Julien Couturier
email: couturier@cerege.fr

Pierre Tamba Oularé

Blanche Collin

Claire Lallemand

Isabelle Kieffer

Julien Longerey

Perrine Chaurand

Jérôme Rose

Daniel Borschneck

Bernard Angeletti

Stéven Criquet

Renaud Podor

Hamed Pourkhorsandi

Guilhem Arrachart

Clément Levard
email: levard@cerege.fr

Yttrium speciation variability in bauxite residues of various origins, ages and storage conditions

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

Introduction

The global demand for metals is constantly increasing, both in terms of quantity and diversity (OECD, 2019;[START_REF] Zepf | Materials critical to the energy industry[END_REF]. This increase is linked to the growth of the world's population and also to the emergence of new societal needs, which consume large quantities of these resources. This is particularly true for sectors such as defense and the digital and environmental transition which makes some metals with specific physico-chemical properties highly strategic (European Commission, 2020;International Energy Agency, 2021) or even "critical" for a number of non-producing countries (British Geological Survey, 2015;[START_REF] Grohol | Study on the Critical Raw Materials for the EU[END_REF][START_REF] Hatayama | Criticality Assessment of Metals for Japan's Resource Strategy[END_REF]; U.S. Geological [START_REF] Survey | 2022 Final List of Critical Minerals[END_REF].

Rare earth elements (REEs), considered as one of the most critical elements according to European and American agencies [START_REF] Grohol | Study on the Critical Raw Materials for the EU[END_REF]; U.S. Geological [START_REF] Survey | 2022 Final List of Critical Minerals[END_REF], are the focus of particular attention. The REE group includes metals from the lanthanide family (Z = 57 -71), as well as yttrium (Y, Z = 39) and scandium (Sc, Z = 21) due to their similar physico-chemical properties. REEs are usually subdivided into two subgroups, light rare earth elements (LREEs), comprising lanthanides from lanthanum (La, Z = 57) to europium (Eu, Z = 63) and heavy rare earth elements (HREEs), including Y and lanthanides from gadolinium (Gd, Z = 64) to lutetium (Lu, Z = 71). This arbitrary distinction has no scientific basis because there is no clear physico-chemical separation between these groups, rather a progressive change in properties and behaviours, including in ionic radii [START_REF] Gschneidner | Physical properties of the rare earth metals[END_REF]. Their particular electronic configuration gives them specific electromagnetic properties, making them essential for many applications in electronics, manufacturing, medicine, and renewable energy, among others [START_REF] Balaram | Rare earth elements: A review of applications, occurrence, exploration, analysis, recycling, and environmental impact[END_REF]. China controls almost the entire REE value chain [START_REF] Gauß | Rare Earth Magnets and Motors: A European Call for Action. A report by the Rare Earth Magnets and Motors Cluster of the European Raw Materials Alliance[END_REF], making the supply of REEs worldwide extremely vulnerable, as revealed in 2010, when China's quota policy causes a "REE crisis" in Europe and the US [START_REF] Chen | sustainability What Happens after the Rare Earth Crisis: A Systematic Literature Review[END_REF].

Beyond these economic and geopolitical considerations, primary extraction also poses often neglected environmental and social problems [START_REF] Eheliyagoda | A method to assess national metal criticality: the environment as a foremost measurement[END_REF], due to the huge quantities of energy required and of waste generated [START_REF] Adewuyi | Methods of Ore Pretreatment for Comminution Energy Reduction[END_REF][START_REF] Farjana | A review on the impact of mining and mineral processing industries through life cycle assessment[END_REF], as well as social conflicts and accidents [START_REF] Goodland | Responsible mining: The key to profitable resource development[END_REF][START_REF] Scheidel | Environmental conflicts and defenders: A global overview[END_REF]. All these impacts are further amplified by the general decline in ore grades [START_REF] Prior | Resource depletion, peak minerals and the implications for sustainable resource management[END_REF].

Faced with the ever-increasing demand for critical metals, the depletion of resources and the environmental and social crises associated with their extraction, a paradigm shift is urgently needed for the sustainable production of these metals. In particular, in the context of circular economy, there is a need to develop processes for extracting metals from secondary sources.

Since 2010 and the "REE crisis", the search for secondary sources of REEs has become a hot research topic with almost 350 papers published in 2022 whereas before 2010, fewer than 10 papers were published on this topic per year (Figure 1 A). This vast literature can be divided into two main categories. First, papers related to concentrated wastes (i.e. that contain REE concentrations above 1 wt%), which consist mainly in end-of-life products or product manufacturing scraps, and account for the majority of publications. In this category, permanent magnets are the most widely studied followed by waste from electrical and electronic equipment (WEEE), batteries, phosphors, catalysts or polishin g powders [START_REF] Belfqueh | Evaluating organic acids as alternative leaching reagents for rare earth elements recovery from NdFeB magnets[END_REF][START_REF] Ramprasad | Strategies and options for the sustainable recovery of rare earth elements from electrical and electronic waste[END_REF][START_REF] Yang | Selective extraction and recovery of rare earth metals from phosphor powders in waste fluorescent lamps using an ionic liquid system[END_REF]. Second, diluted wastes (i.e. that contain REE concentration below 1 wt%) are usually more complex matrices [START_REF] Binnemans | Towards zerowaste valorisation of rare-earth-containing industrial process residues: A critical review[END_REF] that are potentially more difficult to exploit given the low concentrations of REEs but which also attract considerable attention. This category includes mining and industrial wastes such as bauxite residues (BRs), phosphogypsum, coal fly ash, acid mine drainage, mine tailings or wastewater [START_REF] Binnemans | Towards zerowaste valorisation of rare-earth-containing industrial process residues: A critical review[END_REF][START_REF] Dupont | Recycling of rare earths from NdFeB magnets using a combined [Hbet][Tf2N][END_REF][START_REF] Hermassi | Recovery of rare earth elements from acidic mine waters: An unknown secondary resource[END_REF][START_REF] Peiravi | A Review of Rare-Earth Elements Extraction with Emphasis on Non-conventional Sources: Coal and Coal Byproducts, Iron Ore Tailings, Apatite, and Phosphate Byproducts[END_REF]. In this category, BRs are one of the most frequently cited and studied as a potential source for REEs (20-35% of identified papers in the last five years). waste" category contains the keywords: "magnet", "WEEE", "phosphor", "battery", "catalyst", "polishing waste". The "Diluted waste" category contains the keywords: "Bauxite residues", "phosphogypsum", "coal fly ash", "mine drainage", "mine tailings", "wastewater". (B) Conceptual scheme of the difference in properties in diluted and concentrated waste.

