# Evaluating organic acids as alternative leaching reagents for rare earth elements recovery from NdFeB magnets

Sahar Belfqueh, Alain Seron, Simon Chapron, Guilhem Arrachart, Nour-Eddine Menad

<figure><img src="image_1.png" /></figure>

## To cite this version:

Sahar Belfqueh, Alain Seron, Simon Chapron, Guilhem Arrachart, Nour-Eddine Menad. Evaluating organic acids as alternative leaching reagents for rare earth elements recovery from NdFeB magnets. Journal of Rare Earths, 2022, 10.1016/j.jre.2022.04.027. hal-03711357

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https://brgm.hal.science/hal-03711357v1

Submitted on 6 Nov 2024

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1 Evaluating organic acids as alternative leaching reagents for rare earth
2 elements recovery from NdFeB magnets

3 Sahar Belfqueh a,b, Alain Seron a, Simon Chapron a, Guilhem Arrachart b, Noureddine Menad a

4 <sup>a</sup> BRGM, Direction de l’Eau, de l’Environnement, des Procédés et Analyses, Orléans, France.

5 <sup>b</sup> ICSM, Univ. Montpellier, CEA, CNRS, ENSCM, Marcoule, France

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7 *Corresponding author: saharbelf@gmail.com (Sahar Belfqueh); n.menad@brgm.fr (Nourredine Menad)

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9 Abstract

10 This study proposes an advanced leaching method using organic acids to recover rare earth
11 elements (REEs) from NdFeB permanent magnets from end-of-life computers hard disk drives
12 (HDDs). The end-of-life HDDs were first dismantled in order to recover NdFeB magnets,
13 which were then thermally demagnetized at 350°C during 30min before crushing in a ball mill
14 under inert atmosphere. Scanning Electron Microscopy/Energy Dispersive X-ray Spectroscopy
15 (SEM/EDS) analysis performed on the NdFeB magnets showed the heterogeneous structure
16 containing the major matric phase Nd₂Fe₁₄B and the rich-REEs phase containing Nd and Pr
17 oxides. Additionally, X-Ray Diffraction (XRD) and Mossbauer Spectroscopy (MS) analysis on
18 the ground NdFeB magnet showed that grinding NdFeB magnets under inert atmosphere helps
19 to minimize its oxidation. Chemical analysis showed that composition of the ground sample
20 was Nd: 22.8 wt%, Pr: 3.3 wt%, Dy: 1.2 wt%, Fe: 62.6 wt%, Co: 1.5 wt%, B: 0.9 wt%, Ni: 0.6
21 wt%. Diagrams of speciation and equilibrium phases (Eh vs. pH) were calculated to determine
22 the predominance of the formed species in the REEs-organic acids systems. The influence of
23 the organic acid type (acetic acid, formic acid, citric acid and tartaric acid), the acid
24 concentration (10%, up to saturation), and the solid/liquid S/L ratio (0.5-10%) on NdFeB
25 magnets leaching were investigated employing an optimal experimental design conceived by
26 the statistical software JMP. Acetic acid (CH₃COOH) showed the highest leaching performance
27 of REEs, allowing over 90% leaching yields for Nd, Dy and Pr in the acid concentration (mol/L)
28 range of 1.6 – 10 mol/L and the S/L ratio (%) range of 0,5 – 5 using a temperature of 60°C. The
29 results presented in this investigation suggest that REEs could be recovered from magnets of
30 end-of-life HDDs using an eco-friendly method assisted by organic acids.
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**Graphical abstract**

<figure><img src="image_2.png" /></figure>

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NdFeB permanent magnets were extracted from end-of-life hard disk drives, characterized, then ground under inert atmosphere. NdFeB magnets powder was then leached in organic acid solutions. Acetic acid was efficient to leach rare earth elements Nd, Pr and Dy.

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**Keywords**

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NdFeB magnets, Rare earth elements, Leaching, Organic acids, Acetic acid.

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**1 Introduction**

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Due to their high economic importance and supply risks, the European Commission consider the rare earth elements as critical elements¹. The recovery by recycling of industrial waste from technological equipment, and in particular from end-of-life products and waste electrical and electronic equipment "WEEE" could allow access to a significant source of REEs².

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Among WEEE, NdFeB permanent magnets represent the largest application of REEs both in tonnage and in market value³. NdFeB magnets are the most widely used type of REEs based permanent magnets thanks to their high magnetic performances. The main rare earths contained in NdFeB magnets are Neodymium (Nd), Praseodymium (Pr) and Dysprosium (Dy). The REEs content of these magnets is about 30%, which is much higher compared to that of natural REEs ores which ranges from around 0.2% to 1.4%⁴. The European Rare Earths Competency Network (ERECON) suggests NdFeB magnets as priority sector for REEs recycling taking into account the current size of the sector, the future demand, the potential value of the waste stream, the difficulty to find a substitute and the criticality of the REEs used⁵.

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NdFeB magnets are mainly found in wind turbine generators, computers Hard disk drives (HDDs), compressors in air conditioners, electrical vehicles, etc... Their amount varies widely based on the application. Among these different sources, ERECON considers HDDs as the priority in the context of recycling NdFeB magnets. This ranking was made, taking into
account the availability and quantity of the end-of-life (EOL) products, REEs fraction in the product and the ease of recovery ⁵.

For all the reasons mentioned above, the NdFeB magnets contained in EOL hard disk drives are becoming the center of REE recycling. However, despite their significant recycling potential, the recycling of REEs from permanent magnets remains unindustrialized due to numerous obstacles⁶. A status report made in 2011 regarding the recycling of metals claims that REEs recycling rates were globally <1%⁷. Key points can challenge the validity of recycling and need to be considered:

* Difficulty of HDDs dismantling due to compact and complex design,

* Compositional variation of NdFeB magnets even within the same application,

* Costly recycling processes due to strict requirements of the market of REEs in regards of the degree of purity,

* Difficulty of the individual separation of REEs due to their similar chemical properties,

* Presence of unwanted impurities such as high content of Fe and low contents of Co, B and Ni,

Various methods have been studied in order to recover REEs from NdFeB magnets. These methods can be classified into direct reuse⁸, hydrogen derepitation⁹, pyrometallurgical methods¹⁰, hydrometallurgical methods¹¹⁻¹⁴ and, combined pyro- and hydrometallurgical methods¹⁵⁻¹⁷. All these options come with pros and cons.

The present study is particularly interested in the leaching step as part of hydrometallurgical methods. In general, hydrometallurgy processing consists in leaching NdFeB magnets by a chemical attack, with acidic reagents as well as ionic solvents¹⁸. The obtained mineral concentrate is then subjected to a separation step using selective precipitation¹⁹,²⁰, liquid-liquid extraction²¹,²² or a combination of both of these techniques. The hydrometallurgical method offers significant advantages such as being adjustable to all types of NdFeB wastes and applicable to magnets with large variations in composition, besides allowing the separation of all metals with very high level of purity in order to allow reusing in new technologies.

