Phase Equilibrium Study of Rare Earth Oxide–Fluoride Salt System: A Review

Abstract

The applications of rare earth metals and alloys are becoming increasingly widespread and there is a strong market demand. Currently, most of the production enterprises adopt the fluoride–oxide system for electrolytic preparation of rare earth metals and alloys. 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. This paper outlines the research methods and experimental results on the phase equilibria of the RE₂O₃-REF₃-LiF system. The characteristics and existing problems in the current phase equilibrium study are analyzed. The solubility data of RE₂O₃ are expressed in the forms of ternary and pseudo-binary phase diagrams of the RE₂O₃-REF₃-LiF system, providing theoretical guidance for the establishment of an accurate and reliable rare earth electrolysis system database and the optimization of electrolytic processes.

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].

In recent years, with the momentum of technological innovation and the ongoing revolution in global manufacturing, there have been significant changes in the consumption structure of REEs, with an increasing production of rare earth metals such as La, Ce, Nd, Pr, and Y [3,4,5]. The production of rare earth metals and alloys is an important component of the rare earth industry. Rare earth metals, being highly reactive, are usually produced from chloride or oxide raw materials using two major methods: metallothermic reduction and molten salt electrolysis. Compared with thermal reduction, molten salt electrolysis is a relatively economical method as it allows continuous production and easy control of product quality. It is currently widely used in the production of single rare earth metals, such as La, Ce, Pr, and Nd, and mixed rare earth metal alloys [6,7,8,9].

The production of rare earth metals and alloys by molten salt electrolysis can be divided into two categories: a chloride melt system and an oxide–fluoride melt system. The chloride melt system produces a large amount of generated toxic fumes such as Cl₂ during the electrolysis process and has higher energy consumption, which does not comply with the low-carbon environmental concept. Moreover, the high vapor pressure of chloride melts and low metal recovery severely limit the development of chloride electrolysis, leading to the gradual elimination of this method domestically and internationally [10,11,12].

The technology for producing rare earth metals through oxide–fluoride melt system electrolysis has developed rapidly after resolving the corrosion resistance of fluoride salt on electrolytic cell materials. The electrolysis process achieves automated temperature control, feeding, and vacuum metal suction [13,14,15]. This process has stable raw materials, low pollution to the atmosphere, high current efficiency, and high rare earth recovery rate, which further promotes its technological development. After 2000, scaling up and automation of electrolytic cells have reached industrialized stable production levels [16]. The fluoride electrolysis system uses a LiF-REF₃ mixture as the electrolyte (with the content of REF₃ near the LiF-REF₃ eutectic point) and rare earth oxide as the feed material. A small amount of RE₂O₃ is dissolved in the fluoride electrolyte, and is reduced to rare earth metals at the cathode, while oxygen is released at the anode, reacting with the carbon anode to form CO₂ or CO. Although fluoride salts have a high melting point and strong corrosiveness, optimized electrolytic cells can avoid problems such as low metal recovery and difficulty in slag–metal separation. Moreover, they do not produce harmful chlorine gas. Therefore, most production companies currently use the oxide–fluoride electrolysis system to prepare rare earth metals [17,18].

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 [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 [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 [24,25].

A phase diagram is a graphical representation that quantitatively describes the states of phases in a system with respect to temperature, pressure, and composition [26]. Phase diagrams provide a visual reflection of thermodynamic information such as liquidus lines and primary crystal phases for different components in a system [27]. Pseudo-ternary and pseudo-binary phase diagrams have been widely applied in various fields such as metallic materials, ceramics, cement, refractories, and metallurgical industries. The solubility of rare earth oxides in the fluoride system is essentially the content of RE₂O₃ in the liquid phase saturated with the primary phase. Expressing the solubility of rare earth oxides in the fluoride system using phase diagrams not only allows the summary and comparison of the data obtained under various conditions but also enables the establishment of a thermodynamic database for the REF₃-LiF-RE₂O₃ system based on experimental studies. The use of phase diagrams of the REF₃-LiF-RE₂O₃ system helps in selecting appropriate compositions of molten salts (REF₃:LiF) and electrolysis temperatures for molten salt electrolysis as needed. It also provides a theoretical basis for developing reasonable process routes for the production and resource recovery of rare earth metals and alloys [28,29,30,31,32,33].

