Thermodynamics of Oxygen in Molten Nd–Fe–B Alloy for Production of Low-Oxygen Nd–Fe–B Magnet

Abstract

Oxidation of the Nd-rich phase in Nd–Fe–B magnet alloys is known to deteriorate their coercivity. Therefore, it is important to prevent the dissolution of oxygen into the Nd–Fe–B magnet alloy during the manufacturing process. This requires the knowledge of the properties of oxygen in Nd–Fe–B magnet alloys, which has not been investigated yet. In this study, the oxygen solubility of Nd–Fe–B alloy at 1673 K was measured, and the effect of boron concentration on the affinity between oxygen and Nd–Fe–B alloy was analyzed. The standard Gibbs energy for the dissolution of oxygen into the molten Nd–Fe–B alloy at 1673 K was derived from experimental results, which indicated that the addition of boron into the molten Nd–Fe alloy decreased the affinity between oxygen and the alloy. The thermodynamic cause of this effect of boron is discussed, and a method to suppress oxygen dissolution into Nd–Fe–B alloy during the melt manufacturing process is suggested.

Fig. 3 Dependence of oxygen solubility of molten Nd–Fe–B alloys at 1673 K on boron concentration.

1. Introduction

Nd–Fe–B magnets with the Nd₂Fe₁₄B main phase are of great importance in industry owing to their excellent magnetic properties.^1–5) They are used in various applications such as hard disk drives, motors in consumer electronics, and motors of hybrid vehicles. In particular, the demand for hybrid vehicles and hence Nd–Fe–B magnet–based motors has soared because of growing environmental concerns. Since the coercivity of ordinary Nd–Fe–B magnets is low at typical operating temperatures of motors (∼200°C), Nd–Fe–B magnets for such use are usually enhanced their coercivity by the addition of dysprosium or terbium.^6–11) However, dysprosium and terbium are distributed unevenly around the world and are thus easily subject to heavy price fluctuation. Therefore, it is highly desirable to develop other methods to enhance the coercivity of Nd–Fe–B magnets without using dysprosium and terbium.

Hono et al.¹²⁾ reported that grain refinement of Nd–Fe–B magnets enhances their coercivity. However, too small a grain size deteriorates the coercivity, and the critical grain size strongly depends on the oxygen concentration in the Nd–Fe–B magnet alloy.¹³⁾ This phenomenon is reportedly caused by the oxidation of the Nd-rich phase; it is a structure of the grain boundary of Nd–Fe–B magnets and plays an important role in the high coercivity of the magnet.¹⁴⁾

Therefore, it is important to sustain the dissolution of oxygen into the Nd–Fe–B magnet alloy during the manufacturing process to further enhance its coercivity by grain refinement. In this regard, the knowledge of the properties of oxygen in Nd–Fe–B alloys becomes crucial. Oshino et al.¹⁵⁾ determined the oxygen solubility of molten Nd–Fe alloy; however, the effect of the introduction of boron into the Nd–Fe alloy on the properties of oxygen in the alloy is not well understood. Hence, this study aims to measure the oxygen solubility of Nd–Fe–B alloy and elucidate the thermodynamic effect of boron on the oxygen dissolved in Nd–Fe–B alloy. Further, we consider the manufacturing process for low-oxygen Nd–Fe–B magnets.

2. Experimental Procedure

The Nd–Fe–B alloy was prepared from neodymium rods (99.5% purity), iron lumps (99.9% purity), and boron lumps (99.8% purity) by the arc melting method. The weighed compositions of the Nd–Fe–B alloy are shown in Table 1, wherein the first row lists the composition of the Nd₂Fe₁₄B main phase and the remaining are alloys with a constant Nd concentration of 16.5% but varying B concentrations. All of the Nd–Fe–B alloys in Table 1 are in the liquid phase at the experimental temperature of 1673 K, as confirmed by the Nd–Fe–B phase diagram.¹⁶⁾ The prepared Nd–Fe–B alloy, whose weight is 30 g, was inserted into an Nd₂O₃ crucible (23 mm inner diameter, 29 mm outer diameter, and 55 mm height), and the Nd₂O₃ crucible was placed in an iron holder (30 mm inner diameter, 40 mm outer diameter, and 90 mm height). The iron holder was purged with argon gas and sealed by welding an iron lid. This iron crucible was inserted into an electronic furnace under an argon-gas atmosphere at 1673 K and held for various preset durations of 24 to 144 h; the holding times are listed in Table 1.

