Zeinab Chour

Baptiste Laubie

Jean Louis Morel

Ye-Tao Tang

Marie-Odile Simonnot
email: marie-odile.simonnot@univ-lorraine.fr

Laurence Muhr

Basis for a new process for producing REE oxides from Dicranopteris linearis

Keywords: Agromining, hyperaccumulator plant, hydrometallurgy, leaching, EDTA, REE speciation

Dicranopteris linearis (also known as Dicranopteris dichotoma) is a fern that grows naturally on the tailings of former rare earth element (REE) mines in southern China. It accumulates these elements in its aerial parts at concentrations that classify this plant as hyperaccumulator. The main objective of this research is to design a process to recover REEs directly from the dry biomass, without burning it. This process involves three steps: (i) extraction of REEs from the dry plant by leaching with a solution containing acid and/or complexing agents, (ii) precipitation of REEs with oxalate and (iii) calcination to prepare REE oxide. A methodology based on speciation calculation made it possible to determine operating conditions for precipitation by taking into account the influence of the species present according to the extraction method. Simulations were carried out using Chess software, allowing the calculation of the composition of a multicomponent solution at thermodynamic equilibrium. These operating conditions were then validated experimentally. REE extraction from the dry plant was significantly improved under acid conditions (with H 2 SO 4 ) or with a strong complexing agent such as ethylenediaminetetraacetic acid (H 4 EDTA). After optimization of the precipitation conditions, REE precipitation yields were above 90%. After calcination, the final solid (REE oxide) contained ca 69% of the REEs present in the initial biomass. The use of sulphuric acid as an extracting agent resulted in the recovery of a solid composed of 52 wt % of REEs (based on metal content). Thus, this study proposes a new recovery route for these strategic elements with a REE concentration factor from soil to final solid of 2500.

Introduction

Rare earth elements (REEs), including the 15 lanthanides as well as yttrium and scandium, share similar chemical properties. In recent years, they have been widely used in functional materials (especially in green and electronic technologies), as catalysts or as diagnostic reagents for magnetic resonance imaging, etc. [1]. The disparity of their resource around the world requires increasing extraction yields from primary ores, but also increasing their recovery from secondary materials (e.g. phosphogypsum from phosphoric acid production or red mud from bauxite) [START_REF] Binnemans | Recycling of rare earths: a critical review[END_REF][START_REF] Jha | Review on hydrometallurgical recovery of rare earth metals[END_REF]. Among these secondary resources, low grade soils and tailings from old mines could be suitable for REE recovery. However, new concentration processes have to be developed to be economically and environmentally competitive. Agromining represents a promising means of achieving this goal.

Agromining is an emerging phytotechnology, which uses natural and local hyperaccumulating plants to "harvest" metals [START_REF] Van Der Ent | Agromining: farming for metals[END_REF]. The plants, which accumulate metals in their aerial parts at very high levels, are already being used to produce nickel from ultramafic soils, which are not concentrated enough for conventional mining industry [START_REF] Bani | Element Case Studies: Nickel[END_REF][START_REF] Simonnot | Processing of bio-ore to products[END_REF]. The extraction yield is over 100 kg of nickel per hectare in Mediterranean climate (with Alyssum murale [START_REF] Bani | The effect of plant density in nickel-phytomining field experiments with Alyssum murale in Albania[END_REF] and is very promising in tropical areas (with Phyllanthus rufuschaneyi) [START_REF] Nti Nkrumah | The first tropical 'metal farm': Some perspectives from field and pot experiments[END_REF]. The metal is then generally recovered by hydrometallurgical processes from biomass ashes after burning [START_REF] Simonnot | Processing of bio-ore to products[END_REF]. The combustion stage removes organic matter and concentrates the metal. It also generates energy, which can be wittingly used. The direct extraction of the metal from the plants, without burning, has also been reported [START_REF] Vaughan | Characterisation and hydrometallurgical processing of nickel from tropical agromined bio-ore[END_REF][START_REF] Guilpain | Speciation of nickel extracted from hyperaccumulator plants by water leaching[END_REF]. The main advantages of this route are to limit the issue of gas treatment after metal contamination, and to use biomass after metal extraction for other applications (e.g. composting, anaerobic digestion, etc.). However, part of the soluble organic matter is co-extracted, which implies the development of specific processes to recover the metal [START_REF] Guilpain | Speciation of nickel extracted from hyperaccumulator plants by water leaching[END_REF].

The general objective of this work is to develop the agromining of REEs. Several hyperaccumulating plants have been identified worldwide [START_REF] Liu | Element case studies: rare earth elements[END_REF], the concentration threshold being set at 0.1wt% of the dry biomass. One of them, Dicranopteris linearis (also known as Dicranopteris dichotoma) is a fern growing in southeastern China (subtropical climate). It is found naturally on the tailings of former mines (ionic adsorption clay deposits), at a plant density that makes large-scale cultivation possible.

While the interactions soil nutrients/D. linearis and metal translocation in the fern are fairly well documented [START_REF] Liang | A review of fractionations of rare earth elements in plants[END_REF][START_REF] Shan | Accumulation and uptake of light rare earth elements in a hyperaccumulator Dicranopteris linearis[END_REF][START_REF] Liu | Co-deposition of silicon with rare earth elements (REEs) and aluminium in the fern Dicranopteris linearis from China[END_REF], only one process for the extraction and purification of REEs has been reported. Recently, it has been demonstrated that the recovery of REE mixtures is possible by direct extraction, without burning the plant [START_REF] Chour | Recovery of Rare Earth Elements from Dicranopteris linearis by an enhanced ion exchange leaching process[END_REF]. The recovery step consists of nitric acid extraction followed by adsorption of the elements on an ion exchange resin. Selective elution with nitric acid solutions of several concentrations allows recovery of aqueous REEs with a yield of ca 75% and a purity close to 80%. The main impurity is aluminium (Al), which the fern contains in large quantities; actually, this fern is also an hyperaccumulator of Al. Other strategies should therefore be applied to avoid this contamination, and among them, the precipitation of REE-oxalate (C 2 O 4 2-) seems to be relevant. These intermediates are often studied to produce concentrated solids (REE-oxides) after calcination [START_REF] Qi | Hydrometallurgy of Rare Earths, Extraction and Separation[END_REF]. One of the main advantages of this strategy is the high efficiency of selective REE precipitation. In addition, solids after combustion are relatively pure, due to the transformation of oxalate with few residues (a molecule composed only of carbon and oxygen).