In summary, the study of the phase equilibria of the rare earth oxide–fluoride melt systems is of great significance for establishing a thermodynamic database for molten salt electrolysis systems. The accurate and reliable information will be used for the optimization of the existing processes, development of new processes, and comprehensive utilization of rare earth molten salt electrolysis slags. This article provides a systematic summary and comparison of the research methods and experimental data on the phase equilibria of the RE₂O₃-REF₃-LiF system, laying the foundation for standardized research methods and expression formats for the solubility of rare earth oxides in the fluoride system.

2. Methodology for the Phase Equilibrium Study of the RE₂O₃-REF₃-LiF System

2.1. Isothermal Saturation Method

The isothermal saturation method is widely used to determine the solubility of RE₂O₃ in REF₃+LiF molten salt at a given temperature by adding excess RE₂O₃ powder to a known proportion of REF₃ + LiF melt and analyzing the concentration of RE₂O₃ in the supernatant after reaching equilibrium [34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54]. Figure 1 shows the schematic diagram of solubility determination using the isothermal saturation method. This method is favored due to its ease of operation and direct measurement of solubility data. However, the isothermal saturation method involves a series of issues, including equilibrium time, sampling, analysis, and side reactions.

In theory, REF₃ + LiF molten salt has relatively low viscosity, and stirring is often employed during the measurement of RE₂O₃ solubility to accelerate the reaction. Hu et al. [39] demonstrated through experiments and calculations that, under the stirring condition of 150 r/min at 1030 °C, Nd₂O₃ can reach dissolution equilibrium in a 90% NdF₃-9.5% LiF-0.5% RE₂O₃ solution within 30 min. Figure 2 illustrates the time required for Nd₂O₃ and La₂O₃ to reach saturation in the NdF₃-LiF and NaF₃-LiF system under different conditions, respectively. The relationships between the dissolved La₂O₃ and time in the %LiF-%NaF (680 °C) [46] and between the dissolved Nd₂O₃ and time in the %NdF₃-%LiF system (800 °C) are shown in the figure. It can be clearly seen that saturation is reached in 3 h for Nd₂O₃ at 800 °C [35] and in 8 h for La₂O₃ at 680 °C [46]. This indicates that the dissolution of RE₂O₃ in REF₃-LiF molten salt is complex.

In order to increase the dissolution rate of RE₂O₃, finer powders are typically added, which can result in the slow settling of undissolved oxide particles. During sampling of the supernatant, there is a possibility of inadvertently collecting and analyzing undissolved solid RE₂O₃, leading to a false result. Some researchers [19,37] have realized this issue and conducted X-ray diffraction (XRD) analysis of the cooled salt to confirm the presence of undissolved RE₂O₃ in the supernatant. However, the sensitivity of XRD is insufficient to detect undissolved RE₂O₃ in the supernatant. SEM observation could provide direct evidence. However, it was not used in these studies.

Most of the studies employed inductively coupled plasma (ICP) or chemical titration methods to analyze the concentration of rare earth elements in the supernatant after the equilibration, and then compared it with the initial REF₃-LiF molten salt to determine the concentration of the dissolved oxide [46,47,49]. Some researchers directly analyzed the oxygen content in the supernatant and converted it to the concentration of the rare earth oxide [40]. These analytical methods assumed that there were no side reactions during the dissolution process, and that the total amount of Li and F in the molten salt remained constant. The increase in the rare earth ion concentration after the addition of oxide corresponded to its solubility. However, several studies [36,37,42] have found that, when excessive RE₂O₃ was added to the molten salt, the concentration of rare earth ions in the liquid phase decreased. As shown in Figure 3a,b, the concentrations of the rare earth ions at their maximum determined the solubility of the rare earth oxides. This behavior of RE³⁺ variation introduced significant uncertainty in the results obtained from the isothermal saturation method.

