Daniele Preziosi

S Homkar

C Lefevre

N Viart

M Salluzzo

Unusual anisotropic magnetic orbital moment obtained from x-ray magnetic circular dichroism in a multiferroic oxide system

The electric field control of d-electron magnetism in multiferroic transition metal oxides is attracting widespread interest for the underlying fundamental physics and for next generation spintronic devices. Here, we report an extensive study of the 3d magnetism in magnetoelectric Ga 0.6 Fe 1.4 O 3 (GFO) epitaxial films by polarization-dependent x-ray absorption spectroscopy. We found a nonzero integral of the x-ray magnetic circular dichroism (XMCD), with the sign depending upon the relative orientation between the external magnetic field and the crystallographic axes. This finding translates into a sign reversal between the average Fe magnetic orbital and spin moments. Large Fe displacements, among inequivalent octahedral sites, lower the symmetry of the system producing anisotropic paths for the Fe-O bondings giving rise to a large orbital-lattice interaction akin to a preferential crystallographic direction for the uncompensated, or averaged among different sites, magnetic orbital moment. The latter may lead to a partial reorientation of the magnetic orbital moment under an external magnetic field that, combined with the ferrimagnetic nature of the GFO, can qualitatively explain the observed sign reversal of the XMCD integral. The results suggest that control over the local symmetry of the oxygen octahedra in transition metal oxides can offer a suitable leverage over the manipulation of the effective orbital and spin moments in magnetoelectric systems.

follows that understanding how SOC couples the electron spin angular momentum to the electron orbital angular momentum in multiferroic TMOs is a necessary step toward a rational design of novel ultralow-switching-energy multiferroic-based devices.

Fe 3+ -based oxides, being characterized by a 3d 5 electronic configuration, should exhibit a zero magnetic orbital moment * daniele.preziosi@ipcms.unistra.fr (μ L ) as is found, for example, in the case of γ -Fe 2 O 3 nanopar-50 ticles [9]. However, a nonzero μ L , parallel to the magnetic 51 spin moment (μ S ), was reported in the case of magnetoelectric 52 gallium ferrite (GaFeO 3 ) single crystals [10], where Fe 3+ ions 53 occupy only octahedral (O h ) sites. This result was interpreted 54 as a consequence of intrinsic FeO 6 crystalline distortions, 55 capable of removing the parity symmetry of the 3d orbitals via 56 anisotropic Fe 3d-O 2p hybridization paths. Similarly, Tseng 57 et al. by using the sum rules reported a nonzero μ L parallel to 58 μ S in -Fe 2 O 3 nanoparticles [11].

59

In this work, we report polarization-dependent x-ray ab-60 sorption spectroscopy (XAS) measurements, and in particular 61 Fe L 3,2 -edges x-ray magnetic circular dichroism (XMCD) 62 data, on magnetoelectric Ga 0.6 Fe 1.4 O 3 (GFO) epitaxial films. 63 The 0.4 excess of Fe increases the ferrimagnetic transition 64 above room temperature. This Fe doping allows also a certain 65 amount of Fe 3+ in tetrahedral (T d ) sites (see, for example, 66 Table I). By applying the sum rules to the XMCD data we 67 find that the magnetic orbital moment is anisotropic with 68 a direction parallel or antiparallel to the net magnetic spin 69 moment depending on the orientation between magnetic field 70 and crystallographic axes. We explain the nonzero value of the 71 net μ L and the abnormal change of orientation with respect 72 to the average μ S , as a consequence of a direction-dependent 73 compensation between μ L and μ S along different crystal axes 74 of inequivalent (differently distorted) Fe sites. Here, the Fe 75 ions moving away from the gravity center of the octahedral 76 cage set a strong orbital-lattice interaction that, for large 77 TABLE I. Cationic distributions of Fe 3+ and Ga 3+ over the four different cationic sites of the GFO orthorhombic structure. Experimental values (as taken from Ref. [17]), and theoretical ones as expected from the Ga 0.6 Fe 1.4 O 3 formula. octahedra mainly along the b axis when a magnetic field (H) is applied along the perpendicular direction (i.e., the c axis). For the opposite situation, which sees H applied along the b axis, the Fe displacements along the c axis are less energetically favorable and, most likely, controlled by the nature of the intrinsic distortion of the FeO 6 octahedra. The latter have one of the eight faces oriented in the ac plane, and are trigonally distorted along the b axis, which is also the threefold rotational axis of the trigonal symmetry (D 3d ) [START_REF] Khomskii | Transition Metal Compounds[END_REF]. Here, the t 2g Fe 3+ orbitals are transformed into a g 1 and e π g states, and the e g doublet becomes a unique e σ g state, as schematically shown in Fig. 1(b). The growth orientation of the GFO onto the STO is sketched in the inset of Fig. 1(a), where the bulk ac plane becomes stabilized on the substrate's surface and the bulk b axis coincides with the surface normal.

Ga1(T d ) Ga2(O h ) Fe1(O h ) Fe2(O h ) Sum
To test the quality of our GFO thin films we performed magnetic measurements via vibrating sample magnetometry (Quantum Design, MPMS). Figure 1(c) shows the temperature dependence of the magnetization acquired with a magnetic field of 0.1 T oriented in both in-plane (ac plane) and out-of-plane (b axis) directions. While the Curie temperature of about 356 K is the same for both geometries, the net magnetic moment is strongly anisotropic with the hard axis along the b axis (out-of-plane direction). The saturated magnetic moment measured at 10 K and 6.5 T is 0.78 ± 0.08 μ B /Fe (see Fig. S2 of the Supplemental Material [START_REF][END_REF]). The relative cationic distributions, reported in Table I, have been determined in previous resonant elastic x-ray scattering (REXS) measurements performed on GFO thin films obtained from the same ceramic target [17] as in this study. Oxygen K-edge XAS measurements as a function of the linear polarization were used to compare the electronic structure of our GFO films to stoichiometric GaFeO 3 single crystals. The spectra show a strong polarization dependence reflecting a strong orbital in-plane/out-of-plane anisotropy. XAS at the O K-edge is related to the degree of covalency in the system, hence, reflecting the oxygen projected unoccupied density of states [START_REF] De Groot | [END_REF]. In Fig. 2 the material density. In the case of our GFO thin films we 211 calculated the x-ray penetration depth values from our XAS 212 spectra as reported in the Supplemental Material [START_REF][END_REF]. As a 213 result of this calculation we used in NI (GI) the values of 19.3 214 (24.5) nm and 83.2 (76.8) nm for the L 3 and L 2 edges, respec-215 tively. The overall acquired XAS signal well reproduces the 216 features of the Fe L 3,2 -edges of GaFeO 3 single crystals [10] 217 demonstrating the high quality of our thin films. However, by 218 a closer look at the XAS spectra [see inset of Fig. 3 Also in this case we can highlight a good agreement with data reported for GaFeO 3 single crystals showing similar features, alike the two negative peaks at L 3 and a positive feature at L 2 (Fig. S5 of the Supplemental Material [START_REF][END_REF] shows the two XMCD spectra superimposed). By focusing on the integral sign of the XMCD, while in GI we recover a negative value (corroborating the reported results for bulk GaFeO 3 ), in NI we surprisingly observe a positive integral value. To guarantee a quantitative analysis of this finding any drawbacks linked to the practical application of the sum rules need to be excluded.

Indeed, the extrapolation of absolute values for orbital and practically zero [17], rendered the same integral sign variation 277 as for doped GFO thin films (see Fig. S1 of the Supplemental 278 Material for more details [START_REF][END_REF]). Importantly, we obtain the 279 result that sum rules can formally hold also for our doped 280 GFO thin films. In this framework, the integral of the XMCD 281 is proportional to the average orbital moment [27,28], and we 282 get the unexpected result that the relative orientation of the 283 calculated average orbital and spin moments depend upon the 284 crystallographic direction. [10]. In this picture μ L is linked to the magnitude/direction of 297 the Fe off-centering with respect to the FeO 6 center of gravity, 298 and to fully orient it along H, one should assume that the Fe 299 displacements can take place along all the crystallographic 300 directions within the distorted FeO 6 octahedra. As a matter 301 of fact, our XMCD data [cf. Fig. 3(c)], verified on several 302 samples and showing a sign reversal of the XMCD integrals, 303 tell us that this is not the case and, on the contrary, inform 304 us of a possible large lattice-orbital effect characterizing the 305 most distorted Fe1 and Fe2 sites of our GFO thin films.