Bauxite residues (BRs), also known as "red mud" when hydrated, are wastes generated during the production of alumina using the Bayer process. During this process, the primary bauxite ore, rich in aluminium (Al), is digested with concentrated soda under pressure, leaving a highly alkaline and sodic residue at the end of the process. BRs are mainly composed of iron oxide but also contain a cocktail of toxic and critical metals [START_REF] Borra | Recovery of Rare Earths and Other Valuable Metals From Bauxite Residue (Red Mud): A Review[END_REF][START_REF] Smith | The processing of high silica bauxites -Review of existing and potential processes[END_REF]. REEs, which are naturally present in bauxite ore, are concentrated in BRs as a result of the Bayer process and can reach more than 2500 mg/kg (2500 ppm) [START_REF] Qu | Bioleaching of rare earth and radioactive elements from red mud using Penicillium tricolor RM-10[END_REF][START_REF] Rayzman | Red mud revisited -Special paper on scandium potential[END_REF][START_REF] Wagh | Occurrence of scandium and rare earth elements in Jamaican bauxite waste[END_REF], which makes BRs a potentially good secondary source [START_REF] Deady | Rare Earth Elements in Karst-Bauxites: a Novel Untapped European Resource?[END_REF] with many advantages over concentrated waste (Figure 1 B). First, BRs represent a huge potential reserve of REEs: for every ton of alumina produced, between 1 and 2 tons of BRs are generated [START_REF] Borra | Recovery of Rare Earths and Other Valuable Metals From Bauxite Residue (Red Mud): A Review[END_REF]. Today, it is estimated that approximately 170 Mt of BRs are generated each year, i.e. producing a global stockpile exceeding 4 billion tons [START_REF] Evans | The History, Challenges, and New Developments in the Management and Use of Bauxite Residue[END_REF]International Aluminium Institute, 2023). These stocks are generally easily accessible, as they are located in storage sites close to alumina plants. Moreover, with their very fine granulometry (Gräfe et al., 2011), BRs require little grinding pre-treatment, which is often described as the most energyconsuming stage of the primary extraction processes [START_REF] Adewuyi | Methods of Ore Pretreatment for Comminution Energy Reduction[END_REF]. However, although this residue appears to be an interesting alternative for the production of REEs, the variability of the physico-chemical properties of these residues is an obstacle to the development of a universal process of REE extraction. Several parameters may cause physico-chemical variations in the stocks of BRs available worldwide. First, essentially two types of bauxite ores are used as inputs in the Bayer process: lateritic bauxites, which account for 90% of the mineable reserves, and karstic (or karst) bauxites [START_REF] Freyssinet | Ore-Forming Processes Related to Lateritic Weathering[END_REF]. Both derive from similar processes of alteration and sedimentation (weathering, transportation and deposition), leading to the formation of an Al-rich ore. The difference lies in their bedrock lithology: lateritic bauxite deposits overlie aluminosilicate rocks while karstic deposits overlie carbonate rocks [START_REF] Bardossy | Karst Bauxites: Bauxite Deposits on Carbonate Rocks[END_REF]. Second, differences in the efficiency of the Bayer process due to different Al mineralogy depending on the type or quality of the bauxite ore and variabilit y in the implementation of the Bayer process, may result in variable amounts of Al remaining in the mine tailings. The conditions and time of storage of the residues may also affect their physico-chemica l properties. When not directly discharged into the seas and oceans, BRs are stored in different ways ranging from dry storage in the open air to storage in the form of sludge in retention ponds [START_REF] Evans | The History, Challenges, and New Developments in the Management and Use of Bauxite Residue[END_REF][START_REF] Fourrier | Les résidus de bauxite de Provence : propriétés physico-chimiques et influence sur la formation et le fonctionnement des sols[END_REF][START_REF] Power | Bauxite residue issues: I. Current management, disposal and storage practices[END_REF]. Aging of BRs can also induce physico-chemical variability since some residue deposits may be more than 100 years old: the Bayer process was invented at the end of the 19th century [START_REF] Borra | Recovery of Rare Earths and Other Valuable Metals From Bauxite Residue (Red Mud): A Review[END_REF]. Consequently, treatment or remediation attempts (cover layers, organic or inorganic amendment, etc.) have been undertaken at many sites sometimes leading to revegetation of the site despite particularly hostile conditions for life [START_REF] Di Carlo | Soil quality and vegetation performance indicators for sustainable rehabilitation of bauxite residue disposal areas: A review[END_REF]. This variability also results in marked differences in chemical composition and mineralogy as reported in the literature [START_REF] Borra | Recovery of Rare Earths and Other Valuable Metals From Bauxite Residue (Red Mud): A Review[END_REF][START_REF] Evans | The History, Challenges, and New Developments in the Management and Use of Bauxite Residue[END_REF][START_REF] Ma | Circular economy and life cycle assessment of alumina production: Simulation-based comparison of Pedersen and Bayer processes[END_REF][START_REF] Xue | A review of the characterization and revegetation of bauxite residues (Red mud)[END_REF]. Although the chemical and mineralogical variability is fairly well documented for major elements such as Fe and Al, very little information is available on REE speciation (i.e., the chemical environment) in BRs. Also, most studies that do address REE speciation are based on a microscopic approach (using electron probe microanalyses (EPMA) or scanning electron microscopy coupled with energy dispersive X-ray spectrometry (SEM/EDS)) and rely on elemental co-localization to identify REE bearing phases, which are based on assumptions, rather than on direct speciation analyses [START_REF] Gentzmann | Investigation of scandium in bauxite residues of different origin[END_REF][START_REF] Ochsenkiihn-Petropulu | Recovery of lanthanides and yttrium from red mud leaching by selective[END_REF][START_REF] Rivera | A Study of the Occurrence of Selected Rare-Earth Elements in Neutralized-Leached Bauxite Residue and Comparison with Untreated Bauxite Residue[END_REF][START_REF] Vind | Rare earth element phases in bauxite residue[END_REF]. In addition, existing studies rarely investigate the influence of origin of the bauxite ore, or the time and conditions of storage of BRs. Indeed, detecting low concentration phases and elements in such complex matrices is far from easy, plus detailed characterisation of REEs in BRs requires state of the art facilities such as synchrotron sources.

In the present study, the physico-chemical properties, chemical composition, mineralogy and yttrium speciation of ten BR samples with different origins, ages and storage conditions were characterised.

Yttrium was used as a proxy for HREEs thanks to its similar physico-chemical behaviour [START_REF] Borst | Adsorption of rare earth elements in regolith-hosted clay deposits[END_REF][START_REF] Lallemand | Potential of Ligand-Promoted Dissolution at Mild pH for the Selective Recovery of Rare Earth Elements in Bauxite Residues[END_REF][START_REF] Pingitore | Round Top Mountain rhyolite (Texas, USA), a massive, unique Y-bearing-fluorite-hosted heavy rare earth element (HREE) deposit[END_REF]. Improving knowledge of the REE speciation in BRs and the factors that influence it will pave the way for the development of extraction processes that account for the specificity of the targeted BRs in terms of origin, storage conditions and time [START_REF] Deady | Rare Earth Elements in Karst-Bauxites: a Novel Untapped European Resource?[END_REF]. Such perspectives are discussed in light of our results. The sample bauxite residues were categorized in two types: those generated from a lateritic-type bauxite ore located in Guinea (Boké region), and those generated from a karstic-type bauxite ore located in the south of France (Provence region), hereafter referred to respectively as "lateritic BRs" and "karstic BRs" for the sake of simplicity. These ten residues were collected from four different tailing sites: three in France (Gardanne "Gar", Vitrolles "Vit", Marseille "Mar") and one site in Guinea "Gui" (Fria plant site) from three alumina production plants which use the Bayer process. Samples were collected at several places: (i) directly at the end of the alumina extraction process (E suffix), after the filter press (L-BR-Gar-E) or the last scrubber (L-BR-Gui-E), (ii) from open-air storage sites (A suffix) at the surface (maximum 30 cm depth) of the deposits (L-BR-Gar-A, K-BR-Vit-A, K-BR-Mar-A, K-BR-Gar-A), one of which in a heavily vegetated area (suffix V) (K-BR-Vit-V), (iii) from a storage site under a vegetated capping layer (suffix L), at a depth of 1 m below the surface (K-BR-Mar-L) and (iv) from wet storage sites (suffix W) as lagoon or retention basin (L-BR-Gui-W, K-BR-Vit-W). The storage conditions and aging times (from 0 to 100 years) of the residues are detailed in Table 1 andFigure 2. The initial lateritic bauxite ore (L-B) sample was supplied by Alteo company, a producer of alumina at the Gardanne site which, at that time, used lateritic bauxite ores imported from Guinea. No bauxite ore of karstic origin representative of the studied karstic BR samples was used in the present study because either the plant concerned had closed down or the supply had been switched to lateritic bauxite ores, as was the case in Gardanne between the 1970s and 1990s [START_REF] Arnaud | Les Gueules Rouges. Un siècle de bauxite dans le Var. 1st edition CDDP du Var, 1989 and augmented reedition by Association des Gueules rouges du Var[END_REF].