2.2. Primary Crystallization Temperature Method

The primary crystallization temperature method involves complete melting of the RE₂O₃-REF₃-LiF mixture, followed by the determination of the crystallization temperature at which the primary phase precipitates during the cooling of the melt [55,56,57]. Figure 4 shows the classic heating and cooling curves of a certain material, where T_f represents the temperature at which complete melting occurs during heating, and Tn represents the temperature at which the primary crystalline phase begins to precipitate during cooling.

Liu et al. [55] and Zhu et al. [56] utilized the primary crystallization temperature method to measure the solubility of rare earth oxides in REF₃-LiF molten salt. As shown in Figure 5, when different amounts of Nd₂O₃ (0, 1.10, 1.77, 3.39 wt.%) were added to NdF₃-LiF molten salt (82.6–17.4 wt.%), the corresponding primary crystallization temperatures were 830, 957, 979, and 1053 °C, respectively [55].

The primary crystallization temperature of a given composition melt is its liquidus temperature. Therefore, the measurement of RE₂O₃ solubility in REF₃-LiF molten salt using the primary crystallization temperature method can be attributed to the phase equilibrium study of the RE₂O₃-REF₃-LiF system. As depicted in Figure 6, the primary crystallization temperature curves obtained by adding different amounts of La₂O₃ to 83 wt.% LaF₃-17 wt.% LiF molten salt represent the pseudo-binary phase diagram of (LaF₃ + LiF)-La₂O₃. When the La₂O₃ concentration is below 0.6 wt.%, the liquidus temperature of the sample decreases with increasing La₂O₃ concentration. When the La₂O₃ concentration exceeds 0.6 wt.%, the liquidus temperature of the sample increases with increasing La₂O₃ concentration. In other words, the solubility of La₂O₃ in 83 wt.% LaF₃ + 17 wt.% LiF increases with increasing temperature. The (83 wt.% LaF₃ + 17 wt.%)-La₂O₃ system has a minimum eutectic temperature of 1041 °C at a La₂O₃ concentration of 0.6 wt.% [56]. The pseudo-binary phase diagram of (83 wt.% NdF₃ + 17 wt.%)-Nd₂O₃ is also present in Figure 6 for comparison. It can be concluded that the eutectic temperature is slightly higher and the eutectic point moves to higher Nd₂O₃ direction in the NdF₃-LiF-Nd₂O₃ system than the LaF₃-LiF-La₂O₃ system.

Using the primary crystallization temperature method to measure the solubility of RE₂O₃ in REF₃-LiF molten salts allows for the correlation of this physical property with the thermodynamic data, thereby systematically establishing and understanding the relationship between melt composition and temperature. However, this method needs to overcome some limitations in order to obtain accurate results. Firstly, it is essential to ensure that the RE₂O₃-REF₃-LiF melt is completely in the liquid phase, from which the primary crystallization temperature is determined by the thermal effect during cooling. When a large amount of sample is used for measuring the thermal effect, the sample composition can be verified after the experiment. However, the thermal effect during the primary phase crystallization is not significant, leading to an inaccurate measurement of the temperature. A DSC device may give an accurate thermal effect measurement, but the sample is small and its composition may be inaccurate. Furthermore, this method cannot directly measure the composition of the primary crystalline phase, thus is unable to obtain complete thermodynamic data.