In 1993, Lyman and Palmer¹¹ developed one of the first hydrometallurgical methods for NdFeB magnets recycling. Their method allows complete leaching of NdFeB magnet powder in a 2 mol/L sulfuric acid (H₂SO₄) solution using a solid to liquid (S/L) ratio of 10%. The leachate was then treated by selective precipitation. The used leaching conditions resulted in a leachate with a pH of 0.2, which prevented Fe from precipitating. Using higher acid concentrations and S/L ratios resulted in the precipitation of Nd and Fe because their solubilities were exceeded.

More recently, other mineral acids such as hydrochlorydric acid (HCl) and nitric acid (HNO₃) have shown their effectiveness due to the complete leaching of NdFeB magnets ²³. Although very effective, nitric acid led to the production of nitrate-rich effluents, which are difficult to treat. Although they are very effective in dissolving magnets, these strong mineral
96 acids have the major drawback of being delicate to handle and of having a potential strong
97 environmental impact.

98 Using organic acids as leaching reagents could be a good substitution to mineral acids
99 because they are easier and less dangerous to handle, lead to lower emissions of poisonous gas,
100 and have lower acidities and easier degradability.

101 In 2016, Behera and Parhi<sup>24</sup> investigated the kinetics of Nd leaching from NdFeB scraps
102 using acetic acid (CH<sub>3</sub>COOH). This study shows that using acetic acid in concentrations higher
103 than 0.4 mol/L, to treat NdFeB magnets at a solid/liquid ratio of 1% and a temperature of 80°C
104 leads to successful Nd leaching with yields over 99% along with the co-leaching of Fe. Menad
105 et al.<sup>25</sup> confirm the efficiency of acetic acid in leaching Nd (> 90%) out of NdFeB magnets after
106 7 hours. It was also efficient in leaching Dy (> 90%) and Fe (> 90%), and selective towards Ni
107 (0%), contained in protective surface coating, which could be recovered in the solid phase after
108 filtration.

109 In 2018, Gergoric et al.<sup>26</sup> studied the leaching of roasted NdFeB magnets using acetic
110 acid and citric acid. The highest leaching yields were obtained with 1 mol/L citric acid (C<sub>6</sub>H<sub>8</sub>O<sub>7</sub>)
111 (where Nd, Dy and Pr were totally leached after 24 h) and 1 mol/L acetic acid (where > 95% of
112 Nd, Pr and Dy were leached) using a solid/liquid ratio of 3%. However, other metals showed
113 similar trends and no selective leaching was achieved between REEs and Fe, B and Co. A more
114 recent study<sup>21</sup> considered maleic (C<sub>4</sub>H<sub>4</sub>O<sub>4</sub>), glycolic (C<sub>2</sub>H<sub>4</sub>O<sub>3</sub>) and ascorbic (C<sub>6</sub>H<sub>8</sub>O<sub>6</sub>) acids for
115 REEs leaching out of NdFeB magnets. Yields of 95% were reached for Nd, Dy and Fe using a
116 concentration of 1 mol/L of maleic acid and glycolic acid and a solid/liquid ratio of 1% after 7
117 hours. Ascorbic acid was less efficient at room temperature, but increasing the leaching
118 temperature to 70°C allowed reaching similar values than those observed with maleic and
119 glycolic acids. Again, Fe was co-leached along with REEs in all cases.

120 In a more recent study, Reisdorfer<sup>27</sup> investigated the leaching of roasted and unroasted
121 NdFeB magnets using malic acid and citric acid in order to recover Nd. Both of those acids
122 have shown good leaching behavior on unroasted NdFeB powder. Using citric acid at 1 mol/L,
123 a temperature of 90°C, and a solid/liquid ratio of 5% allowed the leaching of 73% of Nd after
124 1 hour. In the same conditions, after 6 hours, the leaching of 99% of Nd is obtained using malic
125 acid. While the leaching of the unroasted NdFeB powder showed no selectivity between Nd
126 and Fe, the leaching of the roasted NdFeB powder provided good selectivity, but the Nd
127 leaching yield decreased.

128 Based on these studies, the use of organic acids seems to be very effective in the leaching
129 of REEs from NdFeB magnets and can therefore be a good alternative to strong mineral acids.
130 The overall cost and ecological impact of the global process can also be reduced if the organic
131 acids are provided from agro-industrial wastes such as wastewater from food industries<sup>27</sup>. The
132 leaching methods using organic acids present in the literature are summarized in Table 1.

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<table><caption>Table 1 Summary of operational conditions for REEs hydrometallurgical recovery from NdFeB magnets using organic acids.</caption><thead><tr><th>Material</th><th>Leaching agent(s)</th><th>Optimal experimental conditions</th><th>Leaching yields</th><th>Reference</th></tr></thead><tbody><tr><td>Pulverized NdFeB powder 106–150 µm</td><td>Acetic acid</td><td>S/L ratio = 1% [Acid] > 0.4mol/L T° = 80°C</td><td>Nd 99% Fe was co-leached</td><td>24</td></tr><tr><td>Ground NdFeB powder</td><td>Acetic acid</td><td>S/L ratio = 5% [Acid] = 1.6mol/L T° = 30°C</td><td>Nd, Pr, Dy > 90% Fe(II) 20%</td><td>25</td></tr><tr><td>Hydrogen decrepitated NdFeB powder <355 µm, roasted at 400°C for 1.5h</td><td>Acetic acid, Citric acid</td><td>S/L ratio = 3% [Acid] = 1 mol/L T° = 25°C</td><td>Nd, Pr, Dy > 95% Fe, Co and B were co leached</td><td>26</td></tr><tr><td>Hydrogen decrepitated NdFeB powder <355 µm, roasted at 400°C for 1.5h</td><td>Glycolic acid, Maleic acid, Ascorbic acid</td><td>S/L ratio = 1% [Acid] = 1 mol/L (Glycolic acid and maleic acid) T° = 50°C</td><td>Nd, Dy, Pr 95% Fe was co-leached</td><td>21</td></tr><tr><td>NdFeB powder <400 µm, roasted at 900°C for 8h</td><td>Malic acid, Citric acid</td><td>S/L ratio = 5% [Acid] = 1 mol/L (Malic acid) T° = 90°C</td><td>Nd 99%</td><td>27</td></tr></tbody></table>

However, more in-depth studies must be considered to better highlight the potential of organic acids as leaching agents. The current state of art reveals a lack of experimentations regarding the behavior of less abundant rare earths (Dy, Pr...) and other elements (Co, B, Ni...) contained in NdFeB magnets. Moreover, the process parameters such as acid concentration and solid/liquid ratio are studied in narrow intervals.

