Phase Equilibrium Studies in the RE2O3-REF3-LiF System: Comparison
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Please note this is a comparison between Version 1 by Jinfa Liao and Version 2 by Catherine Yang.

The solubility of rare earth oxides in molten salt directly affects the selection of operational parameters in the electrolysis process. When the added amount of RE2O3 is less than its solubility, it leads to a decreased electrolytic efficiency. Conversely, an excessive amount of oxide is prone to settle at the bottom of the electrolytic cell, impeding smooth production. The RE2O3 solubility in the fluoride salt can be represented by the phase equilibrium of the RE2O3-REF3-LiF system. The isothermal lines in the primary phase field of rare earth oxide represent the solubility of the oxide in the fluoride salt at the corresponding temperature.

  • rare earth
  • molten salt electrolysis
  • phase equilibrium
  • solubility

1. Introduction

Rare earth metals and alloys are increasingly used in the field of new materials, and there is a strong market demand. Rare earth elements have unique physical and chemical properties due to their special electronic structures, such as excellent optical and electrical properties, magnetic properties, and active chemical properties. With the development of modern science and technology, REEs have become indispensable key materials for high-tech and novel functional materials [1][2][1,2].

In the process of producing rare earth metals through oxide–fluoride melt system electrolysis, REF3 and LiF form an electrolyte with a low melting point, low density, and high electrical conductivity. Under the action of electrical current, the dissolved RE2O3 is converted to rare earth metals and oxygen at the cathode and anode, respectively. As the electrolysis process progresses, the dissolved RE2O3 in the molten salt is continuously consumed, requiring continuous addition of RE2O3 to maintain a high concentration in the electrolyte [3][4][5][19,20,21]. When the amount of RE2O3 added to the molten salt is lower than its solubility, the electrolysis efficiency and productivity are low. Conversely, if the amount of RE2O3 added to the molten salt exceeds its solubility, the excess RE2O3, being denser than the REF3-LiF melt, tends to form deposits at the bottom of the electrolytic cell, increasing the cell resistance, affecting the metal purity, and even seriously impeding the smooth progress of production [6][7][22,23]. Therefore, the solubility of RE2O3 in the REF3-LiF-RE2O3 system provides the essential data for establishing a suitable feeding system in electrolytic production, playing an important role in improving electrolysis efficiency and maintaining the effective volume of the electrolytic cell. However, there have been significant differences in the solubility data of RE2O3 in the fluoride system, and the semi-empirical models developed based on these data have difficulty in accurately predicting the solubility of rare earth oxides [8][9][24,25].