2.3. Square Wave Voltammetry Method

Molten salt is a conductive system, and its conductivity is closely related to the composition. Chen et al. [57] and Keller [58] have determined the solubility of rare earth oxides in fluoride salts using electrochemical methods. Chen et al. [57] used square wave voltammetry to measure the solubility of Nd₂O₃ in the NdF₃-LiF (90%:10%) molten salt system at 1100, 1150, and 1200 °C. After adding an excess amount of Nd₂O₃ powder to the molten NdF₃-LiF (90%:10%) and stirring for 5 min, the square wave voltammetry curve was continuously measured using an electrochemical workstation. Then, a Gaussian fit was used to obtain a clearer fitting graph. The upper layer of the reacted salt was taken for XRF analysis to determine the concentration of Nd₂O₃ in the molten salt. Figure 7 shows the voltametric square wave graph of the NdF₃-LiF (90%:10%)-Nd₂O₃ (5%) molten salt system at 1200 °C. As the dissolution time increases, the peak current density of the square wave voltammetry curve also increases, indicating an increase in the concentration of neodymium oxide with time. The increase in peak current density becomes insignificant after 3.5 h. Therefore, the concentration of Nd₂O₃ in the molten salt at 3.5 h is taken as the solubility value. Based on the standard curve of Nd₂O₃ concentration versus peak current density shown in Figure 7, the concentration of Nd₂O₃ in the molten salt can be obtained from the measured peak current density.

Square wave voltammetry allows for determining the time required for rare earth oxide to reach dissolution equilibrium and enables the measurement of the dissolution rate of oxides in a sealed system during continuous measurements. This avoids the influence of sampling and analysis on the molten salt system during the experimental process, as well as the errors generated from analyzing multiple sample components. However, when analyzing the composition of the upper layer of salt after the experiment, it is necessary to confirm that an undissolved RE₂O₃ solid phase is not present.

Although the reactants during the electrolysis of the RE₂O₃-REF₃-LiF molten salt system are the dissolved RE³⁺ and O²⁻ species, all studies focus on the solubility of RE₂O₃ in the molten salt. However, multiple studies have shown that, when RE₂O₃ is added to the REF₃-LiF molten salt, it completely forms REOF and there is no RE₂O₃ phase present in the system [36,56]. Therefore, from a thermodynamic perspective, the primary crystalline phase is in equilibrium with the liquid phase of RE₂O₃ + REF₃ + LiF is REOF rather than RE₂O₃. Both the isothermal saturation method and the square wave voltammetry method require the addition of excess oxide to maintain dissolution equilibrium in the molten salt. However, as shown in Figure 2 and Figure 3, when excess RE₂O₃ is added, the concentration of RE³⁺ in the molten salt decreases with increasing RE₂O₃ as the formation of REOF consumes the RE³⁺ in the melt:

RE³⁺ + 3F⁻ + RE₂O₃ → 3REOF

(1)

After reaching the solubility of RE₂O₃, the more RE₂O₃ that is added, the more solid the phase of REOF is formed, and the lower the concentrations of RE³⁺ and F⁻ in the molten salt. Therefore, the solubility alone cannot accurately describe the properties of the RE₂O₃-REF₃-LiF system. Expressing the published solubility of RE₂O₃ in REF₃ + LiF molten salt in the form of a RE₂O₃-REF₃-LiF ternary phase diagram can represent the solubility of RE₂O₃ as a function of temperature and salt composition.

In summary, the experimental equipment is simple in the isothermal saturation method and is easy to operate. However, the samples taken for compositional analysis may include undissolved rare earth oxides during the sampling, which results in an overstated solubility. In addition, the solubility of the RE₂O₃ is usually lower than 5 wt.% and it is difficult to obtain accurate results either by RE difference or oxygen concentration. Square wave voltammetry can measure the concentration and dissolution rate of RE₂O₃ in molten salt continuously, which can reduce the probability of sample contamination. Furthermore, this method has been proven to be sensitive to the concentration of oxygen ions in molten salts, making the obtained data more reliable. However, this method requires complex equipment and careful data analysis, resulting in low productivity. Accurate composition analysis is also important for this technique. The initial crystallization temperature method uses differential thermal analysis to measure the temperature when the primary phase precipitates during the cooling of the melt, thus obtaining the solubility of RE₂O₃ at that temperature. There is no need to collect and analyze the sample in this method, which minimizes the uncertainty associated with the sampling and compositional analysis. The sample composition depends on careful preparation. The thermal effect during primary crystallization is not significant, and the measured initial crystallization temperature can be inaccurate. Therefore, this method requires careful sample preparation and thermal analysis. All these experimental techniques were developed to measure the solubility of RE₂O₃ in the molten salt rather than phase equilibrium study. SEM or EPMA need to be used to identify the primary phase, which is essential information for a phase equilibrium study.