Hence, the present study investigates the leaching of REEs and other elements from EOL NdFeB powder using acetic, citric, formic and tartaric acids through a multi-parametric study which includes wide conditions of acid concentration and S/L ratio. The study follows a
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design of experiments technique. Before conducting the leaching experiments, the NdFeB

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magnets were characterized using different analytical techniques before and after their pre-

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treatment. This step is crucially important because the magnets' quality and pre-treatment

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conditions can have a huge influence on the leaching efficiency of REEs.

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## 2 Materials and methods

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### 2.1.1 Sample preparation

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Various brands of EOL Hard Disk Drives (HDDs) were obtained from a French

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recycling industry company. After sampling a ton of HDDs to get a representative sample of a

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few HDDs, the NdFeB magnets were manually recovered and then demagnetized by heat

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treatment above the Curie temperature, at 350°C, in Muffle furnace. Finally, the demagnetized

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magnets were crushed using a hammer and then ground in a ball mill, in order to obtain particles

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smaller than 100µm ready for chemical processing. Crushing and milling were done in an inert

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atmosphere as a safety precaution to prevent the pyrophoric character²⁸ of NdFeB magnets and
to consequently minimize their oxidation.

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### 2.1.2 Material characterization

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Scanning electron microscopy and energy dispersive X-ray spectroscopy (SEM/EDS)

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analysis using a Jeol 7000 instrument were undertaken on a broken and a polished section of

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NdFeB magnet for targeted analysis of sample surfaces. In order to determine their chemical

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composition, representative samples of NdFeB magnets extracted from HDDs were digested in

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aqua regia and the solution was then analyzed using microwave plasma atomic emission

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spectrometer (MP-AES). The crystalline phases present in the NdFeB powder and the leach

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residues were identified by X-Ray diffraction (XRD) using a Bruker D8 Advance. Moreover,

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⁵⁷Fe Mossbauer spectroscopy was performed to analyze the initial iron oxidation states

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contained in NdFeB magnet powder samples, which were ground in an inert atmosphere. A

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diagram summarizing the pre-treatment and characterization of NdFeB magnets is shown in

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Figure 1.
<figure><img src="image_3.png" /><figcaption>Figure 1 Flow chart of NdFeB magnets pretreatment and characterization.</figcaption></figure>

### 2.1.3 Leaching procedure

In order to predict species formed from NdFeB magnet powder during the leaching process, thermodynamic calculations were carried out using the geochemical software pHreeqC (version 3.0) with the equilibrium constants of the LLNL database (Lawrence Livermore National Laboratory) for REEs and MINTEQ database for Fe(II) and Fe(III). Eh-pH diagrams were built using the HSC Chemistry 7 software. Nd₂Fe₁₄B phase is not available in HSC's and pHreeqC's databases. Therefore, each element was entered as an elemental substance, and calculations were based on the composition of the magnet used in this study.

Due to the limited database on REEs complexes, only speciation of REEs in acetic acid was performed. Speciation calculations using pHreeqC were performed between pH 1 and 13 at 30°C and atmosphere pressure of 1 atm. Further calculations using HSC were performed between pH 0 and 14 and Eh between -2 and 2 Volts at 30°C and 1 atm pressure.

Various leaching tests were performed on the NdFeB magnet powder using formic acid, acetic acid, citric acid and tartaric acid. The leaching experiments were carried out in closed Erlenmeyer flasks immersed in a thermostatically controlled back and forth stirring water bath in order to adjust the temperature as required for each experiment. Typically, 50 mL of organic acid solution of the desired concentration were added to the Erlenmeyer flasks. Then, the NdFeB magnet powder was added to the acid solution.
The start of the experiments (t = 0 min) is taken into account when the flasks were placed in the thermostatically controlled stirring water bath. Leaching time was held constant at 24h to ensure maximum leaching of metals. Minimum agitation speed required to keep all particles in suspension (200 rpm) was applied during the leaching step.

After completing the leaching time, the leachates, containing the dissolved elements, were separated from solid residues by centrifugation at 10000rpm for 5 minutes, then filtered using 0.45 µm filters and finally diluted in a 4% HNO₃ solution to submit them for the metal concentrations determination by MP-AES analysis. The leaching residues were dried in an oven at 60 °C for 24 h and then characterized by XRD.

### 2.1.4 Design of experiments

The design of experiment (DOE) was used to study the effect of three parameters: Solid to Liquid (S/L) ratio, acid concentration and temperature, on the leaching efficiency of the REEs coming from NdFeB magnet.

The leaching yield of elements was calculated as below:

$$ \%Y = \frac{C_i - C_f}{C_i} \qquad \text{Eq. 1} $$

Where Cᵢ is the expected initial concentration of the considered element in the leachate if considering total leaching of such element from the NdFeB magnet and Cf is the concentration of this element in the leachate.

In order to determine effects of independent parameters on the leaching of REEs from NdFeB magnet powder, an optimal design consisting of 15 runs was performed. The JMP v14.1 statistical data analysis software was used to consider the optimal design experiment through the regression analysis of the obtained data. The parameter levels are given in Table S1 (supporting information). The acid concentrations used for the high-level experiments are the ones obtained at saturation while for the low level the concentrations considered are ten times more diluted. The experiments were done in triplicate and the design of experiments was used for each organic acid tested at two different leaching temperatures (30°C and 60°C).

## 3 Results and discussion

### 3.1 Characterization of the NdFeB magnets

Preliminary characterization was performed on the EOL NdFeB magnets in order to check the quality and to determine the chemical and phase composition of the waste, which can both greatly affect the leaching efficiency of REEs.

First, the chemical composition of the NdFeB sample used in this study was determined; the results are summarized in Table 2. The major elements present in the magnet were Fe, Nd, Pr, Dy, Co, B and Ni constituting 93 wt% of the magnet. These results are in agreement with other works¹⁹,²⁹,³⁰.
<table><caption>Table 2 Chemical composition of NdFeB magnets.</caption><thead><tr><th>Elements</th><th>B</th><th>Co</th><th>Dy</th><th>Fe</th><th>Nd</th><th>Ni</th><th>Pr</th></tr></thead><tbody><tr><td>Wt %</td><td>0.9</td><td>1.5</td><td>1.2</td><td>62.6</td><td>22.8</td><td>0.6</td><td>3.3</td></tr><tr><td>RSD* (%)</td><td>1.4</td><td>3.2</td><td>3.0</td><td>1.4</td><td>7.9</td><td>8.5</td><td>1.9</td></tr></tbody></table>

*RSD: Relative Standard Deviation (ratio of the standard deviation to the mean).

