Optimization of Rare Earth Yield from Fluoride Roasting of Neodymium–Iron–Boron Waste Using Response Surface Methodology

Abstract

To address the critical challenges in pyrometallurgical recycling processes—such as poor feedstock adaptability, high energy consumption during roasting conversion, and the low added value of rare earth products—this study systematically investigated the mechanism and process optimization of ammonium bifluoride (NH₄HF₂) roasting for the recovery of neodymium–iron–boron (NdFeB) waste. Thermodynamic analysis confirmed the feasibility of the conversion reaction between NH₄HF₂ and the rare earth components in NdFeB waste. Single-factor experiments were conducted to examine the effects of roasting temperature, reaction time, and NH₄HF₂ dosage on rare earth recovery. The optimal conditions were a roasting temperature of 600 °C, a reaction time of 120 min, and a NH₄HF₂ dosage of 75 wt%, achieving a rare earth recovery rate of 98.81%. Furthermore, the response surface methodology (RSM) was employed to establish a quantitative model correlating process parameters with recovery efficiency. Variance analysis demonstrated that the model was highly significant (F = 136.94, p < 0.0001), with excellent agreement between actual and predicted values (R² = 0.9944). Factor contribution analysis revealed that NH₄HF₂ dosage had the most pronounced impact on rare earth fluorination, followed by roasting temperature and reaction time. Under optimized conditions, the purified rare earth fluoride obtained after acid leaching reached a purity of 99.43%, providing high-quality raw material for producing high-value-added rare earth products.

1. Introduction

Neodymium iron boron (NdFeB) permanent magnets, as third-generation rare earth permanent magnetic materials, have become indispensable key functional materials in modern industry due to their excellent magnetic properties (high magnetic energy product, high coercivity), favorable cost–performance ratio, and outstanding machinability [1]. These materials are widely used in high-tech fields such as new energy vehicle drive motors, wind turbine generators, medical magnetic resonance imaging (MRI) equipment, precision sensors, and consumer electronics, demonstrating broad market prospects [2].

During the production of NdFeB magnets, approximately 25% of scrap materials are generated through mechanical processing steps such as cutting and grinding. These scraps contain up to 30% rare earth elements (primarily Nd, Pr, Dy, etc.), exhibiting significant resource recovery value [3]. It is noteworthy that traditional rare earth mining and smelting processes face severe environmental challenges: for every ton of rare earth oxide (REO) produced, 60,000 cubic meters of waste gas, 200 cubic meters of acidic wastewater, and 1.4 tons of radioactive waste residue are generated (due to the presence of radioactive elements in most rare earth ores) [4]. Against the backdrop of global low-carbon development strategies, advancing rare earth scrap recycling technologies holds dual significance: on one hand, it can reduce the environmental burden caused by primary mineral resource extraction; on the other hand, it can effectively alleviate pressure on rare earth supply chain security [5,6,7,8,9]. Statistics indicate that the annual production of NdFeB magnets is growing at a rate of 8–10%, with corresponding scrap generation increasing exponentially. This trend has prompted academia and industry to accelerate the establishment of a new rare earth circular economy system [10,11,12].

Current NdFeB scrap recycling technologies are primarily divided into two routes: hydrometallurgy and pyrometallurgy. While hydrometallurgical processes (acid leaching-solvent extraction) can achieve single rare earth oxides with purity > 99%, their inherent limitations hinder sustainable development. First, the multi-stage extraction process results in a lengthy procedure lasting 5–7 days; second, processing one ton of scrap consumes 4–6 tons of concentrated hydrochloric acid and generates 10–15 tons of heavy metal-containing wastewater; furthermore, approximately 10–15% of rare earths are lost in iron slag due to mechanical entrainment, making it difficult to achieve an overall recovery rate exceeding 90% [13,14]. These technical and economic bottlenecks urgently require breakthroughs through process innovation.

The pyrometallurgical recovery process for NdFeB waste utilizes the favorable reaction kinetics under high-temperature conditions. Its principle is based on the differential binding affinity of rare earth elements (REEs) and other elements with sulfur, chlorine, or fluorine. By employing sulfidation, chlorination, or fluorination methods, the occurrence states of the elements are altered, enabling the efficient recovery of REEs [15,16,17,18].

The sulfation roasting–water leaching process consists of two steps [15]: (1) The first is the sulfation roasting of pre-oxidized NdFeB waste using a sulfating agent to convert rare earth oxides into rare earth sulfates, while iron and other impurities remain in oxide form. (2) The second is the water leaching of the sulfation-roasted material. Since rare earth sulfates are water-soluble whereas iron oxides are insoluble, REEs can be separated from other oxide impurities. Liu et al. [16] employed a two-step ammonium sulfate roasting–water leaching method to selectively extract REEs from waste NdFeB magnets. First, the waste NdFeB magnets were oxidized at 800 °C, and then mixed with (NH₄)₂SO₄. The first roasting step was conducted at 400 °C for 1 h, converting 78% of REEs into rare earth sulfates and 22% into insoluble rare earth ammonium sulfates, while iron was transformed into insoluble ferric ammonium sulfate. The second step involved calcination at 750 °C for 2 h to convert the insoluble rare earth ammonium sulfates into soluble rare earth sulfates. The sulfation roasting–water leaching method significantly reduces acid and alkali consumption, offering notable environmental benefits. However, it requires both oxidation roasting and high-temperature roasting, leading to high energy consumption. Additionally, further steps such as precipitating REEs from the leachate with sodium carbonate and subsequent high-temperature calcination are needed, resulting in high production costs and a cumbersome process flow.