3. Phase Equilibrium Studies in the RE₂O₃-REF₃-LiF System

3.1. 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 [59,60]. Solubility data of Nd₂O₃ in the NdF₃-LiF system reported in the literature are summarized in

Table 1. Solubility of Nd₂O₃ in NdF₃-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	[35]
58	42	0.75	15	85	0.12	57	42	0.74	850	[35]
58	42	0.82	15	85	0.13	57	42	0.81	860	[35]
58	42	0.96	15	85	0.15	57	42	0.95	900	[35]
63	37	1.68	18	82	0.29	62	36	1.65	1000	[38]
63	37	2.27	18	82	0.40	62	36	2.21	1050	[38]
63	37	2.57	18	82	0.45	61	36	2.51	1100	[38]
65	35	2.07	19	81	0.37	63	35	2.03	800	[58]
66	34	1.83	20	80	0.34	65	33	1.8	1000	[36]
66	34	1.92	20	80	0.35	65	33	1.88	1050	[36]
66	34	2.03	20	80	0.37	65	33	1.99	1100	[36]
66	34	2.12	20	80	0.39	65	33	2.08	1150	[36]
68	32	1.96	22	78	0.38	67	31	1.92	1000	[35]
68	32	2.59	22	78	0.50	66	31	2.52	1050	[35]
68	32	2.73	22	78	0.53	66	31	2.65	1100	[35]
70	30	9.24	23	77	1.96	64	28	8.46	850	[34]
70	30	1.4	23	77	0.28	69	30	1.38	850	[61]
70	30	4.4	23	77	0.90	67	29	4.21	1050	[61]
70	30	0.68	23	77	0.14	69	30	0.68	750	[38]
70	30	0.8	23	77	0.16	69	30	0.79	800	[38]
70	30	0.92	23	77	0.18	69	30	0.91	850	[38]
70	30	1.11	23	77	0.22	69	30	1.1	900	[38]
70	30	2.8	23	77	0.57	68	29	2.72	1100	[57]
70	30	3.1	23	77	0.63	68	29	3.01	1150	[57]
70	30	3.5	23	77	0.71	68	29	3.38	1200	[57]
72	28	2.07	25	75	0.44	71	27	2.03	1000	[36]
72	28	2.17	25	75	0.46	71	27	2.12	1050	[36]
72	28	2.29	25	75	0.48	70	27	2.24	1100	[36]
72	28	2.4	25	75	0.51	70	27	2.34	1150	[36]
73	27	2.18	26	74	0.47	71	26	2.14	1000	[38]
73	27	2.79	26	74	0.60	71	26	2.71	1050	[38]
73	27	3.08	26	74	0.67	71	26	2.99	1100	[38]
75	25	7.2	28	72	1.69	70	23	6.72	800	[34]
75	25	8.3	28	72	1.96	69	23	7.66	850	[34]
75	25	9.4	28	72	2.24	69	23	8.59	900	[34]