306

As discussed above, the off-centering of the Fe 3+ ions 307 determines a different degree of hybridization between Fe 3d 308 and O 2p states along the main crystallographic axes for each 309 distorted sites, hence, establishing anisotropic Fe 3d-O 2p hy-310 bridization paths. As already shown by Arima et al., Fe 3+ ions 311 sitting in the most distorted Fe1 and Fe2 sites move along the 312 b axis in opposite directions [18] (plain white arrows sketched 313 in Fig. 4). In the absence of H such intrinsic off-centering sets 314 a net μ L along the c axis, opposed to the net μ S for which the 315 contribution from Fe2 and Ga2 sites prevails over the one of 316 Fe1 and Ga1 sites, the latter being mostly occupied by Ga 3+ 317 ions. When we measure the XMCD in GI geometry, being H 318 mostly oriented in the sample plane, the Fe ions readjust their 319 position in the perpendicular direction [18], as exemplified by 320 the blue shaded arrows of Fig. 4(a). As a direct consequence 321

346

This scenario explains the anomalous change of the average orbital moment with the crystallographic direction and has important implication for the physics of this system. In particular, it shows that a strongly correlated oxide may have a direction-dependent average magnetic orbital moment as a result of anisotropic distortions and related lattice-orbital effects, which geometrically control the relative orientation between the spin and orbital moments. Thus, a control over the distortions at each site of the GFO crystal structure would then offer an adjustment knob over the spin-orbit coupling in the system. Furthermore, Elnaggar et al. showed that a noncollinearity between spin and orbital magnetic moments is possible also in magnetite (Fe 3 O 4 ) single crystals [25]. There, an intimate interplay between trigonal distortions, spin-orbit coupling, and exchange interaction was assumed to be at the origin of the noncollinear orbital and spin ordering direction. In GFO thin films, this noncollinearity is mainly linked to the intrinsic Fe off-centering within the distorted FeO 6 octahedra with direct consequences on the magnetoelectric and magnetic properties. We believe that our results will encourage the study of TMO materials exhibiting multiferroic properties to assess their potential in spintronics by performing experiments, such as spin-pumping, ferromagnetic resonance, and/or spin-Seebeck effects, taking into account the relative orientation between H and crystallographic axes.

This work was funded by the French National Research Agency (ANR) through the ANR MISSION ANR-18-CE-CE24-0008-01. D.P. has received support from the initiative of excellence IDEX-Unistra (ANR-10-IDEX-0002-02) from the French national program Investment for the Future. S.H. acknowledges financial support from ANR through Grant No. ANR-17-EURE-0024 EUR QMat. The authors wish to thank F. Choueikani for scientific and technical support at DEIMOS, and L. Joly and J. P. Kappler for preliminary measurements performed at SLS. We deeply acknowledge P. Ohresser, M. Alouani, and P. Sainctavit for fruitful and inspiring discussions regarding the possible mechanism explaining our XMCD data. F. de Groot is acknowledged for advice regarding the atomic multiplet calculations. Finally, the authors are very grateful to S. Grenier for the implementation of the DYNA code used for the calculation of x-ray penetration depths.

  FIG. 1. (a) Conventional GFO unit cell with the four different sites. Inset shows the growth mode onto the STO(111). b also corresponds to the threefold rotational axis of the (b) trigonal distortion. (c) Magnetization curves as a function of temperature for the in-plane and out-of-plane geometries.

FIG. 2 .

 2 FIG. 2. (a) O K-edge XAS spectra acquired with LH and LV polarized light with a sketch of the geometrical setup. Inset shows the spectra for the entire energy range. The A-and B-labeled doublet (solid symbols) is reproduced (dashed line) by two Voigt functions (open symbols). (b) Derived energy diagram and energy splitting of the trigonal crystalline splitting with further degeneracy removal of the e σ g .

  (a) we show O K-edge XAS spectra acquired with linear horizontal (LH) and vertical (LV) polarized light with an incidence angle of about 60 • [grazing incidence (GI) geometry], with respect to the sample normal [see inset of

Fig. 2 (

 2 Fig. 2(a)]. In this geometry, the spectra acquired with LH polarization give mostly information regarding the unoccupied O 2p levels oriented out-of-plane (i.e., parallel to the b axis of the film), while with LV we collect information of the unoccupied O 2p states oriented in the sample plane, i.e., parallel to the a and the c axes, as both directions are essentially indistinguishable [cf. inset of Fig. 1(a)]. Indeed, LH and LV O K-edge spectra acquired in normal incidence (NI) geometry are identical (see Fig. S3 of the Supplemental Material [20]), hence, confirming the GFO growth mode as sketched in the inset of Fig. 1(a). The high-energy region, above 532 eV, is characterized by broad peaks due to the hybridization between O 2p and 4s and 4p Ga and Fe orbitals. On the other side, the prepeak region, up to 532 eV, being related to the O 2p hybridization with Fe 3d orbitals, is the one we analyzed. The two main features, labeled A and B, are roughly associated with the Fe 3d t 2g and e g bands, which within the trigonal crystal field can be linked to (a g 1 , e π g ) and e σ g orbital derived bands [Fig. 2(b)]. Thus, the peak A is a convolution between in-plane (e π g ) and out-of-plane (a g 1 ) derived bands. If the symmetry is further lowered, the e σ g peak can also split. As matter of fact, the data acquired with LH and LV polarizations show a shift in the position of the A and B features which can be quantified by a two-peak Voigt profile (open symbols), shown as red dashed lines in Fig. 2(a). The analysis reveals that the average distance between A and B features, roughly corresponding to the 10Dq crystal field splitting, is of the order of 1.2 eV, while the energy splitting between a g 1 and e π g bands is of the order of 0.02 eV. Larger is the shift of the B peaks (∼0.1 eV), which demonstrates also a removal of the e σ g degeneracy. Furthermore, the strong intensity variation of the A and B peaks measured with LH and LV polarizations suggests a strong anisotropic hybridization among Fe 3d and O 2p orbitals for both in-plane and out-of-plane directions. In Fig. 2(b) we show a tentative energy diagram of the orbital hierarchy derived from the O K-edge XAS spectra analysis. In particular, it emerges that the out-of-plane (a g 1 ) orbitals set higher in energy compared to in-plane ones (e π g ), pointing to a trigonal elongation of the FeO 6 octahedra (see Fig. S4 of the Supplemental Material [20]). Summarizing, our O K-edge measurements confirming the removal of the e σ g orbital degeneracy with an anisotropic Fe 3d-O 2p hybridization path point to a net nonzero μ L value also for our GFO thin films, as already inferred for GaFeO 3single crystals[10]. Here, the result of inner movements of Fe ions brings to a parity symmetry breaking of the 3d electron clouds with a subsequent apparition of a measurable magnetic orbital moment. Finally, it should be mentioned also that while O K-edge spectra cannot be used to precisely determine the values of the crystal field splitting parameters they can give, nevertheless, a good estimation.In order to determine whether the observed anisotropic Fe 3d-O 2p hybridization network induces an orbital moment in our films, we performed XAS and XMCD measurements at the Fe L 3,2 -edges in both NI and GI geometries.

Figure 3 (

 3 Figure 3(a) shows the area-normalized XAS spectra corrected from saturation effects[22]. This correction is fundamental when a quantitative analysis of the magnetic orbital moment is required, and one of the most important parameters to consider is the x-ray penetration depth that depends upon

Figures 3

 3 Figures 3(b) and 3(c) report the XMCD spectra acquired for both NI and GI geometries after the saturation correction.

FIG. 4 .

 4 FIG. 4. (a) Parallel configuration among μ L and μ S and (b) their geometrical construction under magnetic field along the b axis for the antiparallel configuration. The length of the arrow representing the spin moment is proportional to the Fe 3+ occupancy at each site.

TABLE II .

 II Optimized parameters with related weights for XAS spectra.

		10D q	U dd U pd	T e T ab Weight for XAS
	Fe 3+ (O h )	1.2	3.0 6.0 7.5 0.5	1	92%
	Fe 3+ (T d )	1.2	3.0 6.0 7.5 0.5	1	8%

TABLE III .

 III XMCD sum-rules-derived μ L and μ S for NI and GI geometries at 6.5 T. Number of holes in the 3d states equal to 4.8 to account for the CT. , especially in 271 the case of materials containing the magnetic ions in the 272 same nominal oxidation state but in different coordination and 273 symmetry[26] (i.e., mixed occupation of T d and O h sites), as 274 it is for GFO. XMCD measurements performed on undoped 275 GFO thin films, for which the Fe 3+ occupation of T d sites is 276

		μ S (μ B /Fe)	μ L (μ B /Fe)	μ total (μ B /Fe)
	NI	+0.72 ± 0.07	-0.023 ± 0.002	0.70 ± 0.07
	GI	+0.68 ± 0.07	+0.016 ± 0.002	0.70 ± 0.07
	spin moments is particularly challenging [25]

  Table III reports the average μ L 285 and μ S values, as obtained from sum rules, for both NI and 286 GI geometries. Within the systematic error that accompanies 287 the application of the sum rules of about 10%-20%, we found 288 that the external magnetic field is strong enough to align μ S 289 along both crystallographic directions, but this does not hold 290 for μ L which, within errors, has values that do not overlap. 291 As already discussed by Kim et al., intrinsic Fe displacements 292 within the most distorted O h sites of the GFO orthorhombic 293 crystal structure are responsible for a nonzero μ L . The latter 294 extending perpendicular to the off-centering direction is a 295 result of the anisotropic electron cloud around the Fe ions 296

site, hence, promoting a net μ L parallel to the net μ S and 323 confirming our experimental finding in GI geometry. On the


Davey Margot Zielinski

Laurent Cassayre

Nicolas Coppey

Béatrice Biscans

Pilot-Scale Lanthanide Precipitation from Sulfate-Based Spent Ni-MH Battery Leachates: Thermodynamic-Based Choice of Operating Conditions Published as part of a Crystal Growth and Design virtual special issue in Celebration of the Career of Roger

Access to critical metals required for high-performance technologies, particularly, the light rare earth elements (REEs = La, Ce, Nd, Pr), has become a major challenge for importdependent economies such as the European Union. In this regard, the recycling of spent nickel metal hydride (Ni-MH) batteries by hydrometallurgical processes can serve as an attractive secondary source of REEs. In such processes, precipitation of REEs from pregnant leach solutions (PLS) in sulfate media using Na 2 SO 4 is often reported. However, little consideration is given as to whether and how sodium ions influence the precipitation efficiency and selectivity. This work focuses on a better understanding of the precipitation process by coupling pilot-scale (2 L) experiments on industrially sourced PLS containing 50 g/L of Ni and 17 g/L of REEs, with thermodynamic modeling, to assess the influence of temperature (25 °C < T < 60 °C) and the Na/REEs molar ratio (0.8:1 < Na/REEs < 3.2:1). Equilibria calculations were performed using OLI Systems Inc. software whose database covers rare earth sulfate compound properties and an accurate description of the aqueous electrolytes. Highly selective precipitation was obtained at 60 °C and for a Na/REEs molar ratio of 4:1. A lanthanide-alkali solid solution was identified by multianalytical characterization.

