Introduction

Since the Nd15Fe77B7 alloy with high energy product (287 kJ/m3), remanent magnetization (1.23 T) and coercivity (0.96 T) was discovered by Sagawa et al.,[1] sintered Nd-Fe-B permanent magnets have been used widely in many industrial fields, such as voice coil motors for hard disk drives and motors for hybrid/electric vehicles.[2-8] Subsequently, Nd13Fe81B6 alloy with high energy products (403 kJ/m3) prepared by sintering process was reported.[9] However, the relatively low intrinsic coercivity (μ0Hc = 1.2 T) and low operating temperature (585 K) of Nd-Fe-B permanent magnets are still practical obstacles in the application of wind power generators and traction motors.[10] The most effective solution of the improvement of the coercivity is the addition of expensive heavy rare earth elements (e.g. Dy, Tb) to Nd-Fe-B magnets.[11-13] For example, Nd13Dy2B6Febal alloy was studied to be higher coercivity (1.823 T) after sintered at 1243 K for 20 h,[14] while the coercivities of Nd12−x Dy3Tb x Fe78B7 alloys increase from 1.7 to 2.0 T with increasing Tb content.[15]

On the other hand, different heat-treatment processes (e.g. sintering, post-sintering and annealing) have a significant influence on the coercivity of Nd-Fe-B permanent magnets.[16,17] The coercivity of Nd-Fe-B magnet increases from 1.464 to 1.671 T by post-sintering annealing.[18] The coercivity of Nd11.7Pr2.8Fe76.9B6.0Al0.5Cu0.1O2.1 alloy was measured to be 1.118 T after post-sintering annealed at 873 K for 1 h.[19] The coercivity of (Nd, Pr)29.5Dy2.0B1.0Al0.2Co0.8Cu0.1Febal alloy increases from 1.170 to 1.450 T after two annealing processes (1138 K for 2 h/793 K for 4 h).[20]

To better understand the effect of sintered/heat treatment process on magnetic properties of Nd-Fe-B permanent magnets, the information of phase equilibria and crystal structures of intermetallic compounds in the Nd-Fe-B ternary system are indispensable. Therefore, the purpose of the present work was to study phase equilibria of Nd-Fe-B ternary system at 873 and 1073 K using key alloy samples and x-ray diffraction (XRD) and scanning electron microscopy (SEM) with energy dispersive spectrometry (EDS).

Literature Information

The Fe-Nd Binary System

The Fe-Nd phase diagram was reviewed by Massalski[21] and assessed thermodynamically by Zhang et al.[22] In the Fe-Nd binary system, there are α-Fe, γ-Fe, δ-Fe, α-Nd and β-Nd as stable solid solution phases, Nd2Fe17 with Th2Zn17 structure[23] as an intermetallic compound. The Nd-Fe phase diagram was later revised,[24,25] because a new intermetallic compound Nd5Fe17 with P63/mcm space group was found to be stable.[26,27] In addition, the intermetallic compound NdFe2 reported by Chaban et al.[5] was not confirmed to be stable.[24-27] Recently, the thermodynamic assessment of the Nd-Fe binary system was performed by Ende et al.,[28] which agrees well with the experimental results.[24]

The Fe-B Binary System

The Fe-B binary system was studied by Portnoi et al.[29] and then was calculated by Ende et al.[28] According to the experimental information,[29] α-Fe, γ-Fe, δ-Fe, β-B and two intermetallic compounds, FeB and Fe2B with a narrow homogeneity range (about 1 at.%), as stable compounds exist in Fe-B binary system.

The Nd-B Binary System

The Nd-B binary phase diagram was reported by Liao et al.[30] and was thermodynamically assessed by Ende et al.[28] There are several stable phase: α-Nd, β-Nd, Nd2B5, NdB4, NdB6, NdB66 and β-B. The binary intermetallic compounds Nd2B5 (Sm2B5-type) and NdB4 (ThB4-type) were found by x-ray diffraction examination of single crystals.[31,32] Storms et al.[33] reported the composition ranges of NdB6 (CaB6-type) are 3.41 at.% B at 1600 K and 4.92 at.% B at 2000 K.

