Experimental Investigation and Thermodynamic Modeling of the B₂O₃-FeO-Fe₂O₃-Nd₂O₃ System for Recycling of NdFeB Magnet Scrap

The binary B₂O₃-Nd₂O₃ system has been investigated in several works.[4‐8] Three stable compounds are known in this system: NdBO₃,[4] NdB₃O₆,[5] and Nd₄B₂O₉.[7] The melting point of all these compounds have been determined in the previous works. The melting point of NdBO₃ was revised several times from the first measurement by Levin et al.[4] through the work by Roth et al.[9] to the final estimate of 1885 K ± 5 K (1612 °C) by Levin.[6] All these measurements were performed using the quenching method (QM). The melting point of NdB₃O₆ was determined to be 1428 K ± 5 K (1155 °C) by the same method in the work by Levin.[6] The melting point of Nd₄B₂O₉ was measured by Ji et al.[7] using differential thermal analysis (DTA) and found to be 1568 K ± 5 K (1295 °C).

NdBO₃ has a eutectic reaction with NdB₃O₆ where the eutectic temperature was found to be 1416 K (1143 °C) by Levin[6] and 1423 K ± 2 K (1150 °C) by Goryunova.[8] NdB₃O₆ has a monotectic reaction with liquid B₂O₃ at 1421 K ± 5 K (1148 °C) according to Levin et al.[5] and 1427 K ± 1 K (1154 °C) according to Goryunova.[8] Levin et al. used the QM for all their measurements while Goryunova used DTA. Ji et al.[7] found Nd₄B₂O₉ to react eutectically with Nd₂O₃ and NdBO₃ where the eutectic temperatures were found by DTA to be 1508 K ± 5 K (1235 °C) and 1483 K ± 5 K (1210 °C), respectively.

There are no studies on the thermal properties of Nd₄B₂O₉. Ji and Xi[10] have investigated NdBO₃ and NdB₃O₆. In this study, they determined the Gibbs energies of NdOF, NdBO₃, and NdB₃O₆ using electromotive force (EMF) measurements. One separate EMF measurement cell was used to determine the Gibbs energy of NdOF, while two EMF cells were used to determine the Gibbs energies of NdBO₃ and NdB₃O₆ simultaneously. Each cell configuration was as follows: Cell-1 “O₂, MgO + MgF₂//CaF₂//NdOF + Nd₂O₃, O₂”, Cell-2 “O₂, MgO + MgF₂//CaF₂/ NdOF + NdBO₃ + NdB₃O₆, O₂”, and Cell-3 “Cr + Cr₂O₂//ZrO₂//NdBO₃ + NdB₃O₆ + B.” It should be noted that cell-2 was incorrectly written in the original manuscript of Ji and Xi (Nd₂O₃ was listed instead of NdBO₃), but according to their discussion in the manuscript, the cell configuration should be as described above. The measured Gibbs energy for NdOF from the first cell was used for determination of the Gibbs energies of NdBO₃ and NdB₃O₆.

The Gibbs energies of NdBO₃ and NdB₃O₆ derived by Ji and Xi[10] were initially tested for the thermodynamic assessment, but it was impossible to reproduce the phase diagram using these values. The main problem was that the entropy of formation reported by Ji and Xi was too large. In addition, the Gibbs energy they used for Cr₂O₃ is different from the current literature value.[11] A closer examination of the work by Ji and Xi also revealed that the expression for the EMF for the third cell is slightly off-set from their measured values. The revised expression of their cell voltage should be

Ji and Xi[10] did not investigate the chemical stability of their cells after the experiments. Careful examination of the EMF cell configurations of Ji and Xi showed that their EMF “Cell-3” may be thermodynamically unstable for determination of the targeted cell reaction. A recent assessment of the neodymium-boron system by Van Ende and Jung[12] was combined with the Gibbs energies measured by Ji and Xi for NdBO₃ and NdB₃O₆. The calculated equilibria showed that NdBO₃ and NdB₃O₆ are stable in equilibrium with NdB₆ in the temperature range where Ji and Xi investigated the Gibbs energy, instead of pure boron as assumed by them. This means that there is a very high probability that the EMF measurements were not performed as they originally designed them. Considering that NdB₆ is the stable phase instead of B, their cell reactions were in the present study re-evaluated as

To keep the internal consistency of the FactSage database, the Gibbs energy of NdB₆ was taken from Van Ende and Jung,[12] and the Gibbs energy of Cr₂O₃ was taken from Degterov and Pelton.[11] The resulting Gibbs energies of formation of NdBO₃ and NdB₃O₆ from pure Nd₂O₃(s) and B₂O₃(l) were found to be These Gibbs energies are more negative than those originally estimated by Ji and Xi.[10] It should be noted that these evaluations are only based on the thermodynamic reactions. For the real cell reactions, however, kinetics is involved—hence it is not possible to make sure that these revised reactions occurred in their actual experiments. Therefore, even these revised data were not highly weighted in the present optimization.

