Anisotropic Fractal Dimension of Nd-Fe-B Permanent Magnets Fracture Surface

Abstract

In this work, SEM image analysis and fractal dimension calculations are carried out on the fractures obtained under the same conditions for N50-type with high remanence, 30EH-type with high coercivity, and isotropic commercial Nd-Fe-B permanent magnets. It is further proved that the fractal dimensions of the fractures parallel and perpendicular to the c-axis for Nd-Fe-B permanent magnets are different. In other words, there is anisotropy in fractal dimension. In addition, it was discovered for the first time that the difference between the fractal dimensions D⊥ and D∥ of N50-type magnet with high remanence is large, and the difference between the fractal dimensions D⊥ and D∥ of the 30EH-type magnet with high coercivity is small, indicating that both remanence and coercivity are sensitive parameters with the microstructure. The difference in the fractal dimension of the fracture will provide new insights for studying the relationship between the magnetic properties and the microstructure of permanent magnetic materials. The anisotropic fractal dimension of the fracture will serve as a new performance parameter in the research of Nd-Fe-B permanent magnets.Keywords: Nd-Fe-B, Fractal dimension, Anisotropy, Performance parameterIntroductionThe magnetic properties of permanent magnets are closely related to the microstructure. However, researchers have seldom focused on the fractal characteristics of fractures in Nd-Fe-B permanent magnets. In fact, it is significant to study the fractal dimension of the fractured microstructure of permanent magnets with statistical self-similarity. Zhu et al. [1] reported the line-measuring dimension of fracture cracks of N50-type permanent magnets, and pointed out that the fractal dimension perpendicular to the c-axis and parallel to the c-axis has some anisotropic trends, but the difference in anisotropy is not obvious. In this work, N50-type, 30EH-type, and isotropic magnets are selected as the research objects. The anisotropic characteristics in fractal dimension of permanent magnets fractures parallel and perpendicular to the c-axis are explored.ExperimentalN50-type, 30EH-type, and isotropic commercial Nd-Fe-B permanent magnets were selected as the research specimens. A Zeiss field emission scanning electron microscope (FE-SEM) was used to observe the fracture morphology of all samples. The fractal dimensions of the fractures were calculated by the method of box counting dimension based on the image processing function of MATLAB.Results and DiscussionThe fractal dimensions of different types of magnet fractures parallel and perpendicular to the c-axis are summarized in Fig. 1. The difference ΔD between the fractal dimension D⊥ and D∥ of N50-type and 30EH-type magnets are 0.0856 and 0.0311, respectively. However, there is almost no difference in the fractal dimension of the isotropic magnet. In a word, the fractal dimension of the magnet oriented by the magnetic field has obvious anisotropy. The fractal dimension can be used as a research method to prove the anisotropy of magnets. The internal microstructure of magnet has a great influence on the magnetic parameters such as remanence, coercivity, and maximum energy product. Comparing the difference in fractal dimensions between N50-type and 30EH-type magnets, it can be found that N50-type magnet with higher remanence has larger anisotropic fractal dimensions, while 30EH-type magnet with higher coercivity has smaller anisotropic fractals dimension. The difference in ΔD of different magnets is inherently related to remanence and coercivity, which indirectly indicates that remanence and coercivity are sensitive parameters of microstructure.ConclusionsThe calculation on fractal dimensions of the fractures for the N50-type and 30EH-type commercial Nd-Fe-B permanent magnets along different crystalline axes demonstrates that the fractal dimensions of the fracture of the permanent magnet are anisotropic. So that the fractal dimension of the fracture can be used as a method to characterize the anisotropy of Nd-Fe-B magnet, which specifically characterizes whether the magnet has anisotropy, the magnitude of remanence and coercivity, and even the level of magnetic properties. **