Mechanics of Materials
Thermodynamics of Oxygen in Molten Nd–Pr–Fe–B Magnet Alloy at High Temperature
2022 Volume 63 Issue 10 Pages 1437-1442
Details
2022 Volume 63 Issue 10 Pages 1437-1442
Neodymium magnets are widely used as high-performance magnets, but there is a problem that thermal demagnetization is relatively significant because of low Curie temperature. Prevention of oxidation for the Nd-rich phases in the grain boundary phase to which improve coercivity is required. Since oxygen dissolution occurs mainly during melting in alloy preparation process, it is necessary to know the affinity between the molten magnet alloy and oxygen. For the proper understanding of this process in practical use, neodymium magnets are made by replacing some of the Nd with Pr in order to cut costs, so the investigation of the system including Pr is required. In this study, Nd–Pr–Fe–B molten alloys and Nd2O3 crucibles were equilibrated in a sealed system, and oxygen solubility was investigated as a function of alloy compositions. It is confirmed that the affinity between the alloy and oxygen increases as the rare earth concentration increases. On the other hand, little effect of Pr ratio was found on the affinity between the molten Nd–Pr–Fe–B magnet and oxygen. It indicates that Nd and Pr have the similar effects on the affinity of the Nd–Pr–Fe–B magnet to oxygen. In addition, as a way to utilize the thermodynamic data obtained in this report, we did calculations regarding deoxidation to prevent oxidation of the Nd-rich phase.
The neodymium magnet was invented by Sagawa et al. in 1982,1) and has much higher magnetism than the various types of magnets used until then. In recent years, neodymium magnets have been widely used as motor materials for hybrid cars and electric vehicles, which are expected to become more popular as a countermeasure to environmental problems. However, the problem with neodymium magnets is that they have a relatively low Curie temperature of approximately 315°C, which can lead to performance degradation due to thermal demagnetization.
The metallurgical structure of neodymium magnets is composed of Nd2Fe14B phase as main phases and the Nd-rich phase as grain boundaries. Hono et al.2) reported that while coercivity is known to increase as the grain size of the main phase decreases, it falls short of the coercivity expected to be obtained by grain refinement when the grain size decreases below 1 µm in their previous magnetic studies.3–11) In addition, Hono et al. observed sintered Nd–Fe–B magnets by FIB-SEM and reported that the presence of Nd-rich phase at grain boundaries contributed to the improvement in coercivity. In the sample with decreased coercivity, oxidation of the Nd-rich phase was observed and disturbed uniform distribution of the Nd-rich phase. This oxidation can also occur during sintering. A countermeasure is to reduce the amount of dissolved oxygen in the alloy. Oshino et al.12) determined the standard Gibbs energy change of oxygen dissolution reaction into molten Nd–Fe alloys as a typical parameter, and Nakazawa et al.13) also determined that of oxygen dissolution reaction into molten Nd–Fe–B alloys. These studies suggest that Nd is the dominant element in terms of the affinity for oxygen.
In industrial neodymium magnets, Pr is used. Pr is obtained by separating it from Nd in the same rare earth ore. The reason why Pr is used is due to the cost savings of not separating Nd and Pr. In terms of magnetism, Betancourt et al.14) measured the magnetic properties of (Ndx,Pr1−x)2Fe14B and reported that maximum energy product was largest at x = 0.75. Morimoto et al.15) found that the substitution of up to 40 mol% of Nd with Pr in HDDR-processed Nd–Fe–B magnets improved the coercivity while maintaining the remanent magnetization under the same HDDR processing conditions. Thus, Nd–Pr–Fe–B magnet alloys are one of the important materials for practical use and future magnet research, and thermodynamic studies of neodymium magnets including Pr are important for process improvement.
Therefore, the purpose of this study is to measure the solubility of oxygen molten Nd–Pr–Fe–B alloys at high temperature to determine the standard Gibbs energy change of oxygen dissolution reactions into the molten alloys and to determine their affinity for oxygen.
