Segregation of Al and its effect on coercivity in Nd-Fe-B

Nd-Fe-B permanent magnets have been widely applied since the invention such as in consumer electronics, electric/hybrid vehicles, and robotics.^1–6 However, the coercivity of Nd-Fe-B magnets decreases with temperature. One approach to improve coercivity is to increase the magnetocrystalline anisotropy of Nd₂Fe₁₄B (2:14:1) phase through a partial replacement of Nd by Dy or Tb.^7–10 Another approach is to tailor the microstructure through grain size refinement and/or grain boundary phase (GBP) engineering.^11–15 Since Dy and Tb have become critical, more research attentions are now being paid to engineer microstructure to enhance coercivity in Nd-Fe-B magnet.

Typically, Nd-Fe-B sintered magnets are prepared by liquid phase sintering (1030–1080 °C) and quenching, followed by a post-sinter annealing (500–600 °C). The 2:14:1 phase in as-sintered Nd-Fe-B magnet should have fine grain sizes (3–5 μm). The post-sinter annealing promotes homogenous distribution of the low melting point Nd-rich phase at the grain boundaries (GB) of the 2:14:1 phase. The fine grain size of the 2:14:1 and Nd-rich GBPs are responsible for high coercivity in Nd-Fe-B magnet.^11,12 The typical GPB has a thickness of several nanometers and a composition of Nd_1-xFe_x with x = 0.2–0.7.^16,17 Nd_1-xFe_x shows soft ferromagnetic properties when x > 0.3, with up to 10 kG magnetization at x = 0.6.¹⁷ The soft ferromagnetic Nd–Fe GBP results in inter-grain exchange coupling and reduces coercivity in Nd-Fe-B magnet. A small amount of alloying element such as Al, Ga and Cu is often added to enhance the coercivity in Nd-Fe-B magnet.^15,18–20 These alloying elements usually segregate at GB, mix with Nd–Fe phase, and form the Nd-Fe-M type GBPs (M = Al, Cu and Ga). The Nd-Fe-M may crystallize into Nd₆Fe₁₃Si-type tetragonal structure (6:13:1) during post-sinter annealing.^21–24 The low melting point of the 6:13:1 phase enables post-sinter annealing to be performed at low temperatures, hence offers better wettability with the 2:14:1 grains and promotes a homogenous distribution of GBP. The tetragonal phase of Nd₆Fe_13-xM_1+x (M = Al, Ga, Cu, etc.) has a layer-like structure and displays antiferromagnetic (AFM) properties.²⁵ The magnetic behavior of Nd₆Fe₁₃M may be directly related to the enhancement of coercivity in Nd-Fe-B magnet. In addition to segregating at the GB, Al, Ga and Cu may also react with the 2:14:1 matrix phase and modify the intrinsic magnetic properties.^26–28 The partitioning behavior of the alloying elements is expected to change the hard magnetic properties of the 2:14:1 and the GBP, thus affect the coercivity of the magnet.

In this work, to understand the role of these alloying elements, we have theoretically investigated the segregation of Al (as an example) and its effect on the coercivity in Nd-Fe-B sintered magnet. The substitution of Fe by Al in Nd₂(Fe, Al)₁₄B and Nd₆Fe_13-xAl_1+x, and the effect on magnetic properties were studied from first principles DFT (density functional theory) calculation. We also performed micromagnetic simulations (MS) to investigate how coercivity correlates with the 6:13:1 at GB and the Al-rich Nd₂(Fe, Al)₁₄B thin shell on the 2:14:1 grain surface. Combining the DFT and MS results, we discuss the role of Al in enhancing coercivity in Nd-Fe-B magnets.

The first principle DFT calculations were performed using a Linear-Combination of Pseudo-Atomic Orbital (LCPAO) method implemented in OpenMX code.^29,30 The generalized gradient approximation (GGA) of Perdew–Burke–Ernzerhof (PBE) functional³¹ was employed to treat the exchange correlation. The 4f electrons of Nd are treated as open-core state. The open core pseudopotential is generated by assuming that the 4f-states are part of the core states. The basis sets are s3p2d1f1, s3p2d1, s2p2d1, s2p2d1 for Nd, Fe, B and Al with cutoff radius of 8.0, 6.0, 7.0 and 7.0 atomic unit (a.u.), respectively. All the structures were fully relaxed with the convergence of the total energy and force better than 10⁻⁷ Hartree and 10⁻⁴ Hartree/Bohr, respectively. The number of k points for Brillouin zone integration are 7 × 7 × 5 and 5 × 5 × 3 for Nd₂(Fe,Al)₁₄B and Nd₆(Fe,Al)₁₃Al, respectively.