INTRODUCTION

Because of their unique physicochemical properties, rare earth elements (REEs) have become key constituents of highperformance technologies and energy storage materials ranging from permanent magnets to electronic equipment, superconductors, polishing powders, pigments, and rechargeable battery electrodes, thus giving them undeniable worldwide economic importance. [START_REF] Kim | Aqueous stability of thorium and rare earth metals in monazite hydrometallurgy: Eh-pH diagrams for the systems Th-, Ce-, La-, Nd-(PO 4 )-(SO 4 )-H 2 O at 25[END_REF][START_REF] Blengini | Study on the EU's List of Critical Raw Materials -Final Report[END_REF] Certain authors forecast an annual increase of the global demand for REEs of +8% from 2017 to 2025. [START_REF] Leguérinel | Competition entre secteurs industriels pour l'acces aux matieres premieres[END_REF] The term "rare" is a misnomer, the more abundant REEs such as lanthanum (La), cerium (Ce), neodymium (Nd), and praseodymium (Pr) being almost as concentrated in Earth's crust as more common metals such as Cu, Ni, or Co. [START_REF]Rare Earth Elements  Critical Resources for High Technology[END_REF] However, exploitable ore deposits are very dilute, and, consequently, REEs are only supplied from a few sources around the globe. [START_REF] Lister | Recovery of Rare Earth Elements from Recycled Hard Disk Drive Mixed Steel and Magnet Scrap[END_REF] As of 2020, China dominates the REEs market and provides more than 86% of the global supply. [START_REF] Blengini | Study on the EU's List of Critical Raw Materials -Final Report[END_REF] High supply risks induced by this uneven distribution make light REEs some of the most critical metals, according to the European Commission's 2021 report on Critical Raw Materials. [START_REF] Blengini | Study on the EU's List of Critical Raw Materials -Final Report[END_REF] Hence, it is crucial for highly import-dependent economies such as the European Union, to seek more locally sourced REE production. To this regard, spent nickel-metal hydride (Ni-MH) batteries can serve as an attractive secondary source of REEs. Indeed, the anode active mass of Ni-MH batteries is made of mischmetal where light REEs (La, Ce, Nd, and Pr) are alloyed with other metals (Ni, Co, Al, and Mn). The valuable powder extracted after crushing spent Ni-MH batteries can contain up to 15 wt % REEs. [START_REF] Zielinski | A multi-analytical methodology for the characterization of industrial samples of spent Ni-MH battery powders[END_REF][START_REF] Meshram | Process optimization and kinetics for leaching of rare earth metals from the spent Ni-metal hydride batteries[END_REF][START_REF] Larsson | Dissolution and characterization of HEV NiMH batteries[END_REF][START_REF] Ebin | Physical separation, mechanical enrichment and recycling-oriented characterization of spent NiMH batteries[END_REF] Given that over a billion Ni-MH battery units have been placed on the market worldwide each year in the past decade [START_REF] Pillot | The Rechargeable Battery Market and Main Trends 2016-2025[END_REF] and that a compound annual growth rate (CAGR) of 2.6% for the global Ni-MH battery market is predicted between 2017 and 2022, [START_REF]Global Nickel-Metal Hydride (Ni-MH) Battery Market[END_REF] recycling of spent Ni-MH batteries has the potential to offer a significant feedstock for secondary REE production. However, because of technical (maturity of recycling processes) and economic (volatility of raw materials prices) aspects, the contribution of recycling to the market demand is still very low. As of 2020, the end-of-life recycling input rate of La, Ce, Nd, and Pr are respectively <1%, <1%, <1%, and <10%. [START_REF] Blengini | Study on the EU's List of Critical Raw Materials -Final Report[END_REF] In the past decade, numerous academic and industrial research groups have focused on developing more efficient hydrometallurgical processes for the recovery of REEs from spent Ni-MH batteries. In a traditional process, spent batteries are transformed into a powder enriched in valuable elements thanks to thermal and mechanical pretreatment steps. [START_REF] Zielinski | A multi-analytical methodology for the characterization of industrial samples of spent Ni-MH battery powders[END_REF][START_REF] Wang | Development of a highly efficient hydrometallurgical recycling process for automotive Li-ion batteries[END_REF] The powder is then leached in a mineral acid (HCl, HNO 3 , or H 2 SO 4 ) where REEs are solubilized in the pregnant leach solution (PLS) along with various other metal elements such as Ni, Co, Mn, Al, Fe, or Zn. [START_REF] Zielinski | Leaching mechanisms of industrial powders of spent nickel metal hydride batteries in a pilot-scale reactor[END_REF] The bottleneck of the hydrometallurgical process is then to selectively separate these elements from each other. The type of mineral acid selected for leaching depends on the downstream separation process: generally, sulfuric media is chosen when precipitation is the preferred separation method, whereas hydrochloric or nitric systems are chosen when solvent extraction is preferred. [START_REF] Lister | Recovery of Rare Earth Elements from Recycled Hard Disk Drive Mixed Steel and Magnet Scrap[END_REF] In this work, we have focused on selective precipitation as a recovery process. Elemental concentrations [g/L] obtained from a selection of the recent literature (2009-2021) having studied the leaching of spent Ni-MH battery powders in sulfuric media are summarized in Table 1. These data show rather wide concentration variations, which can be attributed to the leaching process parameters (solid-liquid ratio, leaching time). The leachates contain predominantly Ni (up to 50 g/L), while REEs represent roughly one-third of the Ni content.

A review of the literature shows that REEs can be precipitated in the form of oxalates or hydroxides by adding oxalic acid [START_REF] Pietrelli | Characterization and leaching of NiCd and NiMH spent batteries for the recovery of metals[END_REF][START_REF] Zhang | Hydrometallurgical process for recovery of metal values from spent nickel-metal hydride batteries[END_REF][START_REF] Yang | Rare earth element recycling from waste nickel-metal hydride batteries[END_REF] or a base, [START_REF] Pietrelli | Rare earths recovery from NiMH spent batteries[END_REF] respectively, to the PLS. Under such conditions, however, the pH shift of REEs at around 6 is above that of other metals in solution (i.e., Fe, Al, Co, Ni, Mn, Zn), which does not yield good separation ratios. An alternative consists of precipitating REEs in the form of sparingly soluble monohydrated double sulfates MREE(SO 4 ) 2 • H 2 O (M = K, Na; REE = La, Ce, Nd, or Pr) by the addition of Na + or K + ions according to the precipitation reaction (eq 1). [START_REF] Meshram | Process optimization and kinetics for leaching of rare earth metals from the spent Ni-metal hydride batteries[END_REF][START_REF] Ahn | Valorization of waste NiMH battery through recovery of critical rare earth metal: A simple recycling process for the circular economy[END_REF][START_REF] Liu | Synergistic recovery of valuable metals from spent NiMH and Liion batteries[END_REF][START_REF] Porvali | Lanthanide-alkali double sulfate precipitation from strong sulfuric acid NiMH battery waste leachate[END_REF][START_REF] Porvali | REE (III) recovery from spent NiMH batteries as REE double sulfates and their simultaneous hydrolysis and wet-oxidation[END_REF]

+ + + → + + - (1)
The precipitation of sodium-lanthanide double sulfates is usually favored over that of potassium-lanthanide double sulfates since the solubility of the former is an order of magnitude lower than the latter, at room temperature. [START_REF] Lokshin | Solubility of double alkali metal (Na, K) rare-earth (La, Ce) sulfates in sulfuric-phosphoric acid solutions at 20°C[END_REF][START_REF] Lokshin | A Study of the Solubility of Yttrium, Praseodymium, Neodymium, and Gadolinium Sulfates in the Presence of Sodium and Potassium in Sulfuric-Phosphoric Acid Solutions at 20°C[END_REF] In that case, the pH of the sulfate-based PLS is usually adjusted to 1.5-3.5 with a concentrated NaOH (3-10 M) solution [START_REF] Meshram | Process optimization and kinetics for leaching of rare earth metals from the spent Ni-metal hydride batteries[END_REF][START_REF] Ahn | Valorization of waste NiMH battery through recovery of critical rare earth metal: A simple recycling process for the circular economy[END_REF][START_REF] Bertuol | Spent NiMH batteries  The role of selective precipitation in the recovery of valuable metals[END_REF][START_REF] Pietrelli | Rare earths recovery from NiMH spent batteries[END_REF][START_REF] Innocenzi | Recovery of rare earths and base metals from spent nickel-metal hydride batteries by sequential sulphuric acid leaching and selective precipitations[END_REF][START_REF] Rodrigues | Hydrometallurgical separation of rare earth elements, cobalt and nickel from spent nickelmetal-hydride batteries[END_REF] or a mixture of NaOH/Na 2 CO 3 [START_REF] Nan | Dismantling, Recovery, and Reuse of Spent Nickel-Metal Hydride Batteries[END_REF][START_REF] Nan | Recovery of metal values from a mixture of spent lithium-ion batteries and nickel-metal hydride batteries[END_REF] as it is believed that solely increasing the pH leads to the precipitation of REE double sulfates. Under optimal conditions, a highly selective precipitation of sodium-REE double sulfates with respect to other metals in solution is obtained.

