Ultrasound-assisted acetic acid leaching of rare earth elements from spent NdFeB permanent magnets: process optimization and kinetic analysis

Abstract

Spent NdFeB permanent magnets (SPM) represent an important secondary resource of rare earth elements (REEs), yet the simultaneous recovery of praseodymium (Pr) and dysprosium (Dy) using environmentally benign lixiviants remains underexplored. An ultrasound-assisted acetic acid leaching (UAL) process was developed for the recovery of Pr and Dy from pre-processed SPM. A four-factor Box–Behnken Design was used for process optimisation, and the developed model predicted maximum leaching efficiencies of 96.31% for Pr and 86.85% for Dy at 60.48% ultrasound amplitude, 1.42% pulp density, 2.51 M acetic acid, and 84.59 min. Analysis of variance indicated a decreasing influence of the variables on Pr leaching, whereas ultrasound amplitude exerted the greatest influence on Dy recovery, consistent with its comparatively lower accessibility within the NdFeB matrix. Although Pr consistently exhibited higher leaching efficiency than Dy, both REEs followed comparable leaching behaviour throughout the investigated operating range. Kinetic analysis showed a shrinking core model to adequately describe the leaching process, indicating diffusion through the reacted layer as the predominant rate-controlling step. The proposed mechanism explains the contribution of acoustic cavitation towards improved mass transfer and REE dissolution. The optimised process further demonstrated appreciable REE recovery at elevated pulp density, indicating its potential for operation under higher solid loading conditions. The findings demonstrate that UAL provides an effective route for the simultaneous recovery of REEs from SPM while offering mechanistic understanding of sustainable rare earth recycling processes.

Spent NdFeB permanent magnets (SPM) represent an important secondary resource of rare earth elements (REEs). This study demonstrates ultrasound-assisted recovery of praseodymium (Pr) and dysprosium (Dy) using an environmentally benign lixiviant.

1. Introduction

Rare earth elements (REEs), comprising the fifteen lanthanides together with yttrium and scandium, possess unique magnetic, optical and catalytic properties that have made them indispensable to modern technologies.¹ They play a crucial role in electric vehicles, wind turbines, advanced electronics, defence systems and energy-efficient technologies, and are therefore considered essential for the global transition towards a low-carbon economy.² Consequently, the global REE market is expected to witness sustained growth over the coming decade, driven by the increasing deployment of clean energy technologies and electrification.³ Despite their relatively widespread occurrence, economically viable REE deposits are limited, and their extraction is often associated with high energy consumption, environmentally intensive processing and the generation of radioactive waste containing thorium and uranium.² Furthermore, the geographical concentration of REE production and processing has raised concerns regarding long-term supply security, leading several countries, including India, the United States, Australia and members of the European Union, to identify REEs among their critical minerals for strategic resource security.^2,4,5 This growing emphasis on resource security also aligns with the United Nations Sustainable Development Goals (SDGs), particularly SDG 9 (Industry, Innovation and Infrastructure) and SDG 12 (Responsible Consumption and Production), which encourage sustainable resource utilisation and circular material management. Consequently, the recovery of REEs from secondary resources has emerged as an important strategy for supplementing primary mining while improving resource sustainability.

The increasing demand for REEs has intensified interest in secondary resources, particularly electronic waste (e-waste), which represents one of the fastest-growing waste streams worldwide. Effective recycling of such complex secondary resources generally requires appropriate pretreatment and separation strategies before subsequent metal recovery.⁶ Annual e-waste generation is projected to reach 74.7 million tonnes by 2030, driven by the rapid replacement of electronic devices.⁷ Among the various secondary resources, spent NdFeB permanent magnets (SPMs) recovered from hard disk drives (HDDs), electric vehicles, wind turbines and electronic equipment are considered one of the most promising sources of REEs because of their relatively high metal content and uniform composition. Compared with primary ores containing REEs, SPMs contain ∼30 wt% rare earth elements, making them an attractive urban mine for REE recovery.⁸ The European Rare Earths Competency Network has therefore identified HDD magnets as a priority recycling stream owing to their established collection infrastructure and potential to reduce dependence on primary mining.⁹ Commercial NdFeB permanent magnets generally contain 25–28 wt% neodymium (Nd), 4–6 wt% praseodymium (Pr) and 1–2 wt% dysprosium (Dy). While neodymium has received considerable attention because of its relatively higher abundance and commercial demand, Pr and Dy are critical REE for the manufacture of high-performance magnets. Pr improves magnetic performance, whereas Dy enhances coercivity and thermal stability required for demanding applications such as electric vehicles and wind turbines.^10,11 Despite their strategic importance, studies addressing the recovery of Pr and Dy remain comparatively limited, particularly with respect to process optimisation, kinetic modelling and mechanistic understanding of their leaching behaviour.

Hydrometallurgical leaching is one of the most widely adopted approaches for recovering REEs from secondary resources because of its high extraction efficiency and operational simplicity. Conventional leaching systems predominantly employ mineral acids such as hydrochloric, nitric and sulphuric acids, which effectively dissolve REEs but often require high reagent consumption, co-leach substantial amounts of iron from the NdFeB matrix, and generate acidic effluents requiring further treatment.^10,12 These limitations have encouraged increasing interest in biodegradable organic acids, which offer comparatively milder operating conditions, lower environmental impact and the potential for reagent regeneration.² Among the available organic lixiviants, acetic acid has attracted considerable attention because of its availability, low toxicity, favourable complexation behaviour with REEs and ability to effectively dissolve the Nd₂Fe₁₄B phase.⁹

Recent studies have demonstrated the applicability of organic acids for REE recovery from SPMs.² However, these investigations have primarily focused on Nd recovery, prolonged leaching durations or conventional leaching systems, while systematic optimisation of the simultaneous recovery of Pr and Dy remains limited. Furthermore, mechanistic understanding of their dissolution behaviour and kinetic evaluation has received comparatively less attention. Understanding the leaching kinetics is essential for identifying the rate-controlling mechanism and facilitating future reactor design and scale-up.^10,13,14 These limitations highlight the need for environmentally benign and process-intensified leaching strategies capable of improving the recovery of REEs from SPMs.