The micromagnetic simulation is based on Landau–Lifshitz–Gilbert equation (LLG) and has been an effective approach to simulate magnetic properties in ferromagnetic materials.^32–34 This approach has been applied to investigate the rare earth magnets, e.g., Nd-Fe-B.^35–38 Our micromagnetic simulation are performed using a finite difference (FD) micromagnetic code MuMax^3,39,40 Here, the finite-difference cell size is 1 × 1 × 1 nm³ for all the calculations. For the calculation of the magnetic hysteresis loop, we adopted a field step of 2 mT. The total energy minimization was performed using a conjugate gradient method with a converge criterion of normalized magnetization change less than 10⁻⁶. The material parameters for micromagnetic simulation are listed in Table I.^{6,17,24,26,41}

Figure 1 shows the Al occupation probability P_i at the different Fe sites as a function of temperature. Al prefers to enter the site of 4c at ground state. With increasing temperature, 4c site occupation decreases as more Al atoms occupy other sites, especially the 8j₂ site. At high temperature (e.g., 1400 K), the P_i values are almost same (33%) for the 4c and 8j₂ sites. There are also some Al atoms distributed at the 16k₂ site (20%). At high temperature, the thermal energy (∼kT) promotes the random distribution of Al at the different Fe sites. Since the Nd-Fe-B alloy are often prepared using high temperature processes, such as induction melting (∼1573 K), it is expected that Al atoms distribute at the 4c, 8j₂ and 16k₂ sites, in real magnets. This prediction is in good agreement with neutron diffraction experiments.²⁶ The preferential occupation of Al is also responsible for the anisotropic change of unit cell size with increasing Al content in 2:14:1.

With the Al segregation at GB and its small solubility in the 2:14:1 phase, it can form the Al-rich 2:14:1 shell on the Nd₂Fe₁₄B grain surface. The Al-rich 2:14:1 shell may modify the magnetization reversal in Nd-Fe-B magnet during the demagnetization process. To understand the effect of doping Al on the magnetization of 2:14:1, the atom resolved magnetic moments of Nd₂Fe_14-xAl_xB are calculated and listed in Table III. Since the 4f electron are treated with a core-hole method, the magnetic moment contributed by the 4f electrons in Nd is taken as its theoretical value based on Hund’s rule, while the other contributions (6s, 5d electrons) are directly computed from DFT calculations. The calculated total magnetic moment of Nd is −2.58 μ_B and −2.51 μ_B at the 4f and 4g sites, respectively, slightly larger than the experimental values of −2.30 μ_B and −2.25 μ_B,⁶ respectively (Table III). As expected, the replacement of Fe by non-magnetic Al will reduce the magnetization of 2:14:1 phase. The calculated average atomic magnetic moment at the 4c site reduces from 2.47 μ_B/atom (at x = 0) to 1.79 μ_B/atom (at x = 0.25) upon Al doping in Nd₂Fe_14-xAl_xB. The doped Al atom shows a small induced negative moment of −0.25 μ_B/atom. The doped Al also slightly reduces the magnetic moment at the other sites, which is ascribed to the electronic hybridization between the neighboring Fe and Al atoms. A similar trend is also observed for the Al at the 8j₂ site (Table III). In addition to the reduction of magnetization, it was reported that doping Al can slightly enhance the magnetocrystalline anisotropy (MCA) of 2:14:1 phases.⁶ The reduced magnetization and enhanced MCA increase the energy barrier for the nucleation of magnetic domain during magnetization reversal, which will be discussed later in the Sec. III C.