2. Nd2O3-NdF-LiF System

Due to the importance of neodymium–iron–boron magnetic materials, there has been an increasing amount of research on the phase equilibrium of the Nd2O3-NdF-LiF system, which is relevant to the production of neodymium through molten salt electrolysis [10][11][59,60]. Solubility data of Nd2O3 in the NdF3-LiF system reported in the literature are summarized in Table 1. Figure 18 summarizes the solubility data of Nd2O3 in the NdF3-LiF system and annotates these data in the Nd2O3-NdF-LiF ternary phase diagram. It can be observed that large amounts of experimental data have been published in the range of 750–1200 °C and 60–90 wt.% NdF3. In the liquid phase, the concentration of Nd2O3 mostly remains below 5 wt.% and increases with the temperature and percentage of NdF3. However, the solubility data published by Wu et al. [12][34] significantly deviate from other data, with a decrease in Nd2O3 concentration as NdF3 increases, indicating the unreliability of these data. The abundance of experimental data shown in Figure 18 indicates the importance of phase equilibrium research in the Nd2O3-NdF-LiF system, both in terms of theoretical significance and practical applications, which has attracted numerous researchers to invest substantial efforts into studying this area. However, there are significant differences and even contradictions among these experimental data [12][13][14][15][16][17][18][19][20][21][22][23][34,35,36,37,38,39,55,56,57,58,61,62], as detailed in the following two figures.
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Figure 18.
Liquidus points on the phase diagram of the NdF
3
-LiF-Nd
2
O
3
system in the NdF
3-rich corner (experimental data from [12][13][14][15][16][17][18][19][20][21][22][23]).
-rich corner (experimental data from [34,35,36,37,38,39,55,56,57,58,61,62]).
Table 1.
Solubility of Nd
2
O
3
in NdF
3
-LiF fluoride melts.
wt.% mol% Normalization (wt.%) T.  
NdF3 LiF Nd2O3 NdF3 LiF Nd2O3 NdF3 LiF Nd2O3 (°C) Ref.
58 42 0.54 15 85 0.08 57 42 0.54 800 [13][35]
58 42 0.75 15 85 0.12 57 42 0.74 850 [13][35]
58 42 0.82 15 85 0.13 57 42 0.81 860 [13][35]
58 42 0.96 15 85 0.15 57 42 0.95 900 [13][35]
63 37 1.68 18 82 0.29 62 36 1.65 1000 [16][38]
63 37 2.27 18 82 0.40 62 36 2.21 1050 [16][38]
63 37 2.57 18 82 0.45 61 36 2.51 1100 [16][38]
65 35 2.07 19 81 0.37 63 35 2.03 800 [21][58]
66 34 1.83 20 80 0.34 65 33 1.8 1000 [14]
Figure 29 represents the solubility data of Nd2O3 in the NdF3-LiF molten salt at 1100 and 1150 °C, plotted on the ternary phase diagram. According to all the available literature, at the same NdF3/LiF ratio, the solubility of Nd2O3 increases with increasing temperatures, and connecting the solubility data at the same temperature should obtain a smooth liquidus line (isotherm). However, it is difficult to determine a consistent liquidus line at 1100 and 1150 °C, based on the data shown in the figure. Some data points indicate a higher solubility of Nd2O3 at 1100 °C compared with 1150 °C. The estimated 1100 and 1150 °C isotherms are shown in the figure. These contradictory data not only pose challenges for production technicians but also cannot be used for developing thermodynamic databases.
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Figure 29.
Liquidus points and estimated 1100 and 1150 °C isotherms on the phase diagram of NdF
3
-LiF-Nd
2
O
3 system (experimental data from [14][15][16][17][20]).
system (experimental data from [36,37,38,39,57]).
Figure 310 shows the solubility data of Nd2O3 in the NdF3-LiF system on a pseudo-binary phase diagram of Nd2O3-(NdF3 + LiF), with NdF3/LiF ratios of 2.3 and 3.3. It can be observed that the liquidus temperatures increase sharply with an increase in the concentration of Nd2O3. For every 1 wt.% increase in Nd2O3, the liquidus temperature rises by approximately 150 °C. In other words, the solubility of Nd2O3 is not sensitive to temperature, as increasing the temperature by 150 °C only results in a 1 wt.% increment in Nd2O3 solubility. The current consensus in the research is that, at the same temperature, a higher NdF3/LiF ratio leads to a greater solubility of Nd2O3. From the figure, it can be observed that at lower temperatures (800–900 °C), the solubility of Nd2O3 in NdF3/LiF = 3.3 is higher than that in NdF3/LiF = 2.3. However, at higher temperatures (1100–1150 °C), the solubility of Nd2O3 in NdF3/LiF = 3.3 is lower than that in NdF3/LiF = 2.3, indicating a significant discrepancy in the experimental data among different researchers. The dashed lines in the figure represent the estimated liquidus lines corresponding to NdF3/LiF ratios of 2.3 and 3.3, based on the experimental data.
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Figure 310.
Pseudo-binary phase diagram of NdF
3
-(LiF + Nd
2
O
3
) at fixed NdF
3/LiF of 2.3 and 3.3 [13][14][20].
/LiF of 2.3 and 3.3 [35,36,57].