The selective chlorination method for recycling waste magnets exploits the strong reactivity between REEs and chloride ions, which readily form chlorides. Under conditions where other ions do not participate in the reaction, REEs in the waste react to form rare earth chlorides, thereby separating them from impurity ions. Currently, chlorinating agents such as FeCl₂, NH₄Cl, and MgCl₂-KCl are commonly used. Shirayama et al. [17] employed magnesium chloride as a reaction medium to extract Nd and Dy from NdFeB waste. The waste was thoroughly mixed with MgCl₂ and reacted at 1000 °C for 12 h. Although the extraction rate of REEs exceeded 80%, excess MgCl₂ and byproduct magnesium had to be removed via vacuum distillation. The chlorination separation method is effective for minimally oxidized waste but performs poorly for heavily oxidized waste. Additionally, the resulting chlorides are hygroscopic and difficult to store. The excessive use of chlorinating agents not only worsens the working environment but also corrodes equipment. Further processing is also required to obtain individual rare earth elements.

Extensive research has also been conducted on molten salt extraction to recover REEs from both oxidized and non-oxidized NdFeB magnets. In this method, mixtures of fluoride or chloride salts are used to dissolve oxidized or non-oxidized magnets, producing rare earth metals or alloys. Abbasalizadeh et al. [18] also employed molten salt extraction to selectively dissolve REEs from NdFeB magnets in a molten fluoride electrolyte. They investigated the effects of different fluxing agents (AlF₃, ZnF₂, FeF₃, Na₃AlF₆) on the selective dissolution of REEs in the LiF-NdFeB system. The results showed that these fluxing agents were suitable as fluorinating agents to form rare earth fluorides (REF₃), which could then be used for the cathodic deposition of rare earth metals. This method is suitable for large-scale industrial production, but the high reaction temperature imposes stringent requirements on the reactor.

Compared to hydrometallurgical processes, pyrometallurgical recovery offers advantages such as a shorter process flow and environmental friendliness. However, it suffers from poor raw material adaptability, high energy consumption, low REE recovery rates, insufficient product purity, and long reaction times, hindering its industrial application [19]. Current pyrometallurgical processes urgently require improvements in the following areas. (1) Poor raw material adaptability: The waste typically must have low impurity content, requiring inspection and classification to ensure the main components meet recovery standards [20,21]. (2) Low product purity: Pyrometallurgically recovered REE products often contain impurities, yielding only rare earth–transition metal alloys with limited applications [22]. Among these, the fluorination roasting–acid leaching process is considered one of the pyrometallurgical methods capable of overcoming these technical challenges.

A comparative study on fluoride calcination technology in the recycling of neodymium–iron–boron scrap materials indicates that while both the ZnF₂ and NaBF₄ calcination systems can achieve rare earth recovery rates exceeding 95%, there are significant differences between them [23,24]. The ZnF₂ system requires the addition of 100% ZnF₂ and roasting at 850 °C for 90 min, with its high energy consumption and large dosage addition being obvious drawbacks, whereas the NaBF₄ system only requires a 65% addition rate and roasting at 600 °C for 30 min to achieve similar results. It is noteworthy that both systems introduce impurity ions into the leachate, increasing the difficulty of subsequent purification of ferric chloride hexahydrate (FeCl₃·6H₂O).

In comparison, the NH₄HF₂ calcination system demonstrates unique advantages: the fluoride residues primarily consist of metal fluorides, significantly reducing the pressure on acid leaching solution treatment; the generated NH₃ can be recycled, effectively reducing exhaust gas treatment costs; more importantly, NH₄HF₂ decomposes into HF and NH₃ at low temperatures between 200 and 400 °C, releasing active fluorine that rapidly reacts with rare earth oxides to form rare earth fluorides, thereby avoiding energy consumption issues associated with high temperatures.

Currently, significant gaps remain in the research on the recovery of rare earth elements from NdFeB waste via fluoride roasting, particularly in the optimization of process parameters and the elucidation of reaction mechanisms, which urgently require breakthroughs. This study innovatively applies NH₄HF₂ roasting technology to the field of NdFeB waste recycling for the first time, developing a novel process route of “NH₄HF₂ roasting–acid leaching purification.” Through the systematic investigation of the roasting reaction process between NdFeB waste and NH₄HF₂, combined with thermodynamic analysis and response surface methodology (RSM), the thermodynamic mechanisms of rare earth fluorination roasting in this system were elucidated for the first time, revealing the synergistic interactions among key process parameters and successfully determining the optimal process conditions. This research not only provides a solid theoretical and experimental foundation for the application of pyrometallurgical processes in NdFeB waste recycling but also pioneers the use of NH₄HF₂ in this field.

2. Experimental Materials and Equipment

2.1. Materials

The NdFeB scrap used in the experiment was taken from a NdFeB scrap recycling enterprise in Jiangxi. The content of oxides in the scrap is shown in

Table 1. Oxide content contained in NdFeB wastes.

Component	REO	Fe2O3 *	Al2O3	CoO	K2O	ZnO	CuO	NiO	Na2O	MgO	B2O3
Content (wt%)	26.98	68.94	1.81	0.50	0.49	0.27	0.23	0.19	0.18	0.2	0.29

* Determination by chemical analytical methods.

, and the X-ray diffraction (XRD) spectrum of the scrap is shown in Figure 1. The content of rare earth oxides in the scrap is 26.98%, and the content of iron trioxide and other small amount of metal elements is 68.94%. Additionally, as shown in

Table 2. Rare earth compositions of NdFeB wastes.