To overcome the inherent mass transfer limitations associated with conventional hydrometallurgical leaching, several process intensification strategies have been investigated to improve REE recovery from secondary resources.¹⁵ Among these approaches, ultrasound-assisted leaching has attracted considerable attention because it enhances solid–liquid interactions without requiring severe operating conditions or altering the chemistry of the lixiviant.¹⁶ The application of ultrasonic waves generates acoustic cavitation, where the formation, growth and implosive collapse of microbubbles produce localized high temperature and pressure, microjets and shock waves at the solid–liquid interface.¹⁷ These effects enhance particle fragmentation, improve lixiviant accessibility, reduce diffusion limitations and accelerate mass transfer, thereby improving REE dissolution and reducing the overall leaching time.¹⁶ Recent studies have demonstrated the effectiveness of ultrasound in enhancing metal recovery from secondary resources through the combined mechanical and sonochemical effects of cavitation.¹⁸ Despite these developments, the application of ultrasound-assisted organic acid leaching for the simultaneous recovery of Pr and Dy from SPMs has received limited attention. Therefore, the present study investigates the simultaneous recovery of Pr and Dy from SPMs using ultrasound-assisted acetic acid leaching (UAL) through statistical optimisation, kinetic modelling and mechanistic evaluation.

2. Materials and methods

2.1. Reagents

The standard acids used were nitric acid (HNO₃) of 65 wt% (14.3 M) and hydrochloric acid (HCl) at 37 wt% (12.0 M), both purchased from Finar. Acetic acid (99%) was obtained from Avra, India. The organic acids, mineral acids, and other chemicals utilised in the study were of analytical grade and used as received from the manufacturers, without further purification.

2.2. Substrate and its preprocessing prior to leaching

Non-functioning HDDs from computers and laptops were collected from e-waste collectors in Hyderabad, India. The HDDs were manually opened, and the SPMs were separated from the drive assemblies. Magnets collected from HDDs of different makes, storage capacities and production periods were pooled as the feed material. The collected SPMs were thermally demagnetised at 350 °C for 1 h to facilitate subsequent size reduction, following conditions reported in earlier studies.^14,19 The demagnetised magnets were allowed to cool to room temperature in a vacuum desiccator before being fragmented into smaller pieces. The fragmented SPMs were then ground using a ball mill (Anton Paar, Germany) at 4 Hz for 60 min in a 50 mL grinding container using one stainless-steel ball of approximately 25 mm diameter (62.57 g). Around 5–6 g of demagnetised SPM was used per batch, corresponding to a ball-to-powder ratio of approximately 10.4–12.5 : 1. The resulting powder was passed through a standard 212 µm sieve, and the fraction below 212 µm (upper particle-size limit in the study) was collected and used for the leaching experiments.¹⁹ The elemental composition of the raw SPM powder, including REEs and other constituent metals, was determined following the US EPA SW-846 Method 3050B.²⁰

2.3. Design of experiments for the ultrasound-assisted leaching of REE using acetic acid

For the UAL experiments, a movable ultrasound probe (UP400St, Hielscher, Germany) was utilised. This probe operates at a fixed frequency of 24 kHz and has a variable power and amplitude range of 20% to 100%. It features an 18 mm-diameter titanium probe. Intermittent manual agitation was used to resuspend the particles during leaching, with fluid motion generated by the ultrasonic waves providing additional mixing. The leaching temperature was controlled under near-ambient conditions using a jacketed beaker connected to a recirculating chiller to minimise the temperature rise associated with ultrasonic irradiation, as illustrated in Fig. S1.²¹ Acetic acid was employed as the leaching agent or the lixiviant.

A 4-factor Box–Behnken Design (BBD) was used for experimental design and regression modelling to optimise REE leaching from SPM powder. Ultrasound amplitude (A), pulp density (B), acetic acid concentration (C), and leaching time (D) were selected as the independent variables. The three levels of investigated values (+1, 0, −1) 20, 50, and 80%; 1, 3, and 5%; 1, 2.5, and 4 M; and 30, 75, and 120 min for A, B, C, and D, respectively. The selected levels were based on preliminary experiments and relevant literature. The leaching efficiencies of Pr and Dy were considered as the response variables. The total number of experimental runs was determined using eqn (1), while the response was fitted using the second-order polynomial model described in eqn (2). Detailed descriptions of the model terms have been reported elsewhere.²²

N = 2k (k − 1) + C_o 1

where, k = number of factors (here, 4), C_o = number of central points (here, 3)

2

where, Y is the predicted response, β₀, β_i, β_ii, and β_ij are regression coefficient, X_i, X_ii, and X_ij are independent variables, k is the number of factors (independent variables), and e₀ indicates model error. The Design Expert (version 11.0.3) was used to analyse the experimental data. Based on the analysis of variance (ANOVA) and quadratic polynomial statistical models, residual errors, various graphs, and data predictions were calculated and estimated.

2.4. Leaching kinetics and leaching mechanism

The kinetic study of the leaching process for ultrasonication-assisted experiments was conducted in duplicate, using the optimised leaching conditions. The experimental data obtained under the optimised leaching conditions were analysed using the shrinking sphere model (SSM), shrinking core model (SCM) and Avrami model as described in eqn (3)–(5).^13,23–25 To further evaluate the applicability of the kinetic models and identify the rate-controlling step governing REE leaching, additional experiments were conducted at different temperatures under the optimised operating conditions. The obtained rate constants were subsequently used for Arrhenius analysis and estimation of activation energy eqn (6).²⁶ The fitting quality of all three models was assessed using the determination coefficient (R²) with OriginPro 9.0.

Shrinking sphere model:

1 − (1 − X)^1/3 = k_ct 3

Shrinking core model:

4

Avrami model:−ln(1 − X) = Ktⁿtaking log on both sides,

ln(−ln(1 − X) = ln K + n ln t 5

where, X is the fraction of REEs leached at time t, k_c is the apparent rate constant for a surface chemical reaction (min⁻¹), k_d is the apparent rate constant for diffusion through the solid product layer (min⁻¹), n is the order of the reaction, and K is the reaction constant (min⁻¹).Arrhenius equation:

6

where, k is the apparent reaction rate constant (min⁻¹), A is the pre-exponential factor, E_a is activation energy (kJ mol⁻¹), R is the universal gas constant (J (mol⁻¹ K⁻¹), and T is the absolute temperature.