In their recent experimental work, Porvali et al. demonstrated that the precipitation of REE double sulfates in sulfuric media does not depend so much on pH but rather on the Na + and SO 4 2-concentrations in solution. [START_REF] Liu | Synergistic recovery of valuable metals from spent NiMH and Liion batteries[END_REF][START_REF] Porvali | Lanthanide-alkali double sulfate precipitation from strong sulfuric acid NiMH battery waste leachate[END_REF][START_REF] Porvali | Nickel Metal Hydride Battery Waste: Mechanohydrometallurgical Experimental Study on Recycling Aspects[END_REF] ratios without necessarily increasing the pH value and, thus, preventing coprecipitation of other metals. The fact that the solubility of sodium-REE double sulfates decreases when the quantity of Na 2 SO 4 in solution increases is linked to the common ion effect. [START_REF] Lister | Recovery of Rare Earth Elements from Recycled Hard Disk Drive Mixed Steel and Magnet Scrap[END_REF] In all of the studies regarding REE double sulfate precipitation from solutions obtained from leaching spent Ni-MH battery powders in sulfuric media, experimental results are very promising but are seldom correlated with thermodynamic equilibria calculations. Yet, thermodynamic simulations could help explain the observed precipitation mechanisms, optimize the conditions of REE extraction, and better design the recycling process. In the rare occasions where thermodynamic calculations are implemented, authors rely on models that do not take into account the complexity of the chemical system. For instance, some models do not represent the nonideality of the concentrated aqueous phase (and thus calculations are made for very diluted solutions). [START_REF] Kim | Aqueous stability of thorium and rare earth metals in monazite hydrometallurgy: Eh-pH diagrams for the systems Th-, Ce-, La-, Nd-(PO 4 )-(SO 4 )-H 2 O at 25[END_REF][START_REF] Porvali | Nickel Metal Hydride Battery Waste: Mechanohydrometallurgical Experimental Study on Recycling Aspects[END_REF] Other models implement thermodynamic databases that cover the subsystem REE-(H 2 SO 4 )-H 2 O (REE = La, Ce, Nd, or Pr) but do not consider the presence of sodium ions and therefore the possibility of precipitating sodium-REE double sulfates. [START_REF] Ahn | Valorization of waste NiMH battery through recovery of critical rare earth metal: A simple recycling process for the circular economy[END_REF] Thermodynamic consideration of the more complex systems REE 2 (SO 4 ) 3 -Na 2 SO 4 -H 2 SO 4 -H 2 O (REE = La, Ce, Nd, or Pr) has been made possible thanks to the recent (2019) modeling work of Das et al. [START_REF] Das | Rare earth sulfates in aqueous systems: Thermodynamic modeling of binary and multicomponent systems over wide concentration and temperature ranges[END_REF] and the implementation of the corresponding thermodynamic data in the database of the OLI Systems Inc. software. One of the originalities of the present work, therefore, lies in the fact that we performed thermodynamic calculations representative of the experimental precipitation system using OLI Systems Inc. given the recent update of thermodynamic data relative to rare earth double sulfates. Thermodynamic equilibria were simulated for concentrated aqueous solutions consisting of spent battery leachates, over a wide range of temperature (25 °C < T < 60 °C) and added moles of Na 2 SO 4 (0 mol < Na 2 SO 4 < 0.32 mol). The modeling results were used as a guide for a parametric study to assess the influence of two main operating parameters on REE precipitation efficiency: temperature (25 °C < T < 60 °C) and final Na/REEs molar ratio (0.8:1 < Na/ REEs < 3.2:1).

Precipitation experiments were carried out in a 2 L pilotscale semibatch reactor, which constitutes another originality of this work compared to previous studies. Indeed, in the referenced literature, smaller reactor volumes of 100 mL, [START_REF] Porvali | Nickel Metal Hydride Battery Waste: Mechanohydrometallurgical Experimental Study on Recycling Aspects[END_REF] 250 mL, 15 500 mL, [START_REF] Meshram | Process optimization and kinetics for leaching of rare earth metals from the spent Ni-metal hydride batteries[END_REF] or 1 L 14 are reported, which do not offer scalable precipitation conditions at industrial scale in terms of hydrodynamics and energy dissipation in the reactor. The objectives of the precipitation experiments reported in this article were to (i) better understand precipitation mechanisms at stake (precipitation kinetics, comparison with thermodynamic equilibria), and (ii) verify the truly selective nature of REE precipitation with respect to other metals when working with a PLS particularly concentrated in nickel ([Ni] ≈ 52 g/L) compared to most previous studies (Table 1). Furthermore, the crystals obtained in all precipitation experiments were characterized to investigate their structure, morphology, and purity.

MATERIALS AND METHODS

Pilot-Scale Setup of the Precipitation Experiments.

Approximately 600 kg of cylindrical-type spent Ni-MH batteries were thermally deactivated, crushed, and sieved at the industrial facilities of SNAM (France) according to the protocol described in our previous work. [START_REF] Zielinski | A multi-analytical methodology for the characterization of industrial samples of spent Ni-MH battery powders[END_REF] The black mass (BM) powder obtained after this thermomechanical treatment was prewashed in H 2 SO 4 -H 2 O media at pH 6 to solubilize residues of alkali metals (Na, K) from the electrolyte and dried at 80 °C in an oven overnight. The prewashed BM powder was then leached in a 10 L semibatch reactor according to the procedure described elsewhere (H 2 SO 4 -H 2 O, pH 1, 40 °C, solid-liquid ratio 15%). [START_REF] Zielinski | Leaching mechanisms of industrial powders of spent nickel metal hydride batteries in a pilot-scale reactor[END_REF] After 27 h of leaching, insoluble residues were filtered out from the solution. A total of five leaching batches were carried out under the same conditions in order to provide a sufficient amount of leachate solution to perform precipitation experiments. For each precipitation experiment, 300 mL of solution from each leaching batch were mixed to obtain a total volume of approximately 1.5 L of initial solution. The mixed leachates used as initial solutions for the precipitation experiments were analyzed by inductively coupled plasma-optical emission spectroscopy (ICP-OES, PerkinElmer Optima 8300), and average elemental concentrations [g/ L] are reported in Table 1.

Precipitation experiments were conducted in a 2 L jacketed semibatch baffled glass reactor equipped with a four-blade stirrer (Teflon, d = 7 cm in diameter). A total of 1.5 L of initial leachate solution was added into the reactor and regulated at a constant temperature (± 0.01 °C) using an ultracryostat instrument device (Thermo HAAKE circulator P2-CT50L). A constant mixing rate of 400 rpm was applied, ensuring sufficient mixing of the solution and a power dissipation in the reactor of approximately 6.9 × 10 -1 W/m 3 of suspension. [START_REF] Zwietering | Suspending of solid particles in liquid by agitators[END_REF] The pH was carefully monitored (±10 -4 ) using a pH sensor (Mettler Toledo probe). For all experiments, an aqueous precursor solution of Na 2 SO 4 -H 2 O (Na 2 SO 4 anhydrous powder, Sigma-Aldrich, >99.0% purity) was prepared at a fixed concentration of 2.87 M and maintained at 40 °C on a heating plate with magnetic stirring. To initiate the precipitation experiments, the precursor solution was added to the heated PLS at a constant flow rate of 7 g• min -1 in a simple jet, using a membrane pump (ProMinent) connected to the servo control system LabMax (Mettler Toledo).

The effect of two process parameters on REE precipitation was studied: precipitation temperature (T = 25, 40, and 60 °C, for a fixed final Na/REEs molar ratio of 3.2:1) and final Na/REEs molar ratio (0.8:1 < final Na:REEs molar ratio <3.2:1, at 60 °C). Na/REEs molar ratios are defined according to eq 2, in which n(Na)added V(Na 2 SO 4 , t) is the number of moles of Na added in the reactor at time t (derived from the volume of precursor solution V(Na 2 SO 4 ) added in the reactor at time t), and ∑n(La,Ce,Nd,Pr) t 0 is the sum of the moles of La, Ce, Nd, and Pr in the initial PLS. n n (Na/REEs) (Na)added (La, Ce, Nd, Pr)

V t t (Na SO , ) 2 4 0 = ∑ (2)
Since for all the precipitation experiments, the same Na 2 SO 4 precursor solution with the same Na 2 SO 4 concentration was added at the same flow rate, Na/REEs molar ratios were increased by increasing the total addition time of Na 2 SO 4 . This implies an initial "semi-batch" period where the Na/REE molar ratio increases linearly as precursor solution is added, followed by a "batch" period where precipitation proceeds without further addition of the precursor solution, and the Na/REE molar ratio is fixed. Final Na/REEs molar ratios are calculated using (eq 2) considering the total added volume of precursor solution, corresponding to the end of the "semi-batch" period (t 0 is the initial time of the experiment).

The suspension was regularly sampled throughout the experiments (about 7 mL per sample) and filtered on 0.45 μm cellulose syringe filters. The elemental concentrations of the 10 following metals were determined by ICP-OES (PerkinElmer Optima 8300): Ni, Co, Mn, Fe, Al, Zn, La, Ce, Nd, and Pr. The experimental proportion of each element remaining in solution P (i,t)exp [%] at sampling time t was calculated according to eq 3 where C mas (i,t) is the mass concentration of element i in solution at sampling time t [mg/L], V sol,t 0 is the initial PLS volume [L], V precursor,t is the total volume of Na 2 SO 4 solution added at sampling time t [L], ∑V sample,t is the accumulative volume of suspension extracted from the reactor at sampling time t [L] and C mas (i, t 0 ) is the mass concentration of element i in the initial PLS [mg/L]. Mass losses due to evaporation of the solution and/or gas generation were considered negligible.