Component	CeO2	Pr6O11	Nd2O3	Sm2O3	Gd2O3	Dy2O3	Ho2O3	La2O3
Content (wt%)	28.82	10.90	51.57	1.91	3.53	2.29	0.79	0.18

, the rare earth composition of the neodymium–iron–boron scrap can be seen, with neodymium trioxide (Nd₂O₃), cerium oxide (CeO₂), praseodymium oxide (Pr₆O₁₁), and gadolinium oxide (Gd₂O₃) accounting for 94.82% of the total rare earth elements. The results of the XRD analysis indicate that the iron and rare earths in the NdFeB waste mainly consist of ferric oxide and rare earth oxides.

2.2. Analytical Characterization

In this study, the feedstock was roasted in a KSL-1200X muffle furnace manufactured by Hefei Kejing Materials Technology Co. (Hefei, China). The rare earth content in the feedstock, the concentration of rare earths in the leach solution, and the fluorinated rare earth content in the leach slag were measured using an ICAP-PRO instrument manufactured by Thermo Fisher Scientific (Waltham, MA, USA). The calibration and verification of ICP Spectrometer: Certified Reference Materials (CRM) standard solutions are used, covering the concentration range of the target elements. Calibration Curve: This includes 5 concentration points (blank, 5 ppm, 10 ppm, 20 ppm, 40 ppm) with a linear correlation coefficient (R²) > 0.999. Accuracy and Error Range: This is verified through spike recovery (90–110%) and repeated measurements (RSD < 5%). The total iron content in neodymium–iron–boron scrap samples is tested using the titration method after reduction with titanium trichloride. The micromorphology of the leach slag was analyzed using a field emission scanning electron microscope model MLA650F manufactured by FEI (Hillsboro, OR, USA). The physical compositions of the raw material, roasted sand, and acid leaching slag were analyzed using an Empyrean type X-ray diffractometer manufactured by Panalytical (Almelo, The Netherlands). The main test specifications and parameters of the instrument were as follows: the target material was Cu-Kα (λ = 0.15406 nm), which was tested in a continuous scanning mode (2θ = 10–90° in steps of 0.013°). The calibration and verification of the XRD analyzer ensured the 2θ error < 0.01°. The consistency of detector response is validated using standard samples with a detection limit of 1–2 wt%. Peak position reproducibility is confirmed through triplicate scans of the same sample (RSD < 1%). The Gibbs free energies of the chemical reactions were calculated using the HSC6.0 software developed by Outotec (Espoo, Finland) and the temperature was set to 0–1000 °C. We fixed all input parameters (temperature, pressure, component concentration, thermodynamic database version) and performed two independent calculations using HSC Chemistry (restarting the software each time to eliminate cache effects). The data from each calculation are completely identical.

2.3. Experimental Procedures and Methods

Figure 2 shows the experimental flowchart for investigating the roasting process of NdFeB scrap with NH₄HF₂. After crushing and grinding, the NdFeB scrap was thoroughly mixed with 15–95% NH₄HF₂ and continuously roasted in a muffle furnace at a constant temperature of 500–700 °C for 30–150 min. Since fluorine atoms tended to combine with hydrogen atoms under strongly acidic conditions to form hydrofluoric acid, the roasted clinker was finely ground and then added to deionized water in a three-neck flask at a liquid-to-solid ratio of 50 mL/g. The mixture was stirred at 25 °C in a constant-temperature water bath at 150 rpm for 60 min; this was followed by filtration to remove the generated FeF₃. This step prevents the subsequent acid leaching process from producing hydrofluoric acid, which could react with rare earth oxides and interfere with the exploration of fluorination roasting conditions. The water-washed residue was dried at 80 °C for 12 h, after which 9 M hydrochloric acid solution was added at a liquid-to-solid ratio of 4 mL/g. The mixture was then placed in an 80 °C constant-temperature water bath and stirred continuously at 150 rpm for 2.5 h. Upon completion of the leaching process, the acid leachate was filtered while hot, and the filter residue finally dried at 80 °C for 12 h.

The acid leachate of the roasted products was diluted with 5% nitric acid, and the concentration of rare earth elements was determined using a full-spectrum direct-reading inductively coupled plasma optical emission spectrometer (ICAP-PRO). The leaching rate was calculated as the ratio of the element content in the leachate to that in the raw NdFeB scrap material, with the rare earth leaching rate was calculated using Equation (1) and the total rare earth leaching rate was calculated using Equation (2). Since rare earth oxides and oxyfluorides are soluble in hydrochloric acid while fluorinated rare earth compounds remain insoluble and are retained in the leaching residue, the yield of fluorinated rare earths was calculated using Equation (3).

$${\mathrm{X}}_{\mathrm{i}}={\displaystyle \frac{\mathrm{V}{\mathrm{C}}_{\mathrm{i}}}{\mathrm{m}{\mathsf{\omega }}_{\mathrm{i}}}}$$

(1)

Equation (1):

• X_i—leaching rate of rare earth “i” (%);
• V—volume of leachate (L);
• C_i—concentration of rare earth “i” in the leach solution (g/L);
• m—weigh the mass of NdFeB scrap (g);
• ω_i—content of rare earth “i” in NdFeB waste (%).

$$\mathrm{X}={\displaystyle \frac{\mathrm{VC}}{\mathrm{m}\mathsf{\omega }}}$$

(2)

Equation (2):

• X—total rare earth leaching rate (%);
• C—total concentration of rare earths in the leach solution (g/L);
• ω—total content of rare earths in the roasting product (%).

η = 1 – X

(3)

in Equation (3):

• η—rare earth recovery rate (%);
• X—total rare earth leaching rate (%).

