Theoretical modeling of densification during activated solid-state sintering

Abstract

Activated solid-state sintering relies on the addition of low concentrations of grain boundary segre-gating species to increase diffusion rates. In this article, enhanced diffusion through an activated layer at the grain boundaries has been modeled for the case of tungsten sintered with transition element additions. Both constant heating rates and isothermal sintering are considered. As in classical treatments, sintering is divided into three stages, but modifications are proposed based on recent observations and theories regarding packing coordination, pore morphology, pore location, grain growth, and pore-grain boundary separation. The intermediate and final stages of sintering are al-lowed to overlap based on the amount of closed porosity to account for both pore closure early in the process and the gradual increase in packing coordination with densification. Mean curvature theory is used to estimate pore curvature during the intermediate stage of sintering. In the final stage, pores are modeled on both the corners of a tetrakaidecahedron and on its square facets. The pore location has only a small effect on densification, while the grain boundary mobility is more of a factor. The model allows pore-grain boundary separation to match experimentally measured grain sizes. The model predictions are compared to dilatometer curves of pure tungsten and tungsten sintered with additions of Co, Fe, Ni, and Pd. For the Co- and Fe-activated samples, the model is modified to account for an increase in diffusional activation energy due to dissolution of the activator in tungsten.