( )

P C i t V V V C i t V 100 ( , ) ( , )
After 1 h, the suspension was filtered on a P3 borosilicate glass Buchner filter (4 L capacity), and the solid fraction was rinsed several times with demineralized water at room temperature. The obtained crystals (typically 65 g per experiment) were dried in an oven at 80 °C overnight before in-depth characterization using multiple techniques: scanning electron microscopy (SEM, JEOL JSM 7100F), laser diffraction (Malvern MS 3000), powder X-ray diffraction (XRD, D8 Bruker, 20°< 2θ < 80°, CuKα radiation, 1.5418 Å), thermogravimetric analysis (TGA, TA Instruments Q600, N 2 (g), 25-600 °C, 5 °C/min, Pt crucible), microwave digestion (CEM MARS 6, 250 °C for 1 h in HCl/HNO 3 1:2, 1 g of powder in 30 mL), and ICP-OES (PerkinElmer Optima 8300, analysis of the 12 following elements: La, Ce, Nd, Pr, Na, S, Ni, Co, Mn, Al, Fe, Zn).

2.2. Thermodynamic Modeling. Thermodynamic equilibria calculations were used as a guide to delimit the studied range of operating conditions (temperature, final Na/REE molar ratios) and to compare theoretical concentrations in solution with experimental ones. Simulations were performed using the commercial software OLI Systems Inc., which implements the mixed-solvent electrolyte (MSE) model for concentrated electrolytic solutions [START_REF] Wang | A speciation-based model for mixed-solvent electrolyte systems[END_REF] and features specifically the thermodynamic description of the systems REE 2 (SO 4 ) 3 -Na 2 SO 4 -H 2 SO 4 -H 2 O (REE = La, Ce, Nd, or Pr). [START_REF] Das | Rare earth sulfates in aqueous systems: Thermodynamic modeling of binary and multicomponent systems over wide concentration and temperature ranges[END_REF] This numerical tool allows the calculation of equilibria concentrations and speciation of the different species in an aqueous system, with respect to several parameters such as temperature and Na/REEs The metallic elements of the simulated PLS were introduced as sulfates either in the form of MSO 4 (M = Ni, Co, Mn, Fe, Al, or Zn) or M 2 (SO 4 ) 3 (M = La, Ce, Nd, or Pr) in a volume of H 2 O, in proportions corresponding to the experimental elemental concentrations in the PLS given in Table 1. A certain quantity of H 2 SO 4 was also added to adjust the SO 4 2-total content of the experimental solution. Then, for a given temperature (25 °C < T < 60 °C), the simulation consisted of adding an increasing volume of the Na 2 SO 4 solution to the initial PLS in order to simulate the experimental "semibatch" period, within a Na/REEs molar ratio range of 0:1-3.2:1. The output of the simulation provides the equilibrium proportion of each element which has precipitated P (i,n(Na 2 SO 4 ),T) eq) [%], as defined in eq 4, for a given temperature and a given amount of Na 2 SO 4 added. The nature of the phases and the proportions of the elements in the solid fraction are also computed. i k j j j j j j y

{ z z z z z z P n i n i 100 1 ( ) ( ) i n T ( , (Na SO ), )eq liquid,eq syst 2 4 = * - (4)
where n(i) liquid,eq is the number of moles of element i in aqueous solution, and n(i) syst is the total number of moles of element i in the system at temperature T with respect to the Na/REEs molar ratio.

According to the definitions provided in eq 3 and in eq 4, P (i,n(Na 2 SO 4 ,T)eq and P (i,t)exp are comparable quantities accounting respectively for the measured and calculated proportion of element i (Ni, Co, Mn, Fe, Al, Zn, La, Ce, Nd, Pr) having precipitated from the PLS.

RESULTS AND DISCUSSION

3.1. Thermodynamic-Based Choice of Operating Conditions. Results of the thermodynamic simulations indicate that within all operating conditions (25 °C < T < 60 °C; 0:1 < Na/REEs < 3.2:1) no metal element other than the REEs should precipitate, which proves the theoretical highly selective nature of this technique. The proportion of each REE which should precipitate (calculated according to eq 4) with respect to the Na/REEs molar ratio for different temperatures is plotted in Figure 1; the vertical dotted lines correspond to the final Na/REEs molar ratios selected for the experiments. When considering the sole impact of temperature without any addition of Na 2 SO 4 , all REEs are soluble at 25 and 40 °C (Figure 1a,c). However, at 60 °C, around 45% of La should precipitate, contrary to Nd, Pr, and Ce which remain soluble (Figure 1e). This corresponds to a precipitation of 30% of the REEs contained in the leachate. The model predicts that the solid phase which should form at 60 °C in the absence of Na 2 SO 4 consists of an hydrated lanthanum sulfate La 2 (SO 4 ) 3 • 9H 2 O which precipitates according to eq 5. This corresponds to the fact that the solubility of La 2 (SO 4 ) 3 •9H 2 O is regressive with increasing temperature [START_REF] Das | Rare earth sulfates in aqueous systems: Thermodynamic modeling of binary and multicomponent systems over wide concentration and temperature ranges[END_REF] and that our PLS is close to La saturation.

2La 3SO 9H O La (SO ) 9H O 3 (aq) 4 (aq) 2 2 43 2 ( s ) 2 + + → • + - (5)
When the Na 2 SO 4 solution is added to the leachate, the model indicates that, at 40 and 60 °C, Ce and Pr should not precipitate when the Na/REEs molar ratio is at least lower than 0.66:1 at 40 °C (Figure 1c) and at least lower than 0.87:1 at 60 °C (Figure 1e). On the other hand, at 40 °C and for a Na/REEs molar ratio of 0.66:1, 68% of La, and 78% of Nd should precipitate (Figure 1c); at 60 °C and for a Na/REEs molar ratio of 0.87:1, 93% of La, and 89% of Nd should precipitate (Figure 1e). It is worth to note that, under such conditions, the calculations suggest that a selective precipitation could be achieved, where La and Nd can be precipitated, whereas Ce and Pr remain in solution.

In the presence of Na 2 SO 4 , results of the thermodynamic calculations indicate that REEs form a monohydrated sodiumlanthanide double sulfate REENa(SO 4 ) 2 •H 2 O (REE = La, Ce, Nd, or Pr), which precipitates according to eq 6 balanced out for 1 mol of Na 2 SO 4 .

+ + + → • + - (6)
According to the simulations, the solid fraction obtained is therefore a mixture of pure REE double sulfates, where the relative molar contents of each REE [mol %] within the solid fraction can be determined according to eq 7. As can be seen in Figure 1d,f, at 40 and 60 °C for Na/REEs molar ratios of 0.66:1 and 0.87:1, respectively, the solid fraction is composed of 90 mol % La and 10 mol % Nd.

For Na/REEs molar ratios greater than 1: In light of the above results, we carried out an experiment at 60 °C with a low final Na/REEs molar ratio of 0.8:1 to study the potentially selective precipitation of La and Nd with respect to Ce and Pr. Moreover, the overall objective being to extract a maximum of REEs during this precipitation step, we have also carried out experiments at 60 °C at higher final Na/ REEs molar ratios of 1.7:1 and 3.2:1. Finally, experiments were carried out at 25 and 40 °C for a final Na/REEs molar ratio of 3.2:1 to investigate the influence of temperature on the kinetics of precipitation. Under such operating conditions, thermodynamic simulations suggest it is possible to extract more than 95% of REEs if equilibrium is reached and that identical proportions of REEs are expected in the solid fraction regardless of the temperature.

3.2. Precipitation Experiments. 3.2.1. Influence of the Final Na/REEs Molar Ratio. The influence of the final Na/ REEs molar ratio (0.8:1 < Na/REEs < 3.2:1) on REE precipitation was studied at a constant temperature of 60 °C. Throughout the experiments, pH evolution in the reactor was monitored, and results are described in Figure 2a. A simultaneous drop of pH is observed when the REE concentrations start to decrease (Figure 2a). With this observation, we show for the first time that pH monitoring can serve as an indicator of REE precipitation initiation. An induction period can thus be thus determined, which is about 3 min for all experiments carried out at 60 °C.

This sudden drop of the pH value could be explained by the displacement of the dissociation equilibrium of hydrogen sulfate HSO 4 -as described in eq 8.

HSO H SO 4 4 2 ↔ + + - - (8)
Indeed, when REE double sulfates precipitate according to eq 6, 3 mol of sulfate ions SO 4 2-is consumed when 1 mol of Na 2 SO 4 reacts. As a result, the dissociation equilibrium of hydrogen sulfate is likely to shift and liberate H + ions according to eq 8, which induces a drop in pH. On the opposite, when the solid's solubility limit is reached, the addition of Na 2 SO 4 shifts the dissociation equilibrium toward HSO 4 -, which gradually increases the pH value.