2.5. Evaluation of leaching performance at elevated pulp density

To understand the behaviour of the leaching system under higher solid loading conditions, additional experiments were conducted at a pulp density of 5% (50 g L⁻¹). The operating conditions were selected based on the BBD predictions, and leaching studies were performed using acetic acid solutions (1 M and 3 M), while maintaining the remaining process variables at their respective values. Experiments were carried out both in the presence and absence of ultrasonication to evaluate its influence on REE recovery. The leaching behaviour was monitored over time to assess the effect of acid concentration and ultrasound under higher pulp density. The obtained results were subsequently compared with the predicted values to evaluate the applicability of the developed approach at higher solid loading.

2.6. Downstream precipitation and calcination

The REEs dissolved in the pregnant leachate were recovered by manually and continuously adding a slight excess of oxalic acid in a dropwise manner using a pipette to induce precipitation.²⁴ During reagent addition, the suspension was stirred continuously at 600 rpm for 30–40 min while maintaining the temperature between 30–35 °C. Following precipitation, the mixture was filtered through a 0.45 µm nylon membrane to separate the solid oxalate phase from the filtrate. The concentrations of residual metals in the filtrate were subsequently determined to evaluate the extent of REE precipitation. The recovered oxalate precipitate was vacuum dried at 60 °C and then calcined at 800 °C for 2 h to obtain mixed rare earth oxides.²⁷ Phase identification of both the oxalate precipitate and the calcined product was also carried out.

2.7. Analytical methods and calculations

After the leaching process, the pregnant leachate was centrifuged at 10 000 rpm for 10 min to separate the solid residue from the liquid phase. The supernatant was then diluted appropriately (typically 50-1000-fold), filtered using 0.22 µm nylon filter paper. The concentrations of the target rare earth elements in the prepared solutions were determined using inductively coupled plasma-mass spectrometry (ICP-MS; Agilent 7850, Agilent Technologies, USA), with data processing carried out in Mass Hunter software. The leaching efficiency (%E) was calculated using the eqn (8), where C_l denotes the concentration of the individual REEs in the leachate and C_i for the initial concentration of REEs in raw SPM obtained using US EPA SW846 method 3050B.²⁸

Leaching efficiency = (C_l/C_i)× 100 8

Prior to ICP-MS measurement, all prepared solutions were brought to a final matrix of 2% (v/v) HNO₃. Quantification was performed against certified multi-element calibration standards prepared in 2% (v/v) HNO₃, covering a concentration range of 0.5–550 ppb. The instrument was equipped with a Scott double-pass spray chamber, a concentric glass nebulizer, and a collision cell. The principal operating parameters comprised a plasma power of 1550 W, plasma gas flow of 15 L min⁻¹, auxiliary gas flow of 0.9 L min⁻¹, RF matching voltage of 1.80 V, sampling depth of 8.0 mm, nebulizer gas flow of 1.07 L min⁻¹, makeup gas flow of 0.10 L min⁻¹, and helium collision-gas flow of 4.3 mL min⁻¹. A nickel sampling cone was employed, and the spray chamber was maintained at 2 °C throughout the analytical runs. Instrument performance was monitored over the course of the analytical sequence using calibration blanks, calibration-check standards, and an internal standard (Sc). The Sc response remained within the 80–120% acceptance range, attesting to consistent instrumental performance during analysis. All measurements were performed in triplicate, with precision expressed as relative standard deviation (%RSD). Calibration linearity, limit of detection, estimated limit of quantification, and standard recovery were likewise evaluated as indicators of analytical method performance (Tables S1and S2). Phase identification of the SPM powder, solid residues, and products obtained downstream of the leaching process was carried out using a powder X-ray diffractometer (XRD; Bruker, United States). Diffraction patterns were recorded using Cu Kα radiation over a 2θ range of 20–70° at a scanning rate of 2°/min.

3. Results and discussion

3.1. Characterization of the NdFeB magnet from HDDs

The preprocessing of SPM was done through thermal demagnetisation and ball milling. The demagnetisation prevents magnetic re-agglomeration of the broken powder during ball milling and leaching, which could otherwise decrease the reactive surface area and compromise experimental consistency. The demagnetised magnets were ball-milled and sieved to get an average particle size of ≤212 µm. Smaller particle sizes increase surface area, thereby improving exposure of the REE centres. This allows for more effective interaction with acetic acid, facilitating the efficient mobilisation of metals and contact between the REEs and the leaching solution.²⁹

The elemental composition in raw SPM is shown in Table 1 with Fe (60.9 wt%), Nd (26.4 wt%), Pr (4.9 wt%), Dy (1.8 wt%), Ni (1.5 wt%), and B (1.4 wt%) as the principal components. These major element proportions are consistent with available literature.⁹ The higher nickel content detected in this study originated from Ni–Cu–Ni triple-layer coating serving as an anti-corrosion barrier commonly applied to commercial NdFeB magnets to improve corrosion resistance.³⁰ This coating was maintained, ensuring that the leaching results are relevant across a wider range of applications. The XRD spectra in Fig. S2a and b represent the demagnetized SPM before leaching and the solid residue recovered after UAL, respectively. Fig. S2a showed tetragonal Nd₂Fe₁₄B as the predominant crystalline phase in the demagnetized SPM.⁹ The major diffraction peaks, before and after leaching, corresponds to the reference Nd₂Fe₁₄B peak positions obtained from the Materials Project database (mp-5182).³¹ The XRD pattern of the solid residue after UAL (Fig. S2b) showed differences in peak intensity and the number of distinct diffraction peaks compared with the initial SPM, reflecting modifications in the solid material following the leaching process.

Table 1. Elemental composition of SPM used in the present study^a.

Elements	Nd	Pr	Dy	B	Fe	Al	Co	Ni	Cu	Ga	Gd
Mass fraction (wt%)	26.40 ± 4.5	4.85 ± 0.7	1.83 ± 0.2	1.41 ± 0.2	60.98 ± 6.4	0.26 ± 0.03	0.71 ± 0.1	1.58 ± 0.3	0.12 ± 0.002	1.03 ± 0.1	0.17 ± 0.03

^a±SD.