Box–Behnken experimental design (BBD) is a response surface analysis method based on spherical spatial design, which is widely used in the optimization of various process parameters [25,26]. BBD is suitable for optimization experiments with fewer factors, and each factor can be taken at three levels, which are expressed by the corresponding codes as (−1, 0, 1) [27]. The BBD response surface methodology was used to further analyze the effects of factors and their interactions on the significance of rare earth recovery rates, and to optimize the process conditions for roasting to recover rare earths. Based on the results of 17 groups of designed experiments, analysis of variance (ANOVA) was performed using the RSM method and the quadratic polynomial shown in Equation (4) was obtained by fitting [28].

$$\mathrm{y}={\mathrm{a}}_0+\sum _{\mathrm{i}=1}^3{\mathrm{a}}_{\mathrm{i}}{\mathrm{x}}_{\mathrm{i}}+\sum _{\mathrm{i}=1}^3{\mathrm{a}}_{\mathrm{ii}}{\mathrm{x}}_{\mathrm{i}}^2+\sum _{\mathrm{i}=1}^2\sum _{\mathrm{j}=\mathrm{i}+1}^3{\mathrm{a}}_{\mathrm{ij}}{\mathrm{x}}_{\mathrm{i}}{\mathrm{x}}_{\mathrm{j}}+\mathsf{\epsilon }$$

(4)

where y is the response value of RSM (rare earth recovery rate), a₀ is the intercept term obtained by least squares regression ANOVA, a_i is the first-order linear coefficient, a_ii is the squared effect between the factors, a_ij is the quadratic effect between the factors, and x_i and x_j are the uncorrelated factors, which are the random error terms caused by the inconsistency between the model predicted values and the actual measured values.

In this experiment, the response surface methodology was used to explore the effects of the roasting factors and their interactions on the significance of the rare earth recovery rates, and the process parameters obtained from the one-factor roasting experiments were optimized to obtain the best roasting process parameters.

3. Results and Discussion

3.1. Thermodynamic Analysis of Roasting Reactions

The main chemical reactions in the roasting process of the NdFeB waste–NH₄HF₂ system are shown in

Table 3. Chemical reactions in the roasting process of NdFeB waste–ammonium hydrogen fluoride system.

No.	Reactions
1	3NH4HF2 + Nd2O3 = 2NdF3 + 3NH3(g) + 3H2O(g)
2	3NH4HF2 + Ce2O3 = 2CeF3 + 3NH3(g) + 3H2O(g)
3	3NH4HF2 + Gd2O3 = 2GdF3 + 3NH3(g) + 3H2O(g)
4	3NH4HF2 + La2O3 = 2LaF3 + 3NH3(g) + 3H2O(g)
5	9NH4HF2 + Pr6O11 = 6PrF3 + 9NH3(g) + 9H2O(g) + O2(g)
6	3NH4HF2 + Dy2O3 = 2DyF3 + 3NH3(g) + 3H2O(g)
7	3NH4HF2 + Ho2O3 = 2HoF3 + 3NH3(g) + 3H2O(g)
8	NH4HF2 = NH3(g) + 2HF(g)
9	6HF(g) + Nd2O3 = 2NdF3 + 3H2O(g)
10	6HF(g) + Ce2O3 = 2CeF3 + 3H2O(g)
11	6HF(g) + Gd2O3 = 2GdF3 + 3H2O(g)
12	6HF(g) + La2O3 = 2LaF3 + 3H2O(g)
13	18HF(g) + Pr6O11 = 6PrF3 + 9H2O(g) + O2(g)
14	6HF(g) + Dy2O3 = 2DyF3 + 3H2O(g)
15	6HF(g) + Ho2O3 = 2HoF3 + 3H2O(g)
16	3NH4HF2 + Fe2O3 = 2FeF3 + 3NH3(g) + 3H2O(g)
17	6HF(g) + Fe2O3 = 2FeF3 + 3H2O(g)

, and the calculated results are shown in Figure 2.

Figure 3a demonstrates that as the reaction temperature increases, the Gibbs free energy (${\mathsf{\Delta }\mathrm{G}}_{\mathrm{T}}^{\mathsf{\theta }}$) of reactions 1–7 shows a monotonically decreasing trend while remaining negative throughout, indicating that the direct reaction between rare earth elements in NdFeB waste and NH₄HF₂ to form rare earth fluorides is thermodynamically spontaneous, and elevated temperatures significantly promote the reaction progress. Notably, the ${\mathsf{\Delta }\mathrm{G}}_{\mathrm{T}}^{\mathsf{\theta }}$ of reaction 8 undergoes a transition from positive to negative at 225 °C, marking this characteristic temperature point as the threshold for the significant decomposition of NH₄HF₂. Although the ${\mathsf{\Delta }\mathrm{G}}_{\mathrm{T}}^{\mathsf{\theta }}$ values of reactions 9–15 remain negative across the entire temperature range, their absolute values gradually decrease with increasing temperature, suggesting that while the reaction between rare earth elements in NdFeB waste and HF gas (generated from NH₄HF₂ decomposition) to form rare earth fluorides is thermodynamically feasible, the driving force weakens at higher temperatures. Particularly, reaction 16 maintains consistently negative ${\mathsf{\Delta }\mathrm{G}}_{\mathrm{T}}^{\mathsf{\theta }}$ values at 600 °C, whereas reaction 17 remains positive, demonstrating that the reaction between Fe₂O₃ in the waste and NH₄HF₂ is thermodynamically favorable at 600 °C, while the reaction with HF gas is non-spontaneous. The enlarged view in Figure 3b reveals more detailed patterns: below 225 °C, the ${\mathsf{\Delta }\mathrm{G}}_{\mathrm{T}}^{\mathsf{\theta }}$ values for fluorination reactions between rare earth elements and HF gas are generally lower than those for direct reactions with NH₄HF₂; however, above this critical temperature of 225 °C, the situation reverses, with ${\mathsf{\Delta }\mathrm{G}}_{\mathrm{T}}^{\mathsf{\theta }}$ values for reactions with HF gas becoming higher than those with NH₄HF₂. This phenomenon uncovers an important principle: HF gas generated from NH₄HF₂ decomposition above 225 °C actually diminishes the driving force for rare earth fluorination.

