Phase-field simulation of liquid-phase sintering coupled with a CALPHAD database of Nd-Fe-B-Cu system

The coercivity of Nd–Fe–B sintered magnets is strongly influenced by their microstructure. High coercivity requires a compact microstructure consisting of small Nd2Fe14B (T1) grains uniformly covered with a thin grain boundary phase. To achieve such a microstructure, Nd−Fe−B sintered magnets are typically produced through sintering followed by postsinter annealing. The sintering process is liquid-phase sintering (LPS) because Nd-rich phases in the material liquefy at the sintering temperature (1000–1100 °C). During LPS, densification, grain growth, and liquid phase expansion determine the sintered compact density, T1 grain size, and final liquid phase distribution. The liquid phases, upon cooling to lower temperatures, transform into Nd-rich phases, which serve as a source of Nd for the formation of the thin grain boundary phase during post-sinter annealing. Therefore, predicting the microstructural evolution during LPS is crucial for enhancing the coercivity of Nd–Fe–B sintered magnets. Numerical simulation using the phase-field (PF) method is a promising numerical approach for predicting microstructural evolution during sintering. In our previous study, we have developed a PF model for LPS in multiphase and multicomponent systems. The PF model can analyze the microstructural evolution, including densification of the sintered compact, grain growth, phase transformation, and solute diffusion, by coupling with a CALPHAD database. In this study, we developed a PF simulation framework to analyze the microstructural evolution during LPS of Nd–Fe–B sintered magnets by coupling the PF model with a CALPHAD database of the Nd–Fe–B–Cu quaternary system. The PF simulation framework provided a thermodynamically consistent evolution of the Fe–15Nd–6B–0.1Cu (at%) alloy. By performing PF simulations under several conditions, we investigated key factors to optimize the microstructure leading to enhanced coercivity. In addition, we also investigated the solidification behavior of the T1 phase after sintering by lowering the temperature from the sintering temperature to 600 °C. This work was supported by Materials Open Platform for Permanent Magnet at NIMS.