The aim of this research is therefore to synthetize REE-oxides after direct extraction of REE from the hyperaccumulator D. linearis and precipitation as oxalate. It consists of three steps: (i) a leaching step using extracting agents (organic or inorganic) followed by (ii) a selective precipitation step with oxalate, and (iii) calcination of the intermediate (Fig. 1). Considering that REEs are complexed by carboxylic acids in the plant tissues, the strategy is either to break these complexes using an acid solution or to shift the complexing equilibrium using a more powerful complexing agent than the one present in the plant. Sulphuric and citric acids have been selected for their acidic properties, and H 4 EDTA and citrate for their complexing properties. H 4 EDTA is a well-known complexing agent for REEs [START_REF] Moeller | Observations on the rare earths-LXXIII the heat and entropy of formation of the 1: 1 chelates of N-hydroxyethylethylenediaminetriacetic acid with the tripositive cations[END_REF][START_REF] Wood | The aqueous geochemistry of the rare-earth elements: Critical stability constants for complexes with simple carboxylic acids at 25° C and 1 bar and their application to nuclear waste management[END_REF], as is citrate, which naturally transports REEs in plants through the xylem [START_REF] Shan | Accumulation and uptake of light rare earth elements in a hyperaccumulator Dicranopteris linearis[END_REF]. During precipitation with oxalate, competitive reactions must be taken into account. They are due to the presence of extracting agents introduced in the previous step, and to soluble organic matter (SOM) of the plant, which may interfere. No data are available on the precipitation of REEs by oxalic acid C 2 H 2 O 4 in the presence of high concentrations of sulphate, H 4 EDTA and citrate. The proposed methodology relies on post-extraction stage speciation studies to investigate the feasibility of downstream unit operations. Hence to determine the optimal precipitation conditions (pH and molar ratio), simulations of REE speciation were first performed. In order to validate the model, an experiment was prepared with a synthetic solution of lanthanum (La) (chosen as representative REEs). The simulations were performed under the assumption that SOM plays no role during precipitation. Tests with a real extract allow us to evaluate its role during REEs recovery. The whole process is finally evaluated according to the composition of the REE oxide obtained after calcination.

Materials and methods

Plant material

Samples of Dicranopteris linearis were collected in a former REE mine in Jiangxi Province (China), and dried for 24 h, at 70 °C. The concentration of REEs in the soil was in the range 300 to 700 mg per kg of dry soil [START_REF] Yuan | Accumulation and fractionation of rare earth elements (REEs) in the naturally grown Phytolacca americana L. in southern China[END_REF]. The entire biomass (leaves and stem) was crushed with a blade grinder (SEB type 8100) before use. The median particle size, determined by laser diffraction (Malvern Mastersizer hydro 2000SM), was 369 µm.

Chemicals

Nitric acid (67-69%, Sigma Aldrich) was used for digestion prior to elemental analysis. Dehydrated disodium salt of ethylenediaminetetraacetic acid (99%), ACS reagent citric acid monohydrate (≥ 99.0%) and L(+)-glutamic acid monosodium salt monohydrate (99%) (supplied by Fisher Chemicals) and sulfuric acid (95-98%, Sigma Aldrich) were tested in the leaching step. Oxalic acid dihydrate ACS (≥ 99.5%, Sigma Aldrich) was used for the precipitation step, and synthetic solutions were prepared with lanthanum nitrate hexahydrate (> 98%, ACROS Organics). Deionized (DI) water (Elga -Purelab Option) was used for all experiments.

Elemental and structural analysis

Prior to elemental analysis, the solid and liquid samples were digested in a microwave oven (UltraWave, Milestone) for 40 min with a set-point of 200 °C. Biomass samples or precipitates (ca 0.1 g) were randomly collected and digested by adding 5 mL of concentrated nitric acid (5 repetitions each time). For liquids, 2 mL of nitric acid was added to 2 mL of sample. After digestion, the leachate was introduced into a 50 mL flask with deionized water, then filtered by syringes equipped with filters (Phenomenex, pore size: 0.45 µm) and analysed by ICP-AES (Thermo ICAP6000). Calibration was performed with the custom standard PlasmaCAL (SCP Science) in a 5% vol. HNO 3 matrix. Two ranges of standard solutions were used, one for the REEs and one for the other elements. The major elements were analysed by radial measurement while the minor elements were analysed by axial measurement. Three replicates were made for each sample and a quality test was performed every 10 measurements with a control solution (PlasmaCAL, SCP Science).

X-ray diffraction analyses (XRD) were performed with a D8-Discover diffractometer (Brucker) (cobalt probe). The crystals were identified with PDF-02 databank of ICDD (International Centre for Diffraction Data). EDX (Energy dispersive X-ray spectrometry) analyses were performed with a JSM-6490LV microscope (Jeol).

REE extraction and recovery from biomass

To study the effect of each agent on the efficiency of REE extraction, the fern biomass was leached with six aqueous solutions (solid/liquid ratios S/L = 3 g/100 mL, 2 h, magnetic stirring): deionized water, H 2 SO 4 (0.25 M), citric acid (1 M) (pH = 1.6 and 4.0, adjusted with NaOH), citrate (1M) (pH = 8.0, adjusted with NaOH) and EDTA (0.05 M) (in the following text, EDTA written in italic refer to the generic ethylenediaminetetraacetic acid, whatever its chemical form). The latter complexing agent was added in the disodic form Na 2 H 2 EDTA (to obtain an extraction at pH 4.5 (predominance area of H 2 EDTA 2-). This agent can create a complex with REE, without generating insoluble REE hydroxides (at pH higher than 7-8). Solid particles were separated from solutions using 0.45 μm porosity cellulose filter papers (Whatman). A synthetic solution (ca 300 mL) was prepared, containing lanthanum (La(NO 3 ) 3 , 2.3 10 -3 mol) and Na 2 H 2 EDTA (4 10 -3 mol). The pH adjustment (between 2 and 8.5) was carried out with 1 M HNO 3 solution and oxalic acid was added in a molar ratio of 1 with Na 2 H 2 EDTA (4 10 -3 mol). The final pH was measured. After one hour of mixing, precipitates were filtered and dried. The liquid phases were analysed by ICP.

