## 1 Introduction  
Rare earth elements have some excellent chemical and physical properties, such as light, magnetism, and catalytic and electronic performance, achieving wide applications in many fields, such as electronic components, national defense, and aerospace [1, 2, 3, 4, 5, 6, 7]. With the market demand increasing, the annual production of rare earth oxides has increased from 210,000 to 350,000 tons over the past 5 years [8, 9], leading to an increase in rare earth secondary resources. Many conspicuous secondary resources belong to post-consumer recycling [10], like waste permanent magnets and waste polishing powders [11, 12, 13, 14]. In the pre-consumer recycling field, some resources, like red mud [15, 16], have the potential to be recovered. Rare earth molten salt electrolysis slag is a typical example in the pre-consumer recycling field. The main rare earth production method is rare earth fluoride molten salt electrolysis [17]. In this procedure, approximately 8% of REEs remain in the REMES and about 2200 tons of REMES will be produced each year [18, 19]. Therefore, with the expansion of are earth production, more REMES will be generated. Meanwhile, there is an abundance of valuable elements in REMES, including 10-60% of REEs, 10-25% fluorine, and 2-5% lithium [19]. Therefore, it is essential to recycle it. Due to the presence of fluorine, it is difficult to recover REMES directly by acid leaching. Therefore, the main challenge in recovery methodologies was to manage the fluorine and defluorination via phase reconstruction methods was studied initially [20]. [PERSON] et al. [21] categorized the recovery methodologies of REMES into three types, including alkali mineral phase reconstruction methods, salt mineral phase reconstruction methods, and acid mineral phase reconstruction methods [22; 23; 24]. [PERSON] et al. [25] utilized sodium hydroxide to reconstruct the phases of rare earth compounds and lithium fluoride, transforming them into hydroxides. After the washing and leaching treatments, the optimal leaching efficiencies of the rare earths, fluorine, and lithium were 99.05%, 98.23%, and 99.22%, respectively. [PERSON] [26] utilized borax to reconstruct REMES, generating rare earth oxides and sodium fluoride. After washing and leaching, the leaching efficiency of the REEs exceeded 97%. [PERSON] et al. [27] proposed a method to reconstruct REMES using concentrated sulfuric acid. During the phase reconstruction process, the rare earth compounds and lithium fluoride were converted into sulfates, which would dissolve in water before the next step. Meanwhile, the released HF was collected and utilized to produce hydrofluoric acid. Then, the sulfate solution and hydrofluoric acid were mixed, precipitating rare earth fluorides and lithium fluoride from the solution. In this method, more than 90% of the REEs, Li, and F could be recovered. Additionally, some physical technologies were also used in the recovery of REMES, like microwaves and external electric fields [28; 29]. [PERSON] et al. [29] used NaOH to transform rare earth fluoride into acid-soluble rare earth compounds, assisted with a microwave. Under optimal conditions, the conversion rate of rare earth fluorides reached 99.17%. With the development of these methodologies, many issues have been handled, such as the recovery of lithium and the increase in resource utilization rates, and comprehensive resource recovery has been achieved, including the recovery of Li, F, and REEs. However, because of the defluorination process, the hydrometallurgical process was still the main purification method [30]. This would result in wastewater problems and a long production process, increasing the risk of environmental pollution and production costs. [PERSON] [31] attempted to apply the vacuum distillation method to the recovery of REMES, while vacuum distillation was only utilized to extract LiF, and the extraction of REEs still involved a series of hydrometallurgical methods.