3.2. Response surface method mediated optimization

3.2.1. Experimental design and model development

The experimental responses (Table 2) obtained from the BBD were fitted to second-order polynomial models to establish quantitative relationships between the operating variables and the extraction efficiencies of Pr and Dy as given in eqn (9) and (10). The regression models establish quantitative relationships between the process variables, their interaction and the extraction efficiencies of Pr and Dy.³²

Table 2. Experimental design for UAL and their responses (leaching efficiency of Pr and Dy) based on BBD.

Run	Factors				Response
	Amplitude (%)	Pulp density (%)	Acid conc. (M)	Time (min)	Pr (%)	Dy (%)
1	20	1	2.5	75	73.8801	60.2974
2	80	1	2.5	75	92.311	79.4346
3	20	5	2.5	75	55.5432	48.5317
4	80	5	2.5	75	52.0798	71.4385
5	50	3	1	30	72.7407	44.905
6	50	3	4	30	70.3821	64.0277
7	50	3	1	120	59.3512	62.0312
8	50	3	4	120	88.1857	81.3499
9	20	3	2.5	30	64.5071	34.8221
10	80	3	2.5	30	90.2332	57.9289
11	20	3	2.5	120	65.2444	53.6557
12	80	3	2.5	120	70.3324	77.8355
13	50	1	1	75	78.58	71.2844
14	50	5	1	75	58.1107	50.4116
15	50	1	4	75	90.5703	78.2287
16	50	5	4	75	91.736	58.1772
17	20	3	1	75	89.1708	31.2624
18	80	3	1	75	62.2518	57.3495
19	20	3	4	75	91.9016	54.8756
20	80	3	4	75	79.1723	78.3839
21	50	1	2.5	30	90.7496	75.181
22	50	5	2.5	30	80.0199	43.9656
23	50	1	2.5	120	72.4461	82.041
24	50	5	2.5	120	45.2715	64.9481
25	50	3	2.5	75	89.1989	78.6034
26	50	3	2.5	75	42.9111	79.8236
27	50	3	2.5	75	82.8261	76.7329

It can be understood from the regression coefficients in eqn (9) and (10) that ultrasound amplitude, acetic acid concentration, and leaching time exerted a positive influence on the extraction of both Pr and Dy, whereas pulp density exhibited a negative effect. The positive regulation of ultrasound amplitude (A) can be attributed to the implosion of vapor cavities generated as result of the propagation of ultrasonic wave across the medium. This promotes hydrodynamic mixing, particle surface erosion, increase in pore volume and disruption of the diffusion boundary layer surrounding the solid particles.³³ These effects enables better contact between the lixiviant and the REE sites within the magnet matrix, thereby accelerating metal dissolution.³⁴ Similarly, increasing acetic acid concentration increases proton availability and promotes the formation of soluble acetate complexes, enhancing the leaching process.³⁵ Leaching time (D) also contributed positively to extraction, as prolonged contact between the solid and liquid phases allows greater progression of the dissolution process.¹⁹ However, the negative coefficient associated with pulp density (B) suggests that higher solid loading adversely affects extraction efficiency. Increasing pulp density reduces the effective lixiviant availability per unit mass of SPM³⁶ and may limit cavitation propagation through the slurry due to increased particle concentration.¹⁶ Consequently, mass transfer resistance becomes more pronounced, leading to lower extraction efficiencies.¹⁶ A similar influence of pulp density (solid to liquid ratio) has been reported in several ultrasound-assisted hydrometallurgical processes where excessive solid loading reduced cavitation effectiveness and restricted reagent accessibility.³⁷

Y_Pr = −33.6756 + 1.9002 × A −0.9291 × B + 24.7472 × C + 0.6382 × D −0.0241 × AB −0.0054 × AC + 0.0005 × AD + 0.1158 × BC + 0.0524 × BD + 0.0034 × CD −0.0143 × A² −0.9261 × B² −3.7131 × C² −0.0041 × D² 9

Y_Dy = −34.8886 + 1.7743 × A −3.9908 × B + 26.8292 × C + 0.6593 × D + 0.0157 × AB −0.0143 × AC + 0.0002 × AD + 0.0684 × BC + 0.0392 × BD + 0.0007 × CD −0.014 × A² −0.7415 × B² −4.1879 × C² −0.0040 × D² 10

Interestingly, negative quadratic coefficients (A², B², C²) were obtained for all process variables in both regression models, indicating the presence of curvature in the response surfaces. This suggests that extraction efficiency does not increase indefinitely with increasing parameter values but gradually approaches a plateau, beyond which further increases become ineffective or even detrimental to metal recovery.³⁸ The relatively small interaction coefficients further indicate that the extraction behaviour is predominantly governed by the individual effects of the operating variables, with only limited contributions from variable interactions within the investigated design space. Similar pattern for the interactive effect of process variables was also observed in some recent investigations that extraction cadmium and zinc from zinc industry waste.³⁹ The adequacy and statistical significance of these observations were subsequently evaluated through ANOVA and model validation studies.

3.2.2. Model adequacy and statistical validation

The adequacy of the developed quadratic models was evaluated using ANOVA, and the results are presented in Tables 3 and 4. Both models were found to be highly significant, with model F-values of 67.82 and 14.37 for Pr and Dy extraction, respectively, and corresponding p-values <0.0001. The p value points out the probability that these high F-value has less than 0.01% chance of being generated from random experimental noise. These results agree with observation that the selected process variables significantly describe the extraction behaviour for the UAL process. Among the process variables, ultrasound amplitude influenced the leaching process most for the responses. Acetic acid, time and pulp density followed in the declining order for Pr leaching (Table 3), while only a modest hierarchical difference was observed for Dy extraction for these variables (Table 4). Meanwhile, most interaction terms were statistically insignificant. This observation aligns with the relatively small interaction coefficients observed in the regression equations (eqn (9) and (10)). This again asserts the effect of individual variables on the leaching process compared to their synergistic interactions. Further, the coefficient of model determination (R²) values of 0.9875 and 0.9437 derived for Pr and Dy, respectively, indicates desirable agreement between model predicted and experimental responses.

