M1 Ceramic Sintering and Vitrification

Topic

Ceramic sintering is the process by which the ceramic densifies, occurring via one of two pathways: solid-state diffusion or liquid-phase viscous flow. The presence or absence of a fluxing agent determines which of these two densification pathways is followed. Let us first examine what happens when a flux is present.

The presence of a flux triggers liquid-phase sintering: the flux locally lowers the temperature at which a liquid phase forms between the ceramic particles, and this liquid phase enables densification through viscous flow, as described by the Frenkel equation. This equation establishes that the rate of viscous flow depends directly on the surface tension pulling the particles together and inversely on the viscosity of the liquid resisting that flow; thus, the higher the surface tension and the lower the viscosity, the faster liquid-phase densification proceeds.

Conversely, the absence of such a flux causes densification to occur via the alternative pathway: solid-state sintering, driven by diffusion. In the absence of a liquid phase, atoms from the solid ceramic itself migrate—via diffusion along particle surfaces and grain boundaries—toward the contact points between neighboring particles. To describe this process, the model employs the same solid-state "neck growth" mechanism used for the same purpose in the equivalent model for metals.

In either pathway, the migration of material toward the contact points between particles—whether through liquid-phase viscous flow or solid-state diffusion—causes the growth of the neck connecting each pair of neighboring particles. As the neck grows, the centers of neighboring particles move closer together; this convergence translates—at the scale of the entire component—into linear shrinkage: the more the inter-particle neck grows, the greater the linear shrinkage experienced by the component as a whole.

Beyond causing this linear shrinkage, the sintering process also governs the ceramic's final grain size: as sintering progresses, not only do the necks between particles grow, but the ceramic grains themselves enlarge, following the same grain-growth mechanism during sintering used—for the same purpose—in the equivalent model for metals. Prolonging the sintering process or raising the temperature results in a larger final grain size, whereas stopping it earlier or at a lower temperature yields a smaller final grain size. This final grain size is precisely one of the two microstructural state parameters described in detail by another model in this set.

Thus, this model—based on the ceramic sintering process with which it began (whether liquid-phase sintering due to the presence of a flux or solid-phase sintering in its absence)—determines two consequences that are also linked to the rest of the set: the linear shrinkage resulting from neck growth (which another model in the set tracks experimentally via dilatometry) and the final grain size controlled by the sintering process (which serves as an input for the model describing the ceramic's microstructure).

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