Figure 4 illustrates the schematic diagram of NH₄HF₂ transformation and its mechanistic role in rare earth fluorination reactions. The diagram clearly demonstrates the dynamic evolution of the reaction system: during the low-temperature phase (<225 °C), NH₄HF₂ directly reacts with RE₂O₃ via solid–solid reactions to form REF₃. It is particularly noteworthy that although thermodynamic analysis indicates temperatures above 225 °C reduce the spontaneity of fluorination reactions, when the temperature exceeds 225 °C, NH₄HF₂ undergoes thermal decomposition to generate reactive HF gas, establishing a triphase synergistic reaction system (NH₄HF₂-HF-RE₂O₃). This system significantly enhances rare earth fluorination efficiency through dual reaction pathways: solid–solid and gas–solid interactions. Based on this theoretical understanding and aiming to achieve higher rare earth recovery yields, this study specifically selected 500 °C as the starting temperature in the single-factor experiments, investigating roasting temperature, to systematically examine the influence of roasting temperature on rare earth fluoride conversion rates.

3.2. Effect of Roasting Conditions on Rare Earth Recovery Rates

3.2.1. Effect of Roasting Temperature on Rare Earth Recovery Rates

The experiments were conducted with a fixed roasting time of 120 min and an NH₄HF₂ addition ratio of 75%, systematically investigating the effect of roasting temperature (500–700 °C) on rare earth recovery efficiency. As shown in Figure 5a, when the roasting temperature increased from 500 °C to 600 °C, the leaching rates of all rare earth elements decreased significantly. Notably, at 600 °C, the leaching rates of cerium (Ce), gadolinium (Gd), neodymium (Nd), and praseodymium (Pr) converged to similar levels, indicating the synchronous fluorination conversion of all rare earth components in the NdFeB waste. When the temperature was further increased to 650 °C and 700 °C, the rare earth recovery rates reached 99.15% and 99.21%, respectively, showing only minimal variation compared to the recovery rate at 600 °C and stabilizing at a high level. As illustrated in Figure 5b, distinct diffraction peaks corresponding to NdF₃, CeF₃, PrF₃, and GdF₃ phases were detected at 500 °C, confirming the onset of fluorination reactions between NdFeB waste and NH₄HF₂ at this temperature, albeit with limited rare earth conversion efficiency. When the temperature was elevated to 600 °C, a remarkable intensification of these characteristic peaks was observed, indicating enhanced fluorination kinetics and consequently higher rare earth recovery yields. Notably, further increasing the temperature to 650 °C did not significantly alter the peak intensities of the fluorinated rare earth phases, suggesting reaction equilibrium had been achieved. This observation correlates well with the plateau in rare earth recovery rates at 650 °C. Through the holistic evaluation of process economics, 600 °C was identified as the optimal roasting temperature, balancing reaction efficiency with operational costs.

3.2.2. Effect of Roasting Time on Rare Earth Recovery Rate

The experiment was conducted with 75% NH₄HF₂ addition at a roasting temperature of 600 °C to systematically investigate the effect of roasting duration (30–150 min) on rare earth recovery efficiency. As shown in Figure 6a, extending the roasting time from 30 to 120 min resulted in significant reductions in the leaching rates of all rare earth elements. Correspondingly, the total rare earth leaching rate decreased substantially while the recovery rate showed remarkable improvement. When the roasting time was further extended to 150 min, the recovery rate reached 98.50%, demonstrating negligible difference compared to the result at 120 min. These findings indicate that while prolonged roasting time facilitates the fluorination reaction, the process reaches saturation at 120 min, making the further extension of time practically ineffective for additional recovery rate enhancement. XRD analysis of the roasted products (Figure 6b) demonstrated the progressive intensification of fluorinated rare earth phase diffraction peaks with increasing roasting time from 60 to 120 min, indicating enhanced fluorination conversion efficiency. However, extending the duration to 150 min did not yield further peak enhancement, suggesting reaction equilibrium was attained by 120 min. This behavior correlates well with the plateau in rare earth recovery yields observed beyond 120 min. Through comprehensive techno-economic evaluation accounting for both processing efficiency and operational costs, 120 min was determined to represent the optimal roasting duration for this process.

3.2.3. Effect of NH₄HF₂ Addition on Rare Earth Recovery Rate

The study investigated the effect of NH₄HF₂ dosage (15–95%) on rare earth element (REE) recovery during the roasting process (600 °C, 120 min), with results presented in Figure 7. As shown in Figure 7a, increasing the NH₄HF₂ dosage from 15% to 35% significantly enhanced the total REE recovery rate from 57.55% to 93.39%. Further increasing the dosage to 75% resulted in gradually decreasing leaching rates for individual elements (Ce: 0.32%, Gd: 0.45%, Nd: 0.32%, Pr: 0.37%), with the total leaching rate stabilizing at 1.19% and the recovery rate reaching 98.81%. However, at 95% dosage, the recovery rate slightly decreased to 98.62%, suggesting that excessive additive amounts may marginally impair fluorination efficiency. The optimal NH₄HF₂ dosage was determined to be 75%, at which point the fluorination reaction reached equilibrium. Figure 7b reveals that the diffraction peaks of fluorinated rare earth compounds intensified progressively with NH₄HF₂ additions up to 75%, but plateaued thereafter, further confirming the 75% dosage as the threshold for maximizing REEs conversion.