77	23	1.45	30	70	0.34	76	23	1.43	860	[35]
77	23	1.61	30	70	0.38	76	23	1.58	900	[35]
77	23	2.27	30	70	0.54	75	23	2.22	1000	[36]
77	23	2.39	30	70	0.57	75	23	2.33	1050	[36]
77	23	2.51	30	70	0.60	75	23	2.45	1100	[36]
77	23	2.62	30	70	0.63	75	23	2.55	1150	[36]
78	22	2.45	31	69	0.60	76	21	2.39	1000	[38]
78	22	2.3	31	69	0.56	76	22	2.25	1050	[38]
78	22	3.52	31	69	0.87	75	21	3.4	1100	[38]
80	20	7.29	34	66	1.95	75	19	6.79	850	[34]
81	19	2.49	35	65	0.66	79	19	2.43	1000	[36]
81	19	2.62	35	65	0.70	79	19	2.55	1050	[36]
81	19	2.73	35	65	0.73	79	19	2.66	1100	[36]
81	19	2.78	35	65	0.74	79	19	2.7	1150	[36]
83	17	1.1	39	61	0.31	82	17	1.09	957	[55]
83	17	1.75	39	61	0.49	81	17	1.72	979	[55]
83	17	3.4	39	61	0.97	80	17	3.29	1053	[55]
83	17	3.04	39	61	0.86	81	16	2.95	1000	[38]
83	17	3.36	39	61	0.96	80	16	3.25	1050	[38]
83	17	2.45	39	61	0.69	81	17	2.39	1100	[37]
83	17	4.09	39	61	1.17	80	16	3.93	1100	[38]
84	16	2.7	40	60	0.79	82	16	2.63	1000	[36]
84	16	2.81	40	60	0.82	82	16	2.73	1050	[36]
84	16	2.92	40	60	0.86	81	16	2.84	1100	[36]
84	16	3.05	40	60	0.90	81	16	2.96	1150	[36]
85	15	3.28	42	58	1.00	82	15	3.18	1050	[39]
85	15	3.88	42	58	1.18	82	15	3.74	1100	[39]
85	15	4.54	42	58	1.39	81	14	4.34	1150	[39]
88	12	3.82	49	51	1.29	85	12	3.68	1050	[38]
88	12	4.54	49	51	1.54	84	11	4.34	1100	[38]
88.5	11.5	3.74	50	50	1.29	85	11	3.61	1050	[39]
88.5	11.5	4.23	50	50	1.46	85	11	4.06	1100	[39]
88.5	11.5	4.71	50	50	1.63	85	11	4.5	1150	[39]
88.5	11.5	7.4	51	49	2.66	82	11	6.89	1200	[62]
90	10	4.2	54	46	1.54	86	10	4.03	1100	[57]
90	10	4.4	54	46	1.61	86	10	4.21	1150	[57]
90	10	4.7	54	46	1.73	86	10	4.49	1200	[57]
92	8	4.2	60	40	1.67	88	8	4.03	1050	[39]
92	8	4.62	60	40	1.84	88	8	4.42	1100	[39]
92	8	4.97	60	40	1.99	88	8	4.73	1150	[39]