Materials and methods

Materials and sampling

Before the experiments began, all the samples were dried at between 60-70 °C then manually ground to < 125 µm using an agate mortar and homogenized. The resulting dry materials were stored at ambient pressure and temperature.

Characterisation of the samples

pH and conductivity

For pH and electrical conductivity measurements, aqueous suspensions with a 1/5 solid/liqu id ratio (1 g of material in 5 mL of distilled water) were prepared according to ISO 10390:2021.

Measurements were made at 20 °C with two replicates after 2 h of stirring and 24 h of decantation.

Chemical composition

Preparation and bulk chemical analyses were conducted at CEREGE (France). The samples were digested by alkaline fusion using 100 mg of sample mixed with 500 mg of previously dried flux (49.5% lithium tetraborate, 49.5% lithium metaborate, 1% LiBr) and placed in an oven (Malvern Panalytical Claisse LeNeo) to undergo specific high refractory material digestion (up to 1050 °C for 22 min). The resulting fusion pearl was immediately dissolved in 40 mL of nitric acid (3-4 wt%). After appropriate dilution in distilled water, trace elements (<1000 µg/L) were analysed by inductively coupled plasma mass spectrometry (ICP-MS, Perkin Elmer 300X quadrupole) and major elements (>1000 µg/L) were analysed by inductively coupled plasma optical emission spectroscopy (ICP-OES Perkin Elmer Optima 4300 DV).

Three replicates were made of each analysis, and the results (concentration in mg/kg dry weight) are expressed along with the average and the standard deviation of the three samples.

Mineralogy

Mineralogy was performed by X-ray diffraction (XRD) at 40 kV and 40 mA on a PANalytical X'Pert Pro (Malvern Panalytical, UK) diffractometer equipped with a rear monochromator and a cobalt anticathode ( = 1.79 Å) at CEREGE (France). Powder samples were deposited on low background silicon plates with a drop of ethanol and scanned from 5 to 75° (2θ) with a step size of 0.033° and a total counting time of 3 h. The sample was rotated at 15 rpm during analysis to improve the statistics. Phase identification was performed using the X'pert Highscore plus software (Malvern Panalytical) with the PDF-2 ICDD (International Center for Diffraction data, Powder Diffraction Files 2) and COD (Crystallography Open Database).

Microscale observations

Microscale observations were performed using a Quattro S Environmental Scanning Electron Microscope (ThermoFisher) coupled with a XFlash6 / 100 Energy Dispersive X-ray Spectrometer with Quantax 400 software (Bruker) (SEM/EDS) (ICSM, France). The L-BR-Gui-E and K-BR-Mar-A powder samples were embedded in resin (Araldite 2020) and then polished (using silicon carbide and diamond) with oil. The cross-sections were then coated with carbon, and copper tape was used to ensure good conduction during microscopy. Series of elemental distribution maps (12×12 and 15×15, ×500 magnification) were first recorded (30 kV, 200 kcps, 20 min for each) to locate particles or grains containing Y over a large area (6-8 mm²). Once the particles were identified, EDS point analyses (15 kV, 100 kcps, 1 min), as well as EDS elemental maps of the selected areas (12 kV, 50 kcps, 20 min) were performed. Finally, quantitative-EDS elemental maps were performed to avoid interference between elements. These maps were produced by integrating 8×8 pixels from the qualitative EDS maps to increase the counting statistics and reduce calculation time.

Yttrium speciation by X-ray absorption spectroscopy (XAS)

XAS spectra at Y K-edge (17.038 keV) were recorded at the European Synchrotron Radiation Facility (ESRF, Grenoble, France) on beamline BM30 (CRG-FAME beamline) [START_REF] Chaurand | Insights into Yttrium speciation in bauxite residue before and after unconventional leaching experiments[END_REF].

Incoming photon flux energy was modulated using a Si(220) double crystal monochromator and higher harmonics were suppressed using Rh-curved mirrors. The data were collected in the step-by-step mode with a beam size of 200×150 µm.

Samples of bauxite ore and BRs were prepared as pure pellets (~30 mg), and model compounds were prepared as pellets diluted with polyvinylpyrrolidone (PVP). For the latter, the dilution ratio with PVP was calculated to obtain an optimal ∆µ 𝑡ℎ𝑒𝑜𝑟𝑖𝑡𝑖𝑐𝑎𝑙 of 1 with ABSORBIX software (v3.02) [START_REF] Michalowicz | MAX: Multiplatform Applications for XAFS[END_REF].

During the experiment, incoming X-ray beam energy was calibrated and regularly checked using a reference metal foil of Y. Each sample was measured in an He cryostat at 10-20 K to prevent beam damage. Spectra were obtained in fluorescence mode for bauxite ore and BR samples (average of 3 to 9 scans depending on the signal to noise ratio), and in transmission mode for model compounds (1 to 3 scans), except for the Y-doped hematite model compound which was run in fluorescence mode due to the relatively low concentration of Y. XAS spectra (XANES and EXAFS) were recorded from 16.85 to 17.58 keV (k = 12 A -1 ) with an energy step of 5 eV between 16.85 and 17 keV (1s counting time), of 0.5eV from 17 to 17.085 keV and a k step of 0.05 A -1 from 17.085 to 17.58 keV. Calibration, merging and normalization were performed with XAS-Viewer software (Larch, v0.9.65) [START_REF] Newville | Larch: An Analysis Package for XAFS and Related Spectroscopies[END_REF].

A library of Y reference compound spectra was used to identify Y species in bauxite ore and BRs [START_REF] Couturier | Y K edge XAS transmission and XAS fluorescence of Yttrium components at 20K[END_REF]. The library consisted of commercial references (purity >99. Linear combination fitting (LCF) of the XANES region was performed from 17000 to 17220 eV with a maximum of three components (adding a fourth component did not improve fits) using XAS Viewer software (Larch, v0.9.65) [START_REF] Newville | Larch: An Analysis Package for XAFS and Related Spectroscopies[END_REF]. The reduced-chi-square value (𝜒 𝑟𝑒𝑑 2 ), which accounts for degrees of freedom in the fit, was used to compare the relative quality of two fits that use the same interval but a potentially different number of variables. A change between two fits is considered statistically significant when the ratio of their two reduced-chi-square is greater than two standard deviations, according to the reference [START_REF] Kelly | Analysis of Soils and Minerals Using X-ray Absorption Spectroscopy[END_REF]. In our case, this criterion was used to identify all fits that were significantly identical to the best fit, which were then defined as "good fits". The value of the criterion was 1.185 and was obtained with the number of points in the fitting interval (N = 237-239) and the number of variables in the fit (V = 3-4). pH and conductivity varied widely among the samples (Figure 3, Table S1). The bauxite ore sample (L-B) had an almost neutral pH and very low conductivity (<300 µS/cm), whereas the BRs had alkaline pH ranging from 8.4 to 12, and strongly varying conductivity, i.e. from 266 µS/cm to >4 mS/cm (saturation value). The high variability observed is nevertheless consistent with that reported in the literature [START_REF] Gräfe | Bauxite residue issues: III. Alkalinity and associated chemistry[END_REF][START_REF] Snars | Evaluation of bauxite residues (red muds) of different origins for environmental applications[END_REF].

Results and discussion

pH and electrical conductivity

The alkaline nature and high conductivity of BRs are due to the contact between bauxite ore and concentrated soda during the Bayer process. In addition to solubilizing Al, excess OH -and Na + ions in the residue are responsible for the high pH and conductivity [START_REF] Di Carlo | Soil quality and vegetation performance indicators for sustainable rehabilitation of bauxite residue disposal areas: A review[END_REF][START_REF] Gräfe | Bauxite residue issues: III. Alkalinity and associated chemistry[END_REF].

