New solutions describing the formation of interparticle necks in solid-state sintering

Abstract

The formation of a neck between spherical particles by surface and grain boundary diffusion is modelled by three independent methods. First, an accurate numerical solution is provided. Second, closed-form similarity solutions are derived, which are exact for short times in the limiting cases of small and large δD s/ δD b ratios. Third, approximate analytical solutions are developed based on a thermodynamic variational principle. The latter method is probably the most versatile on e, since its results are formulated as coupled evolution equations for the neck size and the center-to-center approach of the spheres. As such they are well suited to deal with variable stress and temperature histories as encountered by the material during inhomogeneous sintering. Where the similarity solutions are valid (zero stress, short times, small or large δD s/ δD b), they confirm the results of the approximate method. Compared to the fully numerical method the approximate method usually works well, also for complex stress histories, but has its limitations when the stress becomes tensile and the neck shrinks rapidly in a crack-like mode.