Table 3. ANOVA of quadratic response surface model for Pr extraction (%) from UAL.

Source	ANOVA for Pr extraction (%)
	Sum of squares	df	Mean square	F-value	p-value
Model	5953.29	14	425.23	67.82	<0.0001	Significant
A-amplitude	1969.07	1	1969.07	314.05	<0.0001
B-pulp density	577.54	1	577.54	92.11	<0.0001
C-acid conc	1145.84	1	1145.84	182.75	<0.0001
D-time	1087.60	1	1087.60	173.46	<0.0001
AB	8.33	1	8.33	1.33	0.2714
AC	0.2398	1	0.2398	0.0382	0.8482
AD	2.13	1	2.13	0.3401	0.5706
BC	0.4832	1	0.4832	0.0771	0.7860
BD	88.97	1	88.97	14.19	0.0027
CD	0.2147	1	0.2147	0.0342	0.8563
A 2	880.91	1	880.91	140.50	<0.0001
B 2	73.19	1	73.19	11.67	0.0051
C 2	372.26	1	372.26	59.37	<0.0001
D 2	373.06	1	373.06	59.50	<0.0001
Residual	75.24	12	6.27
Lack of fit	74.57	10	7.46	22.40	0.0435	Significant
Pure error	0.6659	2	0.3330
Cor Total	6028.52	26
SD (standard deviation)	2.5040
R-sq (coefficient of the model determination)	0.9875

Table 4. ANOVA of quadratic response surface model for Dy extraction (%) from UAL.

Source	ANOVA for Dy extraction (%)
	Sum of squares	df	Mean square	F-value	p-value
Model	5433.32	14	388.09	14.37	<0.0001	Significant
A-amplitude	1608.37	1	1608.37	59.56	<0.0001
B-pulp density	989.98	1	989.98	36.66	<0.0001
C-acid conc	797.05	1	797.05	29.52	0.0002
D-time	850.61	1	850.61	31.50	0.0001
AB	3.55	1	3.55	0.1316	0.7231
AC	1.66	1	1.66	0.0616	0.8082
AD	0.2878	1	0.2878	0.0107	0.9195
BC	0.1686	1	0.1686	0.0062	0.9383
BD	49.86	1	49.86	1.85	0.1992
CD	0.0096	1	0.0096	0.0004	0.9853
A 2	864.51	1	864.51	32.01	0.0001
B 2	46.92	1	46.92	1.74	0.2120
C 2	473.54	1	473.54	17.54	0.0013
D 2	351.84	1	351.84	13.03	0.0036
Residual	324.04	12	27.00
Lack of fit	319.20	10	31.92	13.17	0.0726	Not significant
Pure error	4.85	2	2.42
Cor Total	5757.36	26
SD (standard deviation)	5.1965
R-sq (coefficient of the model determination)	0.9437

Therefore, the statistical indicators and model validation results confirm the developed quadratic models to be reliable for evaluating the effects of operating variables and identifying optimum leaching conditions for Pr and Dy recovery.⁴⁰ These observations are similar in line with coorelation understood during leaching of copper and zinc from spent automotive catalyst using nitric acid.¹⁸

3.2.3. Effect of process variables on Pr and Dy leaching

The individual effects of ultrasound amplitude, pulp density, acetic acid concentration and leaching time on the leaching of Pr and Dy are presented in Fig. 1 and 2. In general, the leaching efficiencies of both metals decreased with increasing pulp density, whereas higher ultrasound amplitude, acetic acid concentration and leaching time enhanced metal recovery. Although similar response patterns were observed for Pr and Dy, the extent of leaching varied among the process variables under comparable operating conditions. Among the investigated variables, ultrasound amplitude exerted the strongest influence on the leaching behaviour of both metals, consistent with the ANOVA results presented in Tables 3 and 4. The influence of the individual process variables is discussed in the following sections.

Fig. 1. Effect of individual process variables on Pr extraction predicted by the developed BBD model: (a) ultrasound amplitude, (b) pulp density, (c) acetic acid concentration, and (d) leaching time.

Fig. 2. Effect of individual process variables on Dy extraction predicted by the developed BBD model: (a) ultrasound amplitude, (b) pulp density, (c) acetic acid concentration, and (d) leaching time.

The effect of ultrasound amplitude on Pr and Dy extraction is shown in Fig. 1a and 2a, respectively. Increasing the amplitude from 20% to approximately 60–70% resulted in a marked improvement in extraction efficiency for both REEs. The sharp increase observed within this range indicates that cavitation intensity plays a vital role in governing the dissolution process during the initial phase.³⁷ However, beyond the optimum amplitude, the rate of increment gradually declined and the response curves approached a plateau. This behaviour suggests that increasing ultrasonic intensity beyond a threshold provides reduced benefit towards metal dissolution. The reduced incremental gain at higher amplitudes may be associated with excessive cavity generation, leading to coalescence and acoustic shielding effects that lower the efficiency of energy transfer within the liquid medium.⁴¹ In addition, the progressively lower availability of readily leachable REE phases could also have contributed to this behaviour.¹⁶

Fig. 1c and 2c shows the influence of acetic acid concentration on the leaching of Pr and Dy, respectively. Increasing the acid concentration enhanced the leaching efficiencies of both REEs. This improvement can be attributed to the greater availability of protons for mobilising the metals from the NdFeB matrix, followed by coordination of acetate ions with the dissolved Pr³⁺ and Dy³⁺ species through their carboxylate groups, thereby stabilising the REEs in the aqueous phase as soluble REE-acetate species.¹⁴ This facilitated the mobilisation of Pr and Dy into the aqueous phase through the formation of soluble REE-acetate complexes with increasing acid concentration. However, the increase in leaching with incremental acid concentration diminished at higher concentrations. The availability of readily leachable REE phases might have become increasingly limited, restricting the acid's capacity to increase metal dissolution or complexation further.² Consequently, only marginal improvements in leaching efficiency were observed beyond the optimum concentration.