The morphological aspect of a broken piece of NdFeB magnet without coating²⁵ was studied by SEM/EDS (Figure 2). This image shows that such magnets are mainly made up of small sized tetrahedral grains (of approximately 5µm diameter/length) corresponding to the Nd₂Fe₁₄B matrix according to the EDS analysis. Intergranular spaces are filled with the inter-granular phases, which are rich in oxidized REEs (Nd, Pr, Dy).

<figure><img src="image_4.png" /></figure>

<caption>Figure 2 SEM/EDS image showing morphological and chemical aspects of a NdFeB magnet.</caption>

Sintered magnets are sensitive to humid environments and are usually coated with Ni. Figure 3 shows the Ni protective coating of the characterized NdFeB magnet, which consists in a layer of approximately 23 µm thick. Other types of coatings of sintered NdFeB magnets are known to be used such as Zn, Al, Sn or Cu³¹. However based on the chemical composition (Table 2) and SEM/EDS analysis, none of these metals was found, indicating that Ni coating is the main coating of NdFeB magnets used in this study.
<figure><img src="image_5.png" /><figcaption>Figure 3 Backscattered-Electron (BSE) imaging and EDS graph of the NdFeB magnet polished surface showing the size and chemical composition of the Ni coating.</figcaption></figure>

For further characterization, the polished section of an NdFeB magnet was studied by SEM/EDS. The chemical contrast of the magnet's polished section is presented in Figure 4 (left, top). The latter shows the heterogeneous microstructure of the material. The compositions of the polished section at the specific locations 1, 2 and 3 were analyzed using EDS mapping and are listed in Table 3.

The chemical maps show that Fe is the most abundant element in the dark grey phase (1) in which it represents around 71.9%. This phase also contains around 22.1% of Nd. Indeed, this corresponds to the hard magnetic matrix phase Nd₂Fe₁₄B, which makes up to 94% of the weight of the system. Commonly, the Nd₂Fe₁₄B phase contains 72% Fe and 27% Nd, but in this magnet, a small part of Nd has been substituted with Pr due to its close properties and lower price.

Nd and Pr are concentrated in the grain boundaries (light grey (2) and medium grey (3) phases). These phases represent the rare earth-rich boundary phase, which contains more than 60% of Nd, and more than 19% of Pr. The phase (3) is slightly more oxidized than the phase (2) since the oxygen (O) weight percentage is a little bit higher. Indeed, during the sintering process, oxygen can be infused into this rare earth-rich boundary phase due to its high reactivity. As a result, rare earth oxides are formed such as NdO, Nd₂O₃ and NdO₂ phases³². The presence of Nd₂O₃ and Pr₂O₃ phases was also confirmed by XRD on the ground magnet (see below).

In addition, the elemental mapping shows that the Co distribution is concentrated in phase (1), which means that Co was mainly added in the Nd₂Fe₁₄B matrix phase. A portion of Fe is usually substituted by Co in order to raise the magnet's Curie temperature and reduce the rate at which the magnetic field strength changes as a function of temperature ³³.

Furthermore, the SEM/EDS analysis on the broken section and the polished section of demagnetized NdFeB magnets show that their microstructure is identical to a raw magnet's microstructure³⁴. This indicates that the prior heat treatment for demagnetization would not have an effect on the leaching step of the NdFeB magnets.
<figure><img src="image_6.png" /><figcaption>Figure 4 High-resolution EDS mapping of the main elements on the NdFeB magnet polished surface showing the material's chemical contrast.</figcaption></figure>

<table><caption>Table 3 Elemental composition of domains 1-3 mentioned in Figure 4 determined by EDS.</caption><thead><tr><th rowspan="2">Elements</th><th colspan="2">1 (Dark grey)</th><th colspan="2">2 (Light grey)</th><th colspan="2">3 (Medium grey)</th></tr><tr><th>Wt %</th><th>mol %</th><th>Wt %</th><th>mol %</th><th>Wt %</th><th>mol %</th></tr></thead><tbody><tr><td>Fe</td><td>71.9</td><td>86.3</td><td>2.0</td><td>3.0</td><td>3.1</td><td>3.5</td></tr><tr><td>Nd</td><td>22.1</td><td>10.3</td><td>63.7</td><td>37.1</td><td>62.3</td><td>27.6</td></tr><tr><td>O</td><td></td><td></td><td>9.0</td><td>47.2</td><td>15.0</td><td>60.0</td></tr><tr><td>Pr</td><td>5.7</td><td>2.7</td><td>21.4</td><td>12.8</td><td>19.6</td><td>8.9</td></tr><tr><td>Co</td><td>0.3</td><td>0.7</td><td></td><td></td><td></td><td></td></tr></tbody></table>

First, a small quantity of NdFeB magnets was ground under ambient atmosphere. This experiment highlighted the pyrophoric character (spontaneous self-ignition under ambient conditions) of NdFeB magnets. Thus, NdFeB magnets were then ground under inert atmosphere (N₂) for safety reasons. The resulting magnet powders from the grindings under these two different atmospheres were characterized by XRD in order to see if the exposure of NdFeB magnets to oxygen during the grinding process induces structural changes. Figure 5 illustrates the XRD patterns of the ground NdFeB magnets and Table S2 (supporting information) gathers the amounts of the identified crystalline phases.
<figure><img src="image_7.png" /><figcaption>Figure 5 XRD graph of ground NdFeB magnets. Sample A: in an inert atmosphere, sample B: in air atmosphere.</figcaption></figure>

When ground under inert atmosphere (sample A), the dominant phase present in the resulting powder is the hard magnetic phase Nd₂Fe₁₄B in addition to low quantities of rare earth oxides. On the other hand, when ground under air atmosphere (sample B), the XRD pattern shows new peaks corresponding to Fe and NdFeO₃. This must have been caused by the decomposition and the partial oxidation of the Nd₂Fe₁₄B phase.

Indeed, during the magnets oxidation, the NdO present in the rare-earth rich boundary phase transforms into Nd₂O₃ according to the reaction (Eq. 2) and the Nd₂Fe₁₄B oxidation occurs through two reactions (Eq. 3) and (Eq. 4). In addition, Fe₂O₃ and Nd₂O₃ combine to form the mixed oxide NdFeO₃ (Eq. 5)³⁵. The formation of such mixed oxides is problematic since these phases are not soluble under mild conditions and can cause a decrease of REEs leaching rates³⁶,³⁷.

$$2 \text{NdO} + 1/2 \text{O}_2 (\text{g}) \rightarrow \text{Nd}_2\text{O}_3 \qquad \text{Eq. 2}$$

$$\text{Nd}_2\text{Fe}_{14}\text{B} + 3/2 \text{O}_2 (\text{g}) \rightarrow \text{Nd}_2\text{O}_3 + 14 \text{Fe} + \text{B} \qquad \text{Eq. 3}$$

$$2\text{Fe} + 3/2 \text{O}_2 (\text{g}) \rightarrow \text{Fe}_2\text{O}_3 \qquad \text{Eq. 4}$$
$$Fe_2O_3 + Nd_2O_3 \rightarrow 2 NdFeO_3$$

Eq. 5

Therefore, NdFeB magnets must be ground under inert atmosphere in order to avoid the pyrophoric character of NdFeB magnets, and the formation of mixed oxides such as NdFeO₃, which hinder the REEs leachability under mild conditions.

