Rare-earth sintered permanent magnets based on neodymium (Nd₂Fe₁₄B) are widely used in traction motors of electric vehicles, wind-turbine generators, and other electrical systems requiring high magnetic-energy density. This parameter is directly governed by both the intrinsic crystal properties and the microstructural features of the polycrystal [1]. During technological heat treatment, residual type-II stresses develop in grain-boundary regions and triple-junction pockets (TPJ) as a result of mechanical interactions between the matrix grains and secondary phases, driven by differences in their physico-mechanical properties, thermal strains, and possible phase transitions with temperature change. Variations in interatomic spacing within the Nd₂Fe₁₄B lattice can significantly modify the magnetocrystalline anisotropy of a stress-free crystal, thereby directly affecting the magnetic properties of the material [2, 3]. In this study, finite-element modelling was employed to assess deformation levels under various scenarios of crystal–crystal interaction within the microstructure, ranging from planar contact between two anisotropic bodies to the interaction of inclusions of different shapes and properties embedded in an anisotropic Nd₂Fe₁₄B crystal [4]. At the current stage, we use the specialised computational package OOF2, designed for analysing 2D microstructures. Since the most typical configuration involves the junction of three grains, greater attention was given to a pocket geometry approximating a triangular shape (see figure 1). The calculations account for thermal strains arising during cooling after annealing at 500 °C. 

Extreme strain values are observed in triple-junction regions and, for the geometries studied and selected candidate materials (Cu, Nd), reach approximately ±0.01…0.024 (Cu) and ±0.04…0.011 (Nd), depending on pocket shape, inclusion type, and crystal orientation. The affected zone extends from roughly one-half to one-tenth of the characteristic pocket size. Larger strain magnitudes correspond to convex pocket geometries, stiffer inclusion materials, and higher thermal mismatch. The estimated impact of such strains on coercivity is on the order of 10%, underscoring the importance of accounting for mechanical effects in magnet design.

References

[1] Kronmüller H. et al.; Journal of Magnetism and Magnetic Materials, 1988, 74, 291.

[2] Murakami Y. et al.; Acta Materialia, 2015, 101, 101-106.

[3] Yi M. et al.; Physical Review, 2017, 8, 014011, 1-11.

[4] Sasaki T. et al.; Acta Materialia, 2016, 115, 269–277. 

Acknowledgement

This work has been funded by the European Union (EU) under Horizon Europe (101129888 GREENE). Views and opinions expressed are of the authors(s) and don't necessarily reflect those of the EU or the European Commission and HaDEA (both 'granting authority'). Neither the EU nor the granting authority can be held responsible for them.