THEORETICAL MODELING OF DENSIFICATION DURING ACTIVATED SOLID-STATE SINTERING

Activated solid-state sintering relies on the addition of low concentr ations of grain boundary segregating species to increase diffusion rat es. In this article, enhanced diffusion through an activated layer at the grain boundaries has been modeled for the case of tungsten sintere d with transition element additions. Both constant heating rates and i sothermal sintering are considered. As in classical treatments, sinter ing is divided into three stages, but modifications are proposed based on recent observations and theories regarding packing coordination, p ore morphology, pore location, grain growth, and pore-grain boundary s eparation. The intermediate and final stages of sintering are allowed 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 esti mate pore curvature during the intermediate stage of sintering. In the final stage, pores are modeled on both the corners of a tetrakaidecah edron and on its square facets. The pore location has only a small eff ect on densification, while the grain boundary mobility is more of a f actor. The model allows pore-grain boundary separation to match experi mentally measured grain sizes. The model predictions are compared to d ilatometer curves of pure tungsten and tungsten sintered with addition s of Co, Fe, Ni, and Pd. For the Co- and Fe-activated samples, the mod el is modified to account for an increase in diffusional activation en ergy due to dissolution of the activator in tungsten.