3.3. Optimization of NH₄HF₂ Roasting Process Conditions by Response Surface Methodology (RSM)

3.3.1. Box–Behnken Experimental Design

While response surface methodology (RSM) cannot elucidate chemical reaction mechanisms, it serves as an efficient tool for experimental parameter optimization with minimal experimental runs. As an integration of mathematical and statistical approaches, RSM identifies optimal parameter ranges through modeling analysis and establishes corresponding predictive models to determine optimal conditions [29,30]. Compared with full factorial and single-factor experiments, RSM demonstrates superior performance in optimization precision. Among various RSM designs (Box–Behnken Design (BBD), Central Composite Design, and Plackett–Burman Design), the BBD method is particularly advantageous for characterizing the individual and interactive effects of experimental factors on response variables, while effectively mapping the relationship between factors and responses—making it ideal for optimization studies with limited factors [31].

In this study, the BBD-based RSM was employed to systematically evaluate factor effects and their interactions on rare earth recovery rates, ultimately optimizing the NH₄HF₂ roasting process. The experimental design center points were set as follows: roasting temperature 600 °C, duration 90 min, and NH₄HF₂ dosage 65%. The complete factor levels and corresponding coding scheme for the RSM design are presented in

Table 4. Experimental design levels and factors based on RSM principles.

Levels	Factors
	Roasting Temperature (°C)	Roasting Time (min)	NH4HF2 Dosage(%)
−1	500	30	35
0	600	90	65
1	700	150	95

.

3.3.2. BBD Experimental Results

Response surface experiments were conducted based on the BBD principle and the results are shown in

Table 5. Box–Behnken design matrix and rare earth recovery rates.

Run	Roasting Temperature (°C)	Roasting Time (min)	NH4HF2 Dosage (%)	Rare Earth Recovery Rate (%)
1	700	90	35	88.07
2	600	90	65	97.80
3	600	90	65	97.76
4	600	90	65	96.19
5	500	30	65	87.16
6	600	150	35	86.50
7	500	90	35	74.98
8	700	150	65	97.01
9	600	150	95	99.14
10	700	90	95	96.88
11	700	30	65	98.44
12	600	90	65	97.57
13	600	30	95	96.97
14	600	30	35	84.80
15	500	150	65	92.59
16	600	90	65	97.33
17	500	90	95	95.11

.

3.3.3. Statistical Analysis and Analysis of Variance

The ANOVA results for the regression model of rare earth recovery rate from NdFeB waste are presented in

Table 6. ANOVA table for response surface quadratic modeling.

	Sum of		Mean	F	p-Value
Source	Squares	df	Square	Value	Prob > F	significant
Model	702.34	9	78.04	136.94	<0.0001
A-Roasting temperature (°C)	116.62	1	116.62	204.65	<0.0001
B-Roasting time (min)	7.74	1	7.74	13.58	0.0078
C-Mass ratio of NH4HF2 to raw material (%)	361.18	1	361.18	6351	<0.0001
AB	11.80	1	11.80	20.70	0.0026
AC	32.04	1	32.04	56.23	0.0001
BC	0.0558	1	0.0558	0.0980	0.7634
A2	46.22	1	46.22	81.11	<0.0001
B2	0.1989	1	0.1989	0.3490	0.5732
C2	116.45	1	116.45	204.35	<0.0001
Residual	69	7	0.5699
Lack of Fit	2.22	3	0.7416	1.68	0.3072	not significant
Pure Error	1.76	4	0.4411
Cor Total	706.33	16
Fit Statistics
Std. Dev.	0.7549		R2		0.9944
Mean	93.20		Adjusted R2		0.9871
C.V.	0.8100		Predicted R2		0.9457
PRESS	38.35		Adeq Precision		41.9437

. The model demonstrates a highly significant performance (F-value = 136.94, p < 0.0001), indicating only a 0.01% probability of noise interference, which confirms the model’s exceptional reliability [32,33]. The model exhibits outstanding goodness of fit with R² = 0.9944 and adjusted R² = 0.9871, explaining 99.44% of the variance in rare earth recovery rates. The close agreement between predicted R² (0.9457) and adjusted R² further validates the model’s predictive capability [34]. The signal-to-noise ratio (Adeq Precision) of 41.94, significantly exceeding the threshold value of 4, confirms the excellent model resolution, suitable for process optimization. Experimental precision evaluation shows a coefficient of variation (C.V.) of merely 0.81%, demonstrating the high reproducibility and reliability of the experimental data.

Single-factor analysis reveals that roasting temperature (A, F = 204.65, p < 0.0001) and NH₄HF₂ addition amount (C, F = 6351, p < 0.0001) are the dominant factors influencing rare earth recovery, with the additive amount showing particularly significant effects. Although roasting time (B, F = 13.58, p = 0.0078) demonstrates statistical significance, its actual contribution is relatively minor. Interaction analysis indicates significant synergistic effects between temperature and additive amount (AC, F = 56.23, p = 0.0001), as well as between temperature and time (AB, F = 20.70, p = 0.0026), while the interaction between time and additive amount (BC) is insignificant (p = 0.7634). Quadratic term analysis shows that both temperature (A²) and additive amount (C²) quadratic terms are highly significant (p < 0.0001), suggesting nonlinear optimization windows for process parameters where excessively high temperatures may reduce recovery rates.

Model validation results show a lack-of-fit p-value of 0.3072 (> 0.05), confirming no significant factors were omitted and the model fits well. The low pure error (0.4411) further verifies excellent experimental repeatability. Based on these findings, this study recommends prioritizing the optimization of the NH₄HF₂ addition amount and roasting temperature as key process parameters, while fully leveraging their significant synergistic effect (AC). By establishing a coordinated control mechanism between roasting temperature and additive amount, the rare earth recovery rate can be effectively enhanced. This model not only elucidates the quantitative relationship between process parameters and recovery rate, but also provides a scientific optimization framework and reliable theoretical guidance for the resource recovery of NdFeB waste materials.