As discussed above, the Al atoms segregated at the GB may enter the 2:14:1 lattice and/or mix with Nd–Fe to form Nd-Fe-Al GBP with a 6:13:1 type tetragonal structure. To undertand the effect of Al on the formation of 6:13:1 and its correlation with coercivity, the formation energy and magnetic properties of Nd₆Fe_13-xAl_1+x at GB have been calculated.

E₆₁₃₁, E_Nd, E_Fe and E_Al are the total enegy of Nd₆Fe_13-xAl_1+x, hexagonal Nd, bulk Fe and Al, respectively.

As shown in Table IV, the formation energy is negative and the absolute value increases slightly from 0.14 to 0.19 eV/atom with increasing x, implying that the excess Al can further stablize the 6:13:1 phase. The partial replacement of Fe by Al almost linearly reduces the average atomic magnetic moments at the Fe 16l₂ site with increasing x (Table IV). Further, the average atomic moment at the other Fe sites sightly decreases too. This is related to the electron hybrid between Al and its neigbhoring Fe atoms. The formation of the antiferromagnetic 6:13:1 phase depletes the Fe at GB and reduces the amount of the ferromagnetic Nd–Fe GBP phase in Nd-Fe-B magnet, which may enhance coercivity.

The magnetization reversal process includes the nucleation of the reversal magnetic domain and the propagation of the domain wall (DW) in the magnet. In Nd-Fe-B sintered magnet, the nucleation of reversal magnetic domain prefers to occur on the grain surface with weak MCA and/or large demagnetization field. The GBP inhibits the propagation of DW across GB. Higher nucleation field and larger DW pinning field at the GB results in higher coercivity in the Nd-Fe-B magnet. As discussed above, the segregation of Al at GB often induces the formation of the 6:13:1 Nd-Fe-Al GBP and the Al-rich 2:14:1 shell on the surface of 2:14:1 grain. We investigate the effect of the 6:13:1 phase at the GB and the 2:14:1 Al-rich shell on the nucleation- and pinning-field in Nd-Fe-B magnet using micromagnetic simulations.

Figure 3(a) shows an ideal two-grain microstructure model of Nd-Fe-B magnet. The two grains of 2:14:1 are separated by a thin layer (4 nm) of Nd-Fe-Al GBP. Also there exists a thin layer of Al-rich 2:14:1 (2 nm) between the 2:14:1 grain and the Nd-Fe-Al GBP. A domain wall is created in one 2:14:1 grain (Grain-1). The micromagnetic simulation indicates that the critical pinning field is about 35 kOe [Fig. 3(b)]. For the microstructure without the Al-rich 2:14:1 layer and Nd-Fe-Al type GBP, but with an Nd–Fe type GBP, the pinning field sharply reduced to 22 kOe. Further, for the sample with an Nd-Fe-Al GBP but without Al-rich 2:14:1 layer, the calculated pinning field is about 31 kOe. The results indicate that the formation of 6:13:1 GBP can substantially enhance the pinning field while the Al-rich 2:14:1 thin layer can further increase the barrier energy of DW depinning in Nd-Fe-B magnet. The reason is that the soft ferromagnetic Nd–Fe GBP increase exchange coupling between neighboring 2:14:1 grains and facilitate the DW propagation from one grain to the neighboring ones. The 6:13:1-like GBP has much lower magnetization, which weakens the inter-grain exchange interaction and increases the energy barrier for DW across the GB. The reduced magnetization of Al-rich 2:14:1 layer displays similar but moderate contribution to the enhancement of the pinning field of DW.