The effect of pulp density on the leaching of Pr and Dy is presented in Fig. 1b and 2b, respectively. Increasing the pulp density adversely affected the leaching efficiencies of both metals, particularly at higher solid loadings. This behaviour can be attributed to the lower availability of acid relative to the increasing amount of solid present at higher pulp densities, thereby limiting metal dissolution.³⁷ In addition, higher particle concentrations may hinder cavitation propagation within the slurry, thereby limiting ultrasound-assisted dissolution.¹⁶ The leaching of Dy appeared more sensitive to variations in pulp density, despite exhibiting response patterns similar to those of the other process variables, consistent with the ANOVA results (Table 4). The lower abundance and often association with Dy-enriched grain-boundary or shell regions within the NdFeB matrix may partly explain this observation,⁴² making reagent accessibility increasingly important for its dissolution under high solid loading conditions.

The leaching time shows a positive influence on the leaching efficiency for both the REEs as shown in Fig. 1d and 2d, where prolonged exposure to lixiviant and ultrasonic wave enhanced mobilization of the metals from the NdFeB matrix. The improvement was more pronounced during the initial stages of leaching, after which the rate of metal recovery gradually decreased. This behaviour suggests that a substantial fraction of the readily accessible REE-bearing phases had already dissolved at longer reaction times, thereby limiting the extent of further recovery. Therefore, these observations indicate that ultrasound amplitude and acetic acid concentration exert a greater influence on REE dissolution than pulp density and leaching time under the investigated conditions. Although the individual effects were more pronounced, the combined influence of the operating variables was further examined using response surface and contour plots generated from the developed models.

3.2.4. Interactive effects of process variables on Pr and Dy extraction

The three-dimensional response surface plots generated from the developed quadratic models were used to evaluate the interactive effects of the operating variables on Pr and Dy leaching (Fig. 3 and 4). Consistent with the ANOVA results, the response surfaces indicate that the individual effects of the process variables were more pronounced than their interaction effects. Nevertheless, the interaction terms contributed towards defining the optimum operating region, and the response surfaces provide valuable insight into the combined influence of the variables on REE recovery.²¹

Fig. 3. Response surface plots showing the interaction of process variables on Pr leaching.

Fig. 4. Response surface plots showing the interaction of process variables on Dy leaching.

Among the combinations investigated, the interaction between ultrasound amplitude and acetic acid concentration produced the most pronounced response surfaces for both Pr and Dy extraction (Fig. 3a and 4a). The extraction efficiencies increased progressively with increasing amplitude and acid concentration, reaching a broad optimum region at approximately 60–70% amplitude and 2.8–3.4 M acetic acid. Similar behaviour was observed for the amplitude-time (Fig. 3d and 4d) and acid concentration–time (Fig. 3e and 4e) combinations, where increasing both variables enhanced metal recovery up to an optimum range, beyond which only marginal improvements were observed. The dome-shaped response surfaces are consistent with the negative quadratic coefficients obtained in the regression models, indicating the existence of an optimum operating region rather than a continuous increase in leaching efficiency with increasing parameter values.³⁸ Moreover, the significance of individual effects of the operating variables is further emphasized by the symmetrical and relatively smooth nature of the response surface, while the interaction effects contributed to a comparatively lesser extent.

In contrast, response surfaces involving pulp density (Fig. 3b, c, f, 4b, c and f) exhibited a declining trend with increasing solid loading. The adverse influence of pulp density on metal recovery remained evident irrespective of the associated operating variable. The highest leaching efficiency were consistently achieved at lower pulp densities, even when the beneficial effects of the other variables partially compensated for this decline. This observation agrees with the single-factor analysis and highlights the importance of maintaining sufficient lixiviant availability for effective REE dissolution. Nonetheless, the similar response surface profiles obtained for both REEs indicate that they responded comparably to variations in the operating parameters. However, Pr exhibited slightly higher leaching efficiencies throughout the investigated operating range. The response surfaces further confirmed that optimum REE recovery could be achieved through a balanced combination of ultrasound amplitude, acetic acid concentration and leaching time while maintaining a relatively low pulp density. The predictive capability of the models was further assessed by comparing the experimental and model-predicted values shown in (Fig. 5). A close clustering of data points around the diagonal line for both Pr and Dy indicates significant agreement between predicted and experimental value. The reduced scattering for Pr is consistent with the higher R² value compared to slightly wider scatter for Dy leaching, reflecting difference in predictive accuracy of corresponding models.

Fig. 5. Comparative interpretation of experimental and model-predicted values for (a) Pr and (b) Dy leaching.

The response surface analysis identified a well-defined optimum operating region for Pr and Dy leaching. The BBD optimisation predicted maximum leaching efficiencies of 96.31% for Pr and 86.85% for Dy at an ultrasound amplitude of 60.48%, pulp density of 1.42%, acetic acid concentration of 2.51 M, and leaching time of 84.59 min. These optimised conditions provide a statistically validated condition for the simultaneous recovery of both REEs. Although previous studies have reported Pr and Dy recovery from SPM, greater emphasis has generally been placed on Nd recovery.^14,37 Meanwhile, the simultaneous recovery of Pr and Dy through ultrasound-assisted leaching has remained largely unexplored (Table 5). The optimised recoveries obtained in the present study are within the range of those reported for organic acid-based leaching systems (Table 5), while being achieved through a statistically optimised ultrasound-assisted process under a comparatively shorter leaching duration. The favourable leaching performance obtained under the optimised conditions demonstrated the potential of the developed process and provided the basis for the subsequent kinetic and mechanistic investigations.

Table 5. Comparative summary of reported hydrometallurgical leaching of REEs from SPM under different operating conditions.