Nd–Pr–Fe–B alloys which were prepared by arc melting was provided by collaborating company. Nd2O3 crucible (TEP corporation, purity 99.9%, outer diameter 29 mm, inner diameter 21 mm, height 40 mm) was used as the crucible. Iron holder (S25C, outer diameter 45 mm, inner diameter 35 mm, height 90 mm) was used as a container for sealing.
2.2 Equilibrium experimentThe alloy sample was placed in Nd2O3 crucible and inserted into an Ar gas-filled iron holder for weld sealing. The specimens were held at 1450°C or 1400°C in an electric resistance furnace. The atmosphere in the furnace was Ar–10%H2 to prevent oxidation of the iron holder. After holding the specimens for the specified time, the alloy sample was cooled by water and cut out.
2.3 Sample analysisThe microstructure of samples obtained by the equilibrium experiment were observed by SEM-EDS. The alloy samples were analyzed for composition by ICP-OES and oxygen solubility by inert gas fusion non-dispersive infrared absorption method. The interface oxide was observed between the alloy and the Nd2O3 crucible, which was scraped off for composition analysis by ICP-OES and phase identification by XRD (source: CuKα).
Table 1 shows the compositions of the alloy samples after the experiments, measured by ICP-OES. In this experiment, it shows to reach equilibrium that the oxygen solubility and the alloy composition are constant with respect to time. However, the compositions after the experiment are not stable in the same experiment temperature and holding time because of absorption by the Nd2O3 crucible. Therefore, instead of using the value of oxygen solubility versus holding time, we confirm whether equilibrium was reached by examining the process of decreasing oxygen solubility. Figure 1 shows SEM images of the alloy specimens after the experiment at 1450°C. After 48 h holding, the oxides are observed throughout the alloy specimens. On the other hand, the sample held at 168 h shows almost no oxide. It indicates that the interfacial oxide between the alloy and the crucible is thickened.
SEM images of alloy samples after experiment at 1450°C. (a) 48 h holding (b) 168 h holding.
These results indicate that when the alloy sample melts in the experimental process, excess oxygen in the alloy reacts with Nd and Pr to form oxides. This oxides diffuse and are expelled by adsorption on the Nd2O3 crucible. It is thought to reduce the oxygen solubility in the alloy and reach equilibrium. In accordance with this idea, equilibrium is expected to be reached after 168 h of holding at 1450°C. In other samples with different total amounts of Nd/Pr and the rare earth concentration, the amount of change in Nd and Pr is similar, and the process to equilibrium is the same, so equilibrium is expected to be reached after 168 h of holding at 1450°C. In addition, SEM observation of the sample held at 1400°C for 168 h after holding at 1450°C for 168 h shows that the oxides in the alloy are expelled in the same process, and it can be considered that equilibrium is reached by this combination of holding temperature and time.
In this study, the alloy microstructure is observed for each experiment to confirm that equilibrium is reached in each experiment and that there are no oxides in the alloy that would affect the analysis.
3.2 Determination of oxide phase equilibrated with Nd–Pr–Fe–B alloyIn this study, the thickened area observed between the Nd2O3 crucible and the alloy sample after the experiment, as also seen in Fig. 1, is considered to be the equilibrium oxide phase. Since this interfacial oxide is also in contact with the alloy sample and the gas phase in the iron holder, it is involved in the equilibrium reaction that determines the equilibrium oxygen partial pressure in the system. Figure 2 shows the results of XRD analysis of the interfacial oxide of the alloy sample after the 1450°C experiment. The peaks are consistent with those of Nd2O3 and Pr2O3, and no other peaks are identified. The obtained peak is located in the middle of these oxide peaks and is considered to be due to single phase. Similar results are also obtained by XRD on samples with different Nd/Pr. This suggests that the equilibrium oxide phase is (Nd,Pr)2O3.
X-ray diffraction pattern of equilibrium oxide.
Table 2 shows the oxygen solubility obtained by analysis of the alloy samples after the experiment, the values of equilibrium oxygen partial pressure, and the calculated values of ΔG°. In this table, the oxygen solubility tends to increase as the rare earth concentration increases.