3. La2O3-LaF-LiF System

Figure 411 presents the solubility data of La2O3 in the LaF3-LiF system annotated on a ternary phase diagram based on the summary of the literature data shown in Table 2. Within the range of 948–1250 °C and 60–90 wt.% LaF3, the solubility of La2O3 in the LaF3-LiF system ranges from 1.3 to 3.4 wt.%. With an increase in temperature and LaF3, there is a tendency for the solubility of La2O3 to increase, but the change is not significant [14][24][25][26][36,40,41,42].
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Figure 411.
Liquidus points shown on the phase diagram of LaF
3
-LiF-La
2
O
3
system in LaF
3-rich corner (experimental data from [14][24][25][26]).
-rich corner (experimental data from [36,40,41,42]).
Table 2.
Solubility of La
2
O
3
in LaF
3
-LiF fluoride melts.
wt.% mol% Normalization (wt.%) T.  
LaF3 LiF La2O3 LaF3 LiF La2O3 LaF3 LiF La2O3 (°C) Ref.
65 35 1.4 20 80 0.26 64 35 1.38 950 [24][40]
65 35 1.58 20 80 0.29 64 34 S 1000 [24][40]
65 35 1.78 20 80
[
36
]
0.33 64 34 1.75 1050 [24][40]
65 35 1.94 20 80 0.36 64 34 1.9 1100 [24][40]
65 35 2.1 20 80 0.39 64 34 2.06 1150 [24][40] 66 34
65 35 1.79 20 80 0.33 64 34 1.76 1000 [14][36]
65 35 1.87 20 80 0.35 64 34 1.84 1050 [14][36]
65 35 1.94 20 80 0.36 64 34 1.9 1100 [14][36]
65 35 2.01 20 80 0.37 64 34 1.97 1150 [14][36] 1.92 20 80 0.35 65 33 1.88 1050
70 30 1.54 24[ 76 0.3214 69][ 3036]
1.52 950 [24][40]
48] 70 30 1.76 24 76 0.36 69 29
65 35 0.5 25 75 0.12 65 351.73 1000 [24 0.5 831 [28][63]
65 35 1.79 25 75 0.45 64 34 1.76 850 [29][48]
65 35 0.59 25 75 0.15 65 35 0.59 850 [28][63]
65 35 0.8 25 75 0.20 65 35 0.79 882 [28][63]
65 35 0.8 25 75 0.20 65 35 0.79 900 [28][63]
65 35 2.11 25 75 0.53 64 34 2.07 900 [29][48]
65 35 0.88 25 75 0.22 65 34 0.87 900 [28][63]
65 35 1.65 25 75 0.41 64 34 1.62 1000 [28][63]
65 35 2.96 25 75 0.75 63 34 2.87 1000 [29][
90
10
3.2
54
46
1.19
87
10
3.1
1200
[
24
]
[
40
]
90 10 3.5 54 46 1.30 87 10 3.38 1250 [24][40]
Figure 512 annotates the solubility data of La2O3 on a pseudo-binary phase diagram of La2O3-(LaF3 + LiF), with the LaF3/LiF weight ratios of 1.9 and 3.2. It can be observed that the liquidus temperature increases sharply with an increase in the concentration of La2O3. For every 1 wt.% increase in La2O3 in the melt, the liquidus temperature rises by approximately 300 °C. In other words, the solubility of La2O3 is not sensitive to temperature, as increasing the temperature by 300 °C only results in a 1 wt.% increment in La2O3 solubility. At the same temperature, a higher LaF3/LiF weight ratio leads to a greater solubility of La2O3, but scattered data make it difficult to obtain precise liquidus lines. The dashed lines in the figure represent the estimated liquidus lines corresponding to LaF3/LiF weight ratios of 1.9 and 3.2, based on the experimental data.
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Figure 512.
Pseudo-binary phase diagram of (LaF
3
+ LiF)-La
2
O
3
at fixed LaF
3/LiF of 1.9 and 3.2 [14][24][25].
/LiF of 1.9 and 3.2 [36,40,41].