Evolution of both the experimental and simulated concentrations [mol/L] of REEs with respect to time for different final Na/REEs molar ratios at 60 °C, are compared in Figure 3. The proportions of other metals (Al, Co, Fe, Mn, Ni, Zn) remaining in solution after 1 h of precipitation are given in Table SI.1. Overall, it can be seen that, experimentally, increasing the final Na/REEs molar ratio enhances the amount of REEs which precipitate. Indeed, after 1 h of precipitation at 60 °C, a total of 73.4% REEs has been recovered for a final Na/REEs molar ratio of 0.8:1, 92.9% REEs for a ratio of 1.7:1, and 99.2% REEs for a ratio of 3.2:1. At 60 °C, it is not desirable to seek a further increase of the final Na/REEs molar ratio as nearly maximal REE precipitation efficiency is reached. Similar results have been obtained by Liu et al. (2019) who studied the precipitation of REE-Na double sulfates by the addition of Na 2 SO 4 in a solution originating from sulfuricbased leaching of industrially treated spent Ni-MH batteries. [START_REF] Liu | Synergistic recovery of valuable metals from spent NiMH and Liion batteries[END_REF] Their study shows that, after 1 h of precipitation at 70 °C, 74% of REEs precipitate for a 1:1 final Na/REE molar ratio, 88% for a 2:1 molar ratio, and 98% for 4:1 molar ratio. Moreover, our results show that at 60 °C and for a final Na/REEs molar ratio of 3.2:1, selective REE precipitation conditions are obtained since less than 5% of the other metals present in solution have precipitated (Table SI.1

.).

As can be seen on Figure 3a,b, thermodynamic equilibrium is reached for La and Nd after 1 h of precipitation at 60 °C when the final Na/REEs molar ratio is 3:2:1. Indeed, experimental and thermodynamic concentrations of La are both 0.0005 mol/L, and those for Nd are 0.0000 and 0.0001 mol/L, respectively, which corresponds to the precipitation of 99.3% La and 99.7% Nd. On the other hand, for lower final Na/REEs molar ratios of 0.8:1 and 1.7:1, thermodynamic equilibria for La and Nd is not reached after 1 h of precipitation: only 71.7% La and 74.1% Nd have precipitated experimentally for a molar ratio of 0.8:1, whereas simulations predict a precipitation of up to 90.9% La and 87.0% Nd. For a final Na/REEs molar ratio of (1.7:1), only 92.4% La and 93.5% Nd have precipitated experimentally, whereas simulations Pr at 60 °C, for final Na/REEs molar ratios of 0.8:1 (green), 1.7:1 (yellow), and 3.2:1 (red). Vertical lines correspond to the end of the "semibatch" period. The equilibrium at time t is calculated for a system defined by the initial content of the reactor + amount of added Na 2 SO 4 solution at time t.

predict up to 98.1% La and 97.2% Nd. This indicates slower precipitation kinetics when final Na/REEs molar ratios are decreased, and that for these lower ratios 1 h of precipitation is not enough to reach equilibria.

On the other hand, results indicate that more Ce precipitates experimentally than the quantities predicted by the model, at 60 °C and for all final Na/REEs molar ratios (Figure 3c). Similar observations can be drawn for Pr, particularly for a final Na/REEs molar ratio of 0.8:1 (Figure 3d). For instance, after 1 h of precipitation at 60 °C with a final Na/REEs molar ratio of 0.8:1, 79% Ce and 70% Pr have precipitated, whereas simulated thermodynamic equilibria suggest they should not precipitate.

Consequently, the predicted selective precipitation of La and Nd with respect to Ce and Pr at 60 °C for a final Na/REEs molar ratio of 0.8:1 was not achieved in our experiments. Similar results have been reported by Lister et al. ( 2021) who studied the recovery of Nd, Pr, and Dy contained in hard disk drives by leaching in HCl and precipitating REEs as double sulfates using Na 2 SO 4 . [START_REF] Lister | Recovery of Rare Earth Elements from Recycled Hard Disk Drive Mixed Steel and Magnet Scrap[END_REF] The authors also used the OLI Systems Inc. software to simulate their experimental system, and in some cases observed significant recovery of some REEs, which was not predicted by the model.

The above discrepancies observed between experimental and thermodynamic concentrations of Ce and Pr in solution are most likely due to the formation of a solid solution, where Ce 3+ and/or Pr 3+ would be inserted or substituted within the crystal structure of NaLa(SO 4 ) 2 •H 2 O and/or NaNd(SO 4 ) 2 • H 2 O. Theoretically, a solid solution could form given that the crystal structures of single phases of NaREE(SO 4 ) 2 •H 2 O (REE = La, Ce, Nd, or Pr) are all trigonal (space group P 3 2 21 or the enantiomorphic analogue P 3 2 21 ). [START_REF] Buyer | Hydrothermal synthesis, crystal structure and spectroscopic properties of pure and Eu 3+ -doped NaY(SO 4 ) 2 •H 2 O and its anhydrate NaY(SO 4 ) 2[END_REF][START_REF] Wickleder | Inorganic Lanthanide Compounds with Complex Anions[END_REF][START_REF] Blackburn | Sodium lanthanum(III) sulfate monohydrate, NaLa(SO4)2.H2O[END_REF][START_REF] Blackburn | Redetermination of sodium cerium(III) sulfate monohydrate, NaCe(SO4)2.H2O[END_REF][START_REF] Paul | Characterization, and Crystal Structure Analysis of New Mixed Metal Sulfate NaPr(SO4)-2.H2O[END_REF] Moreover, the existence of solid solutions containing at least two REEs has previously been reported in the literature for other types of compounds such as rare earth oxides, [START_REF] Han | Ce1-xLaxOy solid solution prepared from mixed rare earth chloride for soot oxidation[END_REF] nitrates, [START_REF] Lassin | Modeling the Solution Properties and Mineral -Solution Equilibria in Radionuclide-Bearing Aqueous Nitrate Systems: Application to Binary and Ternary Systems Containing U, Th, or Lanthanides at 25°C[END_REF] or phosphates. [START_REF] Carron | Fractional Precipitation of Rare Earths with Phosphoric Acid[END_REF] Additionally, several authors have reported that stable solid solutions are favorable for adjacent lanthanide pairs (i.e., La-Ce, Ce-Pr, Pr-Nd) in nitrate [START_REF] Lassin | Modeling the Solution Properties and Mineral -Solution Equilibria in Radionuclide-Bearing Aqueous Nitrate Systems: Application to Binary and Ternary Systems Containing U, Th, or Lanthanides at 25°C[END_REF] and phosphate 40 systems. In this case, the solid solution stabilizes the solid phase as opposed to a mixture of pure phases; therefore, a smaller amount of the element remains in solution when it has precipitated in the form of a solid solution than as a mixture of pure phases. [START_REF] Lassin | Modeling the Solution Properties and Mineral -Solution Equilibria in Radionuclide-Bearing Aqueous Nitrate Systems: Application to Binary and Ternary Systems Containing U, Th, or Lanthanides at 25°C[END_REF] As mentioned in section 2.2, the OLI system software does not allow taking into account the thermodynamic properties of solid solutions, which leads to overestimation of the quantities of Ce and Pr in solution. However, even if other software can make it possible to describe equilibria between solid solutions and concentrated aqueous solutions (e.g., Phreeqc, FactSage), there is to our knowledge no consistent thermodynamic description available for quaternary or higher-order systems REE-REE′-Na 2 SO 4 -H 2 SO 4 -H 2 O (REE = La, Ce, Nd, or Pr). The main reason is that thermodynamic data regarding the solid mixtures has not yet been reported in the literature, and hence no model can account for the formation of a solid solution in our system of interest.

Solubility data regarding the quaternary or higher-order systems REE-REE′-Na 2 SO 4 -H 2 SO 4 -H 2 O (REE = La, Ce, Nd, or Pr) have not yet been reported in the literature, and hence the model could not account for the formation of a solid solution and overestimated the quantities of Ce and Pr in solution. However, we can reasonably assume that solid From the solid side, it is interesting to represent the evolution of the relative molar contents [mol %] of REEs in the solid fraction with respect to time, or to the amount of Na 2 SO 4 added, at 60 °C. The proportions obtained both with thermodynamic simulations (calculated according to (eq 7)) and with the experimental results (deduced from the difference between the initial amount of REE in the PLS and the amount in solution) are compared in Figure 4. According to the model, the relative molar contents of REEs in the solid fraction should differ significantly depending on the amount of Na 2 SO 4 added (0 mol < n(Na 2 SO 4 ) < 0.32 mol). Experimentally, during approximately the first 10 min or during the addition of around 0.13 mol of Na 2 SO 4 which corresponds to a Na/REEs molar ratio of 1.46:1, the composition of the solid fraction differs greatly from thermodynamic predictions, particularly in that it contains more Ce and less La than simulated. During this period, the experimental solid fraction is slightly enriched in La (58.5-61.8% mol to 63.5-65.5% mol) to the detriment of Ce (27.7-31.7% mol to 25.9-27.0% mol). After about 10 min, experimental curves flatten out, which indicates that at 60 °C the composition of the precipitate does not depend on time or on the amount of Na 2 SO 4 added (Figure 4). This observation at 60 °C suggests either (i) the formation of a mixture of pure phases of REE-Na double sulfates which maintain the same relative precipitation kinetics during the whole precipitation period or (ii) the formation of an identical single phase in the form of a solid solution. The average relative proportions of REEs in the solid fraction after 1 h are 65.6% mol La, 24.2% mol Ce, 7.5% mol Nd, and 2.5% mol Pr. The proportions of Nd and Pr in the solid fraction are nearly a perfect match to thermodynamic predictions (7.4% mol Nd and 2.4% mol Pr), whereas La and Ce contents are respectively lower and higher than thermodynamic predictions (67.3% mol La and 22.9% mol Ce). Consequently, our results demonstrate that, at 60 °C, the amount of Na 2 SO 4 added or the choice of the final Na/ REEs molar ratio has little influence on the composition of the solid fraction; however, increasing the final Na/REEs molar ratio leads to the extraction of a greater amount of REEs after 1 h (Figure 3). Crystals obtained at the end of each experiment were characterized by various techniques. Size distributions were measured by laser diffraction and show very similar distributions with average mass diameters d 43 in the 22.0-27.0 μm range. Size distributions are coherent with particle morphologies observed by SEM where agglomerates of several microns wide can be distinguished, of which elementary particles are composed of rhombohedra characteristic of the trigonal crystal structure (Figure 5). SEM analyses showed similar crystal morphologies for all experiments. As can be seen in Figure 6a, powder XRD diffractograms of all the precipitates strictly overlap, which confirms that the same solid fraction is obtained as deduced previously from the analysis of the liquid fraction. Narrow peaks indicate precipitates are well crystallized, and the fact that there is no peak splitting strongly suggests the formation of one single phase in the form of a solid solution. The peaks have all been attributed to the pure phases NaLa(SO 4 ) 2 •H 2 O (PDF 01-086-0526) and NaCe-(SO 4 ) 2 •H 2 O (PDF 01-082-1199), with slight deviations from the reference spectra (Figure 6a). No other crystalline phases can be identified. Our XRD results are in agreement with other works which have also precipitated REEs by adding either 3-10 M NaOH [START_REF] Meshram | Process optimization and kinetics for leaching of rare earth metals from the spent Ni-metal hydride batteries[END_REF][START_REF] Ahn | Valorization of waste NiMH battery through recovery of critical rare earth metal: A simple recycling process for the circular economy[END_REF][START_REF] Bertuol | Spent NiMH batteries  The role of selective precipitation in the recovery of valuable metals[END_REF][START_REF] Pietrelli | Rare earths recovery from NiMH spent batteries[END_REF] or Na 2 SO 4 17,18 to sulfate-based solutions originating from the leaching of spent Ni-MH batteries and demonstrate thanks to XRD analyses that precipitates are chiefly composed of REE-Na double sulfates having a mixed crystal composition. However, no accurate chemical formula of the crystals has been reported so far.