The crystal structure information of the stable phases of the binary systems is given in Table 1.

Table 1 Crystallographic data of the stable phases in Nd-Fe-B ternary system
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The Nd-Fe-B Ternary System

The Nd-Fe-B ternary system has been studied extensively, including isothermal sections at different temperatures, vertical sections at different composition conditions and the liquidus projection,[34-39] and then was reviewed by Raghavan[40] and Malfielt et al.,[41] respectively.

As for the isothermal sections of the Nd-Fe-B ternary system, Chaban et al.[5] determined first the phase equilibria at 873 K in the Fe-rich part and at 673 K in Nd-rich part by means of x-ray diffraction and microscopic analysis. Subsequently, partial isothermal sections at 1173 K (Fe-rich), 973 K (Nd-rich),[34,35] 1273 K[36] and at 298 K (room temperature)[37,38] were reported. The solid-liquid equilibria of this ternary system at 1273 K were investigated experimentally by Schneider et al.[36] It is indicated that the two-phase equilibrium, Fe2B + Nd2Fe14B (τ1) is stable at 1273 K. On the other hand, several vertical sections of Nd-Fe-B system were also investigated experimentally.[36,39-43] The four vertical sections (73.3 at.% Fe, 80 at.% Fe, 4 at.% B and at Fe-Nd2Fe14B) were studied by Schneider et al.[36] The experimental results[36] show that the ternary compound Nd2Fe14B (τ1) was considered to be incongruent melting, which is at variance with the congruent formation through the investigation of two vertical sections (6 at.% B and Nd2Fe17-Nd8Fe27B24) reported by Che et al.[39] Three vertical sections of 4 at.% B, 30 at.% Nd and along Fe77B23-Fe27Nd73 were studied experimentally by Knoch et al.[42] Landgraf et al.[43] measured the vertical sections of 60 at.% Nd up to 20 at.% B. Rogl et al.[41] pointed out that the experimental results[43] at high temperature are not reasonable, because the temperature of the last thermal effect close to Nd-Fe binary system is at 1223 K, which is much less than the corresponding binary liquidus temperature (1427 K).

The liquidus projection of the Nd-Fe-B ternary system was investigated experimentally.[41-43] Knoch et al.[42] confirmed the eutectic reaction, L ↔ Nd2Fe14B (τ1) + NdFe4B4 (τ2) + α-Nd, through differential thermal analysis. The liquidus projection was updated by Knoch et al.,[42] because the region of primary crystallization of Nd2Fe14B (τ1) is narrower than the previous results reported by Mastsuura et al.[44]

According to the experimental information mentioned above, three ternary intermetallic compounds, Nd2Fe14B (τ1), NdFe4B4 (τ2) and Nd5Fe2B6 (τ3) are stable in the Nd-Fe-B ternary system. Nd2Fe14B (τ1) was denoted as the Nd3Fe16B by Chaban et al.[5] Herbst et al.[45] determined its crystal structure with space group (P42/mnm) and lattice parameters (a = 0.8804 nm, c = 1.2205 nm) by means of the neutron diffraction. NdFe4B4 (τ2) is a nonmagnetic phase found in Nd-Fe-B magnets. Givord et al.[46] studied that its crystal structure is Ndl.11Fe4B4 structure type with space group (Pccn) and lattice parameters (a = 0.7117 nm, c = 3.5070 nm) through the structure refinement. Nd5Fe2B6 (τ3) with space group (R \( \overline{3} \) m) and lattice parameters (a = 0.5460 nm, c = 2.4272 nm) was reported by Buschow et al. [47] through the structure refinement with x-ray data.