After simulation and determination of optimal precipitation conditions, pH was adjusted to 2.6 (with 1 M NaOH solution) and to 2.3 (with 1 M HNO 3 solution) for H 2 SO 4 and Na 2 H 2 EDTA extracts respectively. In the latter case, this caused the formation of a solid S1, which was separated and analysed (ICP and XRD). Oxalic acid was then added (molar ratio of 0.16 and 1.56, respectively) and the solutions were stirred during 1 h at 20 °C.

Precipitates (S2 and S3 respectively) were filtered, washed with deionized water and dried at 100 °C. They were calcined at 700 °C for 2 h to obtain S4 and S5.

Theory

The addition of oxalic acid to a solution containing REEs and EDTA will affect the speciation . The distribution of the chemical forms of the three species as a function of pH is exhibited in Fig. 2. In this environment, many competitive reactions can take place, including those represented by Equations 1-3. ) forms should be preferred to obtain the insoluble complex REE 2 Ox 3 . However, in the presence of EDTA, the REEs are theoretically complexed at pH higher than 1.9 (Fig. 2). Two other aspects must also be taken into account:

(i) the very low solubility of the precipitate REE 2 Ox 3 (Ks between 5 10 -30 and 4.5 10 - 32 [START_REF] Chung | Solubility of Rare Earth Oxalate in Oxalic and Nitric Acid Media[END_REF]). This implies that the presence of a very small quantity of deprotonated oxalic acid can lead to the formation of the precipitate. The latter inevitably leads to the displacement of reaction 3 in the forward direction;

(ii) only stability constants between EDTA 4-and HEDTA 3-are available. However, due to the EDTA excess introduced during extractions, REEs are complexed in totality with these two forms below pH 2.

Only modelling that takes all these data into account can enable optimum precipitation conditions to be found. Due to the large number of species involved, the Chess software was used [20], after having completed its database with the stability constants given in Table 1. Conventionally, the stability constant of the formation reaction of a species (Eq. 4) is given by Eq. 5. The species present on the left side of the equilibrium, called "basis species", are usually written in their deprotonated form.

Eq. 4

Eq. 5

Results and discussion

Elemental composition of Dicranopteris linearis

The results of the D. linearis elemental analysis are presented in Table 2. Like all plants, the fern is rich in K, Ca, Mg. However, it contains high levels of Si and Al, which is a common characteristic of this plant [START_REF] Nguyen | Dicranopteris linearis, derived phytoliths in soil: Morphotypes, solubility and content in relation to soil properties[END_REF]. The threshold for Al hyperaccumulation is set at 0.1%, indicating that this plant can be considered as Al -hyperaccumulator. Concerning REEs, La, Nd and Ce were the main elements identified. Pr, Sm, Y and Gd were also present but at lower concentrations. The analysis shows that D. linearis can accumulate more than 3 g of REEs per kg of dry biomass (0.30%). This means that this plant batch can be considered as a REE hyperaccumulator (threshold fixed at 1 g kg -1 ).

In the literature, concentration in plant tissues are generally measured between 0.023 and 0.26% [START_REF] Chour | Recovery of Rare Earth Elements from Dicranopteris linearis by an enhanced ion exchange leaching process[END_REF]. The plant studied is therefore very rich. It mainly accumulates light REEs.

Extraction of REEs from D. linearis

The extraction yield of REEs is defined by Eq. 6:

Eq. 6 Experiments were carried out under optimal conditions because the biomass had been finely ground (therefore the diffusion limitations were low), and the solid/liquid ratio was low. The stability constants of REEs with the EDTA ligand are relatively high, with a log K between 15 and 20 [START_REF] Moeller | Observations on the rare earths-LXXIII the heat and entropy of formation of the 1: 1 chelates of N-hydroxyethylethylenediaminetriacetic acid with the tripositive cations[END_REF][START_REF] Wood | The aqueous geochemistry of the rare-earth elements: Critical stability constants for complexes with simple carboxylic acids at 25° C and 1 bar and their application to nuclear waste management[END_REF]. They are certainly higher than those of the various REE related compounds in biomass. The formation of REE-EDTA complexes can thus make it possible to displace the reactions that are at the origin of the interactions between REE and organic matter. Insofar as these interactions help to maintain the REEs within the biomass, this leads to better extraction. In the case of citrates, the stability constants of the REE-citrate complexes are lower. The fact that the equilibria involved do not allow sufficient displacement of the reactions at the origin of these interactions could explain a low extraction. For the other elements, yields in water were low (< 20%), except for K which had a very high extraction yield (> 80%). This was also the case for all the other solutions used. K is known as a very extractable element from hyperaccumulators [START_REF] Guilpain | Speciation of nickel extracted from hyperaccumulator plants by water leaching[END_REF].

The extraction of divalent and trivalent elements was improved by the addition of an acid or a complexing molecule. However, lowering the pH is to be preferred to increase their extraction yields.

In conclusion, even if REEs are directly extractable from biomass with water, higher yields (> 80%) are obtained either with strong complexing agents (EDTA) or with strong acid. These two options were selected for the following.