The chemical compositions [wt %] of the precipitates determined after microwave digestion and ICP-OES analysis (La, Ce, Nd, Pr, Na, S, Ni, Co, Mn, Al, Fe, Zn) as well as TGA (determination of the water content) are detailed in Table 2. For the experiments carried out at 60 °C, very similar compositions are obtained regardless of the final Na/REEs molar ratio. Namely, precipitates contain on average 22.6 wt % La, 7.9 wt % Ce, 2.6 wt % Nd, and 0.6 wt % Pr. This corresponds to relative REE molar contents of 67.3% mol La, 23.3% mol Ce, 7.6% mol Nd, and 1.8% mol Pr, which is coherent with the relative contents deduced from the analysis of the liquid fraction (Figure 4). No traces of Co, Mn, Fe, and Zn were detected (below ICP-OES detection level); however, precipitates contain substantial amounts of Ni and Al, on average 5.7 wt % Ni and 1.8 wt % Al. Consequently, metalbased purities of 81.9 wt % on average are calculated according to eq 9 with wt % i being the relative weight contents [wt %] of metallic elements in the precipitates. The relatively significant impurity uptake observed in our results could be due to the coprecipitation of Ni and Al with REEs. Indeed, Al(OH) 3 and Ni(OH) 2 are known to have pH shifts around 4 and 6.5, respectively. [START_REF] Monhemius | Precipitation diagrams for metal hydroxides, sulphides, arsenates and phosphates[END_REF] 2b. As previously mentioned, the simultaneous drop of pH when REE concentrations in solution start to decrease indicates that pH can serve as an indicator of the induction period. It is interesting to note that the induction period decreases with increasing temperature, namely, 10 min at 25 °C, 8 min at 40 °C, and 3 min at 60 °C. This observation is in agreement with the classical theory of 3D nucleation which stipulates that the induction period is inversely proportional to the logarithm of the supersaturation in solution. 42 Hence, with an increase of the temperature, the supersaturation in solution increases before the beginning of nucleation since the solubility of the REE-Na double sulfates decreases with increasing temperature. [START_REF] Das | Rare earth sulfates in aqueous systems: Thermodynamic modeling of binary and multicomponent systems over wide concentration and temperature ranges[END_REF] Experimental REE concentrations in solution with respect to time at different temperatures are compared with calculated equilibrium concentrations in Figure 7. Because the solubility of REE-Na double sulfates is regressive with temperature, increasing the temperature from 25 to 60 °C greatly increases precipitation efficiency of all REEs and yields faster precipitation kinetics. For example, after 1 h and for a fixed final Na/REEs molar ratio of 3.2:1, 77.6% of the REEs has precipitated at 25 °C, 94.5% at 40 °C, and 99.2% at 60 °C. Moreover, thermodynamic equilibria after 1 h of precipitation is reached only when working at an elevated temperature. After 1 h of precipitation at 25 °C, 74.4% La, 87.6% Ce, 77.5% Nd, and 69.3% Pr have precipitated experimentally, whereas the model predicts precipitation efficiencies of up to 94.4% La, 95.7% Ce, 97.1% Nd, and 88.3% Pr. At 40 °C, 92.9% La, 100.0% Ce, 94.4% Nd, and 84.3% Pr have precipitated experimentally after 1 h, whereas the model predicts precipitation efficiencies of up to 97.9% La, 92.7% Ce, 98.3% Nd, and 91.1% Pr.

Evolutions of the relative molar contents [mol %] of REEs in the solid fraction as deduced from the analysis of the liquid fraction from both the experiments and thermodynamic calculations are represented in Figure 8 with respect to the amount of Na 2 SO 4 added and for different temperatures. When a total of 0.32 mol of Na 2 SO 4 has been added, which corresponds to the final Na/REEs molar ratio of 3.2:1, the model predicts that the same solid fraction should form regardless of the temperature. This is verified by the experiments as the molar ratios are within close ranges for all temperatures: 63.4-66.3 mol % La, 24.2-27.0 mol % Ce, 7.2-7.3 mol % Nd, and 2.2-2.3 mol % Pr. However, although experimentally the same solid fraction appears to precipitate regardless of the amount of Na 2 SO 4 added at 60 °C, this is not the case at 40 and 25 °C. Indeed, the experimental composition of the solid fraction with respect to the amount of Na 2 SO 4 added evolves and more significantly so as the temperature decreases. This observation could indicate that, at 25 and 40 °C, (i) REEs precipitate in the form of a mixture of pure phases of REE-Na double phases, or (ii) the nature of the solid solution depends on both the temperature and the amount of Na 2 SO 4 added. Further research is required on this aspect to determine which hypothesis prevails.

The filtered crystals obtained at different temperatures after 1 h of precipitation show very similar size distributions (22.8 μm < d 43 < 26.1 μm) as indicated by laser diffraction and have precipitated as agglomerates of similar morphology as evidenced by SEM measurements. As represented in Figure 6b, peaks of the powder XRD diffractograms are thin and strictly overlap, suggesting the formation of a solid solution of constant composition for all temperatures after 1 h of precipitation. This observation is confirmed by the fact that crystals have nearly identical chemical compositions [wt %] and metal-based purities [wt %] (Table 2). They are composed on average of 22.1 wt % La, 7.9 wt % Ce, 2.6 wt % Nd, and 0.6 wt % Pr with metal-based purities of about 81.5 wt %.

CONCLUSION

A straightforward pilot-scale process was developed for the selective precipitation of REEs contained within a sulfate-based leachate originating from the industrial treatment of spent Ni-MH batteries. [START_REF] Zielinski | Leaching mechanisms of industrial powders of spent nickel metal hydride batteries in a pilot-scale reactor[END_REF] The main objectives of this study were to (i) better understand the influence of operating parameters on precipitation mechanisms (precipitation kinetics, comparison with thermodynamic equilibria) and (ii) verify the truly selective nature of REE precipitation with respect to other metals when a concentrated Na 2 SO 4 solution is added to a leachate particularly rich in Ni ([Ni] ≈ 52 g/L). One of the originalities of this work is that we performed equilibria calculations in the complex system MSO 4 -REE 2 (SO 4 ) 3 -Na 2 SO 4 -H 2 SO 4 -H 2 O (M = Ni, Fe, Co, Mn, Zn; REE = La, Ce, Nd, or Pr) with high initial concentrations of metal elements thanks to the OLI Systems Inc. software. This model benefits from the recent implementation of thermodynamic data related to REE sulfate compounds properties. [START_REF] Das | Rare earth sulfates in aqueous systems: Thermodynamic modeling of binary and multicomponent systems over wide concentration and temperature ranges[END_REF] Ce, Nd, or Pr) is expected. Results also demonstrate that increasing both temperature and final Na/REEs molar ratios should enhance REE precipitation efficiency because the solubility of the compounds decreases with increasing temperature and amount of Na 2 SO 4 added. Furthermore, at a fixed temperature of 60 °C, the composition of the precipitated solid fraction is predicted to depend on the amount of added Na 2 SO 4 . On the contrary, thermodynamic predictions indicate that, for a fixed final Na/REEs molar ratio of 3.2:1, the composition of the precipitated solid fraction should not vary significantly between 25 and 60 °C.