Thermodynamic assessment of the Nd-Fe-B ternary system was first performed by Hallenmans et al.,[48] and then was revised by Ende et al.[28] using the quasi-chemical model to describe liquid phase. The invariant reactions in the Nd-Fe-B ternary system were given by Raghavan[49] based on the experimental and calculated results,[28] and a schematic liquidus projection with phases of primary crystallization marked close to the B-rich part was presented.

Experimental Procedure

Bulk Nd (99.99% purity), Fe (99.99% purity), B (99.99% purity) and powder Fe (99.99% purity), B (99.999% purity) were used as raw materials. Nd-Fe-B ingots (<60 at.% B) were melted using bulk materials in the arc furnace with a non-consumable tungsten electrode under an inert argon atmosphere. On the other hand, Nd-Fe-B alloys (>60 at.% B) were prepared using powder Fe and B with bulk Nd. The mixed powders of 50 at.% Fe and 50 at.% B were first compressed under the pressure of 8 MPa, and then melted in a high frequency induction melting furnace under high-purity argon. Bulk Nd and Fe50B50 alloy annealed at 1223 K for 120 h in the evacuated quartz tube were melted in the arc furnace. It should be pointed out that the each Nd-Fe-B alloy sample (about 3 g) prepared by the two methods mentioned above was re-melted at least four times in order to ensure compositional homogeneity. The mass loss of the ingot was generally less than 1%.

Alloy samples were sealed into evacuated quartz and annealed (873 K for 1440 h, 1073 K for 960 h) and quenched in ice water. After that, powder samples were analyzed using x-ray diffraction techniques (PLXcel 3D, Co Kα radiation) in the range from 20° to 90°, 2θ with 0.2626 step sizes at 45 kV and 40 mA. The microstructures of alloy samples were examined by scanning electron microscopy (SEM) with energy dispersive spectrometry (EDS). The crystal structures of the phases in the alloys were characterized using Jade 6.5, X’Pert Highscore plus and Fullprof software.

Results and Discussions

The representative XRD patterns and backscattered electron (BSE) images of Nd-Fe-B alloys (Nd15Fe82.5B2.5, Nd5Fe65B30, Nd15Fe35B50 and Nd10Fe20B70) annealed at 873 K for 1440 h and alloys (Nd7.5Fe90B2.5, Nd25Fe72.5B2.5 and Nd25Fe60B15) annealed at 1073 K for 960 h were analyzed and shown, respectively. It should be pointed out that the compositions of Nd and Fe in Nd-Fe-B alloys were shown in Tables 2 and 3, while those of B in Nd-Fe-B alloys were not given. The reason for it is that B as the light element could not be accurately measured quantitatively by EDS. The identified phases in Nd-Fe-B alloys by EDS are only based on the composition measured of Nd and Fe without consideration B content. In addition, the solubility of B in binary/ternary intermetallic compounds and solid solution phases could not be measured quantitatively in this work.

Table 2 Experimental results of the Nd-Fe-B alloys annealed at 873 K for 1440 h
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Table 3 Experimental results of the Nd-Fe-B alloys annealed at 1073 K for 960 h
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Phase Equilibria at 873 K

Figure 1(a) is the XRD pattern of Nd7.5Fe90B2.5 alloy annealed at 873 K for 1440 h. As can be seen, the characteristic peaks of Nd2Fe14B (τ1), Nd2Fe17 and Nd5Fe17 phases are marked well. The ternary intermetallic compound, Nd2Fe14B (τ1), was determined to be Nd2Fe14B structure with space group P42/mnm. Three-phase microstructure of this alloy is also observed in the back scattered electrons (BSE) image of the alloy in Fig. 1(b). Based on the EDS measurements, the compositions of the dark grey phase and the light grey phase are 11.23at.%Nd-88.77at.%Fe (Nd:Fe = 2:15.8) and 20.13at.%Nd-79.87at.%Fe (Nd:Fe = 5:19.8), respectively, which are corresponding to Nd2Fe17 and Nd5Fe17. The white matrix phase with 13.24at.%Nd-86.76at.%Fe is approximately close to theoretical ratio (Nd:Fe = 2:14) and is identified as Nd2Fe14B (τ1). Therefore, the XRD results in Nd7.5Fe90B2.5 alloy are in good agreement with the SEM/EDS examination.