Many parameters can influence both pH and conductivity of the BRs. During the Bayer process, the concentration of the NaOH solution, the quality of the washing steps or the inclusion of a filtration step determine the alkalinity and salinity of the BR at the outlet of the plant, among other things (Power et al., 2011). During storage, locally strong increases in pH and conductivity can occur at the surface of the deposit, resulting in the formation of efflorescence [START_REF] Di Carlo | Soil quality and vegetation performance indicators for sustainable rehabilitation of bauxite residue disposal areas: A review[END_REF][START_REF] Wu | Simulation study for the formation of alkaline efflorescence on bauxite residue disposal areas following the phosphogypsum addition[END_REF], mainly in the form of a thin white layer composed of Na2CO3 and NaHCO3. This phenomenon has already been observed at the Vitrolles site [START_REF] Fourrier | Les résidus de bauxite de Provence : propriétés physico-chimiques et influence sur la formation et le fonctionnement des sols[END_REF] and may explain the high conductivity of K-BR-Vit-A.

However, a decrease in pH and conductivity is most often observed as a function of the storage time of the deposit. The decrease is related to the leaching of alkaline soluble compounds by natural weathering (mainly rainfall), to the slow carbonation of BRs by atmospheric CO2 or even to the activity of microorganisms and plants [START_REF] Cusack | An evaluation of the general composition and critical raw material content of bauxite residue in a storage area over a twelve-year period[END_REF][START_REF] Di Carlo | Soil quality and vegetation performance indicators for sustainable rehabilitation of bauxite residue disposal areas: A review[END_REF][START_REF] Khaitan | Field Evaluation of Bauxite Residue Neutralization by Carbon Dioxide, Vegetation, and Organic Amendments[END_REF][START_REF] Kong | Natural evolution of alkaline characteristics in bauxite residue[END_REF][START_REF] Macías-Pérez | Contrasted microbial community colonization of a bauxite residue deposit marked by a complex geochemical context[END_REF][START_REF] Zhu | Novel predictors of soil genesis following natural weathering processes of bauxite residues[END_REF]. This aging effect was particularly visible in the oldest sample, K-BR-Gar-A. Organic, inorganic, acidic or seawater amendments also lead to the neutralization of BRs, which is one of the most desired effects when the aim is remediation or use of these wastes around the world [START_REF] Fourrier | How Raw and Gypsum Modified Bauxite Residues Affect Seed Germination, Enzyme Activities, and Root Development of Sinapis alba[END_REF][START_REF] Jones | Cation and anion leaching and growth of Acacia saligna in bauxite residue sand amended with residue mud, poultry manure and phosphogypsum[END_REF][START_REF] Khaitan | Neutralization of Bauxite Residue with Acidic Fly Ash[END_REF][START_REF] Khaitan | Field Evaluation of Bauxite Residue Neutralization by Carbon Dioxide, Vegetation, and Organic Amendments[END_REF][START_REF] Klauber | Bauxite residue issues: II. options for residue utilization[END_REF][START_REF] Kong | Acid transformation of bauxite residue: Conversion of its alkaline characteristics[END_REF][START_REF] Menzies | Seawater neutralization and gypsum amelioration of bauxite refining residue to produce a plant growth medium[END_REF][START_REF] Wong | Effects of gypsum and sewage sludge amendment on physical properties of fine bauxite refining residue[END_REF].

Neutralization of BRs is the main factor that enables the natural establishment of micro-organisms and vegetation [START_REF] Di Carlo | Soil quality and vegetation performance indicators for sustainable rehabilitation of bauxite residue disposal areas: A review[END_REF][START_REF] Santini | Spontaneous vegetation encroachment upon bauxite residue (red mud) as an indicator and facilitator of in situ remediation processes[END_REF][START_REF] Xue | A review of the characterization and revegetation of bauxite residues (Red mud)[END_REF], as can be seen at the K-BR-Gar-A and L-BR-Vit-V sites.

The age or storage conditions of the BRs thus appear to have an influence on their pH and conductivity, but many other parameters also come into play, making it difficult to make clear correlation, especially when the history of operations at the site is difficult to trace. S2). The bauxite ore sample (L-B) mainly contained aluminium (Al, 23.1 wt%) and iron (Fe, 14.5 wt%) while BR samples mainly contained Fe (20-39 wt%), Al (5-10%), silicon (Si, 2-6 wt%) and titanium (Ti, 2-5 wt%). The main difference in composition between bauxite ore and the BR samples was due to Al extraction during the Bayer process. The Bayer process was also at the origin of the nonnegligible sodium content (Na, 1.3-5.9 wt%) and calcium content (Ca, 0.8-6.0 wt%) in the BRs, whereas these elements were not present in the L-B sample. The presence of Na is due to digestion of bauxite ore with caustic soda (NaOH) and the presence of Ca to the addition of lime (CaO, Ca(OH)2) during preliminary desilication and causticization [START_REF] Borra | Recovery of Rare Earths and Other Valuable Metals From Bauxite Residue (Red Mud): A Review[END_REF][START_REF] Smith | The processing of high silica bauxites -Review of existing and potential processes[END_REF].

Chemical composition

Among the minor elements, the amount of total REEs (including Y and Sc) in the L-B sample was 218 mg/kg while total REE contents in BRs ranged from 562 to 2702 mg/kg. The enrichment of the REE content in BRs is specific to the Bayer process, as these elements are not released by soda during the process and are consequently concentrated in the residues. Individually, REE concentrations agree with their natural occurrence, ranked in decreasing order: Ce, followed by Y, La, Nd and Sc and the other REEs (Table S2).

Despite the significant differences between the BR samples considered in the present study, in terms of their ore origin, storage conditions, ages, as well as pH and conductivities, variations in the concentrations of the major elements remain limited compared to the variety of compositions reported in the literature [START_REF] Binnemans | Towards zerowaste valorisation of rare-earth-containing industrial process residues: A critical review[END_REF][START_REF] Evans | The History, Challenges, and New Developments in the Management and Use of Bauxite Residue[END_REF][START_REF] Gräfe | Bauxite residue issues: III. Alkalinity and associated chemistry[END_REF][START_REF] Khairul | The composition, recycling and utilisation of Bayer red mud[END_REF][START_REF] Snars | Evaluation of bauxite residues (red muds) of different origins for environmental applications[END_REF][START_REF] Xue | A review of the characterization and revegetation of bauxite residues (Red mud)[END_REF]. In particular, no correlation was found between the variations in the concentration of these elements and their storage time, thereby confirming some findings reported in the literature [START_REF] Cusack | An evaluation of the general composition and critical raw material content of bauxite residue in a storage area over a twelve-year period[END_REF]. However, some slight variations in the composition of BRs can be explained by the history of activities at the storage site concerned or during the implementation of the Bayer process. To give an example, aerial image archives have proven the presence of construction site landfills in the lower part of the Vitrolles tailing site over the last 30 years, which correspond to the areas where the K-BR-Vit-V and K-BR-Vit-W were sampled [START_REF] Fourrier | Les résidus de bauxite de Provence : propriétés physico-chimiques et influence sur la formation et le fonctionnement des sols[END_REF]. The addition of Si and Ca rich materials is probably responsible for lower concentrations of Fe, Al and Ti and higher concentrations of Si and Ca compared to the K-BR-Vit-A sample, which was collected from the upper part of the same tailing site and has never been in contact with these landfills. However, the difference in Al content between L-BR-Gui-E (8.0 wt%) and L-BR-Gar-E (5.6 wt%) could also be due to differences in the quality of the ore and/or in the performance of the Bayer process.