Moreover, Mössbauer spectroscopy was applied to NdFeB magnet powder ground under inert atmosphere in order to study the structural state of iron atoms. The Mössbauer spectrum of the sample and the corresponding Mössbauer parameters are provided in Figure S1 and Table S3 (supporting information).

The Nd₂Fe₁₄B phase has a tetragonal crystal structure with 68 atoms in the unit cell. The Fe atoms in Nd₂Fe₁₄B are located in six types of structure non-equivalent positions: k1, k2, j1, j2, e and c indicated in Table S3. Hence, the Mössbauer spectrum of Nd₂Fe₁₄B can be described in the model of six sextets corresponding to the six possible states of Fe atoms. The spectrum is in good agreement with the six-sextet model of the NdFeB magnet³⁸. However, the spectra reveals an additional doublet corresponding to Fe(III). The presence of this doublet may indicate the presence of little amounts of iron oxides due to the matrix dissociation during the grinding process. Nevertheless, these results show that grinding NdFeB in an inert atmosphere helps minimizing structural modifications in the material since the relative contribution of the doublet to the spectrum does not exceed 2%.

## 3.2 NdFeB magnet powder leaching using organic acids

### 3.2.1 Thermodynamic considerations

Thermodynamic calculations have been performed in order to predict species formed from NdFeB magnet powder during the leaching process. The results showed that Nd, Pr and Dy have similar speciation in acetic acid. For this reason, only speciation calculations of Nd in acetic acid are given as a representative example in the Figure S2 (supporting information). At low pH (<2.5), REEs mainly occur as REE³⁺. Within the pH range of 2.5 – 9.5, REE-acetates (REE(CH₃COO)₃)³⁺, j = 1, 2, 3) are the most dominant species in the solution. Under more alkaline conditions, REEs mainly occur as REEO₂⁻, REEO₂H and REEO⁺.

In addition, speciation calculations were also performed on Fe, the main component of NdFeB magnets (supporting information, Figure S3). At low pH (<2), Fe(III) mainly occurs as Fe³⁺. Between the pH value of 2 and 5, Fe(III) mainly occurs as soluble acetate complexes (Fe(CH₃COO)₃)³⁺, j = 1, 2, 3). Within the pH range of 5 – 8, Fe(OH)₂⁺ is the predominant species and in more alkaline conditions, Fe occurs mainly as Fe(OH)₄⁻.

Fe(II) speciation was also examined showing that at low pH (<2), Fe is mainly in the form of Fe²⁺. Within the pH range of 2 – 8.5, Fe²⁺ and Fe(CH₃COO)⁺ are the predominant species. Within the pH range of 8.5 – 10.5, Fe²⁺ and FeOH⁺ are the predominant species. The most dominant species in more alkaline conditions are FeOH⁺ and Fe(OH)₃⁻.

To sum up, based on the calculations, an illustration of the speciation as a function of pH is provided in Figure 6.
<figure><img src="image_8.png" /><figcaption>Figure 6 Sum up of the speciation of Fe and REEs in acetic acid media as a function of pH.</figcaption></figure>

Furthermore, Eh-pH diagrams for the systems Nd-acetic acid and Pr-acetic acid (supporting information, Figure S4) highlight that soluble complexes are obtained in a large pH range (0 – 10 for Nd and 0 – 7.5 for Pr). Pr and Nd have quite similar stability regions and must have a similar behavior to leaching in this system. In comparison, Fe leaching in acetic acid is only thermodynamically favored in the Eh range of -0.2 – 0.8 Volts and the pH range of 0 – 7.5 in the form of $Fe(CH_3COO)^+$ in diluted and saturated acetic acid solutions (supporting information, Figure S5). Hence, the diagrams show that, generally, Nd and Pr leaching in acetic acid is thermodynamically preferred over Fe leaching.

### 3.2.2 Effect of acid type

Organic acid type such as monocarboxylic acid (formic and acetic acid), dicarboxylic acid (tartaric acid) or tricarboxylic acid (citric acid) has been considered for the leaching of NdFeB magnet powder. It should be mentioned that the leaching behavior of Nd, Pr and Dy is similar regardless of the nature of the acid. Therefore, in order to summarize the results, only the effect of acid type on the leaching of Nd, as representative of the REEs present in NdFeB magnet, is provided. The leaching yields of Nd in each tested acid are illustrated in contour plots as a function of S/L ratio and acid concentration using a temperature of 60°C (Figure 7).

These results show that the nature of organic acid used in the leaching process is a critical parameter that can influence the leaching behavior of REEs in a significant way. The highest leaching efficiencies for REEs were obtained using acetic acid. Overall, based on the REEs leaching yields, the examined organic acid can be ranked in order of decreasing leaching efficiency as follows: acetic acid > citric acid > formic acid > tartaric acid.

In addition to allowing high REEs leaching yields, the use of acetic acid allows the extension of S/L ratio and acid concentration ranges for which more than 90% of REEs are leached as illustrates the green zone of the contour plot on Figure 7 (a). Thus, using acetic acid, efficient REEs leaching (> 90%) is possible under industrially favorable conditions: low acid concentration (1.6 mol/L) and high S/L ratios (10%). These results are validated by the thermodynamic considerations presented above and are in concordance with previous studies²⁴,²⁶.
<figure><img src="image_9.png" /><figcaption>Figure 7 Contour plots showing the effects of S/L ratio and acid concentration on the leaching yield of Nd from the NdFeB magnet powder using different organic acids: (a) acetic acid, (b) formic acid, (c) citric acid and (d) tartaric acid. Colored contour bands represent ranges of the leaching yield values from the lowest values (red) to the highest values (green). Leaching temperature: 60°C; leaching time: 24h.</figcaption></figure>