Experimentally, the drop of pH observed when REE concentrations start to decrease showed for the first time that pH monitoring can serve as an indicator of REE precipitation initiation and allowed the determination of induction periods. Experiments carried out at 25 °C < T < 60 °C for a fixed final Na/REEs molar ratio of 3.2:1 were coherent with thermodynamic predictions: indeed, crystals obtained after 1 h of precipitation showed very similar chemical compositions regardless of the temperature. Experiments carried out at 60 °C and for 0.8:1 < final Na/REEs molar ratios < 3.2:1 were also in reasonable agreement with equilibria calculations; however, in some cases experimental results could not be reconciled with solubility calculations. Namely, results showed that at 60 °C the relative molar contents [mol %] of REEs in the solid fraction remained constant regardless of the amount of Na 2 SO 4 added; in other words, increasing the amount of Na 2 SO 4 added only enhances the quantity of REE extracted but does not modify the nature of the solid fraction as predicted by thermodynamics. This observation strongly suggests the formation of a single solid solution throughout the whole precipitation period at 60 °C in the form of La w Ce x Nd y Pr z Na(SO 4 ) 2 •H 2 O (w + x + y + z = 1), which is backed by the absence of peak splitting in the XRD diffractograms of the crystals obtained after 1 h. Because of the current lack of solubility data regarding the systems REE-REE′-Na 2 SO 4 -H 2 SO 4 -H 2 O (REE = La, Ce, Nd, or Pr), the model used it this study could not account for the formation of a solid solution and therefore in some cases overestimated the quantities of REEs in solution. Further work should include a more detailed structural characterization of the crystals to clarify the nature of the solid solution, as well as solubility studies to determine under which conditions REEs precipitate in the form of a mixture of pure salts or rather as a solid solution. Eventually, mixed double sulfate compounds could be added in the current thermodynamic database in order to improve the quality of the predictions.

Highly selective conditions were obtained after 1 h at 60 °C and for a final Na/REEs molar ratio of 3.2:1, whereby more than 99.2% of REEs precipitate, while more than 95% of the other metals (Ni, Co, Mn, Al, Fe, Zn) remain in solution. These precipitation conditions are totally transferable at the industrial scale leading to a more sustainable process with mild temperature (25 °C < T < 60 °C) and short batch time. Under such conditions, crystals contain 22.5 wt % La, 7.7 wt % Ce, 2.6 wt % Nd, and 0.6 wt % Pr with a metal-based purity of 81.0 wt %. The REE-free solution (70 ppm La, 0 ppm of Ce, 4 ppm of Nd, and 52 ppm Pr) is thus ready for further downstream processing to recover additional valuable metals such as Ni and Co.

■ ASSOCIATED CONTENT

* sı Supporting Information

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.cgd.1c00834.

Proportion of metallic elements remaining in solution after 1 h of precipitation (PDF)

■ AUTHOR INFORMATION

Corresponding Author

Béatrice Biscans -Laboratoire de Génie Chimique, Université de Toulouse, CNRS, INPT, UPS, Toulouse 31432, France; orcid.org/0000-0002-2663-4357; Email: beatrice.biscans@toulouse-inp.fr

  molar ratio. It is worth noting that the model only considers the possibility of forming a mixture of pure phases (i.e., REE-Na(SO 4 ) 2 • H 2 O with REE = La, Ce, Nd, or Pr) but does not consider the possibility of forming solid solutions (i.e., La w Ce x Nd y Pr z Na(SO 4 ) 2 • H 2 O with w + x + y + z = 1).

Figure 1 .

 1 Figure 1. Proportion [%] of La, Nd, Ce, and Pr which should precipitate according to equilibria calculations at (a) 25 °C, (c) 40 °C and (e) 60 °C, and the proportion [% mol] of each REE in the solid fraction at (b) 25 °C, (d) 40 °C and (f) 60 °C (simulations performed with OLI Systems Inc.).

Figure 2 .

 2 Figure 2. Evolution of pH, the proportion of La remaining in solution [%], and moles of Na 2 SO 4 added with respect to time for the experiments carried out (a, c) at 60 °C and with final Na/REEs molar ratios of 0.8:1 (green), 1.7:1 (yellow), and 3.2:1 (red), and (b, d) at 25 °C (green), 40 °C (yellow), and 60 °C (red) for a fixed final Na/ REEs molar ratio of 3:2:1.

Figure 3 .

 3 Figure 3. Evolution of the experimental (dotted lines) and simulated (full lines) concentrations [mol/L] of (a) La, (b) Nd, (c) Ce, and (d)Pr at 60 °C, for final Na/REEs molar ratios of 0.8:1 (green), 1.7:1 (yellow), and 3.2:1 (red). Vertical lines correspond to the end of the "semibatch" period. The equilibrium at time t is calculated for a system defined by the initial content of the reactor + amount of added Na 2 SO 4 solution at time t.

  solutions of REE x REE 1-x ′ (SO 4 ) 2 •H 2 O are likely to form, particularly, solid solutions of the adjacent pairs La x Ce 1-x (SO 4 ) 2 •H 2 O and NdxPr 1-x (SO 4 ) 2 •H 2 O.

Figure 4 .

 4 Figure 4. Comparison of the evolution of the molar ratios [% mol] of REEs in the solid fraction as obtained by thermodynamic simulations (continuous lines) and experiments (dotted lines) at 60 °C and for final Na/REEs molar ratios of 0.8:1, 1.7:1, and 3.2:1, with respect to (a) time and (b) the number of added moles of Na 2 SO 4 . The equilibrium at time t is calculated for a system defined by the initial content of the reactor + amount of added Na 2 SO 4 solution at time t.

  Bertuol et al. (2009) obtained somewhat similar results after precipitating REE-Na double sulfates by adding 5 M NaOH to sulfate-based spent Ni-MH battery leachates, with a 91.93 wt % metal-based purity, 5.93 wt % Ni, and 1.16 wt % Co.

Figure 5 .

 5 Figure 5. SEM micrograph of the crystals obtained after 1 h of precipitation at 60 °C and for a final Na/REEs molar ratio of 3.2:1.

Figure 6 .

 6 Figure 6. Powder XRD diffractograms of crystal obtained after 1 h of precipitation (a) at 60 °C and for final Na/REEs molar ratios of 0.8:1 (green), 1.7:1 (yellow), and 3.2:1 (red) and (b) at 25 °C (green), 40 °C (yellow), and 60 °C (red) for a final Na/REEs molar ratio of 3.2:1.

Figure 7 .

 7 Figure 7. Evolution of the experimental (dotted lines) and simulated (full lines) concentrations [mol/L] of (a) La, (b) Nd, (c) Ce, and (d) Pr for a final Na/REEs molar ratio of 3.2:1 at 25 °C (green), 40 °C (yellow), and 60 °C (red). The vertical line corresponds to the end of the "semibatch" period. The equilibrium at time t is calculated for a system defined by the initial content of the reactor + amount of added Na 2 SO 4 solution at time t.

Figure 8 .

 8 Figure 8. Comparison of the evolution of the molar ratios [mol %] of REEs in the solid fraction as obtained by thermodynamic simulations (continuous lines) and experiments (dotted lines) with respect to the number of added moles of Na 2 SO 4 at (a) 25 °C, (b) 40 °C, and (c) 60 °C.

  1, results indicate that the proportion of each REE which should precipitate increases with increasing Na/REEs molar ratios (Figure1a,c,e). It is therefore preferable to work at elevated Na/ REEs molar ratios in order to precipitate the majority of REEs: for instance, at 60 °C and for a Na/REEs molar ratio of 3.2:1, more than 95% of REEs should precipitate. It is interesting to note that the effect of temperature becomes negligible at sufficiently high Na/REEs molar ratios. Indeed, for a Na/REEs molar ratio of 3.2:1, the proportion of each REE in the solid fraction is relatively equivalent at 25, 40, and 60 °C; namely, the solid fraction consists of 67.3 ± 1.37 mol % La, 7.4 ± 0.09 % mol Nd, 22.9 ± 1.39 % mol Ce, and 2.4 ± 0.09 mol % Pr (Figure1b,d,f). The relative proportions of REEs in the solid fraction are almost equivalent to the relative proportions of REEs in the initial PLS solution: 66.41% mol La, 7.35% mol Nd, 23.56 % mol Ce, and 2.68 % mol Pr.

  Locally high pH gradients in the reactor due to insufficient hydrodynamics could have led to the precipitation of the hydroxide phases. The fact that Ni-or Al-bearing phases were not detected by XRD could suggest that compounds are amorphous and thus not detectable by powder XRD; however, further characterization is required to confirm this hypothesis. If that is the case, crystal purities could be improved by washing the precipitates with hot water or a hot Na 2 SO 4 -H 2 O solution rather than room temperature water because the solubility of Al(OH) 3 and Ni(OH) 2 increases with increasing temperature as opposed to that of REE-Na double sulfates.3.2.2. Influence of Temperature. The influence of temperature (25 °C < T < 60 °C) on REE precipitation was studied for a fixed final Na/REE molar ratio of (3.2:1). The pH was monitored throughout the experiments, and results are detailed in Figure

Table 2 .

 2 Chemical Compositions [wt %] and Metal-Based Purities [wt %] of All the Obtained Precipitates

	chemical composition of the precipitates [wt %]

Simulations were used to guide an experimental parametric study to assess the influence of two operating parameters: temperature (25 °C < T < 60 °C) and final Na/REEs molar ratio (0.8:1 < Na/REEs < 3.2:1).

Modeling results indicate that the grouped selective precipitation of REEs is achievable because no other metal element than the REEs should precipitate and that a mixture of pure REE-Na double sulfates REENa(SO 4 ) 2 •H 2 O (REE = La,

Authors

Margot Zielinski