Equilibrium neck shapes for initial stages of solid-state sintering due to surface diffusion in a disk model of clays

We study equilibrium neck shapes corresponding to initial stages of solid-state sintering, using a microscopic model of clays in which particles have a uniform disk shape with a microscale diameter R and a nanoscale thickness ? = R/100. Particles are stacked on top of each other, forming vertical piles of various heights ranging from h = ? to h = 10?. Pores are formed in the spaces between any three touching piles of the same height. Assuming that surface diffusion is the dominant sintering mechanism and considering a simplified form of the neck configuration, we derive equilibrium neck shapes by minimizing a neck surface free energy when a neck volume V fixed. We allow for the anisotropy of the surface free energy, using a single anisotropy parameter q. We discuss the dependence of the obtained neck shapes on the neck volume V, pore height h, and anisotropy parameter q.