In contrast to major elements, the origin of the bauxite ore has a strong influence on REE content in BRs (657 ± 112 mg/kg (n = 4) for lateritic BRs and 1983 ± 429 mg/kg (n = 6) for karstic BRs). Indeed, karstic bauxites are known to have higher concentrations of REEs than lateritic bauxites [START_REF] Binnemans | Towards zerowaste valorisation of rare-earth-containing industrial process residues: A critical review[END_REF][START_REF] Borra | Recovery of Rare Earths and Other Valuable Metals From Bauxite Residue (Red Mud): A Review[END_REF][START_REF] Vind | Rare earth element phases in bauxite residue[END_REF], and can reach 1000 mg/kg or more [START_REF] Liu | Genesis of REE minerals in the karstic bauxite in western Guangxi, China, and its constraints on the deposit formation conditions[END_REF][START_REF] Mondillo | Rare Earth Elements (REE) in Al-and Fe-(Oxy)-Hydroxides in Bauxites of Provence and Languedoc (Southern France): Implications for the Potential Recovery of REEs as By-Products of Bauxite Mining[END_REF]. This difference has been widely reported and is usually attributed to the "pH-barrier" of the underlying alkaline carbonate rock that tends to favour REE concentration in karstic bauxites [START_REF] Gentzmann | Investigation of scandium in bauxite residues of different origin[END_REF]. Consequently, the difference is carried over to the BRs with concentrations of up to 2702 mg/kg in the K-BR-Mar-L sample, which is more than ten times the average for the earth's crust (∑REEs ≈ 240 mg/kg) [START_REF] Haynes | Section 14 -Geophysics, Astronomy, and Acoustics[END_REF]. The high REE contents in BRs originating from karstic bauxite ores make them promising secondary sources of REEs for the future. In comparison, some natural deposits currently being exploited for their REEs contain less than 1 wt% REEs [START_REF] Davris | Current and Alternative Routes in the Production of Rare Earth ElementsAktuelle und alternative Routen bei der Herstellung von Metallen der Seltenen Erden[END_REF][START_REF] Huang | Characteristics and genesis of ion adsorption type REE deposits in the weathering crusts of metamorphic rocks in Ningdu, Ganzhou, China[END_REF][START_REF] Li | The Genesis of Regolith-Hosted Heavy Rare Earth Element Deposits: Insights from the World-Class Zudong Deposit in Jiangxi Province, South China[END_REF].

The specific karstic/lateritic signature in terms of the chemical compositions of BRs can be also observed in other elements. For example, P, Cr, V, Ga are more abundant in lateritic BRs, while Si, Mg, Mn, Sr, Ni, Pb As, Co are present at higher concentrations in karstic BRs. Finally, among the elements present in the BRs (Table S2), we also noted the presence of significant quantities of Ti (up to >5 wt%), Mg (up to >3000 mg/kg in karstic BRs), Zr (up to >2000 mg/kg), P (up to >2000 mg/kg in lateritic BRs), V (up to >1500 mg/kg in lateritic BRs), Cr (up to >1500 mg/kg in lateritic BRs), Mn (up to >800 mg/kg in karstic BRs), Sr (up to >400 mg/kg in karstic BRs), Ni (up to >300 mg/kg in karstic BRs), which are also considered as critical elements by the European Commission or the USGS [START_REF] Grohol | Study on the Critical Raw Materials for the EU[END_REF] U.S. Geological Survey, 2022), and for which the possibility to use BRs as a secondary source remains to be investigated. For a more in-depth analysis of the observed differences between lateritic and karstic BRs with respect to REEs, chondrite-normalized REE profiles are plotted by normalizing each REE content by the corresponding value in the chondrites [START_REF] Taylor | The Continental Crust: Its Composition and Evolution[END_REF], (Figure 4, Table S3). In order to compare samples independently of their total REE content, the REE profiles are also normalized by the lanthanum value for each sample.

Chondrite-normalized REE profiles

All the BRs showed dominance of LREEs over HREEs, which decreased with an increase in Z, as often reported for bauxites in the literature [START_REF] Das | Trace and REE geochemistry of bauxite deposit of Darai-Daldali plateau, Kabirdham district, Chhattisgarh, India[END_REF]. The Ce and Eu anomalies, defined as the

𝐶𝑒 𝑁 √(𝐿𝑎 𝑁 * 𝑃𝑟 𝑁 )
and

𝐸𝑢 𝑁 √(𝑆𝑚 𝑁 * 𝐺𝑑 𝑁 )
ratios also presented similar values (1.0 to 1.3 and 0.6 to 0.7 respectively), when we compared BR compositions (Table S4). Interestingly, a difference appeared in the behaviour of HREEs depending on the origin of the bauxite ore. Evidence for a relative enrichment of HREEs, also visible on Y, was found in lateritic BRs compared to in karstic BRs. This variation can be characterised by the value of the slope of the REE pattern, defined as the ratio of normalized LaN/LuN values, which is lower for lateritic BRs (4.2 to 4.7) than for karstic BRs (7.4 to 9.5) (Table S4). It is also important to note that the lateritic bauxite ore sample (L-B) followed the same pattern as the lateritic BRs despite a 2 to 4 times lower REE concentration. This supports the conclusion that the differences observed in the HREEs are characteristic of the origin of the bauxite ore, as, when we compared the REE profiles of L-B and lateritic BRs, the Bayer process had no effect on the relative proportions of the REEs.

Differences in REE patterns may be the signature of different speciation [START_REF] Bea | Residence of REE, Y, Th and U in granites and crustal protoliths; implications for the chemistry of crustal melts[END_REF]. Figure 4 suggests that HREEs bearing phases in BRs differ depending on the origin of the bauxite ore. This hypothesis was reinforced by further analysis of the chemical data. For example, the scatterplot between P and HREEs shows that HREEs concentration is correlated with the concentration of P in lateritic BRs, whereas no correlation was apparent in karstic BRs (Figure S2). To identify the HREE-bearing phases and the potential association of HREEs with P in the BRs, the mineralogy of the samples was next examined from a macroscopic and microscopic perspective, as described in the following sections. [START_REF] Baioumy | Factors controlling the geochemical variations of lateritic bauxites formed upon different parent rocks in Peninsular Malaysia[END_REF][START_REF] Bhukte | Geochemical, Mineralogical and Petrological Characteristics of Lateritic Bauxite Deposits formed on Deccan Trap Basalt with Reference to High-level and Coastal (low level) Deposits of Maharashtra[END_REF][START_REF] De Oliveira | THE LATERITIC BAUXITE DEPOSIT OF RONDON DO PARÁ: A NEW GIANT DEPOSIT IN THE AMAZON REGION, NORTHERN BRAZIL[END_REF][START_REF] Negrão | Mineralogy and geochemistry of a bauxite-bearing lateritic profile supporting the identification of its parent rocks in the domain of the huge Carajás iron deposits, Brazil[END_REF][START_REF] Sidibe | Petrography, mineralogy, geochemistry and genesis of the Balaya bauxite deposits in Kindia region, Maritime Guinea[END_REF][START_REF] Vind | Rare earth element phases in bauxite residue[END_REF], although diaspore (AlO(OH)) may be encountered in certain cases [START_REF] Gu | Mineralogy, geochemistry, and genesis of lateritic bauxite deposits in the Wuchuan-Zheng'an-Daozhen area, Northern Guizhou Province[END_REF]. Also, karstic bauxites (not studied here) often contain boehmite (AlO(OH)) as the main Al phase [START_REF] Kloprogge | Thermal decomposition of bauxite minerals: Infrared emission spectroscopy of gibbsite, boehmite and diaspore[END_REF][START_REF] Mondillo | Rare Earth Elements (REE) in Al-and Fe-(Oxy)-Hydroxides in Bauxites of Provence and Languedoc (Southern France): Implications for the Potential Recovery of REEs as By-Products of Bauxite Mining[END_REF][START_REF] Radusinović | The potential for REE and associated critical metals in karstic bauxites and bauxite residue of Montenegro[END_REF][START_REF] Reinhardt | Geochemistry and mineralogy of rare earth elements (REE) in bauxitic ores of the catalan coastal range, NE Spain[END_REF] even if gibbsite or diaspore phases are the main phases in some non-Mediterranean karstic bauxites (Z. [START_REF] Li | Discovery of the REE minerals in the Wulong-Nanchuan bauxite deposits[END_REF][START_REF] Torró | Geological, geochemical and mineralogical characteristics of REE-bearing Las Mercedes bauxite deposit, Dominican Republic[END_REF].

