This paper presents our recent microstructure characterization work of Nd-Fe-B sintered magnets with the emphasis of the structure and chemistry of Nd-rich phases at grain boundary triple junctions and thin Nd-rich phases formed along grain boundaries. The use of secondary electron imaging through the in-lens type detector combined with the TEM analysis lead to the unambiguous identification of Nd-rich phases at grain boundary triple junctions. Through microstructure characterization of commercial sintered magnet by the correlative characterization and atomic scale high angle annular dark field scanning TEM (HAADF-STEM)combined with energy dispersive spectroscopy (EDS), we have concluded the formation of non-ferromagnetic grain boundary phase along the grain boundaries parallel to the easy axis is one of the keys to increase the coercivity. The trace addition of Ga into Nd-rich Nd-Fe-B magnet demonstrated the substantial coercivity increase by the formation of non-ferromagnetic Nd-rich grain boundary phase.

　After getting detail structural information from Nd-Fe-B permanent magnets by multi-scale structural characterization, we employ finite element micromagnetic simulations to explain how the microstructure influences the magnetization reversals and coercivity. In this paper, the basis of the micromagnetic simulation and how the computing models are constructed are described. Then, the influence of the microstructure such as the grain size, the grain shape, the composition and the anisotropic nature of grain boundary phase on the coercivity of Nd-Fe-B permanent magnets are shown. The results showed that local demagnetization factor decreases as grain size decreases, which is attributed to a higher coercivity in fine-grained anisotropic Nd-Fe-B magnets. It was also found that the reduction of the magnetization of the grain boundary phase, particularly the grain boundaries located parallel to c-axis of Nd₂Fe₁₄B grains, leads to the coercivity enhancement of anisotropic Nd-Fe-B permanent magnets due to a stronger pinning force against magnetic domain wall motion. The coercivity of Nd-Fe-B magnets cannot be enhanced by the reduction of the grain size alone unless the grain are exchange decoupled.

Recently, several experimental studies for sintered Nd-Fe-B magnets have shown that their coercivity can be decisively affected by atomic structures around the grain boundaries in the magnets. In this article, a theoretical review is given on possible coercivity reduction mechanisms in sintered Nd-Fe-B or rare-earth based permanent magnets by focusing on the anomalous local magnetic anisotropy found for Nd ions on interfacial structures, based on first-principles calculations and an effective spin model.

　Fundamental understanding of microstructures of neodymium magnets is indispensable to improve their performance at high temperatures. Thus, it is of significant importance to clarify atomic structures and local magnetic properties of interphase interfaces in microstructures on the basis of electron theory. We studied interfaces between the main phase of neodymium magnets, Nd₂Fe₁₄B, and a subphase NdO_x using massively parallel first-principles electronic-structure calculations with the K computer. In addition to the known effect of Cu addition that is the wettability improvement of the metallic Nd subphase, we identified some of the added Cu atoms at the (001) interface improve the local magnetic anisotropy of Nd at the interface. Furthermore, we found that the Zn substitution, in addition to the Cu and Ga substitutions, for the (001)-surface Fe sites of main-phase grains can stably improve the magnetic anisotropy.

A thermodynamic assessment of the Nd-Fe-Cu system was attempted using the CALPHAD method, to clarify an effect of Cu addition to the permanent magnets based on Nd₂Fe₁₄B phase. The regular solution model was applied to liquid phase and solid solutions. Intermediate compounds were described as stoichiometric phases. The formation enthalpy of δ(Nd₆Fe₁₃Cu) phase was evaluated using the first-principles calculation. The result was introduced to the optimization process with some experimental phase boundary data. In the calculated liquidus projection of the ternary system, it is characteristic that the two-phase separation of the liquid phase exists between Fe-rich and (Nd, Cu)-rich regions. The ternary eutectic reaction E₁: (L)⇔βNdCu+(αNd)+δ occurs in the Nd-rich region and the reaction temperature is estimated about 508.6°C.

The non-equilibrium phase-field method which has recently been proposed by Steinbach et al. was slightly modified, and the improved method was applied to the formation process of grain boundary phase (GBP) in the Nd₂Fe₁₄B polycrystalline microstructure of Fe-Nd-B hard magnet. In particular, we focused on the temporal evolution of morphological changes of GBP in this study, and the results obtained are as follows: (1) The Nd₂Fe₁₄B grains are partially covered with GBP at early stage of aging, however the coverage decreases with aging by Ostwald ripening among GBPs. (2) The coverage area by GBP increases with increasing average composition of Nd in alloy. (3) The interfacial energy density between GBP and Nd₂Fe₁₄B phase greatly affects the morphological change of GBP.