Table 1 Experimental compositions of Nd–Fe–B alloys and holding times.

Subsequently, the iron holder was removed from the furnace and immediately water-quenched.

The cooled iron holder was cut open to retrieve the Nd₂O₃ crucible. Then, the Nd–Fe–B alloy was cut off from the Nd₂O₃ crucible and divided into several bulks of 0.1 g. The divided alloy bulks were polished and treated with ultrasonic cleaning in ethanol, following which the oxygen concentration was measured by the inert gas fusion-infrared absorption method using nickel capsules as the flux. Subsequently, a piece of the alloy was added with 10 ml of nitric acid and dissolved by heating to 100°C. The solution was diluted with pure water by 100 times, and the Nd, Fe and B concentrations in the solution were measured using inductive coupled plasma optical emission spectroscopy (ICP-OES) to determine the composition of the alloy. Finally, the oxide layer between the Nd–Fe–B alloy and Nd₂O₃ crucible was scraped off and analyzed by X-ray diffraction (XRD) using Cu-Kα radiation to identify the equilibrium oxide phase.

3. Results and Discussion

3.1 Determination of the equilibrium time

Figure 1 shows the change in oxygen concentration with holding time for Fe–11.8 at%Nd–5.9 at%B alloy. The error bars in Fig. 1 indicate the standard deviations of the analytical values. Figure 1 shows that the oxygen concentration in the Nd–Fe–B alloy gradually decreases with the extension of the holding time and the corresponding error bars shrink. Oshino et al.¹⁵⁾ reported the same phenomenon for the Nd–Fe system and explained its underlying mechanism as follows. In an equilibrium experiment, excessive oxygen beyond the oxygen solubility of molten Nd–Fe alloy forms Nd₂O₃ inclusions in the alloy, and these inclusions slowly migrate to the surface of the Nd₂O₃ crucible, which leads to a gradual decrease in the oxygen concentration in the molten Nd–Fe alloy. The slow change in the oxygen concentration of the Nd–Fe–B alloy shown in Fig. 1 may have occurred for the same reason. A slight decrease in Nd concentration of the alloy along with the extension of the holding time was also observed, which may have occurred by the emission of Nd₂O₃ inclusions from the alloy. Here, Fig. 1 shows that the holding times of 72 h and 144 h resulted in approximately the same values of oxygen concentrations within the range of their respective error bars. The Nd concentration of the alloy also became constant with the holding times of 72 h and 144 h.

Fig. 1

Change in oxygen concentration with time for Fe–11.8 at% Nd–5.9 at% B alloy.

Therefore, the equilibrium time for the system under study was determined to be 72 h.

3.2 Identification of the equilibrium oxide phase

Figure 2 shows the results of XRD analysis for the oxide layer between the Nd₂O₃ crucible and Fe–11.8 at%Nd–5.9 at%B alloy held for 144 h. The figure shows only the peaks corresponding to the oxide phase of Nd₂O₃. Therefore, the equilibrium oxide phase for the system under study was identified as Nd₂O₃.

Fig. 2

Diffraction spectrum by X-ray for the oxide phase equilibrated with Fe–11.8 at% Nd–5.9 at% B held at 1673 K for 144 h.

3.3 Standard Gibbs energy for the dissolution of oxygen into molten Nd–Fe–B

The determined oxygen solubilities of the Nd–Fe–B alloy are shown in Table 2 and Fig. 3. It should be noted that in Fig. 3, the white plot indicates the oxygen solubility listed at the first row of Table 2, and black plots indicate the values below second row of Table 2 with their average value of Nd concentration. Figure 3 shows that an increase in the boron concentration causes a slight increase in the oxygen concentration of the Nd–Fe–B alloy with the average Nd concentration of 14.5 ± 0.4 at%.

Table 2 Oxygen solubility of molten Nd–Fe–B alloys at 1673 K.

Fig. 3

Dependence of oxygen solubility of molten Nd–Fe–B alloys at 1673 K on boron concentration.