Fig. 1
figure 1

XRD pattern and backscattered electron image of Nd15Fe82.5B2.5 alloy annealed at 873 K for 1440 h

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As shown in Fig. 2(a), Nd5Fe67B33 alloy is composed of three phases, NdFe4B4 (τ2), Fe2B and α-Fe, based on distinguished characteristic peaks of the XRD pattern. The ternary intermetallic compound, NdFe4B4 (τ2), was determined to be RE1.11Fe4B4 structure with space group Pccn. Figure 2(b) shows the three-phase microstructure of this alloy. From EDS results, the composition of the dark phase is 99.07at.%Fe-0.93at.%Nd, which is corresponding to α-Fe, and that of the grey matrix phase is 22.72at.%Nd-77.28at.%Fe, which is approximately close to theoretical ratio (Nd:Fe = 1:4) of NdFe4B4 (τ2). The white phase in Fig. 2(b) is identified to be Fe2B from the XRD analysis.

Fig. 2
figure 2

XRD pattern and backscattered electrons (BSE) image of Nd5Fe67B33 alloy annealed at 873 K for 1440 h

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Figure 3(a) is the XRD pattern of Nd15Fe35B50 alloy annealed at 873 K for 1440 h. It can be seen that the three phases, NdFe4B4 (τ2), Nd5Fe2B6 (τ3) and NdB4, are identified based on distinguished characteristic peaks of the XRD pattern. The ternary intermetallic compound, Nd5Fe2B6 (τ3), was determined to be Pr5Co2B6 structure with space group R \( \overline{3} \) m. Three-phase microstructure of the alloy is also observed in Fig. 3(b). According to the measured compositions by EDS, the composition of the grey matrix phase with 22.14at.%Nd-77. 86at.%Fe and the white phase as stripes with 69.78at.%Nd-30.22at.%Fe is approximately corresponding to theoretical ratios (Nd:Fe = 1:4 and Nd:Fe = 5:2) of NdFe4B4 (τ2) and Nd5Fe2B6(τ3), respectively. The dark grey phase in Fig. 3(b) is considered to be NdB4 on the basis of XRD analysis.

Fig. 3
figure 3

XRD pattern and backscattered electrons (BSE) image of Nd15Fe35B50 alloy annealed at 873 K for 1440 h

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Figure 4(a) is the XRD pattern of Nd10Fe20B70 alloy. The characteristic peaks of the three phases (NdB4, NdB6 and FeB) are well distinguished. Figure 4(b) is the BSE micrograph of the alloy, which shows three-phase microstructure. Due to the difficulty of quantitative measurements of content B in Nd-Fe-B alloys by EDS, it could still identify binary Nd-B compounds and binary Fe-B compounds only from the compositions of Nd and Fe in the different phases. In Fig. 4(b), the content of Fe in the dark grey phase is higher, while that of Nd in other color phases are much higher by EDS measurement. Combined with the XRD analysis in Fig. 4(a), the dark grey phase is identified to be FeB. On the other hand, although the grey phase and the light grey phase in Fig. 4(b) are impossible to be identified only by EDS results, the volume fraction of the grey phase is clearly much more compared with that of the light grey phase. Moreover, the nominal composition of Nd10Fe20B70 alloy is closed to NdB4. Therefore, the grey phase could be identified to be NdB4, while the light grey phase would be NdB6 according to the XRD analysis.