Mineralogy

The effect of the Bayer process transforming bauxite ore into BR is clearly visible on XRD diffractograms. The majority of the Al phases contained in L-B were extracted showing the Fe phases to be predominant in BRs as hematite (Fe2O3) or goethite (FeO(OH)). The decrease in the Al phase in the BRs also brought out minor Ti phases, such as anatase or rutile (TiO2), and Si, as quartz (SiO2) which were masked in L-B due to the limit of detection of this technique (≈1 wt%). Similarly, calcite (CaCO3)

and aluminosilicate phases (cancrinite, sodalite, vishnevite) corresponding to desilication products [START_REF] Gräfe | Bauxite residue issues: III. Alkalinity and associated chemistry[END_REF][START_REF] Radomirovic | Crystallization of sodalite particles under Bayer-type conditions[END_REF][START_REF] Senaputra | The impact of desilication product on bauxite residue flocculation[END_REF] were observed in the XRD patterns of BRs. These results are consistent with data reported in the literature [START_REF] Evans | The History, Challenges, and New Developments in the Management and Use of Bauxite Residue[END_REF][START_REF] Gentzmann | Investigation of scandium in bauxite residues of different origin[END_REF][START_REF] Khairul | The composition, recycling and utilisation of Bayer red mud[END_REF][START_REF] Klauber | Bauxite residue issues: II. options for residue utilization[END_REF].

The mineralogy of all the BR samples was relatively similar, except for some slight variations that mainly depended on the origin of the bauxite ore. Gibbsite (main peak at θ = 21.3°) was not observed from the XRD pattern of karstic BRs. The intensity of the boehmite-related peak (main peak at θ = 16.9°) was more intense in the XRD pattern of karstic BRs than in the XRD pattern of lateritic BRs, confirming reports on karstic bauxites in the literature [START_REF] Kloprogge | Thermal decomposition of bauxite minerals: Infrared emission spectroscopy of gibbsite, boehmite and diaspore[END_REF][START_REF] Mondillo | Rare Earth Elements (REE) in Al-and Fe-(Oxy)-Hydroxides in Bauxites of Provence and Languedoc (Southern France): Implications for the Potential Recovery of REEs as By-Products of Bauxite Mining[END_REF][START_REF] Radusinović | The potential for REE and associated critical metals in karstic bauxites and bauxite residue of Montenegro[END_REF][START_REF] Reinhardt | Geochemistry and mineralogy of rare earth elements (REE) in bauxitic ores of the catalan coastal range, NE Spain[END_REF]. Iron-containing phases were present as a mixture of hematite and goethite, but relatively speaking, the intensity of hematite peaks was far greater than that of the goethite peaks in karstic BRs. The intensity of the aluminosilicate peak (main peak at θ = 16.2°) was also greater in karstic BRs.

In agreement with the chemical composition, the effect of construction site backfill during storage of K-BR-Vit-V and K-BR-Vit-W is visible here due to more intense quartz (θ = 31.0°) and calcite peaks (θ = 34.3°) on the diffraction patterns. Similarly, we attribute the higher gibbsite and quartz peaks in L-BR-

Gui-E and L-BR-Gui-W, compared to the other lateritic BRs on the diffractograms, to the quality of the ore or to the performance of the Bayer process. Indeed, the bauxite ore used at Fria plant is reputed to be of lower quality than that used at the Gardanne plant, due to its higher silica content, which hampers aluminium extraction.

The structural analysis performed by XRD revealed differences in the mineralogy of the major phases of BRs depending on the origin of the bauxite ore, but no other drastic mineralogical variation were found related to the age or storage conditions of the BRs. However, other characterisation techniques are needed to investigate the possible REE phase differences mentioned earlier in more detail3.3. Scanning electron microscopy (SEM) observations coupled with energy dispersive X-ray spectroscopy (EDS) were performed on L-BR-Gui-E and K-BR-Mar-A BRs, as these two samples were assumed to be representative of lateritic and karstic BRs, respectively (Figure 6 and Figure S3). In order to identify the occurrence of the particles in the samples in a representative way, a series of elemental distribution maps (magnification ×500) were performed on large regions of interest (6-8 mm²)

Microscopic and macroscopic evidence of speciation

SEM/EDS observations

for both samples. The analytical conditions chosen allowed the identification of particles with a diameter as small as 500 nm.

In both cases, Y-rich particles were found, co-localized with similar elements. Yttrium was found colocalized with other HREEs (Gd, Dy, Ho, Er, Yb), which supports the classification of Y as HREEs and validates using it as a proxy for HREEs [START_REF] Borst | Adsorption of rare earth elements in regolith-hosted clay deposits[END_REF][START_REF] Lallemand | Potential of Ligand-Promoted Dissolution at Mild pH for the Selective Recovery of Rare Earth Elements in Bauxite Residues[END_REF][START_REF] Pingitore | Round Top Mountain rhyolite (Texas, USA), a massive, unique Y-bearing-fluorite-hosted heavy rare earth element (HREE) deposit[END_REF].

EDS elemental maps show that Y and HREEs are always associated with phosphorus (P), but not associated with major elements (Fe, Al, Ti, Ca < 3 at%) (Figure 6 B, C and D). Moreover, the local chemical micro-analyses show P/HREEs atomic ratios close to 1 and Y/O atomic ratios between 0.15 and 0.25, suggesting the presence of xenotime (YPO4) or churchite (YPO4.2H2O) phases. In rare cases, Si and Zr can also be associated (>3 at%), suggesting traces of zircon (ZrSiO4) associated with xenotime, as well as with Fe from the surrounding matrix. These results are in good agreement with microscopic observations reported in the literature on BRs and bauxites [START_REF] Lallemand | Potential of Ligand-Promoted Dissolution at Mild pH for the Selective Recovery of Rare Earth Elements in Bauxite Residues[END_REF][START_REF] Li | Discovery of the REE minerals in the Wulong-Nanchuan bauxite deposits[END_REF][START_REF] Mordberg | Mineralogy and geochemistry of trace elements in bauxites: the Devonian Schugorsk deposit, Russia[END_REF][START_REF] Radusinović | The potential for REE and associated critical metals in karstic bauxites and bauxite residue of Montenegro[END_REF][START_REF] Reinhardt | Geochemistry and mineralogy of rare earth elements (REE) in bauxitic ores of the catalan coastal range, NE Spain[END_REF][START_REF] Rivera | A Study of the Occurrence of Selected Rare-Earth Elements in Neutralized-Leached Bauxite Residue and Comparison with Untreated Bauxite Residue[END_REF][START_REF] Vind | Rare earth element phases in bauxite residue[END_REF]. All these studies show that Y is found as xenotime or churchite phosphate particles in BRs, as in bauxites, regardless of the origin of their geological ore, although Y has also been detected in mixed phases of REEs in Greek BRs [START_REF] Vind | Rare earth element phases in bauxite residue[END_REF].

Based on this local probe technique, it seems that Y speciation does not differ as a function of the lateritic or karstic origin of the samples and cannot confirm our hypothesis that there is a difference in HREE mineralogy between lateritic and karstic BRs based on REE patterns. However, scanning large sample areas (6-8 mm 2 ) indicated approximately twice as many particles present in the L-BR-Gui-E sample than in the K-BR-Mar-A sample (2.4 and 1.3 particles/mm² respectively) while the Y content was twice lower in the L-BR-Gui-E sample than in the K-BR-Mar-A sample (102 and 226 mg/kg respectively).