Since the equilibrium oxide phase in this experiment is found to be (Nd,Pr)2O3 as mentioned above, the equilibrium oxygen partial pressure can be calculated. The oxidation reactions of Nd and Pr and the standard Gibbs energy changes in these reactions are as eq. (1)–(4).16)
| \begin{equation} \text{2Nd(l)} + \text{3/2 O$_{2}$(g)} = \text{Nd$_{2}$O$_{3}$(s)} \end{equation} | (1) |
| \begin{equation} \Delta G^{\circ} = -1813 + 0.285T\ (\text{kJ/mol}) \end{equation} | (2) |
| \begin{equation} \text{2Pr(l)} + \text{3/2 O$_{2}$(g)} = \text{Pr$_{2}$O$_{3}$(s)} \end{equation} | (3) |
| \begin{equation} \Delta G^{\circ} = -1805 + 0.284T\ (\text{kJ/mol}) \end{equation} | (4) |
Generally, the Gibbs energy change of a reaction is expressed as eq. (5).
| \begin{equation} \Delta G = \Delta G^{\circ} + RT\ln K \end{equation} | (5) |
Here, ΔG° is the standard Gibbs energy change, R is gas constant, and T is Kelvin temperature.
Since ΔG = 0 at equilibrium, the equilibrium constant K is expressed as eq. (6).
| \begin{equation} K = \exp (-\Delta G^{\circ}/RT) \end{equation} | (6) |
The equilibrium constant K is expressed as eq. (7)
| \begin{equation} K = a_{\text{Nd${_{2}}$O${_{3}}$(s)}}a_{\text{Nd(l)}}^{2}/P_{\text{O${_{2}}$}}^{3/2} \end{equation} | (7) |
Here, ai is the activity of i and $P_{\text{O}_{2}}$ is the equilibrium oxygen partial pressure. From the above equation, the equilibrium oxygen partial pressure $P_{\text{O}_{2}}$ is expressed as eq. (8).
| \begin{equation} P_{\text{O${_{2}}$}} = (a_{\text{Nd${_2}$O${_{3}}$(s)}}\exp(\Delta G^{\circ}/RT)/a_{\text{Nd(l)}}^{2})^{2/3} \end{equation} | (8) |
Nagai et al.17) reported the Nd activity in Nd–Fe alloy from 1100°C to 1250°C using double Knudsen cell mass spectrometry. The values of 16 mol%Nd, 49 mol%Nd, and 72 mol%Nd are extrapolated to 1450°C, the experimental temperature in this study. These values are used as a linear relationship to Nd concentration to obtain the rare earth activity as shown in Fig. 3. Since the equilibrium oxide phase is formed at almost the same composition ratio as Nd/Pr in the alloy sample, we consider as the chemical properties of Nd and Pr in Fe are very similar and distribute the activity by the concentration ratio of Nd and Pr.
Relationship between RE concentration and activity of RE at 1450°C.
In this study, since the concentration of Nd2O3 is higher than that of Pr2O3 in the equilibrium oxide phase, the activity of Nd2O3 is determined by the concentration of Nd2O3 obtained from the composition analysis of the equilibrium oxide phase and applying the Raoult rule. The equilibrium oxygen partial pressure is calculated using each of the activity of Nd2O3 obtained as above. The values of equilibrium oxygen partial pressure are shown in Table 2.
The standard Gibbs energy change of oxygen dissolution reaction expresses the relationship between oxygen solubility in Nd–Pr–Fe–B alloys and equilibrium oxygen partial pressure. The reaction of oxygen dissolution into the molten Nd–Pr–Fe–B alloy and its standard Gibbs energy change are expressed as eq. (9), (10).
