The figure on the right presents the simulation results of liquid-phase sintering, performed by applying CALPHAD thermodynamic data of a hypothetical ternary system exhibiting solid–liquid–vapor coexistence to the newly developed phase-field model. This framework is the first liquid-phase sintering phase-field model capable of resolving the rigid-body motion of sintering particles while incorporating grain-boundary contributions to both rigid-body motion and solute diffusion. The present model achieves continuous simulation from the initial to the final stages of liquid-phase sintering. It demonstrates that characteristic microstructural phenomena—specifically, shrinkage between solid particles, capillary-driven liquid penetration into grain boundaries, and liquid-mediated Ostwald ripening—can be analyzed in a unified and seamless manner. Furthermore, the accompanying evolution of elemental concentrations is thermodynamically consistent, confirming the validity and efficacy of the developed phase-field model.

Accurate predictions via phase-field simulations require precise material properties and model parameters; however, such parameters remain unknown for many materials. To address this issue, this study developed a high-fidelity predictive framework by applying data assimilation—a methodology capable of inversely estimating material parameters from experimental observations—to phase-field simulations of solid-state sintering. The schematic on the left outlines the results of this work. Through data assimilation, seven unknown parameters, including the surface and grain-boundary diffusion coefficients of Cu atoms, were successfully estimated simultaneously. By utilizing these estimated parameters, the phase-field model not only accurately reproduced the sintering behavior observed in the reference experimental data, but also successfully predicted the sintering behavior captured in an independent field of view with high fidelity.