In the present optimization, the liquid parameter, \( \Delta g_{{{\text{Nd}}^{3 + } {\text{B}}^{3 + } }} \), was roughly optimized first based on the liquidus of Nd₂O₃ and the miscibility gap in the B₂O₃-rich region. The Gibbs energies of solid stoichiometric compounds were subsequently optimized to roughly reproduce the re-evaluated Gibbs energies of compounds from the EMF data by Ji and Xi[10] and the phase diagram. The entropies of all stoichiometric compounds in the B₂O₃-Nd₂O₃ system were estimated using the Neumann–Kopp rule. This rule was also applied to estimate the heat capacity of the compounds since there are no heat capacity data available for any of them. Then, the value of \( \Delta H_{{298{\text{ K}}}}^{\text{o}} \) for NdBO₃ was adjusted to reproduce the phase diagram. Iterative adjustments of \( \Delta g_{{{\text{Nd}}^{3 + } {\text{B}}^{3 + } }} \) and \( \Delta H_{{298{\text{ K}}}}^{\text{o}} \) of compounds were done until the phase diagram was reproduced within the experimental uncertainty.

The optimized phase diagram from the present study is plotted in Figure 1 along with experimental data by Levin,[6] Ji et al.,[7] and Goryunova.[8] The optimized congruent melting temperature of NdBO₃ is 1885 K (1612 °C), matching the experimentally measured temperature by Levin et al.[6] The eutectic temperature between NdBO₃ and NdB₃O₆ was adjusted to be 1419 K (1146 °C), which is between the values found by Levin et al.[6] and Goryunova[8]. The same was done for the monotectic temperature, which was adjusted to 1423 K (1150 °C). This gave a melting point of NdB₃O₆ of 1423.5 K (1150.5 °C), which is a bit lower than the value of 1428 K (1155 °C) found by Levin et al.[6] The critical point of the miscibility gap has not been measured, and a tentative value of 1873 K (1600 °C) was set in the present optimization. The eutectic temperature between Nd₂O₃ and Nd₄B₂O₉ was adjusted to the value from Ji et al.[7] of 1508 K (1235 °C). The eutectic between Nd₄B₂O₉ and NdBO₃ from the optimized model was 1487 K (1214 °C), which is slightly higher than the value from Ji et al. of 1483 K (1210 °C). Finally, the melting point of Nd₄B₂O₉ from the optimization was 1519 K (1246 °C), which is significantly lower than the melting point of 1568 K (1295 °C) found by Ji et al.

The optimized Gibbs energies of formations of the stoichiometric NdBO₃ and NdB₃O₆ compounds from Nd₂O₃(s) and B₂O₃(l) are plotted in Figure 2. The original data from Ji and Xi[10] and the revised data from the present study are compared with the optimized results. The best reproduction of the phase diagram was achieved with a somewhat more negative Gibbs energy of NdBO₃ than the revised data from Ji and Xi at 1172 K (899 °C) (−62.6 vs −51.9 kJ mol⁻¹). For NdB₃O₆, the Gibbs energy in the present work was calculated to be almost half of the value measured by Ji and Xi[10] at 1172 K (899 °C) (−74.6 vs −122.9 kJ mol⁻¹). As shown in the phase diagram in Figure 1, NdBO₃ has the most stable congruent melting temperature. This means that most probably the Gibbs energy of formation of NdBO₃ in one mole of the Nd₂O₃-B₂O₃ system should have the lowest value. However, according to the experimental data by Ji and Xi, the gram mole Gibbs energy of formation of NdB₃O₆ has lower value than NdBO₃, which is highly unrealistic and could not reproduce the phase diagram data at all.