| \begin{equation} \text{1/2 O$_{2}$(g)} = \text{$\underline{\text{O}}$($X_{\text{O}}$ in Nd–Pr–Fe–B alloy)} \end{equation} | (9) |
| \begin{equation} \Delta G^{\circ} = -RT\ln (\gamma_{\text{O}}X_{\text{O}}/P_{\text{O${_{2}}$}}^{1/2}) \end{equation} | (10) |
Here, γi is the activity coefficient of component i on Raoult basis and Xi is the mole fraction of component i. In this study, the oxygen concentration in the molten alloy is at most XO = 3.0 × 10−4, so it is assumed to be a dilute solution and the activity coefficient of oxygen is set to unity. Therefore, the standard Gibbs energy change into the molten alloy can be calculated from the oxygen concentration in the alloy and the equilibrium oxygen partial pressure in Table 2, which also shows the calculated values of ΔG°. For the value at 1450°C, Fig. 4 shows the relationship between ΔG° and the concentration of rare earths, and Fig. 5 shows the relationship between ΔG° and the ratio of Pr to rare earths, respectively. Here, the rare earth concentration is the total of Nd and Pr concentration. In Fig. 4, ΔG° tends to decrease as the rare earth concentration increases. In Fig. 5, there is no correlation between the ratio of Pr to rare earth concentration and ΔG°. It means that the effect on the affinity for oxygen is almost the same when Pr and Nd are compared. From these results, the affinity of molten Nd–Pr–Fe–B magnet alloys for oxygen is mainly controlled by the total concentration of rare earth elements.
Relationship between standard Gibbs energy of alloy sample and RE concentration at 1450°C.
Relationship between standard Gibbs energy of alloy sample and Pr ratio at 1450°C.
For the samples at 1450°C and 1400°C that are close in composition, ΔG° for the dissolution reaction of oxygen at 1450°C to 1400°C into the approximately 12.0 mass%Nd–4.3 mass%Pr–Fe–1.3 mass%B melting alloy can be calculated if the compositions are considered nearly identical. Based on this idea, ΔG° of the dissolution reaction of oxygen is calculated as eq. (11).
| \begin{align} \Delta G^{\circ} & = -410.4 + 0.064T\ (\text{kJ/mol})\\ &\quad (\text{1673$\,$K to 1723$\,$K},\\ &\quad\text{12.0$\,$mass%Nd–4.3$\,$mass%Pr–Fe–1.3$\,$mass%B}) \end{align} | (11) |
To achieve high coercivity in neodymium magnets, it is important to prevent oxidation of the Nd-rich phase. In this section, we estimate whether oxidation of the Nd-rich phase can occur in the actual manufacturing process and the deoxidation target in alloy preparation to prevent it, using data from this study and previous studies.
Mazilkin et al.18) have investigated oxygen in the Nd-rich phase, the grain boundary phase in the microstructure of Nd–Fe–B permanent magnets. It is known that it is difficult to confirm the presence of oxygen in the thin grain boundary phase by SEM observation, and that it may have been oxidized in the sample preparation. Microstructural observation and crystal structure analysis by TEM and composition analysis by EELS were performed. As a result, the Nd-rich phase was confirmed to take the form of pure Nd, Nd–Fe, Nd2O3, and Nd2O3+Nd, and the composition of metal phase is confirmed to range from about Fe–70 mol%Nd to pure Nd. The main phase, Nd2Fe14B, did not contain much oxygen, while the Nd-rich phase often contained oxygen. This indicates that the oxygen in the alloy oxidizes the Nd-rich phase during the heat treatment of the magnet fabrication process and it affects the magnetic properties.
Therefore, the equilibrium oxygen solubility in the Nd-rich phase is calculated by considering the equilibrium of the Nd oxidation reaction in the two cases where the Nd-rich phase is Fe–77.8 mol%Nd and pure Nd. The oxidation of Nd-rich phase may occur in the sintering and heat treatment processes, and here we consider the sintering temperature of 1050°C and the heat treatment temperatures of 800°C and 500°C. Note that if the Nd-rich phase is Fe–77.8 mol%Nd, it melts at these temperatures, but if it is pure Nd, it melts only at 1050°C. For Fe–77.8 mol%Nd, the equilibrium oxygen partial pressure at each temperature is calculated by the Nd activity that can be calculated by the values of Fe–72 mol%Nd and Fe–93 mol%Nd by Nagai et al.17) Here, Nd2O3 is assumed to exist as a pure solid and the activity is set to unity.