4. Y2O3-YF3-LiF System

Figure 613 presents the solubility data of Y2O3 in the YF3-LiF system annotated on a ternary phase diagram, and the data from the literature are summarized in Table 3 [27][28][47,63]. Within the range of 725–1009 °C and 60–90 wt.% YF3, the solubility of Y2O3 in the YF3-LiF system ranges from 0.45 to 5.09 wt.%. Data published by the same group of researchers indicate that the solubility of Y2O3 in YF3-LiF increases with temperature and YF3. However, as can be seen from the figure, there are significant differences in the data from different researchers. Figure 714 annotates partial solubility data of Y2O3 on a pseudo-binary phase diagram of Y2O3-(YF3 + LiF), with YF3/LiF weight ratios of 1.9 and 5.6. From the figure, it can be observed that the liquidus temperature increases with an increase in the concentration of Y2O3, but the extent of increase is not as significant as in the La2O3-LaF3-LiF and Nd2O3-NdF3-LiF systems. Therefore, the solubility of Y2O3 in the YF3-LiF system increases rapidly with increasing temperature. In principle, at the same temperature, a higher YF3/LiF ratio leads to a greater solubility of Y2O3, but there are significant differences in the data from the two groups of researchers in the figure. The dashed lines in the figure represent the estimated liquidus lines corresponding to the YF3/LiF weight ratios of 1.9 and 5.6, based on the experimental data.
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Figure 613.
Liquidus points shown on the phase diagram of YF
3
-LiF-Y
2
O
3
system in YF
3
-rich corner.
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Figure 714.
Pseudo-binary phase diagram of (YF
3
+ LiF)-Y
2
O
3
at fixed YF
3/LiF of 1.9 and 5.6 [28][29].
/LiF of 1.9 and 5.6 [48,63].
Table 3.
Solubility of Y
2
O
3
in YF
3
-LiF fluoride melts.
wt.% mol% Normalization (wt.%) T.  
YF3 LiF Y2O3 YF3 LiF Y2O3 YF3 LiF Y2O3 (°C) Ref.
58 42 1.17 20 80 0.26 58 41 1.16 725 [29][48]
58 42 1.25 20 80 0.28 58 41 1.23 750 [29][48]
58 42 1.48 20 80 0.33 58 41 1.46 800 [29][48]
58 42 1.87 20 80 0.42 57 41 1.84 875 [29][48]
58 42 2.09 20 80 0.47 57 41 2.05 920 [29][48]
58 42 2.35 20 80 0.53 57 41 2.3 950 [29][48]
58 42 2.87 20 80 0.65 57 40 2.79 1000 [29][48]
65 35 1.28 25 75 0.32 64 34 1.26 750 [29][48]
65 35 0.45 25 75 0.11 65 35 0.45 810 [28][63]
65 35 1.63 25 75 0.41 64 34 1.6 825 [29][
66 34 2.03 20 80 0.37 65 33 1.99 1100 [14][36]
][40] 66 34 2.12 20 80 0.39 65
70 30 1.9433 2.08 1150 [ 2414][ 7636]
0.40 69 29 1.9 1050 [24][40] 68 32 1.96 22 78
700.38 67 31 1.92 1000 [13][35]
30 2.2 24 76 0.45 68 29 2.15 1100 [24][40] 68 32 2.59 22 78 0.50 66 31 2.52 1050 [13][35]
70 30 2.35 24 76 0.49 68 29 2.3 1150 [24][40] 68 32 2.73 22 78 0.53 66 31 2.65 1100
72 28 1.99[13][35]