Precipitation of REEs in EDTA medium with oxalate

REE speciation in presence of EDTA and oxalic acid

To precipitate REEs, oxalic acid was added to the EDTA extract. The co-existence of EDTA and oxalic acid leads to the formation of a large number of chemical species. As the former is a tetraacid and the latter a diacid, the concentrations of the different chemical forms depend on the pH. These different forms react with the REEs to form soluble species such as REEEDTA -or insoluble species such as REE 2 Ox 3 , this last compound being the desired one. The concentrations of EDTA 4-and Ox 2-increase with increasing pH, but the precipitation of insoluble REE hydroxides increases at the same time. Therefore, the search for a pH high enough to obtain the Ox 2-form that allows the precipitation of REEs (Eq. 1) under the oxalate form is a compromise to avoid high solubilization of REEs due to the complex formed with EDTA 4-(Eq. 2).

Lanthanum was chosen as a representative REE, and the composition of a solution containing La, oxalate and EDTA was simulated as a function of pH, using Chess software. Results are represented by lines in Fig. 4. The concentration term on the yaxis does not correspond to the conventional definition of concentration. In the Chess nomenclature, for a solid, it is the number of moles of precipitates per litre of solution.

Only the main species are shown in this figure. Under very acid conditions (pH < 1), La is a trivalent cation (La 3+ ). As the pH increases, it reacts with oxalate to form insoluble La oxalate (La 2 (C 2 O 4 ) 3 ), then it is complexed with EDTA (to give soluble LaEDTA -).

Finally, at very high pH (> 12), La hydroxide precipitates. At pH between 1 and 2, La is totally precipitated as oxalate. Above this pH range, LaEDTA -appears to become predominant at pH 4.5, and the only species at pH > 5.3. Precipitate masses and concentrations of La were measured after reaction (confidence intervals were estimated at 10%). The experimental results are plotted in Fig. 4. Overall, a very good agreement was found between the experimental results and the simulations.

Based on these results, it can be concluded that at a pH between 1.2 and 2.

Concentration

(mol/L) pH acid is multiplied by 5, this pH increases to 6. In addition, for a given concentration of La, increasing the addition of oxalic acid limits the formation of La 3+ and increases the pH range (especially at low pH) at which lanthanum can be precipitated.

Precipitation of REEs in biomass extract a) pH adjustment

Firstly, the extract at pH 4.1 was acidified in order to reach the previously defined pH (ca 2.3), resulting in the formation of a first precipitate S 1 (6.5 g L -1 ) from the protonation of EDTA in the H 4 EDTA form, which has a low aqueous solubility. This precipitation was confirmed by XRD analysis (Fig. 5). All identified peaks corresponded to EDTA. No other molecules have been identified. During extraction, the molar ratio EDTA/REEs was approximately 21 so that competitive reactions between REEs and the other elements present in solution did not influence their extraction. This molar ratio could be optimized, however, even in the present conditions, half of the EDTA (45%) can be recovered and reused after filtration. All the peaks correspond to EDTA (except the two marked with an arrow)

Analysis of this solid showed that less than 2% of the REEs were lost at this stage. This percentage was calculated from the amount of initial biomass. Other elements are also identified: 6.5% and 1.5% for P and Ca respectively. For the other elements, only 0.4 to 0.6% of the initial biomass content is found in S 1 . This step could be a way to recycle.

b) REE precipitation using oxalic acid

The addition of oxalic acid caused a decrease in pH. To ensure that the pH is far from the lower limit of precipitation, a large excess was introduced (molar ratio oxalate/REE = 70), giving a final pH of 1.3. The large amount of reagent was also chosen to reduce competition from other cations and SOM (organic carbon concentration: 7.0 ± 0.2 g L -1 ).

The formation of the oxalate precipitate (S 2 ) was instantaneous. After filtration, analysis of the extract showed that REE precipitation was almost complete. Concentrations of Ce, Gd, Pr and Sm were below the detection limit (10 μg L -1 ) and less than 1% remained in solution for the other three main REEs (La, Nd, Y). Thus, this process can recover 65.9 to 72.2% of the REEs present in the initial biomass. The organic matter had no influence on the operations implemented.

The recovered solid (2.56 g L -1 of extract, 42.6 mg g -1 of raw biomass) was washed with deionized water, which removed most of the sodium, coming from the addition of EDTA during extraction. Finally, the precipitate contained 4.62% (27.3 mg) of REEs, which was 13 times more concentrated than the starting plant (Table 3). Calcium was the major impurity in the solid. . Of course, the higher the oxalate/REEs ratio, the higher the concentration of La(C 2 O 4 ) 3 3-(this species is very low when the oxalate/REE molar ratio is less than about 30). Therefore, there are two advantages to not raising the pH of the solution too much: less reagent used and no risk of formation of an ionic REE oxalate compound. Based on these results, the pH of the solution should be set between 2.5 and 3.0 to optimize REE oxalate precipitation. , La(OH) 3

Precipitation of REEs in biomass extract

Following the recommendations determined by simulation, the pH of the extract obtained with D. linearis was first adjusted to 2.6 by NaOH addition (the initial pH was 0.8). After addition of oxalic acid (8 mmol for 0.37 mmol of REE), a precipitate S 3 appeared directly.

After filtration, analysis of the aqueous solutions showed that 90% of REEs precipitated.

The 10% remaining in solution were mainly La and Y. The other elements were also analysed to assess the purity of the REE-oxalate precipitate (Table 4). The mass ratio of REEs in this solid was 52.35%. Identified impurities represent 3.13% by mass. Considering that REEs are precipitated as Ox 3 REE 2 the remainder of this mass corresponded to the oxalate. The main impurity was Na, from the sodium hydroxide solution used to neutralize the extract. A better washing of the solid could certainly reduce this impurity.

These results prove that SOM did not inhibit precipitation under these conditions. The REE content is more than 10 times higher in S 3 (H 2 SO 4 ) than in S 2 (EDTA) (52.4 and 4.62% respectively), while the recovery yields are similar (68.6 and 69.3% respectively). This is due to the presence of EDTA in S 2 .