Oshino et al.12) determined the temperature dependence of ΔG° of the oxygen dissolution reaction for Fe–77.8 mol%Nd. ΔG° at the assumed temperature can be obtained by extrapolations of this. With these values, the equilibrium oxygen solubility can be calculated using eq. (7). For the case of pure Nd, Sano et al.19) obtained the temperature-dependent equation for oxygen solubility in pure Nd, which is used to calculate the equilibrium oxygen solubility.
In comparing the equilibrium oxygen solubility in the molten Nd–Pr–Fe–B obtained in this study, it is necessary to consider how the oxygen in the alloy is distributed and present relative to the main phase and the Nd-rich phase. Assuming that the diffusion distance is $\sqrt{2Dt} $, the diffusion distance of oxygen for 1 hour is 2–3 mm because of the diffusion coefficient of oxygen in iron DO in Fe = 2.0∼5.0 × 10−10 m2/s at 1050°C. Given this, all of the dissolved oxygen is considered to be in the Nd-rich phase. For the 32 mass%Nd–Fe–1 mass%B alloy, the assumed oxygen solubility in the Nd-rich phase is about 11∼14 times the oxygen solubility in the molten alloys. For example, if the oxygen solubility is 100 ppm in the molten alloys, there will be about 1100–1400 ppm of oxygen in the Nd-rich phase at sintering process. Table 3 shows the equilibrium oxygen solubility in the molten alloy for oxidation of the Nd-rich phase obtained by these calculations. If oxygen is dissolved above the values shown in Table 3, the Nd-rich phase is oxidized during sintering or heat treatment at each temperature. Since the oxygen solubility in commonly manufactured neodymium magnets is several hundred ppm, oxidation of the Nd-rich phase is considered to occur. As suggested by the ΔG° of oxygen dissolution reaction into molten alloy at 1450°C obtained in this study, the affinity between neodymium magnets and oxygen is high, and oxidation during sintering cannot be prevented unless melting takes place in an extremely low oxygen environment or some of deoxidation method is performed. The deoxidation target to prevent oxidation during sintering should be 80 ppm or less.
A possible deoxidation method for molten neodymium magnet alloys is to add Ca or NdF3, which are more reactive with oxygen than Nd. Similar to the calculation of the standard Gibbs energy change for the oxygen dissolution reaction described above, ΔG° is calculated for the No. 5 sample with oxygen as the mass fraction. The reaction equation and ΔG° are expressed as eq. (12) and (13).
| \begin{equation} \text{1/2 O$_{2}$(g)} = \text{$\underline{\text{O}}$([mass%O] in Nd–Pr–Fe–B alloy)} \end{equation} | (12) |
| \begin{equation} \Delta G^{\circ} ([\text{mass%O}]) = -359.3\,\text{kJ/mol} \end{equation} | (13) |
| \begin{equation} \text{Ca(l)} + \text{1/2 O$_{2}$(g)} = \text{CaO(s)} \end{equation} | (14) |
| \begin{equation} \Delta G^{\circ} = -658 + 0.113T\ (\text{kJ/mol}) \end{equation} | (15) |
| \begin{equation} \text{2/3 Nd(l)} + \text{1/2 O$_{2}$(g)} + \text{1/3 NdF$_{3}$(l)} = \text{NdOF(s)} \end{equation} | (16) |
| \begin{equation} \Delta G^{\circ} = -661 + 0.101T\ (\text{kJ/mol}) \end{equation} | (17) |
| \begin{equation} \text{Ca(l)} + \text{$\underline{\text{O}}$([mass%O] in Nd–Pr–Fe–B alloy)} = \text{CaO(s)} \end{equation} | (18) |
| \begin{align} \Delta G^{\circ}& = -RT\ln (a_{\text{CaO(s)}}/a_{\text{Ca(l)}}f_{\text{O}}[\text{mass%O}]) \\ &= -104.0\,\text{kJ/mol} \end{align} | (19) |
| \begin{align} &\text{2/3 Nd(l)} + \text{$\underline{\text{O}}$([mass%O] in Nd–Pr–Fe–B alloy)} \\ &\quad + \text{1/3 NdF$_{3}$(l)} = \text{NdOF(s)} \end{align} | (20) |
| \begin{align} \Delta G^{\circ} &= -RT\ln (a_{\text{NdOF(s)}}/a_{\text{Nd(l)}}^{2/3}f_{\text{O}}[\text{mass%O}]a_{\text{NdF${_{3}}$(l)}}^{1/3})\\ & = -127.7\,\text{kJ/mol} \end{align} | (21) |