On the other hand, citric acid allows high REEs leaching yields of up to 95%, but under very specific operating conditions that are not industrially favorable, as can be seen on Figure 7 (c). Moreover, formic acid and tartaric acid are the two least efficient leaching agents, as the highest yields obtained using these acids are 73% and 35% respectively. The reactions between formic acid and NdFeB magnet powder led mainly to the formation of insoluble REE-formates that were disclosed by analyzing the leach residues using XRD (Figure 8). Similarly, for tartaric acid, insoluble Nd hydroxides were found, in small quantities, in the leach residues (Figure 9).
<figure><img src="image_10.png" /><figcaption>Figure 8 X-ray diffraction pattern of the leach residue. Leaching agent: 1.9 mol/L formic acid; S/L ratio: 10%; temperature: 60°C; leaching time: 24h.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Figure 9 X-ray diffraction pattern of the leach residue. Leaching agent: 0.4 mol/L tartaric acid; S/L ratio: 10%; temperature: 60°C; leaching time: 24h.</figcaption></figure>
385 Leaching of metals by organic acids generally occurs through protonation, chelation and ligand exchange reactions. Hence, the leaching could be governed by the acid dissociation extent. This dissociation is quantified by the pKa constant: the lower the pKa value, the higher the dissociation rate. However, acetic acid has the highest pKa (4.76) compared to the other acids with first pKa values of 3.8, 3.1, 3.0 respectively for formic acid, citric acid and tartaric acid. However, metal leaching in organic acids does not only depend on the availability of protons provided by the acid. It is also influenced by the type of counter ions present in the leachate and the stability of the metal complexes formed in the solution. Thus the greater the stability of the formed complexes, the higher the metal leaching yields.

394 Furthermore, from an economic point of view, it should also be noted that acetic acid offers the advantage of being less expensive than citric or tartaric acid.

396 **3.2.3 NdFeB magnet powder leaching using acetic acid**

397 **3.2.3.1 Effect of S/L ratio**

398 In a hydrometallurgical process, the right choice of the S/L ratio is of great importance. Indeed, the optimization of S/L ratio allows a compromise between the efficiency of the leaching process and the cost of the process linked to the equipment's size and design.

401 In this study, the S/L ratio was varied between 0.5% and 10%. The regression model's equations of the leaching process (supporting information, Eq. S1 – Eq. S7) show that the S/L ratio is the most influential factor on the elements leaching compared to acid concentration or temperature. The higher the S/L ratio, the lower the leaching yields of REEs and other elements. This may be because the increase of S/L ratio leads to a decrease in the renewal of the liquid/solid interface at the periphery of the grains, which is a consequence of the decrease in the stirring speed of the solution. This negative influence on leaching efficiency is accentuated in the case of Fe, Ni and Co.

409 The leaching yields of Nd, Pr and Dy in acetic acid are represented in contour plots as a function of S/L ratio and acid concentration using a temperature of 60°C (Figure 10).

411 The contour plots show that the negative effect of the S/L ratio is more important when using high acid concentrations. This is due to the combination of the effect of the S/L ratio (A) factor and the effect of the acid concentration (B) that are both negative, as evidenced by the negative coefficients of the factors A and B in the regression model's equations (supporting information, Eq. S1 – Eq. S7). Furthermore, the effect of the interaction of these two factors (AB) is also negative. Thus, when using a low acid concentration such as 1.6 mol/L, increasing the S/L ratio up to 10% allows maintaining high leaching yields for REEs: 80% for Nd, 75% for Pr and Dy.
<figure><img src="image_12.png" /><figcaption>Figure 10 Contour plots showing the effects of S/L ratio and acid concentration on the leaching yield of (a) Nd, (b) Dy and (c) Pr using acetic acid. Colored contour bands represent ranges of the leaching yield values from the lowest values (red) to the highest values (green). Leaching temperature: 60°C; leaching time: 24h.</figcaption></figure>
### 3.2.3.2 Effect of acetic acid concentration

The effect of acetic acid concentration on the leaching of REEs and other elements was studied in the range of 1.6 mol/L to saturation (16.3 mol/L). As shown by the coefficients of the factor B (acid concentration) on the regression model's equations (supporting information, Eq. S1 - Eq. S7), the acid concentration is the second most influential factor after S/L ratio with a negative effect on the leaching of all elements except for Ni for which the effect is weak and positive.

Contour plots on Figure 10 show that the use of a low acid concentration (1.6 mol/L) allows high REEs leaching yields of around 80% in a wide S/L ratio (%) range 0.5 – 10. As the acid concentration increases, the S/L ratio range for which the REEs leaching is efficient shrinks. Therefore, using a saturated acid solution, REEs leaching yields of around 80% can only be achieved in a S/L ratio (%) range of 0.5 – 4. This may be due to the negative effects of S/L ratio and acid concentration but also to their negative interaction.

When the NdFeB magnet powder is brought into contact with acetic acid solution, the main reactions taking place in the solution can be written as follows:

$$ \mathrm{CH_3COOH(aq) + H_2O \rightleftharpoons CH_3COO^- (aq) + H_3O^+ (aq)} \qquad \textbf{Eq. 6} $$

$$ \mathrm{REE(s) + 3H_3O^+ (aq) \rightleftharpoons REE^{3+} (aq) + 3/2H_2(g) + 3H_2O(l)} \qquad \textbf{Eq. 7} $$

$$ \mathrm{Fe(s) + 2H_3O^+ (aq) \rightleftharpoons Fe^{2+} (aq) + H_2(g) + 2H_2O(l)} \qquad \textbf{Eq. 8} $$

$$ \mathrm{Fe(s) + 3H_3O^+ (aq) \rightleftharpoons Fe^{3+} (aq) + 3/2H_2(g) + 3H_2O(l)} \qquad \textbf{Eq. 9} $$

$$ \mathrm{REE^{3+} (aq) + jCH_3COO^- (aq) \rightleftharpoons REE(CH_3COO)_j (^{(3-j)+} (aq), j = 1, 2, 3)} \qquad \textbf{Eq. 10} $$

The negative effect of acid concentration on REEs leaching may be due to Le Chatelier effect, which predicts that, the dissociation of acetic acid reaction's (Eq. 6) equilibrium will shift to the left as “free” ions concentration increases³⁹. Moreover, when using low acid concentrations, the final pH value of the leachate ranges between 3 and 6, depending on the used S/L ratio. In this pH range, ferric ions are not stable, as they undergo hydrolysis and form goethite as described in the reaction below (Eq. 11). The hydrolysis of ferric ions contributes to proton regeneration, a phenomenon that can improve REEs leaching. Indeed, characterization of the leach residues using XRD, indicated the presence of goethite as shown in Figure 11. It was not possible to identify the non-indexed peaks in Figure 11 using the available database (ICDD: International Centre for Diffraction Data).

$$ \mathrm{Fe^{3+} + 2H_2O \rightleftharpoons FeO(OH) + 3H^+} \qquad \textbf{Eq. 11} $$
<figure><img src="image_13.png" /><figcaption>Figure 11 X-ray diffraction of the leach residue. Leaching agent: 1.6 mol/L acetic acid; S/L ratio: 10%; temperature: 60°C; leaching time: 24h. The non-indexed peaks were not identified.</figcaption></figure>

### 3.2.3.3 Effect of temperature

Based on the regression model's equations (supporting information, Eq. S1 – Eq. S7), the temperature factor shows a positive effect on the leaching of all studied elements (REEs, B, Ni and Co) except for Fe. Compared to the other studied factors, temperature shows the weakest influence on all elements leaching except for Ni for which temperature plays a bigger role than acid concentration. The positive effect of temperature on the leaching of REEs and the other elements is undoubtedly related to the endothermic nature of their leaching reactions.