To evaluate the effect of Al segregation on the nucleation field, we construct a microstructure model with a cube shaped 2:14:1 grain (edge length of 120 nm) covered with a thin layer of Al-rich 2:14:1 (2 nm) and then a layer of Nd-Fe-Al GBP (4 nm). The calculated nucleation field is 55 kOe from micromagnetic simulations. However, the 2:14:1 cube covered with only an Nd–Fe GBP (4 nm) has a nucleation field of about 25 kOe. Since the soft magnetic Nd–Fe GBPs have relative high magnetization (Table I), the low MCA and strong local demagnetization field make them as the preferred nucleation sites during magnetization reversal. On the other hand, the 6:13:1 phase has much lower magnetization (Table I), i.e., smaller demagnetization energy, and little contribution to the reduction of the nucleation field of 2:14:1 grain. Further, the calculated nucleation field is 50 kOe for the 2:14:1 cube with Nd-Fe-Al GBP, but without Al-rich 2:14:1 layer. Compared to Nd-Fe-Al GBPs, the slightly reduced magnetization of Al-rich 2:14:1 layer has similar but weaker effect on nucleation field. The enhancement of nucleation field is mainly contributed by formation of 6:13:1 GBP. The results reveal that the formation of the Al-rich 2:14:1 layer and the Nd-Fe-Al type GBP can substantially enhance the nucleation field. It should be noted that we assumed no other defects in the 2:14:1 cube in the MS calculations. If there are weak MCA local region, the nucleation field may substantially decrease.

The weakest points for magnetization reversal, i.e., the grain boundary regions, determine the coercivity. Whichever is smaller, the pinning- or the nucleation-fields, dictates the coercivity value in the magnet. For the typical ternary Nd-Fe-B magnet, the calculated pinning field (22 kOe) and nucleation (25 kOe), are comparable to the experimental observed values (12-20 kOe).¹¹ The coercivity is mainly controlled by the pinning behavior. If the Nd–Fe type GBP is replaced with Nd-Fe-Al phase, the predicted coercivity is up to 30-35 kOe and much larger than the experimental values. One reason for this difference is that the GBP is generally a mixture of Nd–Fe type GBP and 6:13:1-like phase. Further, the 2:14:1 grains are not completely isolated by the GBP in real magnet. All these microstructure defects reduce the experimentally achieved coercivity. Similar chemical elements such as Cu, Ga, Sn, etc. can also alloy with Nd–Fe to form 6:13:1 type antiferromagnetic or weak ferromagnetic phase.^21–23 Development of novel fabrication method to engineer the segregation of doping elements such as Al, Cu, Ga etc. and the formation of 6:13:1 phase can be a promising approach for improving coercivity in Nd-Fe-B magnet.

Aluminum tends to segregate at grain boundary and promote the formation of antiferromagnetic or weak ferromagnetic Nd-Fe-Al (6:13:1-like structure) phase as indicated by DFT calculations. The formation of Nd-Fe-Al phase depletes Fe and reduces the amount of ferromagnetic Nd–Fe type GBP, which enhances magnetic-isolation of 2:14:1 grains. The 6:13:1-like GBP increases the pinning field of DW at GB from 22 kOe to 31 kOe. In addition, DFT calculations indicate that Al has a small solubility in 2:14:1 and prefers to occupy the 4c and 8j₂ sites, which may result in the formation of Al-rich 2:14:1 shell on grain surface since the segregation of Al at GB. The thin layer of Al-rich 2:14:1 (2 nm) can further enhance the pinning field of DW from 31 kOe to 35 kOe. The nucleation field is 25 kOe, 50 kOe and 55 kOe, when the 2:14:1 grain is surrounded completely with Nd–Fe type GBP (4 nm), Nd-Fe-Al GBP (4 nm), and Nd-Fe-Al GBP (4 nm) plus an Al-rich 2:14:1 shell (2 nm), respectively. The segregation of Al at GB result in the formation of antiferromagnetic (or weak ferrimagnetic) 6:13:1-like GBP and potential Al-rich 2:14:1 layer on the matrix 2:14:1 grain surface, which is responsible for the coercivity enhancement in Nd-Fe-B magnet. Engineering the Al (and/or similar element Cu, Ga, etc.) segregation and the formation of 6:13:1-like phase at GB are potential approaches to enhance the coercivity in Nd-Fe-B magnet.

This work was supported by the Critical Materials Innovation Hub funded by the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, Advanced Materials and Manufacturing Technologies Office (AMMTO). The work was performed in Ames National Laboratory, operated for the U.S. Department of Energy by Iowa State University of Science and Technology under Contract No. DE-AC02-07CH11358.

The authors have no conflicts to disclose.

X. B. Liu: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – original draft (equal). I. C. Nlebedim: Conceptualization (equal); Funding acquisition (equal); Methodology (equal); Project administration (equal); Supervision (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request and CMI approval.