Here, fO is the activity coefficient of Henrian standard state on a 1 mass% basis and [mass%O] is the oxygen solubility in the molten alloy. Consider that CaO or NdOF is solid in this temperature, aCaO(s) and aNdOF(s) are set to unity. Since oxygen is dilute in the molten alloy, fO is set to unity. These values allow us to determine the relationship between the oxygen solubility in the alloy and the activity of Ca or NdF3. Figure 6 shows the relationship of that. From Fig. 6, adding Ca or NdF3 in alloy preparation makes it possible to achieve the deoxidation target of 80 ppm for preventing oxidation during sintering. Although Ca can be widely used since it deoxidizes only by itself, it is necessary to considerably increase the amount of Ca activity to deoxidize to low oxygen concentrations. There is concern about deterioration of cleanliness. On the other hand, the deoxidation by NdF3 is affected not only by NdF3 activity but also by Nd activity, so a high degree of control can be expected. Figure 6 also shows that deoxidation by NdF3 is possible to a lower oxygen concentration.
Dependence of oxygen concentration of molten No. 5 alloy sample deoxidized by additions of calcium and neodymium fluoride at 1723 K on activity of Ca and NdF3.
On the other hand, when the composition of the Nd-rich phase is Fe–77.8 mol%Nd, it is difficult to achieve the deoxidation target of approximately 10 ppm or less for 800°C heat treatment. Therefore, it is considered difficult to prevent oxidation of the Nd-rich phase in the heat treatment even with some technological improvements in the magnet fabrication process. However, if the Nd-rich phase is not oxidized during sintering, uniform distribution to the grain boundary phase can be achieved, and it is possible to achieve improvement in coercivity.
In previous magnetic research, it is known that heat treatment can improve coercivity. Based on the above discussion, it is thought that the Nd-rich phase, which is thinly and uniformly distributed on the grain boundaries without oxidation during sintering, is oxidized by heat treatment to become a nonmagnetic phase, which improves the coercivity. Recently, high-precision analysis has revealed that Fe is contained in the Nd-rich phase, and it is thought that the Nd-rich phase affects the improvement of coercivity as a ferromagnetic phase. However, considering that the Nd-rich phase is oxidized in the heat treatment, the presence of Fe in the Nd-rich phase is a result of composition change to the eutectics, and the oxidation to a nonmagnetic phase in the heat treatment is the main factor for the improvement of coercivity.
Assuming this mechanism of coercivity enhancement, the realistic deoxidation target can be set to the value that the Nd-rich phase is not oxidized during sintering, which is 80 ppm or low. In the industrial process, the standard Gibbs energy change for the oxygen dissolution reaction obtained in this study can be used to study atmosphere control and deoxidation methods to achieve this target value. In addition to this, if the Nd activity in the molten alloy and the activity of oxides are obtained, deoxidation can be predicted more accurately for the industrial process.
In this study, the affinity between the molten alloy and oxygen was investigated by measuring oxygen solubility in molten Nd–Pr–Fe–B alloys at 1450°C and 1400°C using the chemical equilibrium method. Excess oxygen above the equilibrium oxygen solubility precipitates as rare earth oxides in the molten alloy and is discharged from the molten alloy. The oxide phase in equilibrium with the molten Nd–Pr–Fe–B alloy at 1400–1450°C is (Nd,Pr)2O3. By considering the ΔG° of oxygen dissolution reaction into the molten alloy, the affinity between the molten alloy and oxygen increases with increasing rare earth concentration at 1450°C. There is no significant difference in the effect of Nd and Pr on the affinity for oxygen. From the previous study, we estimated that the deoxidation goal to prevent oxidation of the Nd-rich phase during sintering is about 80 ppm, and we investigated deoxidation methods to achieve this value using the thermodynamic data obtained in this report.
