Scaling microstructural processes in the sintering of ionic ceramics
A multi-scale framework, combining a multiphase field formulation and large deformation mechanics, was developed as a stepping stone to perform the data analytics of the microstructural level kinetics of a sintering solid. Relevant microstructural information from this framework, such as grain, stress, and porosity statistics, was scaled up to describe the macroscopic level sintering kinetics. Here, the developed formulation was applied to describe the electric field assisted sintering of Y 2 O 3 . Microstructural inhomogeneities in a multi-granular solid result in the formation of a field of compressive stress networks, which interleave with low compression and weakly tensile regions, defining a scaffolding for sintering concentration regions to develop. A Poisson effect-induced lateral stress network is also naturally self-induced as a result of the mechanical constraints imposed by the sintering apparatus. For long sintering times, localized shear stresses enhancing mass flow along grain boundaries and internal surfaces develop. Three-sided pores are removed by either vacancy transport to the surrounding pores, or move towards the external surfaces through grain boundary diffusion. Four- and higher order-sided pores stabilize because an equal amount of vacancies are gained and lost through the connecting grain boundaries. Grain dewetting contributes to pore coalescence, suggesting that pore kinetics and grain growth are coupled and should be analyzed in concert. The combined sintering and grain growth kinetics define six regimes of sintering behavior: (1) T, the transient regime; (2) E$_Υ$, the surface energy dominated, early sintering regime, where the grain growth exponent, p = 1, and the stress concentration factor, $f$ ~ $1/\hat{ρ}^{4.6}$; (3) E S , the stress dominated, early sintering regime, where p = 1 and $f$ ~ $1/\hat{ρ}^{4}$; (4) I$_Υ$, the surface energy dominated, intermediate sintering regime, where p = 2 and $f$ ~ $1/\hat{ρ}^{4.6}$; (5) I S , the stress dominated, intermediate sintering regime, where p = 2 and $f$ ~ $1/\hat{ρ}^{4}$; and (6) L, the late sintering regime, where p = 3 and $f$ ~ 1. At the macroscopic level, the rapid densification and suppression of grain growth observed in the electric field assisted sintering process is a consequence of the compounding effects of the underlying stress-, transport-, and interfacial-energy-induced energy minimization kinetics, as predicted by the multi-scale framework.