For REEs, when increasing the temperature from 30°C to 60°C, the leaching yields of Nd, Pr and Dy increased from 62% to 85%, 65% to 77% and 53% to 73%, respectively, using a S/L ratio of 10% and an acetic acid concentration of 1.6 mol/L.

Furthermore, as said earlier, being a weak acid, the ability of acetic acid to leach metals is influenced by its degree of dissociation. The higher the temperature, the more the acid dissociates and provides protons and ligands for the leaching process. In the case of acetic acid, the relation between temperature and pKa is parabolic and given by the following equation⁴⁰:

$$pKa - pKm = C (T - \theta)^2 \qquad \text{Eq. 12}$$

Where T is the temperature in degrees Celsius, pKm is the minimum value of pKa at temperature θ, and C is an arbitrary constant of the order of 5x10⁻² degrees. Thus, this could explain why increasing the temperature favors the leaching of REEs, Ni, B and Co in acetic acid.
469

470

471

On the other hand, Fe is the only metal whose leaching is negatively affected by the increase of temperature. This may be due to the fact that increasing temperature favors the precipitation of leached Fe as goethite$^{41}$, which has been observed experimentally.

472

### 3.2.3.4 Leaching behaviour of other elements

473

474

475

476

477

478

Selective leaching of REEs from other elements present in NdFeB magnet powder such as Fe, Ni, B and Co is of great potential benefit to the global hydrometallurgical process. Selective leaching ensures the reduction of purification steps and the maximization of the final product's value. For this reason, the leaching of other elements is investigated and discussed in the following. The leaching yields of Fe, B, Co and Ni in acetic acid at 60°C as a function of acid concentration and S/L ratio are illustrated in the form of contour plots in Figure 12.

<figure><img src="image_14.png" /></figure>

479

480

481

482

483

<caption>Figure 12 Contour plots showing the effects of S/L ratio and acid concentration on the leaching yield of (a) Fe, (b) B, (c) Co and (d) Ni using acetic acid. Colored contour bands represent ranges of the leaching yield values from the lowest values (red) to the highest values (green). Leaching temperature: 60°C; leaching time: 24h.</caption>

484

485

486

487

488

489

490

As seen before, Fe is the most abundant element in NdFeB permanents magnets representing around 63% of its weight (Table 2). According to Figure 12 and the regression model's equations (supporting information, Eq. S4), Fe shows a close leaching behavior in acetic acid to that of REEs. The main difference between REEs leaching and Fe leaching is the S/L ratio's negative effect, which is more pronounced in the case of Fe. Thus, using an acid concentration of 1.6 mol/L, at 60°C, Nd leaching yields are above 80% over a wide S/L ratio (%) range of 0.5 – 10, while Fe leaching yields are above 80% only over an S/L ratio (%) range
491 of 0.5 – 4. Therefore, the use of low acid concentrations (1.6 mol/L) and S/L ratio values
492 between 4% and 10% allows favoured leaching of REEs with yields above 80% compared to
493 Fe whose yield drops to 40% at an S/L ratio of 10%. However, selective leaching of REEs with
494 regard to Fe is difficult to achieve due to the high initial content of Fe in the NdFeB magnet
495 powder.

496 Moreover, Co and B, representing respectively 1.5% and 0.9% of the NdFeB magnet
497 powder, show a close leaching behaviour to that of REEs. As shown by the coefficients of
498 factors A (S/L ratio), B (acid concentration) and C (temperature) of the regression model's
499 equations (supporting information, Eq. S5, Eq. S7), the leaching of Co and B is characterized
500 by a strong negative effect of S/L ratio followed by a less important negative effect of acetic
501 acid concentration and finally by a weak positive effect of temperature. In addition, the effect
502 of S/L ratio is accentuated for the leaching of Co and B compared to REEs. Thus, as in the case
503 of Fe, REEs leaching is favoured over that of Co and B, when using low acid concentrations
504 (1.6 mol/L) and high S/L ratios (10%). Under these conditions, the leaching efficiency of Nd is
505 close to 80% while those of B and Co are around 60% and 26% respectively.

506 Furthermore, the Ni electrolytic coating of the NdFeB magnet, representing around
507 0.6% of the magnet powder shows a very different leaching behaviour, compared to other
508 elements. Indeed, Ni leaching is characterized by a stronger dependence on S/L ratio (Eq. S6)
509 Increasing S/L ratio significantly hinders Ni leaching. In addition, Ni is the only element whose
510 leaching is positively influenced by the increase of acid concentration. Therefore, using low
511 acid concentration and high S/L ratios results in selective leaching of REEs against Ni.

512 4 Conclusions

513 The objective of this study was to investigate the leaching of NdFeB magnet powder
514 from end of life hard disk drive using organic acids as leaching agents. As a first step, NdFeB
515 magnets were characterized before and after the grinding step, in order to determine its chemical
516 and phase composition, which can greatly influence the leaching behavior of REEs. SEM/EDS
517 analysis of the polished section of NdFeB magnets highlighted the presence of two main phases:
518 Nd₂Fe₁₄B matrix phase, which is responsible of the magnetic properties of the material, and the
519 intergranular REEs rich phase. Moreover, a Ni coating envelops the NdFeB magnets used in
520 this study. These magnets were ground under inert atmosphere in order to limit oxidation and
521 avoid their pyrophoric character. X-ray diffraction (XRD) and Mössbauer spectroscopy (MS)
522 analyses confirmed the effectiveness of such a measure in minimizing oxidation during the
523 grinding process. Chemical analysis of the NdFeB powder revealed the presence of
524 approximately 63% Fe, 23% Nd, 3% Pr, 1% Dy, 1.5% Co, 0.9% B and 0.6% Ni.

525 Based on the literature review and the thermodynamic considerations obtained using
526 pHreeqC and HSC, it appears that organic acids can be “eco-compatible” alternatives to strong
527 mineral acids which are traditionally used as REEs leaching agents. For example, speciation
528 calculations show that REEs form soluble complexes in acetic media over a wide pH range.
529 Among the tested organic acids, acetic acid was found to be the most effective for leaching
530 REEs from NdFeB magnet powder under industrially favorable conditions. Thus, using a
531 temperature of about 60°C and a residence time of 24h, acetic acid allowed the leaching of more
532 than 90% of all the REEs (Nd, Pr and Dy) in a range of S/L ratio (%) of 0.5 – 5 and a range of
533 acid concentration (mol/L) of 1.6 – 10. However, under these same conditions, leaching is non-
534 selective as it results in partial co-leaching of Fe, Co and B. The improvement of the selectivity
535 is currently under investigation.