Additionally, while in both samples, most of the particle diameters were smaller than 5 µm, several large particles were found in L-BR-Gui-E, including one particle with a 50 µm diameter (Table S5 and Table S6). This suggests that most of the Y in the K-BR-Mar-A sample is not detectable by SEM and, according to the P vs HREE scatterplot (Figure S2), is probably not associated with P. X-ray absorption spectroscopy (XAS) was performed at bulk scale to specifically characterise the atomic environment of Y species in all the samples, including the phosphate phases and other potential Y-bearing phases not detected by SEM analysis (Y-minerals and absorbed species). Visually, the speciation of Y in samples of lateritic origin is very similar to a xenotime phase. Indeed, linear combination fitting (LCF) of the results of the XANES region (17000 to 17220 eV) confirmed these observations with the strong presence (>34% in all best fits) of medium crystalized xenotime YPO4 (mcxYPO4) (Table S7). For example, the best fit for L-BR-Gui-E consisted in a mixture comprising 57% medium crystalized xenotime YPO4 (mcxYPO4) and 35% hcHA with a very good match (χ² = 0.02) (Figure 8 A). Figure 9 is a statistical study of the LCF results to compare samples with different noise levels and to obtain statistically relevant results. In Figure 9 A, the percentages of occurrence of the main model compounds (with an arbitrary threshold of 25% in the fit) in all the good fits (i.e., all fits that do not statistically differ from the best fit) are plotted for each sample. A quality criterion (Figure 9 C), based on reduced chi-square value (𝜒 𝑟𝑒𝑑 2 ), was used to determine the number of significantly good fits for each sample (Figure 9 B) (see section 2.2.5). Indeed, in the case of a noisy spectrum, a large number of combinations of model compounds can correctly fit the experimental data, as is the case of L-B sample with 11 fits (fit n°1 to fit n°11 in the white area) considered to be good. Thus, it does not seem reasonable to rely only on the best fit.

X-Ray absorption spectroscopy measurements at Y K-edge

Our statistical study confirmed that xenotime YPO4 appears in 100% of good fits of all lateritic samples in the form of mcxYPO4 or less often in the form of hcxYPO4. With the exception of the strong presence of hcHA in L-BR-Gar-A good fits, as well as Y(OH)3, which was present in the majority of L-BR-Gar-E good fits, no other model compounds appear significantly in the good fits of lateritic samples. These results confirm and complement the results of the study by [START_REF] Lallemand | Potential of Ligand-Promoted Dissolution at Mild pH for the Selective Recovery of Rare Earth Elements in Bauxite Residues[END_REF] who proposed speciation of Y as a mixed amorphous and crystalline xenotime phosphate based on the same lateritic material (L-BR-Gar-E).

The speciation of Y in samples of karstic origin clearly differs from speciation in samples of lateritic origin, but is also more difficult to identify than in lateritic ones. Visually, the XANES signals do not reveal a specific structure or if they do, only tenuously. The LCF results of the XANES region showed no clear predominance (Table S7), as illustrated by the best fit for K-BR-Vit-W, consisting, with a very good match (χ² = 0.01) of a mixture of 36% highly crystallized hydroxyapatite (hcHA), 34% Y-doped hematite and 30% Y(OH)3 (Figure 8 B). Our statistical study nevertheless showed that only hcHA, Ydoped hematite, Y(OH)3 and to a lesser extent, Y-adsorbed on montmorillonite, are present in the good fits of karstic BRs (Figure 9 A). In none of the cases, do the xenotime YPO4 compounds stand out, in contrast to in the samples of lateritic origin. To be consistent with XAS responses, Y in karstic BRs could be adsorbed or incorporated into one or more mineral phases, as is the case for Sc in BRs [START_REF] Gentzmann | Investigation of scandium in bauxite residues of different origin[END_REF]. However, Sc speciation is known to diverge from that of other REEs [START_REF] Horovitz | Scandium : its occurrence, chemistry, physics, metallurgy, biology, and technology[END_REF][START_REF] Suss | Specific features of scandium behavior during sodium bicarbonate digestion of red mud[END_REF][START_REF] Vind | Rare earth element phases in bauxite residue[END_REF], so extrapolation to Y behaviour is not feasible.

For example, in their study, Gentzmann et al. show that the geological origin of the ore implies only minor changes in the distribution of Sc in the host mineral phases, which is not the case for Y [START_REF] Gentzmann | Investigation of scandium in bauxite residues of different origin[END_REF]. normalized by the best fit for each sample and significance cut-off criterion. Fits present in the grey area differ significantly from the best fit. (C) Significant criterion formula between two fits, i and j according to the reference [START_REF] Kelly | Analysis of Soils and Minerals Using X-ray Absorption Spectroscopy[END_REF].

Yttrium speciation in the BRs probed by bulk XANES analysis is mainly influenced by the origin of the bauxite ore and tend to corroborate the differences between the lateritic and karstic BRs suggested by the REE patterns, contrary to the microscopic approach. In all samples of lateritic origin, Y was mainly found in the form of xenotime YPO4, which could be distinguished from churchite YPO4, confirming the microscopic observations. Given that YPO4 xenotime particles were also found in karstic BRs using microscopic observation methods, but that the XANES signal indicates that the majority of Y is not in xenotime or churchite phosphate form, we can assume that Y is present in several phases in the karstic BRs. Pellet heterogeneity was also investigated by examining each XANES spectrum collected at different locations in the sample pellet before averaging, confirming the presence of rare YPO4 particles in karstic BRs (2 out of 27 scans collected) resulting in noisier, more intense spectra and exhibiting the xenotime YPO4 features (Figure S4). However, the majority of Y in karstic BRs is probably incorporated in small quantities in other mineral phases (iron oxyhydroxide, hydroxyapatite)

or adsorbed on the surface of other minerals, which would explain why they are not easily detectable by SEM-EDS (below the limit of detection).

However, no variability in Y speciation was detected linked to the storage conditions of the tailings, nor their aging time for a given origin.

Perspectives

The information obtained in this study is crucial for the use of BRs as a secondary source of REEs, particularly for the design and implementation of selective recovery processes.

First, HREE solubility probably differs as a function of origin. Indeed, the observed difference in speciation may affect HREE recovery yields depending on the origin of the bauxite ore. A comparative study of the dissolution behaviour of HREEs from these different BRs is needed to validate this hypothesis. The solubility of HREEs was found to be very low for lateritic BRs [START_REF] Lallemand | Potential of Ligand-Promoted Dissolution at Mild pH for the Selective Recovery of Rare Earth Elements in Bauxite Residues[END_REF] because of the very low solubility of xenotime. Given the higher REE content in karstic BRs than in lateritic BRs and the difference in HREE speciation, it would be interesting to test and compare similar recovery approaches. Second, the marked variability of BR storage conditions and durations does not appear to have a significant effect on HREE speciation which should consequently facilitate the treatment of tailings stored in different conditions and for different storage times at large scales.

Although origin appears to be the only parameter that affects HREE speciation, we recall that some geographical disparities may also exist due to variations in the bedrock lithology of a given origin (lateritic or karstic). In our case, bauxites ore from all lateritic BR samples came from the Boké region in Guinea (West Africa) and bauxite ore from all the karstic BR samples came from the region of Provence (South of France). Therefore, to extrapolate these results worldwide, it is crucial to study potential geological differences, including HREE speciation, for a given origin in other geographica l regions of the world, such as China, Australia, Brazil or India, which are the main generators of BRs at the present time. In addition, some alumina production sites use a mixture of lateritic and karstic bauxites as ore input, e.g., at the Aluminium of Greece plant [START_REF] Vind | Rare earth element phases in bauxite residue[END_REF]. In these cases, it would be impossible to address the link between the origin of the ore and HREE speciation in the BRs.

Finally, a complete understanding of REE speciation in BR remains to be achieved for LREEs, for which no clear speciation has been assigned to date.

Conclusion

The aim of this study was to perform a multi-scale characterisation of different bauxite residues (BRs) as a function of origin of the ore, of the storage conditions and storage time, with a particular focus on the speciation of Y as a proxy of the behaviour of heavy rare earth elements (HREEs).