Material	Acid used	Leaching conditions	Leaching efficiency	Reference
NdFeB magnets	Acetic acid	0.5–5% PD, 24 h at 60 °C, 1.6–10 M acid	≥90% Pr, Dy	9
NdFeB magnets from mobile	Acetic acid	1% PD, 60 min, 0.5 M acid, microwave at 175 °C	65% Pr	14
NdFeB magnets from mobile	Citric acid	1% PD, 60 min, 0.5 M acid, microwave assisted	58% Pr	14
NdFeB powdera	Glycolic acid	1.25% PD, 400 min at 25 °C, 1 M acid, 400 RPM	≥95% Pr, Dy	53
NdFeB powdera	Maleic acid	1.25% PD, 400 min at 25 °C, 1 M acid, 400 RPM	≥95% Pr, Dy	53
NdFeB powdera	Ascorbic acid	1.25% PD, 400 min at 70 °C, 1 M acid, 400 RPM	≥95% Pr, Dy	53
Spent wind turbine magnetb	HCl	10% PD, 500 rpm, 300 min, 95 °C, 0.5 M acid	∼98% Pr, Dy	24
Magnetic sludge waste sample	HCl	8.3%, PD, 80 °C, 120 min, 0.3 M H2O2, 3 M acid	99% Dy	10
Magnetic sludge waste sample	HNO3	8.3% PD, 120 min, 80 °C, 0.3 M H2O2, 3 M acid	99% Dy	10
Spent NdFeB permanent magnets	Acetic acid	1.42% PD, 2.51 M acid, 84.59 min, ultrasound amplitude 60.48%	96% Pr 86% Dy	Present study

^aHydrogen decrepitated and roasted.

^bDemagnetized and roasted.

3.3. Leaching kinetics and model fitting

Kinetic model fitting was performed to identify the rate-controlling step governing the UAL of Pr and Dy from SPM. Among the models employed, the shrinking sphere model assumes that the overall leaching rate is governed by the surface reaction occurring at the solid–liquid interface, whereas the shrinking core model considers diffusion through the reacted layer surrounding the unreacted core as the rate-controlling step. The Avrami model was also considered in the kinetic analysis owing to its reported applicability in heterogeneous solid–liquid leaching systems.^13,43

The fitting results obtained for the REEs are presented in Fig. 6. For both REEs, the SCM exhibited the highest correlation coefficients among the investigated models. The SCM fitting yielded R² values of 0.982 and 0.994 for Pr and Dy, respectively, whereas the corresponding values for the shrinking sphere model were 0.961 and 0.943. Although the Avrami model also provided satisfactory correlations (R² > 0.96), the superior fit obtained with the SCM indicates that diffusion through the reacted layer predominantly governs the leaching process.^13,44 Both REEs appear to possess comparable rate-controlling mechanisms under the investigated conditions, as evident from their similar kinetic characteristics. The gradual increase in REE recovery with leaching time and the high degree of linearity obtained from the SCM plots further support the applicability of diffusion-controlled kinetics for the present leaching system.^44,45

Fig. 6. Kinetic model fitting of Pr and Dy leaching: (a and e) leaching efficiency, (b and f) Shrinking sphere model, (c and g) Shrinking core model, (d and h) Avrami model kinetic plot.

Further, the dependence of leaching behaviour on particle size was investigated to verify the applicability of the SCM (Fig. S3). The decrease in particle size tends to increase the apparent rate constant for both Pr and Dy. This supports the theory that particle size reduction improves the overall leaching rate. Smaller particles provide a larger surface area for contact with the lixiviant and reduce the diffusion distance required for transport of reactants and dissolved species.⁴⁶ Consequently, improved accessibility of the lixiviant to the reactive regions of the magnet particles resulted in faster REE recovery. A linear relationship was observed between the apparent rate constant and 1/d₀² (Fig. S4), with R² > 0.97 for both metals. These observations provide additional support for the diffusion-controlled leaching behaviour, indicating the suitability of the SCM in describing the leaching mechanism of the present system.¹³

The effect of temperature on the leaching kinetics was subsequently examined using the SCM (Fig. S5). An increase in temperature from 298 to 308 K resulted in higher apparent rate constants for both Pr and Dy (Table 6), indicating that elevated temperatures favour REE dissolution. The Arrhenius plots shown in Fig. S6 exhibited good linearity and yielded activation energies of 12.07 and 10.06 kJ mol⁻¹ for Pr and Dy, respectively. These relatively low activation energies are consistent with a diffusion-controlled leaching mechanism, in agreement with the conclusions drawn from the SCM and particle-size studies.⁴⁴ Furthermore, the close agreement between the activation energies obtained for Pr and Dy indicates that both metals are subjected to similar mass-transfer constraints during leaching. The corresponding thermodynamic parameters are provided in Table S3.

Table 6. The fitting parameters of the shrinking core model from for the Arrhenius plot.

Temperature (K)	Pr			Dy
	k (min−1)	ln k	R 2	k (min−1)	ln K	R 2
298	0.00399	−5.52396	0.987	0.00431	−5.44682	0.995
303	0.00444	−5.4171	0.989	0.00477	−5.34541	0.996
308	0.00461	−5.37953	0.989	0.00492	−5.31445	0.996

3.4. Proposed mechanism of REE leaching

The kinetic analysis presented in Section 3.3 suggests that a diffusion-controlled mechanism governs the leaching of Pr and Dy from SPM. During leaching, acetic acid initially interacts with the exposed REE-bearing regions of the NdFeB matrix, resulting in the release of REEs from the magnet matrix and the subsequent formation of soluble REE-acetate species.² According to the SCM, the leached surface gradually develops a reacted layer through which the lixiviant and REE-acetate species must diffuse as the reaction progresses (Fig. 7).

Fig. 7. Mechanistic insight into the UAL process for enhanced REE leaching.

The application of ultrasonic wave facilitates this process through multiple effects. The collapse of cavitation bubbles generates localized turbulence and microstreaming in the microenvironment, thereby reducing diffusion resistance at the solid–liquid interface.¹⁶ In addition, repeated cavitation may promote fragmentation and particle size reduction of the magnet particles, exposing fresh reactive sites for continued dissolution.¹⁷ Localized thermal effects associated with cavitation may further enhance molecular mobility and mass transfer, which is consistent with the favourable influence of temperature observed during the kinetic investigation.⁴⁷ Hence, these effects improve lixiviant accessibility and transport of dissolved species, resulting in enhanced recovery of Pr and Dy from the magnet matrix.

3.5. Performance of REE leaching at elevated pulp density

Although lower pulp densities were found to favour the high REE recovery, understanding the behaviour of the leaching system under higher solid loading conditions is important for future process development. The operating conditions selected for the study were guided by the BBD predictions at a fixed pulp density of 5%. Under this constraint, the model predicted Pr and Dy leaching efficiencies of 89.21% and 75.49%, respectively, at an acetic acid concentration of 3.09 M, ultrasound amplitude of 64.6%, and leaching time of 104.88 min. The predicted conditions were subsequently investigated experimentally to evaluate the leaching performance at higher pulp density (Fig. 8).