We derive the standard Gibbs energy for the dissolution of oxygen into molten Nd–Fe–B, whose reaction is expressed in eq. (1) as follows:   

\begin{equation} \text{1/2O$_{2}$(g)} = \underline{\text{O}}(X_{\text{O}},\ \text{in}\ \text{Nd–Fe–B}). \end{equation} (1)

In the case of equilibrium between molten Nd–Fe–B alloy and solid Nd₂O₃, eqs. (2)–(5) hold.   

\begin{equation} \text{2Nd(l)} + \text{3/2O$_{2}$(g)} = \text{Nd$_{2}$O$_{3}$(s)}, \end{equation} (2)

  

\begin{equation} \Delta G^{\circ}{}_{(2)} = -1813 + 0.285T[\text{kJ${\cdot}$mol$^{-1}$}], \end{equation} (3)

  

\begin{equation} K = a_{\text{Nd${_{2}}$O${_{3}}$(s)}}/(a_{\text{Nd(l)}}^{2}\cdot P_{\text{O${_{2}}$}}^{3/2}), \end{equation} (4)

  

\begin{equation} K = \exp (- \Delta G^{\circ}{}_{(2)}/RT), \end{equation} (5)

where ΔG°₍₂₎ represents the standard Gibbs energy change for the reaction in eq. (2), K represents the equilibrium constant for the reaction in eq. (2), T [K] represents temperature, a_i represents the activity of component i relative to that of the pure substance, $P_{\text{O}_{2}}$ represents the partial pressure of oxygen in the system, and R [kJ·mol⁻¹·K⁻¹] represents the gas constant.

In this study, the activity of Nd₂O₃(s) was unity because the oxide phase equilibrated with the Nd–Fe–B alloy was solid Nd₂O₃. Regarding the activity of Nd in molten Nd–Fe–B alloy, Zhou et al.¹⁸⁾ optimized the thermodynamic parameters for the Nd–Fe–B liquid phase using eq. (6), which gives the Gibbs free energy of mixing for the Nd–Fe–B liquid phase. The optimized thermodynamic parameters¹⁸⁾ are listed in Table 3.   

\begin{align} \Delta G_{\text{Nd–Fe–B}}^{\text{M}} &= RT\sum\nolimits_{i = \text{Nd,$\,$Fe,B}}x_{i}\ln x_{i} \\ & \quad+ x_{\text{Nd}}x_{\text{Fe}}\sum\nolimits_{i = 0}^{2}(x_{\text{Nd}} - x_{\text{Fe}})^{i}L_{\text{Nd,Fe}}^{i}\\ & \quad + x_{\text{Fe}}x_{\text{B}}\sum\nolimits_{i = 0}^{2}(x_{\text{Fe}} - x_{\text{B}})^{i}L_{\text{Fe,B}}^{i} \\ & \quad+ x_{\text{Nd}}x_{\text{B}}\sum\nolimits_{i = 0}^{1}(x_{\text{Nd}} - x_{\text{B}})^{i}L_{\text{Nd,B}}^{i}, \end{align} (6)

where x_i represents the mole fraction of component i.

Table 3 Thermodynamic parameters of molten Nd–Fe–B alloy.¹⁸⁾

The activity of Nd in molten Nd–Fe–B alloy was obtained by substituting eq. (6) and the parameters in Table 3 into the eq. (7).   

\begin{align} a_{\text{Nd}} &= \exp ((\mu_{\text{Nd}} - \mu^{\circ}{}_{\text{Nd}})/RT) \\ &= \exp((\partial \Delta G_{\text{Nd–Fe–B}}^{\text{M}}/\partial n_{\text{Nd}})_{n_{\text{Fe}},n_{\text{B}}}/RT), \end{align} (7)

where n_i represents the number of moles for component i.

The derived values of activity of Nd are listed in Table 4.

Table 4 Calculated neodymium activity for the molten Nd–Fe–B alloy at 1673 K.

The activities of Nd in Table 4 and the unity for the value of the activity of Nd₂O₃ were substituted into eq. (4), and eqs. (3)–(5) were solved simultaneously to derive the oxygen partial pressure $P_{\text{O}_{2}}$ in the equilibrium reaction (eq. (2)). The determined oxygen partial pressures $P_{\text{O}_{2}}$ are shown in Table 5.

Table 5 Oxygen partial pressure for the molten Nd–Fe–B alloy equilibrated with Nd₂O₃ at 1673 K.