Calcination of the oxalate precipitate

To obtain REE-oxides, S 2 and S 3 , obtained from EDTA and sulphuric acid extractions respectively, were burnt. Many parameters can influence the final composition of the solids; to compare the two processes, a calcination step at 700 °C for 2 h was chosen in a first approach. Fig. 8 shows the mass ratios of the various elements identified in the two precipitates after calcination (determined by ICP analyses using the method described in paragraph 2.3.). In the case of EDTA leaching, REEs represented 79.8% of the mass of the calcination residue. The identified impurities were Ca (2.30%) and Al (1.94%) coming from the plant and Na (1.34%) mainly from EDTA. Given that the elements were in the form of oxides (REE 2 O 3 , CaO, etc.) the remainder of this mass mainly corresponded to oxygen.

In the case of H 2 SO 4 leaching, REEs represented 78.9% of the calcination residue mass while the mass ratio of impurities was 5.2% of which 3.8% is Na. It can be noted that the calculated uncertainties are high. They take into account the different stages from the acid leaching to calcination. It is important to note that experiments are carried out with very low masses and that the mass of the final product obtained is 300 times smaller than the initial mass of plant.

The two leaching methods led to close purities with a slightly different impurity profile.

For example, Ca content was slightly higher when EDTA leaching was used (2.3% against 0.4%). This can be explained by the stability of the Ca-EDTA complex.

XRD and EDX analyses showed a better crystallized solid when extraction was performed with sulphuric acid. For example, cerium oxide (Ce 7 O 12 ) was well identified. In the case of an extraction with EDTA, the final solid contains carbon, coming from EDTA calcination.

Conclusion and perspectives

A three-step process involving extraction, oxalate precipitation and calcination has been developed to produce REE oxides from hyperaccumulator D. linearis fern. Proof of concept has been established. Experimental study of the extraction showed that REEs can be extracted from the plant using either EDTA or sulphuric acid. A methodology based on speciation studies was successful in determining the operating conditions for precipitating REEs in oxalate form. The pH range to be maintained, close to pH 2 for both extraction methods, was found to be critical. The experimental study showed that the soluble organic matter was also extracted from the plant but did not inhibit the precipitation of REE oxalate.

Overall, REE purity was similar in solids after calcination (impurity content close to 5 wt%). However, even if extraction yields were higher with EDTA (87.5% against 79. %), the yield for the whole process was higher with H 2 SO 4 (72. % against 60.5%). The final solid contained 0.7 g of REES per g.

Fig. 1 :

 1 Fig. 1: Flowsheet of the proposed process to recover REEs from D. linearis

  REE speciation was investigated and simulated at 25 °C using CHESS (Chemical Equilibrium with Species and Surfaces, version 5.0.8) software [20]. The stability constants of La with EDTA and oxalate were implemented in the default database EQ3/6 (already containing data on La and sulphate interactions) [21].

Fig. 2 :

 2 Fig. 2: Species prevalence as function of pH for REE, oxalic acid and EDTA

Fig. 3

 3 Fig. 3 compares the extraction yield of REEs (Eq. 6) from biomass with the six extracting solutions: deionized water (blank sample), H 2 SO 4 (0.25 M) (strong mineral acid, pH < 0.5), citric acid (1 M) (weak carboxylic acid) at two pHs (1.6 and 4), citrate (1 M) (complexing agent) at pH 8, and EDTA (0.05 M) (strong chelating agent) at pH 4.5.

Fig. 3 :

 3 Fig. 3: Extraction efficiency of REEs (a) and other elements (b) using, H 2 O , citric acid (1 M, pH 1.6) , citric acid (1 M, pH 4) , citrate (1 M, pH 8) , H 2 SO 4 (0.25 M) , and Na 2 EDTA (0.05 M)

Fig. 4 : 2

 42 Fig. 4: Speciation of lanthanum in oxalic acid and EDTA solutions (simulations represented with lines and experimental points with dots): La 3+ , La 2 Ox 3 and , LaEDTA - and , La(OH) 3

Fig. 5 :

 5 Fig. 5: Diffractogram of the solid S 1 obtain after pH adjustment for extraction with EDTA.

Fig. 6 :

 6 Fig. 6: Simulations of lanthanum (1.13 mM) speciation in oxalic acid (80 mM) and sulphate (250 mM) solutions:

Fig. 7 Fig. 7 :

 77 Fig. 7: Distribution (relative to the initial plant content) of REEs after precipitation with oxalic acid in H 2 SO 4 extracts: oxalate precipitates , final solutions

Fig. 8 :

 8 Fig. 8: Elemental composition of the calcinated precipitates: from EDTA extract , from H 2 SO 4 extract

Table 1 :

 1 Stability constants used for speciation determination

	Basis species	Species formed	Log K (25 °C)*
	Ox	2-+ H	+	HOx	-	4.27
	Ox	2-+ 2 H	+	H 2 Ox	5.52
	Ox	2-+ La 3+	LaOx+	6.00
	2 Ox	2-+ La 3+	LaOx 2 -	9.55
	3 Ox	2-+ La 3+	LaOx 3 3-	11.59
	3 Ox	2-+ 2 La 3+	La 2 Ox 3	28.23
	EDTA 4-+ H	+	HEDTA	3-	10.95
	EDTA 4-+ 2 H +	H 2 EDTA 2-	17.22
	EDTA 4-+ 3 H +	H 3 EDTA -	20.34
	EDTA 4-+ 4 H +	H 4 EDTA	22.56
	EDTA 4-+ 5 H +	H 5 EDTA +	24.06
	EDTA 4-+ La 3+	LaEDTA -	17.94
	EDTA 4-+ H	+ + La 3+	LaHEDTA	20.40

*The data is corrected to zero ionic strength using Davies equation.

Table 2 :

 2 Composition in major cations and rare earths in Dicranopteris linearis (wt%) (confidence ranges are determined with 3 replicates)

	Element		Dry biomass
		La	0.128 ± 0.010
		Ce	0.113 ± 0.013
		Nd	0.088 ± 0.014
	REEs	Pr	0.027 ± 0.007
		Sm	0.014 ± 0.002
		Y	0.012 ± 0.002
		Gd	0.007 ± 0.001
		Total	0.389 ± 0.045
		Si	1.65 ± 0.05
	Other	K Al	0.254 ± 0.031 0.205 ± 0.043
	elements	Ca	0.174 ± 0.036
		Mn	0.051 ± 0.012
		Mg	0.048 ± 0.007

  3, REEs precipitate as oxalate, even in the presence of a high concentration of EDTA in solution.