. Figure 8 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. [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 8 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 [34,35,36,37,38,39,55,56,57,58,61,62], as detailed in the following two figures.

Figure 9 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.

Figure 10 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.

3.2. La₂O₃-LaF-LiF System

Figure 11 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. Solubility of La₂O₃ in LaF₃-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	[40]
65	35	1.58	20	80	0.29	64	34	S	1000	[40]
65	35	1.78	20	80	0.33	64	34	1.75	1050	[40]
65	35	1.94	20	80	0.36	64	34	1.9	1100	[40]
65	35	2.1	20	80	0.39	64	34	2.06	1150	[40]
65	35	1.79	20	80	0.33	64	34	1.76	1000	[36]
65	35	1.87	20	80	0.35	64	34	1.84	1050	[36]
65	35	1.94	20	80	0.36	64	34	1.9	1100	[36]
65	35	2.01	20	80	0.37	64	34	1.97	1150	[36]
70	30	1.54	24	76	0.32	69	30	1.52	950	[40]
70	30	1.76	24	76	0.36	69	29	1.73	1000	[40]
70	30	1.94	24	76	0.40	69	29	1.9	1050	[40]
70	30	2.2	24	76	0.45	68	29	2.15	1100	[40]
70	30	2.35	24	76	0.49	68	29	2.3	1150	[40]
72	28	1.99	25	75	0.43	70	28	1.95	948	[41]
72	28	2.08	25	75	0.45	70	28	2.04	968	[41]
72	28	1.64	25	75	0.35	70	28	1.61	980	[42]
72	28	2.17	25	75	0.47	70	28	2.12	988	[41]
72	28	2.01	25	75	0.43	70	28	1.97	1000	[36]
72	28	2.13	25	75	0.46	70	28	2.09	1050	[36]
72	28	2.26	25	75	0.49	70	28	2.21	1100	[36]
72	28	2.37	25	75	0.51	70	28	2.32	1150	[36]
75	25	1.65	28	72	0.38	74	25	1.62	950	[40]
75	25	1.95	28	72	0.45	74	25	1.91	1000	[40]
75	25	2.23	28	72	0.52	73	24	2.18	1050	[40]
75	25	2.5	28	72	0.58	73	24	2.44	1100	[40]
75	25	2.65	28	72	0.62	73	24	2.58	1150	[40]
76	24	2.23	30	70	0.53	75	23	2.18	1000	[36]
76	24	2.12	30	70	0.50	75	23	2.08	1004	[41]
76	24	2.3	30	70	0.55	75	23	2.25	1024	[41]
76	24	1.81	30	70	0.43	75	23	1.78	1035	[42]
76	24	2.36	30	70	0.56	75	23	2.31	1044	[41]
76	24	2.35	30	70	0.56	75	23	2.3	1050	[36]
76	24	2.48	30	70	0.59	75	23	2.42	1100	[36]
76	24	2.58	30	70	0.62	74	23	2.52	1150	[36]
80	20	2.31	35	65	0.61	78	20	2.26	1050	[40]
80	20	2.53	35	65	0.67	78	20	2.47	1100	[40]
80	20	2.75	35	65	0.73	78	19	2.68	1150	[40]
80	20	2.93	35	65	0.78	78	19	2.85	1200	[40]
80	20	3.06	35	65	0.82	78	19	2.97	1250	[40]
80	20	2.56	35	65	0.68	78	19	2.5	1050	[36]
80	20	2.15	35	65	0.57	79	19	2.1	1062	[41]
80	20	2.45	35	65	0.65	78	19	2.39	1082	[41]
80	20	1.97	35	65	0.52	79	19	1.93	1090	[36]
80	20	2.69	35	65	0.71	78	19	2.62	1100	[36]
80	20	2.58	35	65	0.69	78	19	2.52	1102	[41]
80	20	2.78	35	65	0.74	78	19	2.7	1150	[36]
83	17	2.14	39	61	0.62	81	17	2.1	1100	[37]
83	17	2.73	39	61	0.79	81	16	2.66	1050	[36]
83	17	2.85	39	61	0.83	81	16	2.77	1100	[36]
83	17	3.01	39	61	0.88	81	16	2.92	1150	[36]
85	15	2.68	43	57	0.83	83	15	2.61	1100	[40]
85	15	2.85	43	57	0.88	83	15	2.77	1150	[40]
85	15	3.08	43	57	0.96	82	15	2.99	1200	[40]
85	15	3.25	43	57	1.01	82	15	3.15	1250	[40]
90	10	3.2	54	46	1.19	87	10	3.1	1200	[40]
90	10	3.5	54	46	1.30	87	10	3.38	1250	[40]

. 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 [36,40,41,42].

Figure 12 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.