Subsequently, the standard Gibbs energy change for oxygen dissolution into Nd–Fe–B alloy, whose reaction is expressed in eq. (1), is described by eq. (8).   

\begin{equation} \text{1/2O$_{2}$(g)} = \underline{\text{O}}(X_{\text{O}},\ \text{in}\ \text{Nd–Fe–B}) \end{equation} (1)

  

\begin{equation} \Delta G^{\circ}(X_{\text{O}},\ \text{in}\ \text{Nd–Fe–B}) = -RT\ln (f_{\text{O}}X_{\text{O}}/P_{\text{O${_{2}}$}}^{1/2}), \end{equation} (8)

where f_O represents the activity coefficient of oxygen relative to Henry’s standard with mole fraction. Because of the very low values of oxygen solubility of the Nd–Fe–B alloy (Table 2), f_O is assumed to be unity. The oxygen solubilities in Table 2 and oxygen partial pressures in Table 5 were substituted into eq. (8) to derive the standard Gibbs energy change for oxygen dissolution into molten Nd–Fe–B alloy at 1673 K. The derived values are shown in Table 6 and Fig. 4, wherein the white plots indicate the values listed at the first and second rows of Table 6, and black plots indicate the values below third row of Table 6 with their average value of Nd concentration.

Table 6 Standard Gibbs energy for dissolution of oxygen into molten Nd–Fe–B alloys at 1673 K.

Fig. 4

Dependence of standard Gibbs energy for dissolution of oxygen into molten Nd–Fe–B alloys on boron concentration at 1673 K.

For comparison, Table 6 and Fig. 4 also show the values for Nd–Fe alloy calculated from eq. (9), which was reported by Oshino et al.¹⁵⁾ as the standard Gibbs energy change for oxygen dissolution into molten Nd–Fe alloy at 1673 K.   

\begin{align} &\Delta G^{\circ}(X_{\text{O}},\ \text{in}\ \text{Nd–Fe}) \\ &\quad = -298.09 - 201x_{\text{Nd}} - 88x_{\text{Nd}}^{2}[\text{kJ/mol}]. \end{align} (9)

It should be noted that Oshino et al.¹⁵⁾ derived eq. (9) by using the values of Nd activity with the assumption of Raoult’s law for Nd–Fe liquid alloy, but whichever the Nd activity is calculated from eq. (7) or the assumption of Raoult’s law, the difference in ΔG° (X_O, in Nd–Fe) is within 1 kJ. The results in Table 6 and Fig. 4 indicate that the addition of boron into the molten Nd–Fe alloy causes an increase in the value of the standard Gibbs energy change for oxygen dissolution into molten Nd–Fe alloy, which implies that the molten Nd–Fe–B alloy has a lower affinity for oxygen compared to the molten Nd–Fe alloy. However, the addition of boron beyond 3.7 at% seemed not to change the value for a Nd concentration of 14.5 ± 0.4 at%. In addition, the oxygen solubilities for Fe–7.6 at%Nd and Fe–14.5 at%Nd at 1673 K were estimated from their standard Gibbs energy for dissolution of oxygen which were calculated from eq. (9) and shown in Table 6. Using eqs. (3)–(5), (8) and the Nd activity with the assumption of Raoult’s law for Nd–Fe liquid alloy, the oxygen solubilities were calculated and exhibited in Table 7. A comparison between Table 2 and 7 shows that the Nd–Fe alloys have higher oxygen solubilities than the Nd–Fe–B alloys at 1673 K.

Table 7 Estimated oxygen solubility of molten Nd–Fe alloys at 1673 K.

3.4 Effect of boron on the affinity of oxygen for molten Nd–Fe–B alloy

The reason for the lower affinity of oxygen for Nd–Fe–B alloy than for Nd–Fe alloy can be attributed to the interaction among Nd, Fe, B, and O in the molten Nd–Fe–B–O alloy. Figure 5 shows the formation-free energies for the oxides of Nd, Fe, and B projected as the Ellingham diagram,^17,19) and Fig. 6 shows the mixing enthalpies of the molten Nd–Fe alloy^18,20) and molten Nd–B alloy;¹⁸⁾ In Fig. 6, two reported data for the mixing enthalpy of Nd–Fe alloy^18,20) are exhibited, where one is a thermodynamically calculated data¹⁸⁾ and the other is an experimental data determined by calorimetric measurement,²⁰⁾ and the mixing enthalpy of Nd–B alloy¹⁸⁾ is calculated data using Miedema’s method.

Fig. 5

Formation free energy for the oxides of Nd, B, and Fe projected as Ellingham diagram.^17,19)

Fig. 6

Mixing enthalpies of the molten Nd–Fe²⁰⁾ and Nd–B¹⁸⁾ alloys.