Very limited experimental data are available in the iron-saturated FeO-B₂O₃ system. One unpublished study by Kosh et al. is cited in the Slag Atlas.[13] In their study, the compound Fe₃B₂O₆ was indicated but it is not documented anywhere else. The compound FeB₂O₄ has been reported only as a high-pressure phase.[14,15] Block et al.[16] and Kawano et al.[17] reported the last compound indicated by Kosh et al. Fe₂B₂O₅, to be stable at standard atmospheric pressure. From the single crystal growth experiments by Kawano et al., it would be expected that the melting point of Fe₂B₂O₅ is between 1223 K and 1273 K (950°C and 1000 °C).

Kawano et al.[17] also observed that Fe₃BO₅ formed when they were on the FeO-rich side of Fe₂B₂O₅. It should be noted that Fe₃BO₅ also contains iron in the 3+ oxidation state. Kravchuk and Lazebnik[18] also observed Fe₃BO₅ in equilibrium with Fe₂B₂O₅ and iron. Kosh et al. did not indicate the compound FeB₄O₇ in their study, but it has been documented by Kravchuk and Lazebnik,[18] and Rumanova et al.[19] Kravchuk and Lazebnik obtained single crystals of FeB₄O₇ at 973 K (700 °C), and found it to be stable in the whole range from 523 K to 973 K (250 °C to 700 °C).

Dong et al.[20] studied the solid-phase equilibria at 903 K (630 °C) under 95 pct argon + 5 pct hydrogen atmosphere and found FeB₄O₇, FeB₂O₄, and Fe₃BO₅ to be the only existing phases by XRD. These results suggests that FeB₂O₄ may exist as a stable phase even at atmospheric pressure and that Fe₂B₂O₅ may not be stable at lower temperatures. Further studies should be conducted to investigate this, and these results were not used in the present study.

Only one study was found on the thermodynamic properties in the FeO-B₂O₃ system Fujiwara et al.[21] used electrochemical cell measurements to determine the activities of FeO and B₂O₃ at 1473 K, 1573 K, and 1673 K (1200 °C, 1300 °C, and 1400 °C) under iron saturation. They also determined the positions of the liquidus line of FeO and the miscibility gap on the FeO-rich side at these temperatures.

Figure 3 shows the optimized phase diagram of the iron-saturated FeO-B₂O₃ system. The liquid solution parameters of the iron-saturated FeO-B₂O₃ system were adjusted according to the activity measurements by Fujiwara et al.,[21] as shown in Figure 4. In addition, the phase boundaries found by Fujiwara et al. were used for the liquidus of FeO and miscibility gap in the B₂O₃-rich region. The heat capacities and entropies at 298 K (25 °C) of Fe₃BO₅, Fe₂B₂O₅, and FeB₄O₇ were estimated using the Neumann-Kopp rule due to lack of experimental data.

The enthalpy of formation of Fe₂B₂O₅ was adjusted to reproduce the expected melting point of approximately 1248 K (975 °C) from Kawano et al.[17] The enthalpy of formation of Fe₃BO₅ was adjusted to give a tentative melting point of 1373 K (1100 °C), which is low enough to keep Fe₂B₂O₅ as a congruently melting compound and high enough to keep Fe₃BO₅ and Fe₂B₂O₅ existing in equilibrium. Finally, the enthalpy of formation of FeB₄O₇ was adjusted to reproduce the stability up to 973 K (700 °C) found by Kravchuk and Lazebnik.[18]

The optimized phase diagram shows reasonable agreement with available data, but it should be noted that the available phase diagram data are very limited. It can be seen that the estimated diagram by Koch et al.[13] is quite different from the liquidus of FeO by Fujiwara et al.[21] In the present study, more weight was given to the data by Fujiwara et al. The experimental activity data of FeO are very well reproduced by the present optimization, as can be seen in Figure 4.

The phase equilibria of the Fe₂O₃-Nd₂O₃ system were first investigated by Katsura et al.,[25] and they found NdFeO₃ to be the only stable compound. Nielsen and Blank[26] determined the melting point of NdFeO₃ to be 2068 K ± 8 K (1795 °C) in air. That was the only melting point of this compound found in literature.