536 Acknowledgements

537 The authors are grateful to the Occitanie region (RETREAt project – ALDOCT 000443)
538 and the French geological survey (BRGM) for PhD funding and financial support.

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## Supporting Information

<table><caption>Table S1 Experimental domain of the DOE used in the study.</caption><thead><tr><th>Factors</th><th>Type</th><th>Low level : -1</th><th>Median level: 0</th><th>High level : +1</th></tr></thead><tbody><tr><td>S/L Ratio (%)</td><td>Continuous</td><td>0.5</td><td>5.25</td><td>10</td></tr><tr><td>[Formic acid] (mol/L)</td><td>Continuous</td><td>1.9</td><td>10.8</td><td>19.6</td></tr><tr><td>[Acetic acid] (mol/L)</td><td>Continuous</td><td>1.6</td><td>8.9</td><td>16.3</td></tr><tr><td>[Citric acid] (mol/L)</td><td>Continuous</td><td>0.4</td><td>2.1</td><td>3.9</td></tr><tr><td>[Tartaric acid] (mol/L)</td><td>Continuous</td><td>0.4</td><td>2.1</td><td>3.8</td></tr></tbody></table>

<table><caption>Table S2 Phase composition of ground NdFeB determined from the XRD patterns.</caption><thead><tr><th rowspan="2">Phases</th><th>Ground NdFeB</th><th>Ground NdFeB</th></tr><tr><th>in N<sub>2</sub> atmosphere (wt%)</th><th>in air atmosphere (wt%)</th></tr></thead><tbody><tr><td>Nd<sub>2</sub>Fe<sub>14</sub>B</td><td>94</td><td>59</td></tr><tr><td>Fe</td><td>0</td><td>32</td></tr><tr><td>NdFeO<sub>3</sub></td><td>0</td><td>8</td></tr><tr><td>Nd<sub>2</sub>O<sub>3</sub></td><td>6</td><td>1</td></tr></tbody></table>

<figure><img src="image_15.png" /><figcaption>Figure S1 Mossbauer spectra of NdFeB magnets ground in inert atmosphere.</figcaption></figure>
668

669

670

<table><caption>Table S3 Mossbauer parameters of the spectra corresponding to NdFeB powder ground in inert atmosphere.</caption><thead><tr><th>Components</th><th>CS<br>(mm/s)</th><th>Δ<br>(mm/s)</th><th>H<br>(kOe)</th><th>Relative spectral area<br>(%)</th></tr></thead><tbody><tr><td>Doublet Fe (III)</td><td>0.1</td><td>0.83</td><td></td><td>2</td></tr><tr><td>Sextet site k1</td><td>-0.24</td><td>0.002</td><td>298</td><td>28</td></tr><tr><td>Sextet site j2</td><td>-0.122</td><td>0.099</td><td>364</td><td>11</td></tr><tr><td>Sextet site k2</td><td>-0.012</td><td>0.145</td><td>291</td><td>37</td></tr><tr><td>Sextet site e</td><td>-0.04</td><td>0.027</td><td>246</td><td>9</td></tr><tr><td>Sextet site j1</td><td>0.14</td><td>0.35</td><td>334</td><td>10</td></tr><tr><td>Sextet site c</td><td>-0.39</td><td>0.17</td><td>201</td><td>3</td></tr></tbody></table>

671

<figure><img src="image_16.png" /></figure>

672

673

674

675

<caption>Figure S2 Sillén diagram of Nd(III) in acetic acid media at 30°C (calculations made using pHreeqC and LNLL database: Lawrence Livermore National Laboratory). The concentration is expressed in moles per kilogram of solvent (water).</caption>

676
<figure><img src="image_17.png" /><figcaption>Figure S3 Sillèn diagram of (a) Fe(II) and (b) Fe(III) in acetic acid media at 30°C (calculations made using pHreeqC and LNLL/MINTEQ databases. The concentration is expressed in moles per kilogram of solvent (water).</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>Figure S4 Eh-pH diagram of the predominant species of Nd and Pr in diluted acetic acid media (1.6 mol/L):
(a) Nd and (c) Pr and in the saturated acetic acid media (16 mol/L): (b) Nd and (d) Pr at equilibrium at 30°C and 1 atm (HSC 7).</figcaption></figure>
<figure><img src="image_19.png" /><figcaption>Figure S5 Eh-pH diagram of the predominant species of Fe in (a) diluted acetic acid media (1.6 mol/L) and in (b) saturated acetic acid media (16 mol/L) at equilibrium at 30°C and 1 atm (HSC 7).</figcaption></figure>
688 Model fitting of the NdFeB magnet powder leaching using acetic acid

689 Based on the collected experimental leaching data thanks to an optimal design of

690 experiments, the regression models for Nd, Dy, Pr, Fe, B, Ni and Co leaching yields are given

691 below:

$$ \%Nd = 98.29 - 21.86A - 8.92B + 3.57C - 20.46A^2 - 8.61AB + 3.90AC - 1.59BC, R=0.9 \qquad \text{Eq. S1} $$

$$ \%Dy = 91.19 - 24.51A - 7.62B + 4.11C - 16.63A^2 - 6.74AB + 3.68AC - 0.97BC, R=0.99 \qquad \text{Eq. S2} $$

$$ \%Pr = 92.25 - 21.09A - 8.94B + 3.55C - 16.38A^2 - 7.89AB + 1.37AC + 0.34BC, R=0.99 \qquad \text{Eq. S3} $$

$$ \%Fe = 94.73 - 35.11A - 8.26B - 2.09C - 29.84A^2 - 8.26AB - 2.84AC - 0.33BC, R=1.00 \qquad \text{Eq. S4} $$

$$ \%B = 92.33 - 26.75A - 5.07B + 1.28C - 19.09A^2 - 5.06AB + 1.80AC + 0.007BC, R=1.00 \qquad \text{Eq. S5} $$

$$ \%Ni = 10.20 - 42.56A + 0.95B + 4.27C + 32.81A^2 - 0.51AB - 3.57AC + 2.19BC, R=0.97 \qquad \text{Eq. S6} $$

$$ \%Co = 72.10 - 33.74A - 8.19B + 5.87C - 16.57A^2 + 0.90AB - 6.98AC + 4.07BC, R=0.95 \qquad \text{Eq. S7} $$

692 Where A, B and C represent respectively S/L ratio (%), acetic acid concentration (mol/L) and

693 temperature (°C). According to these equations, three interactions (AB, AC and BC), between

694 the three factors A, B and C, are identified. Interactions occur when the effect of one factor

695 depends on the level of the other factor.