	0,010
	0,008
	0,006
	0,004
	0,002
	0,000
	0	2	4	6	8	10	12	14
	The simulations also indicate that as EDTA/C 2 H 2 O 4 molar ratio increases, the pH

corresponding to the total complexation of La with EDTA decreases (from 5.2 to 4.6, when the EDTA concentration is multiplied by 5). Conversely, when the amount of oxalic

Table 3 :

 3 Elemental composition of the precipitate S 2 (%), obtained after oxalic acid addition in the extract with EDTA (confidence ranges are determined with 3 replicates) Stricter pH control and optimization of the amounts of EDTA and oxalic acid used during the extraction would certainly improve the REE content of the S 2 precipitate. Due to the low content (REEs and impurities), it appears that an excessive amount of EDTA has still precipitated. This was confirmed by an XRD analysis of the precipitate, where only

	Element		wt%
	REEs	Total	4.621 ± 0.489
		Ca	0.456 ± 0.012
		P	0.117 ± 0.003
	Other	K	0.043 ± 0.001
	elements	Al Pb	0.029 ± 0.001 0.028 ± 0.001
		Na	0.020 ± 0.001
		S	0.015 ± 0.001

speciation in the presence of H 2 SO 4 and oxalic acid

  As with the previous approach, the objective is to precipitate REEs as oxalate. The insoluble form referred to is La 2 (C 2 O 4 ) 3 . However, in the presence of sulphuric acid, REE sulphate complexes are formed, with REE(SO 4 ) + being the predominant species

	(REE(SO 4 ) 2 -is negligible all the time). A typical simulation of the equilibria is exhibited in
	Fig. 6. The precipitation of REEs as oxalate depends on pH. At low pH, sulphate forms
	solubilize REEs (pH is below the pKa of oxalic acid (1.2), C 2 H 2 O 4 is predominant), while
	hydroxides are formed under alkaline conditions. When the sulphate concentration is
	divided by 2, the pH corresponding to the formation of REE(SO 4 ) + decreases from 2.5 to
	2. Around pH 3.5 -4 and above, two species of oxalate coexist, La 2 (C 2 O 4 ) 3 and
	La(C 2 O 4 ) 3 3-

Table 4 :

 4 Elemental composition of the precipitate S 3 (wt%), obtained after oxalic acid addition in the extract with H 2 SO 4 (confidence ranges are determined with 3 replicates)

		100
	(%)	80
	distribution	40 60
	REE	20
		0
		La	Ce	Nd	Pr	Sm	Y	Gd ∑REEs
				Element		S 3 (wt%)

  The proposed process has a major advantage not to precipitate Al with oxalate (even if more than 50% is extracted). Here, and especially after H 2 SO 4 extraction, the final solid contained only 0.4% Al.Experiments have shown that the choice of H 2 SO 4 as the extraction agent was relevant to EDTA. Yields are better, it is cheaper, and a part of EDTA is burnt (lost) during calcination. Further studies are required to optimize this process (amount of H 2 SO 4 and oxalic acid, combustion temperature etc.). Reducing the quantity of reactants and studying the possibility of recycling certain solutions is necessary to design and scale up a process, which will allow the development of agromining development to recover REEs from secondary resources with more environmentally friendly techniques.

Acknowledgment

The authors would like to thank Bro-Penny (Lebanon) for financial support. They thank LabEx Ressources 21 (ANR-10-LABX-21), Institut Carnot ICEEL (REEcovery Project) and are grateful to Mr. S. Pontvianne for his assistance in the analytical work.


Inès Lacôte

David Gueorguiev

Claudio Pacchierotti

Marie Babel

Maud Marchal

Speed Discrimination in the Apparent Haptic Motion Illusion

Keywords: Apparent Haptic Motion, Tactile speed, Tactile devices

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Haptic illusions are a major tool to enhance tactile stimulations in a large variety of domains [START_REF] Lederman | Haptic perception: A tutorial[END_REF][START_REF] Lederman | Tactile and Haptic Illusions[END_REF]. They are an interesting topic of research as they enable to convey rich sensations with rather simple stimulation techniques. One major illusion is the Apparent Haptic Motion (AHM) illusion. The apparent haptic motion illusion aims at conveying a sensation of continuous movement along the skin when only discrete points are stimulated. In his original work, Burtt [START_REF] Burtt | Tactual illusions of movement[END_REF] found that two distinct vibrotactile stimuli elicited in close proximity on the skin with overlapping actuation were not perceived as localized sensations but rather as a single moving vibration.

Studies regarding AHM were conducted on different body parts [START_REF] Niwa | Determining appropriate parameters to elicit linear and circular apparent motion using vibrotactile cues[END_REF][START_REF] Israr | Control space of apparent haptic motion[END_REF] to test its robustness and understand the essential parameters driving this sensory illusion. The illusion was demonstrated to be effective in conveying directional cues and proved to be robust in both 1D and 2D patterns [START_REF] Park | Rendering Moving Tactile Stroke on the Palm Using a Sparse 2D Array[END_REF], which suggests a potential for providing directional information during navigation tasks. Besides spatial parameters, i.e., the position of the activation points and their distance to each other, temporal aspects have also been studied, so as to deepen the understanding of the illusion mechanisms [START_REF] Kirman | Tactile apparent movement: The effects of interstimulus onset interval and stimulus duration[END_REF][START_REF] Sherrick | Bilateral apparent haptic movement[END_REF]. In this respect, some studies showed that the temporal parameters, i.e., activation delays between motors, were actually not strongly constrained. Indeed, Stimuli Onset Asynchrony (SOA) and Duration of Signals (DoS) that are different from those proposed by Sherrick and Rogers [START_REF] Sherrick | Apparent haptic movement[END_REF], can also efficiently elicit this illusion [START_REF] Israr | Control space of apparent haptic motion[END_REF].