The experimental dataset comprising 17 trials was initially subjected to multiple regression analysis. Subsequently, the coefficients of the approximating polynomial were determined through least squares fitting, yielding the second-order polynomial Equation (5) that describes the rare earth recovery rate from NdFeB waste.

Rare earth recovery rate (%) = 97.33 + 3.82A + 0.9834B + 6.72C − 1.72AB − 2.83AC + 0.1181BC − 3.31A² − 0.2173B² − 5.26C²

(5)

Figure 8 shows a normal probability plot comparing the predicted and actual values of the dependent variable over the selected range of the independent variable. The plot shows a straight line with negligible residual values, indicating a good model fit. The plot also shows that all data points fall within a narrow range, indicating that the data are normally distributed.

3.3.4. Response Surface Analysis

The corresponding two-dimensional contour plots and three-dimensional response surface plots (Figure 9, Figure 10 and Figure 11) were generated based on the regression equations to investigate the interaction effects between different factors. The slope characteristics of the response surfaces provide intuitive indications of each factor’s influence degree: a steeper slope suggests greater impact on rare earth recovery rate, while a gentler slope indicates relatively minor influence [31].

Figure 9 illustrates the interaction between roasting temperature and time. The results demonstrate that (1) at a fixed roasting duration, the rare earth recovery rate increases rapidly with rising temperature before stabilizing, and that (2) at a constant temperature, prolonged roasting time only leads to a gradual increase in recovery rate followed by stabilization. Particularly noteworthy is that when the roasting temperature reaches 650 °C, the recovery rate becomes essentially unaffected by variations in roasting time. Comparative analysis clearly shows that roasting temperature exerts significantly greater influence on rare earth recovery than duration.

As shown in Figure 10, the interaction between roasting temperature and NH₄HF₂ dosage significantly affects rare earth recovery rate, which is primarily reflected in the steepness of the response surface slope. Experimental results demonstrate that within the temperature range of 500–700 °C, as NH₄HF₂ dosage increases, the rare earth recovery rate first rises rapidly and then stabilizes. A higher NH₄HF₂ dosage is more favorable for promoting the fluorination reaction of rare earth elements. Similarly, when NH₄HF₂ dosage is held constant, increasing roasting temperature also causes the rare earth recovery rate to rise rapidly before reaching a stable state. However, comparative analysis reveals that NH₄HF₂ dosage has a more pronounced effect on rare earth recovery rate.

Figure 11 presents the two-dimensional contour plots and three-dimensional response surface analysis results of the interaction between roasting time and NH₄HF₂ dosage. The study demonstrates that when maintaining a constant NH₄HF₂ dosage, extending the roasting time has a minimal impact on the rare earth recovery rate, which remains essentially stable; with a fixed roasting duration, increasing NH₄HF₂ dosage leads to an initial rapid rise followed by gradual stabilization in rare earth recovery. These findings indicate that NH₄HF₂ dosage serves as the predominant factor influencing rare earth recovery, while roasting time exhibits relatively minor effects, with no significant interaction effect observed between the two parameters.

Systematic analysis of Figure 9, Figure 10 and Figure 11 reveals that among the three process parameters (roasting temperature, duration, and NH₄HF₂ dosage), the NH₄HF₂ addition amount demonstrates the most decisive influence on rare earth recovery rate. Experimental data show that with increasing NH₄HF₂ dosage, the recovery rate exhibits a characteristic pattern of rapid initial ascent followed by gradual stabilization, showing excellent consistency with previous single-factor experiment results. Mechanistic analysis indicates that under high-temperature roasting conditions, when NH₄HF₂ exceeds the optimal dosage, the fluorination reaction with rare earth materials reaches chemical equilibrium. The excess NH₄HF₂ undergoes thermal decomposition at elevated temperatures, releasing gaseous byproducts, and thereby causing the recovery rate to plateau. The study confirms that although synergistic effects exist between roasting temperature and NH₄HF₂ dosage, the ultimate maximum recovery rate is predominantly determined by the optimal NH₄HF₂ addition.

Through response surface methodology optimization, the ideal parameters for rare earth fluorination roasting were established as a 631 °C roasting temperature with an 85 min duration and an 82% NH₄HF₂ dosage, achieving a 99.77% rare earth recovery rate. From a green chemistry perspective, these optimized conditions not only ensure high extraction efficiency but also minimize reagent consumption. Repeated verification experiments confirmed that under these conditions, the relative deviation of recovery rates remains below 3%, demonstrating excellent reproducibility and fully meeting industrial production requirements for process stability.

3.4. Acid Leach Analysis

Under optimal process conditions (roasting temperature 631 °C, reaction time 85 min, NH₄HF₂ dosage 82%), the obtained fluorinated roasted clinker was crushed and ground; it was then leached with 9 mol/L hydrochloric acid solution (liquid-to-solid ratio 4 mL/g) at 80 °C for 2.5 h, followed by drying at 80 °C for 12 h. The final rare earth fluoride product achieved a purity of 99.43% (

Table 7. Rare earth fluoride content.

REF	CeF4	PrF3	NdF3	SmF3	GdF3	DyF3	HoF3	LaF3	EuF3	TbF3	ErF3	YF3	Sum
Content (wt%)	32.22	10.33	48.77	1.75	3.20	2.04	0.71	0.18	0.08	0.12	0.02	0.03	99.43

). This product demonstrates outstanding industrial application value: it can be directly used to prepare ultra-high-purity rare earth oxides and metals to meet high-end application requirements; the process flow is significantly simplified, with a product recovery rate reaching 99.77%, far surpassing the level of comparable processes.

