivities, and applied compressive forces are investigated.