Speed perception and impacting parameters

Perception and discrimination of tactile speed has been studied in a large variety of conditions such as textures and vibrations [START_REF] Dallmann | The role of vibration in tactile speed perception[END_REF]. These works mainly realized experiments with a surface sliding under the fingertip, creating a contact and skin stretch. Hence, the literature provides information on the influence of textures and vibrations on speed discrimination for different velocity ranges, going, e.g. from 33 to 120 mm.s -1 [START_REF] Delhaye | Feeling fooled: Texture contaminates the neural code for tactile speed[END_REF][START_REF] Dépeault | Tactile speed scaling: contributions of time and space[END_REF]. The results from [START_REF] Delhaye | Feeling fooled: Texture contaminates the neural code for tactile speed[END_REF][START_REF] Dallmann | The role of vibration in tactile speed perception[END_REF] show that smooth surfaces are systematically felt as sliding slower than textured surfaces, even when presented with an identical sliding velocity. It was found that the Pacinian corpuscles have a crucial role in the discrimination of tactile speed [START_REF] Delhaye | Feeling fooled: Texture contaminates the neural code for tactile speed[END_REF], which explains the impact of material-induced vibrations on speed perception.

Speed perception of the apparent motion illusion

As previously mentioned, various studies confirmed the presence of the AHM illusion at different distances between the stimulation points (the position of the actuators) and with different SOA and DoS, deviating from the parameters indicated by Sherrick and Rogers [START_REF] Sherrick | Apparent haptic movement[END_REF]. Interest has been put to investigate various parameters regarding the spatial and temporal dimensions of the AHM illusion [START_REF] Kirman | Tactile apparent movement: The effects of interstimulus onset interval and stimulus duration[END_REF][START_REF] Niwa | Determining appropriate parameters to elicit linear and circular apparent motion using vibrotactile cues[END_REF], enabling the creation of more complex and informative stimulations. Although other works have focused on determining the optimal actuation timing for conveying the most natural apparent motion, to the best of our knowledge, no study focused on the perception of speed and duration as a source of information in AHM. Understanding the parameters that make two stimulations easily distinguishable could indeed be relevant for tactile communication or navigation. For example, the speed perception of the apparent motion could help representing a moving obstacle or a safe direction to follow.

Contribution

The goal of this paper is to investigate the perception of the velocity conveyed during the AHM illusion. To go further, we also tested the robustness of this perception based on how the stimulation is provided. Indeed, while historically the AHM is conveyed with vibrations, our previous study [START_REF] Lacôte | Tap Stimulation": An Alternative to Vibrations to Convey The Apparent Haptic Motion Illusion[END_REF] suggested that the illusion can also be conveyed by intervals of mechanical pressure. To explore that possibility, we conducted a study with two main objectives. First, we determine and compare the threshold of velocity discrimination for the apparent motion using both vibrations and pressure intervals ("taps") on the skin. Secondly, we study the impact of these modes on the participants' confidence when answering.

User study

This study aims to investigate the ability of discriminating a velocity change in the AHM illusion. The study has been approved by Inria's ethics committee (COERLE Dornell -Saisine 513).

Experimental set-up and stimulation modes

The experimental setup is shown in Fig. 1. It is composed of three custom actuators inspired by the work of Duvernoy et al. [START_REF] Duvernoy | Electromagnetic Actuator for Tactile Communication[END_REF], with a coil as a stator and two magnets glued together in their repulsive position as a mover to increase the magnetic field. The actuators are mounted onto a curved 3D printed hand-rest, positioned in a comfortable bend for the participants. The signals for the three actuators are first created with Matlab and then processed through a National Instrument USB-6343 series controller, which sends them to three amplifiers enabling to deliver a 6.5V signal to the motors, which corresponds to a force of approximately 0.4 N exerted on the hand. This last measure was recorded during a previous study, in which we characterized the force exerted by these actuators with a Nano17 force sensor (ATI, USA). The two magnets of the electromagnetic actuators move upward and downward along the center of the coil, depending on the electrical tension passing through it. This design enables to implement two stimulation modes: (i) a vibratory mode, where the actuators vibrate at 120 Hz, and (ii) a "tap" mode, where the magnets elicit a single impact to the user's skin. The vibrating frequency for (i) was set based on previous studies investigating the apparent haptic motion illusion with vibrotactile stimuli, such as [START_REF] Zhao | Intermanual apparent tactile motion on handheld tablets[END_REF]. Fig. 2 shows the signals imparted to the three motors in the two stimulation modes. In both modes, asynchronous overlapping stimulations are sent to the same three locations on the hand (see Fig. 1). While the duration of activation of the actuators is fixed, we seek to change the time delay between the actuators activation, also called Stimuli Onset Asynchony (SOA). Based on pilot tests and [START_REF] Gallo | Augmented white cane with multimodal haptic feedback[END_REF], we set DoS = 220 ms and the reference SOA = 110 ms in both stimulation conditions. In the following experiment, we tested SOA values of 90%, 80%, 70%, 60% and 50% of the reference SOA, making the comparison SOA values [99, 88, 77, 66, 55] ms.

Experimental design

Stimulations are conveyed between the middle finger and the proximal part of the palm, as shown in Fig. 1. We consider the two stimulation modes presented in Sec. 2.1, vibratory and tap, as well as two directions of motion, proximal-todistal (orange-to-green in Fig. 1) and distal-to-proximal (green-to-orange).

The two modes (vibrations or taps) are tested in two blocks, carried out one after the other. A block is thus made of only vibratory or only tap trials. Each block is composed of 80 trials of which the changing parameters are the SOA and the direction of the motion. A trial is a sequence of the reference signal with a SOA=110 ms and then a comparison signal with a different SOA, both having the same orientation (see also Sec. 2.3). The sequence of two signals is repeated a second time before the participants answer the questions. The order of the signal presentation is pseudo-randomized. Thus, blocks are only differentiated by the type of signal that is provided (vibratory or tap) and the order of the comparison, pseudo-randomized differently for each block and each participant.