25 75 0.43 70 28 1.95 948 [25][41] 70 30 9.24 23 77 1.96 64 28 8.46 850 [
7212] 28[ 2.08 25 75 0.45 7034]
28 2.04 968 [25][41] 70 30 1.4 23 77 0.28 69
72 28 1.6430 1.38 850 [22][61]
25 75 0.35 70 28 1.61 980 [26][42] 70 30 4.4 23 77
720.90 28 2.17 25 7567 29 4.21 1050 0.47[22][61]
70 28 2.12 988 [25][41] 70 30 0.68 23
72 28 2.0177 0.14 25 75 0.4369 30 0.68 70 28750 1.97[16] 1000[38]
[14][36] 48 70 30
720.8 23 77 0.16 2869 2.13 25 75 0.4630 0.79 800 [16][38]
] 70 28
65 35 1.65 25 75 0.41 64 342.09 1050 1.62[14] 1000[36] [28] 70 30
[63] 72 280.92 23 77 0.18 2.2669 25 75 0.49 7030 0.91 850 [16][38]
28 2.21 1100 [14][36
75 25 1.69 35 65 0.51 74 24 1.66] 1000 [28][63] 70 30 1.11 23 77 0.22 69 30
72 28 2.37 25 75 0.51 701.1 900 28 2.32 1150[16][38
79]
[14][36] 21 1.72 40 60 0.57 78 21 1.69 750 [29][48] 70 30 2.8 23 77 0.57 68
75 25 1.65 2829 72 0.38 74 252.72 1100 [ 1.6220 950][57]
[
7924][ 2140] 2.14 40 60 0.71 77 21 2.1 800 [29][48] 70 30 3.1 23 77 0.63 68 29 3.01 1150
75 25 1.95 28 72 0.45 74[20 25] 1.91[
79100057]
[24][40 21] 2.26 40 60 0.75 77 21 2.21 825 [29][48] 70 30 3.5 23 77 0.71
75 2568 29 3.38 2.23 28 72 0.52 73 24 2.18
791200 [20] 21[57]
1050 [ 2.9324 40] 60[ 0.9840] 77 20 2.85 900 [29] 72 28 2.07 25 75 0.44
[48] 75 25 2.571 28 72 0.58 7327 2.03 1000 24 2.44[14][36]
791100 [ 21 3.5224][40] 40 60 1.18 76 20 3.4 950 [29][48] 72 28 2.17 25
7575 0.46 71
7927 252.12 2.65 28 72 0.621050 73 24 2.58 1150[14][36]
21[24][40] 4.9 40 60 1.66 75 20 4.67 1000 [29][48] 72 28 2.29 25 75 0.48 70 27 2.24 1100 [14][36
76]
24 2.23
85 15 3.7230 70 0.53 50 50 1.4575 23 2.18 82 15 3.591000 [14][ 900 [29][48] 72 28 2.4 25 75 0.51 70 27 2.34 1150 [14][36]
36]
76 24 2.12
85 15 1.1930 70 0.50 75 23 502.08 1004 [25][41] 50 0.46 84 15 1.18 900 [28][63] 73 27 2.18 26 74 0.47 71 26 2.14 1000
76 24 2.3 30[ 70 0.5516 75][ 2338]
2.25 1024 [25][
85 1541 1.41 50 50] 0.54 84 15 1.39 929 [28][63] 73 27 2.79 26 74 0.60 71 26 2.71 1050 [16][38]
76 24 1.81 30 70 0.43 75 23 1.78 1035 [26][42]
85 15 1.51 50 50 0.58 84 15 1.49 943 [28][63] 73 27 3.08 26 74 0.67 71
76
8524 2.36 15 4.4526 2.99 1100 [ 3016][ 7038]
0.56 75 23 2.31 1044 [ 50 50 1.7525][41] 81 14 4.26 950 [29][48] 75 25 7.2 28 72
761.69 70 23 6.72 800
85[12][34]
24 152.35 30 70 0.56 75 23 2.3 1050 [14 1.61 50 50] 0.62[ 8436] 15 1.58 964 [28][63] 75 25 8.3 28 72 1.96 69 23 7.66 850 [12]
85[34]
76 24 2.48 30 70 15 1.78 50 500.59 75 23 0.69 83 152.42 1100 [14][36] 1.75 974 [28][63] 75 25 9.4
85 15 1.8828 72 2.24
76 2469 2.58 30 70 0.6223 8.59 900 74 23[12][34]
2.52 1150 [14] 50 50[ 0.7336 83 15 1.85] 988 [28][63] 77 23
80 201.45 30 70 2.31 350.34 76 23 1.43 65860 0.61 78
85 15 5.36 50 50 2.1120 2.26[13][35]
1050 [ 8124][40] 14 5.09 1000 [29] 77 23 1.61 30 70 0.38 76
[48] 80 20 2.5323 1.58 900 [13][35]
35 65 0.67 78 20 2.47 1100 [
