Grain boundary diffusion mechanism in Dy-diffused Nd-Fe-B sintered magnets

Grain boundary diffusion (GBD) is an effective method to enhance the thermal stability of Nd-Fe-B based permanent magnets. When developing a high-performance magnet, it is essential to carry out a study on its mechanisms, in order to reveal the distribution regulation of diffusion solutes and microstructural evolution. In the present work, the phase-field method is applied to investigate the thermodynamic features and the heavy rare-earth Dy migration in a Dy-diffused Nd-Fe-B magnet during the GBD process. In the simulation process, the grain phase transformation and volume diffusion were taken into consideration and the effects of the diffusion mode, initial diffusion source concentration, grain size, and grain boundary (GB) width were explored in a set of magnet models with various grain sizes. An optimized fitting function was introduced to evaluate the solute distribution in grain boundaries and the effective diffusion coefficient. It is shown that the diffusion mode and the GB width have significant impacts on the effective diffusion coefficient. The results provide a theoretical scheme concerning the quantitative evaluation of GBD efficiency based on thermodynamic analysis.