Katsura et al.[25] determined the Gibbs energy of NdFeO₃ using CO₂-H₂ gas equilibration and a solid electrolyte cell, which measured the oxygen partial pressure in the range from 1347 K to 1620 K (1200 °C to 1347 °C). In these experiments, they found NdFeO₃ to decompose to metallic iron and Nd₂O₃. This means that the three phase equilibrium of Fe + Nd₂O₃ + NdFeO₃ occurs in the range from 1347 K to 1620 K (1200 °C to 1347 °C), and no ferrous (Fe²⁺) oxide is involved in this decomposition reaction even at reducing conditions in the presence of metallic iron. Based on the experimental findings they could draw the ternary section of the Fe-Fe₂O₃-Nd₂O₃ system at 1473 K (1200 °C).[27]

The thermal properties of NdFeO₃ at somewhat lower temperatures were recently investigated by Parida et al.[28] They used a Calvet microcaliometer to measure enthalpy increments from 299 K to 1000 K (26 °C to 727 °C). From 1004 K to 1208 K (731 °C to 935 °C), they used a reversible EMF cell to measure the Gibbs energy, and by linear extrapolation to higher temperatures, they found good agreement with the measurements by Katsura et al.[25] Vorobev et al.[29] reviewed available experimental literature where they included one dataset from Russian literature. These data also agree relatively well with the measurements by Katsura et al.[25] and Parida et al.[28]

The calorimetry data by Parida et al.[28] were used for the heat capacity of NdFeO₃. The enthalpy and entropy of NdFeO₃ were also taken from the study by Parida et al. The Gibbs energy of NdFeO₃ used in the present study is presented in Figure 5 along with experimental data.

The model parameter of the liquid solution was optimized in order to reproduce the melting point of NdFeO₃ in air found by Nielsen and Blank[26] of 2068 K ± 8 K (1795 °C). Due to the lack of phase diagram data other than the melting temperature of NdFeO₃, a single parameter of \( \Delta g_{{{\text{Fe}}^{3 + } {\text{Nd}}^{3 + } }}^{\text{o}} \) was optimized. The optimized phase diagram of the Fe₂O₃-Nd₂O₃ system in air is plotted in Figure 6. Two eutectic temperatures of NdFeO₃ + Fe₃O₄ → L and NdFeO₃ + Nd₂O₃ → L are predicted at 1697 K and 1945 K (1424 °C and 1672 °C), respectively.

To the present authors’ knowledge, no experimental phase diagram data are available for the iron-saturated FeO-Nd₂O₃ system. Therefore, key phase diagram experiments were performed in the present study using the classical quenching method (QM) and the differential thermal analysis (DTA) technique.

The reagent chemicals were powders of Fe₂O₃ (99.998 pct, Alfa Aesar), Nd₂O₃ (99.99 pct, Alfa Aesar), and iron (≥99.9 pct, Alfa Aesar). These powders were weighed and mixed to give the targeted compositions with 50 pct excess iron. The reagent chemicals and prepared mixtures were stored in a desiccator filled with silica gel due to the hygroscopic nature of the oxides and the corrosion potential of iron. The moisture content in the reagent Fe₂O₃ was found to be negligible by checking the mass loss (0.09 pct) of a control sample after heating to 398 K (125 °C) in air for 24 hours. The mass loss from the reagent Nd₂O₃ was found to be 0.23 pct after heating to 1273 K (1000 °C) for 3 hours in air. The mixing of reagents for the FeO-Nd₂O₃ mixtures was done for 15 minutes in an agate mortar under 99.9 pct isopropanol. Iron crucibles with outer diameter 6 mm, inner diameter 4 mm, and height 18–20 mm were made from a 99.5 pct pure iron tube (one end was sealed by welding). The tubes were filled with approximately 200 mg of material before they were clamped and welded to sealed capsules.

Three different compositions were prepared: 40FeO-60Nd₂O₃, 60FeO-40Nd₂O₃, and 95FeO-5Nd₂O₃ (compositions in mole percent). The classical quenching experiments were carried out using a vertical tube furnace. In order to prevent oxidation of the iron capsules during the experiment, high-purity Ar gas (6N) was purged into the tube during the experiments. The capsules containing all three compositions were held at 1473 K (1200 °C) for 18 hours. Two samples of 40FeO-60Nd₂O₃ and 60FeO-40Nd₂O₃ were also held at 1673 K (1400 °C) for 6 hours. After targeted equilibration time, the capsules were quenched by dropping directly from the hot zone into a container with water. The capsules were subsequently mounted in epoxy and polished for EPMA. Small amounts of sample were also extracted for XRD analysis.