Figure 5 indicates that Nd has an extremely high affinity for oxygen relative to Fe and B. Therefore, oxygen atoms in molten Nd–Fe–B alloy may attract more Nd atoms than Fe and B atoms, which is also implied by Oshino et al.¹⁵⁾ This hypothesis implies that oxygen atoms in molten Nd–Fe–B and Nd–Fe alloys are mostly surrounded by Nd atoms. Therefore, the affinity between an oxygen atom and the surrounding atoms in molten Nd–Fe–B and Nd–Fe alloys may be almost the same in both of the molten alloys. However, Nd atoms can gather around oxygen atoms only by breaking some of its chemical bonds with surrounding atoms.

Figure 6 shows that the mixing enthalpy of molten Nd–B is lower than that of molten Nd–Fe alloy, which implies that Nd–B bonds are stronger than Nd–Fe bonds. This further implies that more energy is required to cut off the chemical bonds between the Nd atom and the surrounding atoms in the molten Nd–Fe–B alloy than in the Nd–Fe alloy because of the existence of strong Nd–B bonding in the Nd–Fe–B alloy. Considering the above discussion, the energy required to cut off stronger Nd–B bonds is likely the reason for the lower affinity of oxygen for the molten Nd–Fe–B alloy than for the Nd–Fe alloy.

However, the above discussion is inadequate to account for the invariance along with a increase in B concentration of Nd–Fe–B alloy in the standard Gibbs energy change for oxygen dissolution into molten Nd–Fe–B alloy with Nd concentration of 14.5 ± 0.4 at% and B concentrations beyond 3.7 at%. This may be caused by more complicated interactions between the constituent elements, and this requires further investigation.

3.5 Melt manufacturing process for low-oxygen Nd–Fe–B magnet alloy

The molten Nd–Fe–B alloy was found to have a lower affinity for oxygen than the Nd–Fe alloy. Based on this result, the melt manufacturing process for a low-oxygen Nd–Fe–B magnet alloy was examined. In the case of Nd, Fe, and B bulk melted together to produce Nd–Fe–B magnet alloy; it may be preferable to add B bulk before Nd bulk to avoid the formation of the Nd–Fe alloy, which has a higher affinity for oxygen than the Nd–Fe–B alloy of the final composition. The values of the standard Gibbs energy for dissolution of oxygen into Nd–Fe–B alloys at 1673 K in Table 6 indicate that the values for Nd–Fe–B alloy have 7–12 kJ less values than Nd–Fe alloy with the same Nd concentration. According to eq. (8), this difference of 7–12 kJ implies that the Nd–Fe alloy with no boron has an almost 1.6–2.4 times as large value of oxygen solubility as the Nd–Fe–B alloy with the same Nd concentration when exposed to atmosphere with the same oxygen partial pressure at 1673 K. As is already shown at chapter 3-3 in Table 2 and 7, the maximum oxygen solubility for Nd–Fe alloy is also higher than Nd–Fe–B alloy with the same Nd concentration. Since the compositions of Nd₂Fe₁₄B main phase (Fe–11.8 at%Nd–5.9 at%B) is near the ones listed in Table 6, Nd–Fe–B magnet alloy may also apply to above discussion. Therefore, the formation of Nd–Fe alloy during the melt manufacturing process can increase the risk of oxygen dissolution unnecessarily. This risk may be avoided by melting in the following order: Fe, B, and Nd.

4. Conclusion

The oxygen solubility of the molten Nd–Fe–B alloy at 1673 K was measured to investigate the affinity between oxygen and the Nd–Fe–B magnet alloy. The standard Gibbs energy for the dissolution of oxygen into molten Nd–Fe–B alloy at 1673 K was derived from experimental results and compared with the corresponding value for Nd–Fe alloy,¹⁵⁾ which indicated that the addition of boron to molten Nd–Fe alloy decreases the affinity between oxygen and the alloy. The cause of this effect of boron was discussed based on the principles of thermodynamics, and recommendations were provided for the melt manufacturing process of low-oxygen Nd–Fe–B magnet alloy.

Acknowledgment

The authors are grateful to the Elements Strategy Initiative Center for Magnetic Materials for the financial support to this research in the Elements Strategy Project, launched by the Ministry of Education, Culture, Sports, Science and Technology (MEXT).

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