Fig. 8. Effect of acetic acid concentration and ultrasound assistance on (a) Pr and (b) Dy leaching at 5% pulp density.

For both REEs, leaching efficiency increased with increasing reaction time and acid concentration irrespective of the leaching method employed. The UAL consistently outperformed leaching without ultrasound throughout the investigated period. The enhancement became more pronounced at longer reaction times, indicating the beneficial role of ultrasound in maintaining effective leaching even at elevated pulp density. At 110 min, UAL leaching using 3 M acetic acid achieved recoveries of 90.25% and 76.00% for Pr and Dy, respectively, whereas the corresponding recoveries obtained through conventional leaching were substantially lower. The improved performance can be attributed to cavitation effects, particle modification and enhanced mass transfer, which facilitate lixiviant accessibility and transport of dissolved species into the bulk.^16,48

The experimentally obtained recoveries of the REEs closely agreed with the values predicted by the BBD analysis. The results demonstrate that appreciable REE recovery can be maintained even at elevated pulp density, despite the adverse influence of solid loading observed during the optimization study. These findings provide useful insight into the behaviour of the present system under higher solid loading conditions and would assist in guiding future efforts aimed at improving process applicability through reduced acid consumption and shorter processing times.

3.6. Recovery of REEs as oxide product

The dissolved REEs in pregnant leachate from optimized condition were recovered through oxalate precipitation and subsequent calcination to obtain the corresponding oxide product. The precipitation step converted the dissolved REE species into a separable solid phase, thereby providing a simple route for downstream recovery. Comparison of the REE concentrations in the leachate before and after oxalate precipitation showed that approximately 98–99% of the dissolved REEs were recovered into the solid phase, demonstrating the effectiveness of the precipitation process. The obtained precipitate was further calcined to facilitate the decomposition of the oxalate phase and formation of the corresponding rare earth oxides.²⁴

The XRD patterns presented in Fig. S7 confirm the successful transformation of the recovered material during the precipitation–calcination sequence. The diffraction peaks obtained after precipitation can be attributed to the formation of REE oxalate phases, while the calcined product exhibited characteristic reflections corresponding to rare earth oxides. The absence or significant reduction of oxalate-associated peaks following calcination further supports the phase transformation process. These observations demonstrate that the REEs dissolved during UAL can be recovered as oxide products through a straightforward downstream treatment route, thereby illustrating the feasibility of a complete waste-to-product recovery pathway. However, the study acknowledges the need for further refinement of the precipitation and purification steps to improve product quality and facilitate the production of high-purity REE oxides.⁴⁹ Hence, the present study not only demonstrates efficient extraction of Pr and Dy from SPM through UAL, but also establishes a complete recovery pathway from leaching to oxide production. This highlights the potential of the proposed approach as an integrated route for rare earth recovery from end-of-life magnetic materials.

3.7. Sustainability implications and future outlook

The present study demonstrates that UAL can provide a practical approach for the recovery of REEs from SPMs. The use of acetic acid as the lixiviant offers a more environmentally benign alternative to conventional mineral acids while maintaining effective leaching performance under optimised conditions.⁵⁰ The application of ultrasound further enhanced the leaching process by improving mass transfer and reducing the time required for REE dissolution through cavitation-induced process intensification.¹⁶ The moderate operating amplitude together with the shorter leaching duration may partly balance the energy demand associated with ultrasonic irradiation.²¹ More broadly, the design of pretreatment and recovery steps should also consider their environmental consequences alongside their effectiveness in facilitating downstream metal recovery.⁵¹

The developed process also demonstrated appreciable REE recovery at higher pulp density, indicating its potential for further optimisation towards higher solid loading and continuous processing. In addition, the efficient recovery of Pr and Dy, despite their relatively lower abundance in the magnet matrix, highlights the applicability of ultrasound-assisted leaching for recovering REEs from secondary resources. The efficient precipitation of REEs from the pregnant leachate also creates the possibility for future regeneration and reuse of the lixiviant following appropriate solution conditioning. Although mixed rare earth oxides were successfully obtained, further purification steps will be necessary to produce high-purity individual REE oxides suitable for value-added applications while improving the environmental and economic feasibility of the overall process.⁵² Future studies should therefore focus on lixiviant recycling, downstream purification, higher pulp density operation, scalable cavitation systems, and process optimisation guided by techno-economic assessment to facilitate practical implementation of the developed process.

4. Conclusion

Ultrasound-assisted leaching using acetic acid was successfully developed for the recovery of Pr and Dy from SPM. The BBD effectively described the influence of the operating variables and identified the optimum leaching region, demonstrating that ultrasound amplitude, acetic acid concentration and leaching time positively influenced REE dissolution in the decreasing order, whereas increasing pulp density adversely affected the leaching process. The reliability of the optimisation was further confirmed by the close agreement between the experimental observations and the model predictions. The kinetic analysis identified shrinking core model to adequately describe the UAL process for REE leaching, suggesting diffusion through the reacted layer as the predominant rate-controlling step. The proposed mechanistic interpretation further illustrates how acoustic cavitation enhances mass transfer, improves lixiviant accessibility and facilitates REE dissolution from the magnet matrix. Although Pr consistently exhibited higher leaching efficiency than Dy, both REEs followed comparable kinetic behaviour and appeared to share a common diffusion-controlled mechanism. The developed process also showed desirable leaching performance at higher pulp density, providing insights for future process development. Furthermore, the REEs were recovered from the pregnant leachate through simple precipitation-calcination route as mixed oxides which complete the recovery pathway from SPM to recoverable oxide products. Thus, the present study demonstrates a unified process flow combining statistical optimisation, kinetic interpretation, mechanistic understanding, and downstream recovery, providing a scientific basis for the further development of ultrasound-assisted hydrometallurgical strategies for rare earth recycling.

Conflicts of interest

There are no conflicts to declare.

Data availability

All data generated or analysed during this study are included in this published article and its supplementary information (SI). Supplementary information: additional experimental, analytical, kinetic, and quality-control details. See DOI: https://doi.org/10.1039/d6ra06427b.