The physical phase and morphology of the acid leaching products under optimal roasting conditions were characterized by XRD and SEM, as shown in Figure 12 and Figure 13. From the XRD patterns, we determined that the characteristic peaks of the fluorinated rare earths in the acid leaching residue were consistent with the standard peaks of NdF₃, CeF₄, PrF₃ and GdF₃, and there were no impurity peaks, which indicated that the fluorinated rare earths were products with homogeneous structures. The SEM patterns showed that the fluorinated rare earths had granular agglomerated structures.

3.5. Recommendations for the Process

In this study, NdFeB waste was crushed and mixed with 82% NH₄HF₂ and roasted for 85 min at 631 °C. Subsequently, the clinker was washed and roasted for 2.5 h at 80 °C with a liquid–solid ratio of 4 mL/g and 9 M hydrochloric acid to obtain fluorinated rare earths. Hydrochloric acid could be added continuously to adjust the pH of the leaching solution during the operation. After drying, the fluorinated rare earth slag can be used for oxidized roasting or molten salt electrolysis to obtain high-purity oxidized rare earths or rare earth metals. At the same time, the leachate can be concentrated and crystallized to obtain FeCl₃-6H₂O crystal products using reduced-pressure distillation. This process, outlined in Figure 14, can realize the synergistic extraction and comprehensive utilization of NdFeB wastes. It is suitable for industrial applications and has good economic benefits. Process optimization recommendations and challenge analysis for scrap materials from different sources (oxidized scrap/non-oxidized magnets) can be systematically improved in the following aspects. First, in the raw material pretreatment stage, establish classification standards based on scrap characteristics to achieve differentiated processing. In the leaching step, focus on developing a temperature-time synergistic control model to optimize reaction efficiency, while adopting a stepwise acid addition method and a dynamic pH regulation system (maintaining the optimal pH range) to reduce hydrochloric acid consumption and stabilize reaction conditions. For exhaust gas treatment, it is recommended to configure a two-stage series scrubber (NaOH + H₂O₂ combination) to achieve the efficient removal of HF and NH₃. To enhance overall economic efficiency, it is advisable to construct a waste heat recovery system to reduce energy costs and establish a hydrochloric acid regeneration system for resource recycling. In the product treatment stage, the process can be shortened by establishing a direct electrolysis process for rare earth slag, while developing deep-processed FeCl₃ products to increase their added value. These improvement measures need to be implemented synergistically to achieve overall process optimization.

4. Conclusions

This study thoroughly investigated the reaction mechanism and process conditions for the recovery of rare earths in NdFeB wastes by a NH₄HF₂ fluoride roasting process, and the research results can provide experimental and theoretical bases for the promotion of pyrometallurgical technology in NdFeB wastes. The main research results are as follows: Thermodynamic analysis indicates that the fluorination reaction between NH₄HF₂ and rare earth oxides (REOs) in NdFeB waste proceeds spontaneously (${\mathsf{\Delta }\mathrm{G}}_{\mathrm{T}}^{\mathsf{\theta }}$ < 0) within the temperature range of 0–1000 °C. NH₄HF₂ decomposes at 225 °C to generate reactive HF gas, which further promotes the fluorination conversion of rare earth elements. Although the thermodynamic driving force slightly decreases when the temperature exceeds 225 °C, experimental results demonstrate that elevated temperatures significantly improve the reaction kinetics and facilitate the progression of the reaction. The optimal roasting process was obtained by a one-factor experiment, with the addition of NH₄HF₂ of 75%, and roasting conditions of 600 °C and 120 min, and the rare earth recovery rate could reach 98.81%. The influence of each process factor was confirmed using a response surface methodology and it was found that the NH₄HF₂ addition had the greatest influence on the fluorination rate of rare earths, followed by roasting temperature and roasting time. The optimum roasting conditions were determined as 82% NH₄HF₂ dosage, 631 °C, and 85 min. The validation experiments showed that the rare earth recovery could reach 99.77% under the optimum process conditions. The rare earth fluoride obtained after acid leaching achieved a purity of 99.43%, meaning it can be directly used as high-quality raw material for molten salt electrolysis or oxidative roasting processes. The solid-state NH₄HF₂ reagent demonstrates superior safety in storage and transportation, while the simplified process flow (roasting → acid leaching) renders it highly promising for industrial-scale applications. This innovative approach effectively addresses key challenges in conventional pyrometallurgical recycling, including poor feedstock adaptability, high energy consumption, and low product value added. By synergizing fluorination conversion with acid leaching, the process achieves efficient rare earth–iron separation while circumventing the massive wastewater generation characteristic of hydrometallurgical methods. Notably, the NH3 byproduct in off-gases can be recycled, and the crystallized FeCl₃·6H₂O byproduct is valorizable, aligning perfectly with green metallurgy principles. Future research should prioritize mechanistic studies of reaction kinetics to further optimize energy efficiency. Although this process shows promising prospects, its industrial application still requires us to address the following issues: Current research has only been completed on a laboratory scale, and pilot-scale verification is needed to assess equipment corrosion, process stability, and economic viability. NH₄HF₂ is highly corrosive, necessitating safety measures such as HF exhaust scrubbing and NH₃ recovery. A comprehensive cost–benefit comparison with wet processes is required to clarify its commercial advantages. Follow-up research should focus on establishing kinetic models, conducting continuous reactor validation, exploring low-corrosivity reagents like NaF/CaF₂ to reduce safety risks, and quantifying the carbon emission reduction benefits of this process compared to traditional methods.