Sealed iron crucibles containing samples were used for DTA as well. Approximately, 100 mg of mixed material was filled in each iron crucible. These crucibles were made from 99.85 pct pure iron and had the same dimensions as the capsules used for the quenching experiments except for a lower height of 12 mm and a flat bottom. The crucible containing samples was first held at 1273 K (1000 °C) for one hour under 6N argon atmosphere to remove any hydrocarbons, moisture, hydroxide, or carbonates that could have been introduced or formed during mixing. The mass loss was typically 1 mg or less. The opening was then clamped and the crucibles were welded to sealed capsules. The sealed capsules were held at 1723 K (1450 °C) for one hour under argon atmosphere for premelting and homogenization before cooling back to room temperature. Then, the capsules were investigated by DTA using a Netzsch STA 449C Jupiter, where they were held in an alumina cup. The temperature measurements of this apparatus were calibrated against the melting point of gold. The capsules were heated under 98 pct argon + 2 pct hydrogen by 10 K min⁻¹ to 1723 K (1450 °C) and cooled by the same rate back to room temperature. Transition temperatures were determined as the extrapolated onset temperature of the exothermic and endothermic peaks. Eight different compositions in the iron-saturated FeO-Nd₂O₃ system were investigated by DTA.

The experimental results of quenching runs are summarized in Table II, and the results of DTA are summarized in Table III. The stoichiometry of phases after the quenching experiments were determined by EPMA and the phases were confirmed by XRD.

Figure 7 shows the microstructures of two quenched samples from the present study. The microstructure of the capsule containing 95FeO-5Nd₂O₃ after annealing at 1473 K (1200 °C) for 18 hours is shown in Figure 7(a). NdFeO₃ crystals are observed in equilibrium with FeO and iron. The capsules containing 40FeO-60Nd₂O₃ and 60FeO-40Nd₂O₃ still contained unreacted powders even after being held at 1473 K (1200 °C) for 18 hours. The capsules held at 1400 °C for 6 hours had NdFeO₃ in equilibrium with Nd₂O₃ and iron after quenching. The microstructure of the capsule containing 40FeO-60Nd₂O₃ is shown in Figure 7(b). Some regions where Nd₂O₃ and iron were intermixed were observed in between NdFeO₃ grains, as can be seen in Figure 7(b). This seems to happen due to the liquid phase decomposing to Nd₂O₃ and iron during cooling, as explained by the final optimized phase diagram of the Fe-Fe₂O₃-Nd₂O₃ system below. This also indicated that the quench was not rapid enough to form a glass from the liquid phase.

The optimized phase diagram of the iron-saturated FeO-Nd₂O₃ is calculated in Figure 8. As determined from the quenching experiment, there is only one intermediate phase in the FeO-Nd₂O₃-Fe system. Surprisingly, the intermediate phase is not in this section (no ferrous neodymium oxide phase exists), but NdFeO₃ where iron is in ferric state is existing here. That is, the ‘NdFeO₃ + Fe’ mixture is the stable phase in this FeO-Nd₂O₃ section as calculated in Figure 9. This result is consistent with the previous study by Katsura et al.[25] who measured the Gibbs energy of NdFeO₃ from a Fe + Nd₂O₃ mixture, which also led them to report the diagram of the Fe-Nd₂O₃-Fe₂O₃ system in their later study.[27]

The DTA results are also plotted in Figure 8. The extrapolated onset temperature during cooling is very close to the onset temperature during heating in the region between FeO and NdFeO₃. The eutectic temperature for FeO + NdFeO₃ → L was determined as the mean value of onset temperatures during heating and cooling. The mean temperature of all three compositions was 1511.4 K (1238.2 °C). For the compositions between Nd₂O₃ and NdFeO₃, the onset temperatures during cooling were higher than those during heating by 9.7 K on average. The reason for such discrepancy was not further investigated. In the present study, the average of heating and cooling was taken. The mean temperature of all four compositions was 1604.6 K (1331.5 °C). For the composition of 75FeO-25Nd₂O₃ (melting temperature of NdFeO₃), the mean transition temperature was 1615.3 K (1342.1 °C).

A small negative solution parameter was added to liquid FeO-Nd₂O₃ to adjust the phase diagram in accordance with the DTA measurements as shown in Figure 8. No adjustments were necessary apart from this to reproduce the phase diagram.