8524][ 1540] 1.98 50 50 0.77 83 15 1.94 1000 [28][63] 77 23 2.27 30 70 0.54 75 23
80 20 2.752.22 1000 35 65
85 150.73 2[ 5014][ 5036]
78 19 2.68 1150 [24][40 0.77 83 15] 1.96 1000 [28][63] 77
8023 2.39 30 70 0.57 75 23 2.33 1050 [14][ 2036]
2.93 35 65 0.78 78 19 2.85 1200 [24][40] 77
85 15 2.09 50 50 0.81 83 15 2.05 1009 [28][63] 23 2.51 30 70 0.60 75 23 2.45 1100 [14
91 9] 2.2 64 36[36]
1.02 89 9 2.15 1000 [28][63] 77 23 2.62 30 70 0.63 75 23 2.55 1150 [14][36]
78 22 2.45 31 69
80 20 3.06 35 65 0.82 78 19 2.97 1250 [24][40]
80 20 2.56 35 65 0.68 78 19 2.5 1050 [14][36] 0.60 76 21 2.39 1000 [16][38]
78
80 20 2.15 35 65 0.57 79 19 2.1 1062 [25][41] 22 2.3 31
80 2069 0.56 2.45 35 6576 22 0.65 78 192.25 1050 [ 2.3916 1082][38]
[25][41] 78 22 3.52 31
80 20 1.9769 0.87 75 21 353.4 65 0.52 79 191100 [16][38]
1.93 1090 [14][36] 80 20 7.29 34 66 1.95
80 2075 19 6.79 2.69 35 65 0.71 78 19 2.62850 [12][34]
1100 [14][36] 81 19 2.49 35 65 0.66
80 20 2.5879 35 65 0.69 7819 2.43 1000 19 2.52[14][36]
1102 [25][41] 81 19 2.62 35 65 0.70 79
80 20 2.7819 2.55 1050 [14][36]
35 65 0.74 78 19 2.7 1150 [14][36] 81 19 2.73 35 65
830.73 17 2.14 39 6179 19 2.66 1100 0.62 81[ 17 2.114 1100][36]
[15][37] 81
8319 2.78 35 65 170.74 2.73 39 61 0.7979 19 2.7 81 161150 2.66[14] 1050[36]
[14][36] 83 17 1.1 39 61 0.31 82 17 1.09 957
83 17 2.85 39[ 61 0.8318 81][ 1655]
2.77 1100 [14][36] 83 17
83 171.75 39 61 0.49 81 17 1.72 979 [ 3.0118][ 3955]
61 0.88 81 16 2.92 1150 [14][36] 83 17 3.4 39 61 0.97 80
85 15 2.6817 3.29 1053 [ 4318][ 5755]
0.83 83 15 2.61 1100 [24][40 83 17 3.04 39 61 0.86 81 16 2.95 1000 [16][38]
83 17 3.36 39 61 0.96 80 16 3.25 1050 [16][38]
83 17 2.45 39 61 0.69 81 17 2.39 1100 [15][37]
83 17 4.09 39 61 1.17 80 16 3.93 1100 [16][38]
]
85 15 2.85 43 57 0.88 83 15 2.77 1150 [24][40]
85 15 3.08 43 57 0.96 82 15 2.99 1200 [24][40]
85 15 3.25 43 57 1.01 82 15 3.15 1250 [24][40] 84 16 2.7 40 60 0.79 82 16 2.63 1000 [14][36]
84 16 2.81 40 60 0.82 82 16 2.73 1050 [14][36]
84 16 2.92 40 60 0.86 81 16 2.84 1100 [14][36]
84 16 3.05 40 60 0.90 81 16 2.96 1150 [14][36]
85 15 3.28 42 58 1.00 82 15 3.18 1050 [17][39]
85 15 3.88 42 58 1.18 82 15 3.74 1100 [17][39]
85 15 4.54 42 58 1.39 81 14 4.34 1150 [17][39]
88 12 3.82 49 51 1.29 85 12 3.68 1050 [16][38]
88 12 4.54 49 51 1.54 84 11 4.34 1100 [16][38]
88.5 11.5 3.74 50 50 1.29 85 11 3.61 1050 [17][39]
88.5 11.5 4.23 50 50 1.46 85 11 4.06 1100 [17][39]
88.5 11.5 4.71 50 50 1.63 85 11 4.5 1150 [17][39]
88.5 11.5 7.4 51 49 2.66 82 11 6.89 1200 [23][62]
90 10 4.2 54 46 1.54 86 10 4.03 1100 [20][57]
90 10 4.4 54 46 1.61 86 10 4.21 1150 [20][57]
90 10 4.7 54 46 1.73 86 10 4.49 1200 [20][57]
92 8 4.2 60 40 1.67 88 8 4.03 1050 [17][39]
92 8 4.62 60 40 1.84 88 8 4.42 1100 [17][39]
92 8 4.97 60 40 1.99 88 8 4.73 1150 [17][39]