Experimental procedure

Ten persons participated in the experiment. They were all between twenty-one and thirty years old, of which two were women, and one was left-handed. Stimulations were delivered on the dominant hand. Participants were naive about the hypotheses and process of the experiment. Participants carried out the experiment while wearing headphones playing white noise, so as to mask the sound coming from the motors. Indications about the global number of stimulations and questions were given before the experiment. During a trial, participants would receiv, in a random order, (i) the reference stimulation (SOA = 110 ms), delivered with the stimulation mode of the block at hand, and (ii) one of the comparison signals having a different SOA, delivered with the same stimulation mode and same orientation. The identical sequence was played a second time to end a trial. After each trial, the participants answered two questions about what they perceived: (i) "Which one of the two motions was faster?" and (ii) "How certain are you of your answer?" The data collected from the participants were the index of the signal that seemed faster (1 or 2) and their confidence from 0 (no confidence at all) to 100 (total certainty). The mode of the starting block was counterbalanced between participants. At the end of the experiment, participants were also able to give open comments and feedback about their sensations and the experiment in general.

Results

Results are reported in Figs. 3 and4. Fig. 3 shows the rate of correct responses (score), while Fig. 4 shows the reported confidence. These two parameters are the dependent variables of our statistical analysis. As independent variables, we report the results for five SOA levels and four experimental conditions: two directions of motion (proximal-to-distal or distal-to-proximal) and two types of stimulation (vibrations or taps).

Results showed a significant decrease of correct answers when the time delay between actuators, the SOA, increases and thus, gets closer to the reference SOA. This performance trend is observable in all conditions, both in taps and in vibration mode as well as with proximal-to-distal or distal-to-proximal direction patterns. To confirm the visual perception, we performed a Friedman statistical test on the four experimental conditions. The test highlighted the effect of the changing value of the SOA on the participants' performance to discriminate the fastest stimulation they received for the conditions of proximal-to-distal taps, distal-to-proximal taps, proximal-to-distal vibrations and distal-to-proximal vibrations (p < 0.01). An identical Friedman test was performed on the effect the compared SOAs have on the confidence rates. A significant effect was also noted for the four experimental conditions (p < 0.01).

To interpret the effect of the direction (distal-to-proximal or proximal-todistal) and the stimulation mode (tap or vibration), we performed matched-pairs Wilcoxon tests. The test showed no significant effect of the stimulation mode (p > 0.05) but it showed significant differences on the score between the proximal-to-distal and distal-to-proximal direction in tap stimulations (p < 0.01). However, a post-hoc test operated separately for each SOA did not show a significant difference for any of the comparisons. Finally, the matching between performance and confidence was tested by a Spearman correlation test Fig. 5 and was found significant for all conditions, but with a rather low r coefficient of around 0.4.

Discussion and Conclusions

This paper investigated the perception of the velocity of the apparent movement as well as the impact of two experimental conditions: the direction of the AHM and the stimulation mode. We investigated two stimulation modes, standard vibrations and taps to the palm of the hand. We also considered two directions of motion, from the fingertip to the palm and vice-versa. We studied the role of the delay between the activation of the actuators in the perception of velocity As expected, the smaller the delay compared to the reference, the better participants' speed discrimination. However, it was surprising to observe performance around 85% even for the easiest comparison stimuli, for which the SOA was divided by a factor 2 compared to the reference. Another important objective was to determine the matching between participants' performance and their confidence. As expected, the confidence and score correlated but the r coefficient was surprisingly low suggesting that participants struggled to assess their own performance. There was no significant influence of the mode of stimulation on the score or confidence, which showed a similar perception of both modes. Overall, the task was very challenging to participants and a few of them highlighted the difficulty of the task in their free comments. Thus, AHM illusions with different speeds might not be intuitive enough for people to use during everydat navigation tasks; the outcomes of the experiment were quite interesting in terms of haptic perception and confirm that human perception of tactile speed is inaccurate and prone to artefacts. The apparent haptic motion could still become a useful directional cue to integrate in navigation devices for impaired people, e.g., power wheelchairs, walkers, prewalkers [START_REF] Devigne | Power Wheelchair Navigation Assistance Using Wearable Vibrotactile Haptics[END_REF] but modulating the speed might not be very informative. We wish to conduct further experiments, in which we let participants set what they perceive to be the best parameters for the AHM, e.g., duration, delay, intensity.

Fig. 1 .

 1 Fig. 1. Experimental set-up. A) The signals are generated via a controller and then amplified before being played by the custom-built actuators. B) Three electromagnetic actuators are placed on a curved hand-rest. The colored dots show the contact points of the actuators on the hand.

Fig. 2 .

 2 Fig. 2. Signals sent to the three actuators in the two actuation modes. A) Vibratory mode, made of sinusoïdal oscillations at 120 Hz within ramp envelopes. B) "Tap" mode made of single ramp signals. In this Figure, we used DoS = 220 ms and SOA = 110 ms.

Fig. 3 .

 3 Fig. 3. Score when comparing five different SOAs vs. the reference one of 110 ms, across the two directions of motion (proximal-to-distal or distal-to-proximal) and type of stimulation (vibrations or taps). The boxplot gives the median, 25 and 75 percentiles with extrema values.

Fig. 4 .

 4 Fig. 4. Reported confidence of answer when comparing the SOAs, across the two direction of motion (proximal-to-distal or distal-to-proximal) and type of stimulation (vibrations or taps). The boxplot gives the median, 25 and 75 percentiles with extrema values.

Fig. 5 .

 5 Fig. 5. Spearman correlation tests with the corresponding p-values and statistical dependence factors "r". We tested the correlation between the confidence and the score for the different conditions of mode and direction.

Acknowledgment

This work has received funding from the Inria Défi project "DORNELL". The authors thank Georges Daher, PhD student at the ISIR of Sorbonne Université, for his help in creating the experimental setup. They also thank Frédéric Marie, mechatronics engineer at the Laboratoire de Génie Civil et Génie Mécanique (LGCGM) of Rennes, for the design of the 3D printed hand-rest.