3.3. Y₂O₃-YF₃-LiF System

Figure 13 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. Solubility of Y₂O₃ in YF₃-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	[48]
58	42	1.25	20	80	0.28	58	41	1.23	750	[48]
58	42	1.48	20	80	0.33	58	41	1.46	800	[48]
58	42	1.87	20	80	0.42	57	41	1.84	875	[48]
58	42	2.09	20	80	0.47	57	41	2.05	920	[48]
58	42	2.35	20	80	0.53	57	41	2.3	950	[48]
58	42	2.87	20	80	0.65	57	40	2.79	1000	[48]
65	35	1.28	25	75	0.32	64	34	1.26	750	[48]
65	35	0.45	25	75	0.11	65	35	0.45	810	[63]
65	35	1.63	25	75	0.41	64	34	1.6	825	[48]
65	35	0.5	25	75	0.12	65	35	0.5	831	[63]
65	35	1.79	25	75	0.45	64	34	1.76	850	[48]
65	35	0.59	25	75	0.15	65	35	0.59	850	[63]
65	35	0.8	25	75	0.20	65	35	0.79	882	[63]
65	35	0.8	25	75	0.20	65	35	0.79	900	[63]
65	35	2.11	25	75	0.53	64	34	2.07	900	[48]
65	35	0.88	25	75	0.22	65	34	0.87	900	[63]
65	35	1.65	25	75	0.41	64	34	1.62	1000	[63]
65	35	2.96	25	75	0.75	63	34	2.87	1000	[48]
65	35	1.65	25	75	0.41	64	34	1.62	1000	[63]
75	25	1.69	35	65	0.51	74	24	1.66	1000	[63]
79	21	1.72	40	60	0.57	78	21	1.69	750	[48]
79	21	2.14	40	60	0.71	77	21	2.1	800	[48]
79	21	2.26	40	60	0.75	77	21	2.21	825	[48]
79	21	2.93	40	60	0.98	77	20	2.85	900	[48]
79	21	3.52	40	60	1.18	76	20	3.4	950	[48]
79	21	4.9	40	60	1.66	75	20	4.67	1000	[48]
85	15	3.72	50	50	1.45	82	15	3.59	900	[48]
85	15	1.19	50	50	0.46	84	15	1.18	900	[63]
85	15	1.41	50	50	0.54	84	15	1.39	929	[63]
85	15	1.51	50	50	0.58	84	15	1.49	943	[63]
85	15	4.45	50	50	1.75	81	14	4.26	950	[48]
85	15	1.61	50	50	0.62	84	15	1.58	964	[63]
85	15	1.78	50	50	0.69	83	15	1.75	974	[63]
85	15	1.88	50	50	0.73	83	15	1.85	988	[63]
85	15	5.36	50	50	2.11	81	14	5.09	1000	[48]
85	15	1.98	50	50	0.77	83	15	1.94	1000	[63]
85	15	2	50	50	0.77	83	15	1.96	1000	[63]
85	15	2.09	50	50	0.81	83	15	2.05	1009	[63]
91	9	2.2	64	36	1.02	89	9	2.15	1000	[63]

[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 14 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.

3.4. 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 [64,65], MTDATA [66], and Thermo-Calc [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 [24,25] to predict the solubility of rare earth oxides in molten salts based on available experimental data. Figure 15 summarizes the solubility of various rare earth oxides in fluoride salts, where Figure 15a shows the relationship between solubility and temperature, and Figure 15b demonstrates the relationship between the logarithm of solubility and the reciprocal of temperature [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.

Figure 16 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 16, 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. [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 [34,35,39]. The comparison between the predicted and experimental results is shown in Figure 17, with an average error of 8%. However, the error can reach 30% for low solubility cases.

As shown in Figure 8, 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. [25]. Figure 18 compares the solubility calculated by Guo et al.’s model [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.

4. Conclusions

The solubility of rare earth oxides in fluoride salt is essentially the content of RE₂O₃ in the liquid phase saturated with solid oxides in the REF₃-LiF-RE₂O₃ system. This paper systematically summarizes the determination methods and solubility data of rare earth oxides in molten fluoride salt. The solubility data are expressed in the ternary phase diagrams, and a series of pseudo-binary phase diagrams are constructed to evaluate the reported data in the literature. The solubility data reported in the literature, obtained by different authors using different research methods, exhibit significant deviations. In addition, the solubility models proposed in the literature also exhibit significant deviations from experimental data.

Expressing the solubility of rare earth oxides in the fluoride salt system in the form of a phase diagram not only allows for the summarization and comparison of the data obtained under various conditions but also enables the development of a thermodynamic database for the REF₃-LiF-RE₂O₃ system based on phase equilibrium studies. With the development of production technologies and variations of feed structures, more accurate phase equilibrium information directly related to the production of rare earth metals and alloys is required. Reliable techniques for phase diagram determination of REF₃-LiF-RE₂O₃ need to be developed to meet the requirements. Accurate experimental data will also support the development of thermodynamic databases related to rare earth elements.