5. Solubility Model of RE2O3-REF3-LiF System

High-temperature phase equilibrium experiments not only consume a significant amount of time and funding, as mentioned above, they also yield substantial variations in the data among different researchers and experimental methods, which brings confusion to the applications of these data. Various thermodynamic models, such as FactSage [30][31][64,65], MTDATA [32][66], and Thermo-Calc [33][67], have been developed to predict the thermodynamic properties of slags, molten salts, and alloys. The solubility of rare earth oxides in molten salts can theoretically be predicted using thermodynamic models. However, the construction of the core database for these thermodynamic models relies heavily on a large amount of experimental data. The lack of accurate thermodynamic data for rare earth oxide–molten salt systems currently hinders the ability of existing thermodynamic models to predict their properties, including solubility. Researchers have attempted to establish semi-empirical models [8][9][24,25] to predict the solubility of rare earth oxides in molten salts based on available experimental data. Figure 815 summarizes the solubility of various rare earth oxides in fluoride salts, where Figure 815a shows the relationship between solubility and temperature, and Figure 815b demonstrates the relationship between the logarithm of solubility and the reciprocal of temperature [9][25]. It can be observed that the solubility of rare earth oxides in molten salts generally increases with temperature but with significant variations among different systems. For most systems, the logarithm of solubility exhibits a linear relationship with the reciprocal of temperature.
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Figure 815. Solubility of rare earth oxides (sREO) in fluoride melts as a function of temperature: (a) solubility vs. temperature and (b) logarithm of solubility vs. reciprocal of the temperature [9][25].
Figure 916 illustrates the relationship between the solubility of Nd2O3 and Y2O3 and the concentration of rare earth fluoride (REF3). Within the studied concentration and temperature ranges, the solubility of the oxides increases with an increase in the concentration of REF3 in the molten salt. At higher temperatures, the solubility of rare earth oxides is more sensitive to the concentration of REF3 in the molten salt. As shown in Figure 916, the solubility data for different rare earth oxides in fluoride salts exhibit considerable variability, making it difficult to be expressed by a unified model. Guo et al. [9][25] proposed semi-empirical prediction models for each rare earth oxide with available solubility experimental data. For example, they developed a solubility prediction model for Nd2O3 in the NdF3-LiF-(MgF2/CaF2) system using the data from three articles [12][13][17][34,35,39]. The comparison between the predicted and experimental results is shown in Figure 107, with an average error of 8%. However, the error can reach 30% for low solubility cases.
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Figure 916.
Solubility of rare earth oxides in fluoride melts as a function of REF
3 content (data from Refs. [13][17][28][29]).
content (data from Refs. [35,39,48,63]).
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Figure 107.
Relative error between the experimental data and the data calculated with the current model for Nd
2
O
3 solubility [9].
solubility [25].
As shown in Figure 18, the solubility data of Nd2O3 in the NdF3-LiF system reported in the literature are much more extensive than those used by Guo et al. [9][25]. Figure 118 compares the solubility calculated by Guo et al.’s model [9][25] with all the experimental solubility data of Nd2O3 in the NdF3-LiF system. It can be seen that the solubilities calculated by Guo et al.’s model show a big difference compared with the experimental data in low NdF3 fluoride salt.
Metals 14 00314 g018
Figure 118.
Nd
2
O
3
solubility in melts with different NdF
3 concentration and at different temperatures (data from references [12][13][14][16][17][20][22]).
concentration and at different temperatures (data from references [34,35,36,38,39,57,61]).
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