Fig. 4
figure 4

XRD pattern and backscattered electrons (BSE) image of Nd10Fe20B70 alloy annealed at 873 K for 1440 h

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In this work, thirty-three Nd-Fe-B alloys annealed at 873 K for 1440 h were investigated and analyzed using the same method of the identified phases in four typical Nd-Fe-B alloys mentioned above. According to the experimental results as given in Table 2, the phase equilibria of the Nd-Fe-B ternary system at 873 K were constructed as shown in Fig. 5. It consists of 14 single-phase regions, 28 two-phase regions and 16 three-phase regions. It should be noticed that the three-phase equilibrium, NdB66 + FeB + β-B, was not found directly in the present experiments, but was concluded reasonably on the basis of the phase rule and the three-phase region, NdB6 + FeB + NdB66, which was determined from the XRD and SEM/EDS analysis of Nd2.5Fe32.5B65 and Nd2.5Fe27.5B70 alloys. On the other hand, compared with the isothermal section of the ternary system at 873 K reported by Chaban et al.,[5] it is obvious difference that Nd5Fe17 with space group P63/mcm was observed to be stable at 873 K in the present work, which is in agreement with the calculated results.[28] Meanwhile, NdFe2 as a stable intermetallic compound reported by Chaban et al.[5] at 873 K was not found in the present experimental results and the calculated results.[28] In addition, ternary intermetallic compounds, Nd3Fe16B and Nd2FeB3 denoted by Chaban et al.[5] were confirmed as Nd2Fe14B (τ1) and Nd5Fe2B6(τ3) in the present work, respectively, according to the experimental results.[36,45-47]

Fig. 5
figure 5

Phase equilibria of the Nd-Fe-B ternary system at 873 K determined in this work. The three-phase equilibrium, NdB66 + FeB + β-B, was not found directly in the present experiments, but was concluded reasonably on the basis of the phase rule and the three-phase region, NdB6 + FeB + NdB66, which was determined from the XRD and SEM/EDS results of Nd2.5Fe32.5B65 and Nd2.5Fe27.5B70 alloys

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Phase Equilibria at 1073 K

Figure 6(a) indicates clearly the existence of three phases (α-Fe, Nd2Fe17 and Nd2Fe14B) in Nd7.5Fe90B2.5 alloy annealed at 1073 K for 960 h from the XRD pattern. The corresponding three-phase microstructure of this alloy is also shown in Fig. 6(b). According to EDS measurements, the compositions of the dark phase and dark grey phase are 98.84at.%Fe-1.16at.%Nd and 89.47at.%Fe-10.53at.%Nd, respectively, which are α-Fe and Nd2Fe17 without any solubility of B, and that of the white matrix phase with 13.27at.%Nd-86.73at.%Fe is approximately close to the theoretical ratio (Nd:Fe = 2:14) of Nd2Fe14B (τ1). The white matrix phase is thus identified to be Nd2Fe14B (τ1).

Fig. 6
figure 6

XRD pattern and backscattered electrons (BSE) image of Nd7.5Fe90B2.5 alloy annealed at1073 K for 960 h

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Figure 7(a) is the XRD pattern of Nd25Fe72.5B2.5 alloy annealed at 1073 K for 960 h. It can be seen that the three phases, Nd2Fe17, α-Nd and Nd2Fe14B are identified based on distinguished characteristic peaks. The three-phase microstructure is identified from SEM results in Fig. 7(b). Based on EDS results, the compositions of the dark grey phase and the white phase are 11.43at.%Nd-88.57at.%Fe and 98.51at.%Nd-1.49at.%Fe, which are closed to Nd2Fe17 and α-Nd without any solubility of B, respectively. The composition (14.21at.%Fe-85.79at.%Nd) of the light grey phase is considered to be Nd2Fe14B (τ1) according to the same analysis of identified phases in Nd7.5Fe90B2.5 alloy.

Fig. 7
figure 7

XRD pattern and backscattered electrons (BSE) image of Nd25Fe72.5B2.5 alloy annealed at 1073 K for 960 h

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Nd25Fe60B15 alloy consists of three phases, Nd2Fe14B (τ1), NdFe4B4 (τ2) and α-Nd by the XRD pattern analysis as shown in Fig. 8(a), while the BSE micrograph of the microstructure (three-phase) was also given in Fig. 8(b). According to the measured compositions by EDS, the compositions of the dark grey phase with 14.11at.%Nd-85.89at.%Fe and the light grey phase with 23.22at.%Nd-76.78. 22 at.% Fe are approximately corresponding to theoretical ratio (Nd:Fe = 2:14 and Nd:Fe = 1:4) of Nd2Fe14B (τ1) and NdFe4B4 (τ2), respectively. The composition of the white phase is 99.82at.%Nd-0.18at.%Fe, which is closed to α-Nd.

Fig. 8
figure 8

XRD pattern and backscattered electrons (BSE) image of Nd25Fe60B15 alloy annealed at 1073 K for 960 h

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In the present work, nineteen Nd-Fe-B alloys annealed at 1073 K for 960 h were investigated by XRD and SEM/EDS. Using same analysis of identified phases in three Nd-Fe-B alloys mentioned above, the determined experimental results were summarized in Table 3. Based on the phase relationships of nineteen Nd-Fe-B alloys, the phase equilibria of the Nd-Fe-B ternary system (excluding the B-rich part) at 1073 K was constructed as shown in Fig. 9. As can be seen, it consists of 8 single-phase regions, 14 two-phase regions and 7 three-phase regions in the Nd-Fe-rich field investigated in the present work. In addition, it is indicated that some Nd-Fe-B alloys studied in the present work could appear liquid phase at 1073 K according to the Nd-Fe binary system revised by Hallemans et al.[48] However, as shown from XRD patterns and BSE images of Nd-Fe-B alloys (seen in Fig. 6 and 8), liquid phase in alloy samples is impossible to be observed and α-Nd as the solid phase was found. The possible reason for it is the result of the solidification of liquid phase in alloy samples during quenched process after annealed at 1073 K. Based on the EDS/XRD results, the phase equilibria between liquid phase (α-Nd) and other phases were shown using dotted lines in Fig. 9. It should be also noted that the binary intermetallic compound Nd5Fe17 was not found to be stable at 1073 K according to the present experimental results as shown in Table 3.

Fig. 9
figure 9

Phase equilibria of the Nd-Fe-B ternary system at 1073 K determined in this work. Note that liquid phase in the alloy samples is impossible to be observed and α-Nd as the solid phase was found only. Liquid phase would transform to the solid phase (α-Nd) during the solidification in the process of quenching quickly alloy samples into ice water. The phase equilibria related to liquid phase were not measured directly and thus were used dotted lines to show three-phase regions determined, liquid + Nd2Fe17 + Nd2Fe14B (τ1), liquid + Nd2Fe14B (τ1) + NdFe4B4 (τ2), liquid + NdFe4B4 (τ2) + Nd5Fe2B6 (τ3). In addition, the phase boundary of liquid phase was not measured in this work

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Conclusions

On the basis of the microstructure examination and phase analysis of Nd-Fe-B alloys at 873 and 1073 K using XRD and SEM/EDS, the following conclusions in this work could be drawn:

  1. (1)

    The phase equilibria of the Nd-Fe-B ternary system at 873 K in the whole compositional range and 1073 K in the Nd-Fe-rich part were constructed based on the XRD and SEM/EDS results. The experimental results show phase equilibria of the Nd-Fe-B ternary system at 873 K consists of 14 single-phase regions, 28 two-phase regions and 16 three-phase regions, while there are 8 single-phase regions, 14 two-phase regions and 7 three-phase regions at 1073 K except for the B-rich part.

  2. (2)

    The ternary intermetallic compound, Nd2Fe14B with space group P42/mnm as Nd2Fe14B structure type, NdFe4B4 with space group Pccn as REl.11Fe4B4 structure type and Nd5Fe2B6 with space group R \( \overline{3} \) m as Pr5Co2B6 structure type were confirmed. In addition, Nd2Fe17 and Nd5Fe17 are stable at 873 K, while Nd5Fe17 was not found at 1073 K in the present experiments.