We have shown that some physico-chemical properties of BRs, such as pH, conductivity or chemical composition of major elements, vary with the storage conditions and storage time and may partially explain the marked variability of physico-chemical properties of BRs reported in the literature.

More interestingly, this study has shown that other properties of the BRs, such as the mineralogy of the major phases as well as the chemical composition and speciation of the HREEs varied with the origin of the bauxite ore but were not influenced by the storage conditions or by the age of the BRs. Notably, and to our knowledge, for the first time, we were able to link the origin of the bauxite ore, lateritic or karstic, and the speciation of Y. In the case of lateritic BRs, HREEs are mostly present in the form of pure and crystallized phosphate particles (xenotime). In karstic BRs, HREEs are mainly present in a more complex speciation, probably adsorbed or incorporated in other minerals, including iron oxyhydroxide and hydroxyapatite minerals, although some xenotime phosphate particles were also detected (< 25%). Only the complementarity use of macroscopic, microscopic and spectroscopic approaches enabled us to reach a full understanding of Y speciation in these complex residues.

The present study thus paves the way for a study of the potential of BRs for the selective recovery of HREEs in a circular economy context. Our results also underline the importance of considering BRs produced in different parts of the world not as a single material but as incorporating certain disparities as a function of the origin of the ore that may require a range of different extraction processes. It is true for REEs but also for other critical elements including vanadium for example for which such eventual disparities are not documented today.

Figure 1 :

 1 Figure 1: (A) Evolution of cumulative number of scientific papers containing "rare earth elements" and "secondary sources" keywords, from 2007 and 2022, separated into several categories (source Web of Science). The "Concentrated

Figure 2 :

 2 Figure 2: Presentation of the study samples according to the origin of the ore, age, storage conditions and associated nomenclature

  9%): yttrium oxide (Y2O3; Acros Organics), yttrium carbonate (Y2(CO3)3•xH2O; Alfa Aesar), yttrium phosphate (YPO4•xH2O Alfa Aesar) hereafter "medium crystalized xenotime YPO4" or "mcxYPO4", but also synthesized references (see protocols and XRD in SI): yttrium hydroxide (Y(OH)3), yttrium phosphate (YPO4) with different phase and crystallinity (churchite, low and high crystallized xenotime), Yadsorbed on montmorillonite ((Na,Ca)0,3(Al,Mg)2Si4O10(OH)2•xH2O), Y-doped Calcite (CaCO3), Ydoped hematite (Fe2O3), low and high crystallized Y-doped hydroxyapatite (Ca5(PO4)3(OH)).

Figure 3 :

 3 Figure 3: Conductivity of all the samples as a function of pH (solid/liquid ratio = 1/5, 20 °C) (blue = lateritic-type, red = karstic-type).

Figure 4 :

 4 Figure 4: Patterns of chondrite and lanthanum-normalized rare earth elements in all the bauxite residue samples studied here, separated according to the origin of the ore. The normalized spectrum of lateritic bauxite ore sample is plotted for the purpose of comparison. The normalized values come from[START_REF] Taylor | The Continental Crust: Its Composition and Evolution[END_REF]

Figure 5 :

 5 Figure 5: X-ray diffraction patterns of the studied bauxite ore (L-B) and bauxite residue samples sorted by origin of the ore (blue = lateritic-type, red = karstic-type). Identification of the main peaks of the major phases. DSPs: desilication products

Figure 6 :

 6 Figure 6: (A) SEM image (BSE detector) of an yttrium particle found in samples L-BR-Gui-E as an example of lateritic bauxite residue (magnification ×4000) and associated quantitative EDS elemental maps showing the spatial distribution f or (B) iron (C) phosphorus and (D) yttrium (12 kV, 50 kcps, 20 min). (E) EDS spectrum associated to the micro-analyse performed with the incident beam centered at the red cross position on (A) (15 kV, 100 kcps, 1 min).

Figure 7 :

 7 Figure 7: (A) Stacking of Y K-edge XANES spectra of the model yttrium compounds used in the study. (B) Stacking of Y Kedge XANES spectra of all the studied samples sorted by origin of the ore (blue = lateritic-type, red = karstic-type). Spectra of crystallized YPO 4 xenotime model compound is plotted for the purpose of comparison. The main features of the spectra are identified by the dashed lines.

Figure 8 :

 8 Figure 8: Best linear combination fitting (LCF) XANES analysis results for (A) L-BR-Gui-E, as an example of lateritic samples and (B) K-BR-Vit-W, as an example of karstic samples. Fits were performed with Larch software (17000-17220 eV, with a maximum of 3 components).

Figure 9 :

 9 Figure 9: (A) Occurrence of model compounds in all good fits (i.e. significantly identical to the best LCF) performed with Larch software in the XANES region (17000-17220 eV, maximum of 3 components), for all the samples studied. Only model compounds that contributed more than 25% are shown. (B) Changes in the goodness of fit (reduced-chi-square value)

Table 1 :

 1 Detailed description of the samples cited in this article* Supplied by Alteo, the company that currently manages the Gardanne plant. ** Uncertainty concerning the time of use of the storage site. Dry samples collected on the surface and therefore considered to be young (in bold in the table). *** Difficult to determine the exact age of storage of liquid samples in the dam because of potential transfer between young and old residues. Liquid samples collected on the surface can be considered to be relatively young (0-15 years) compared to the age of the dam (40 years).

	Name

of sample Type of sample Origin of bauxite Plant Sampling location Storage conditions Some known detailed conditions Storage time

	L-B	Bauxite ore	Lateritic (Guinea)	/	*	/	/	/
	L-BR-Gui-E	Bauxite residue Lateritic (Guinea)	Fria plant (Guinea)	At the plant (end of process)	End of Bayer process (after the last scrubber)	/	/
	L-BR-Gui-W	Bauxite residue Lateritic (Guinea)	Fria plant (Guinea)	Dote dam, Guinea	Wet storage (Tropical climate)

Table 2 :

 2 Chemical composition by mass of major elements(Fe, Al, Ti, Si, Ca), Y and sum of all REEs (including Y and Sc) present in our samples, obtained by ICP-MS and ICP-OES after alkaline fusion (3 replicates).

	Sample	Fe (wt%)	Al (wt %)	Ti (wt %)	Si (wt %)	Na (wt %)	Ca (wt %)	Y (mg/kg)	ΣREEs (mg/kg)
	L-B	14.51 ± 0.08 23.11 ± 0.04 1.57 ± 0.01	1.00 ± 0.01	0.01 ± 0.02	0.00 ± 0.01	34 ± 2	218 ± 6
	L-BR-Gui-E 31.24 ± 0.11	8.05 ± 0.14	3.26 ± 0.08	2.02*	1.94 ± 0.03	1.16 ± 0.09	102 ± 2	562 ± 15
	L-BR-Gui-W 32.33 ± 1.34	8.73 ± 0.35	3.40 ± 0.18	2.31*	1.98 ± 0.12	1.46 ± 0.11	101 ± 6	563 ± 25
	L-BR-Gar-E 31.48 ± 0.45	5.56 ± 0.11	4.74 ± 0.10	1.97 ± 0.02	2.23 ± 0.09	4.28 ± 0.09	118 ± 0	727 ± 4
	L-BR-Gar-A 31.90 ± 0.23	6.49 ± 0.03	5.15 ± 0.04	1.92 ± 0.02	2.54 ± 0.04	2.82 ± 0.04	123 ± 2	778 ± 13
	K-BR-Gar-A 28.47 ± 0.65	8.97 ± 0.06	2.37 ± 0.03	3.13 ± 0.06	1.28 ± 0.04	3.53 ± 0.05	226 ± 4	1792 ± 24
	K-BR-Mar-A 29.43 ± 1.01	5.60 ± 0.17	4.08 ± 0.14	3.20 ± 0.11	3.06 ± 0.15	4.45 ± 0.02	226 ± 8	2261 ± 74
	K-BR-Mar-L 39.02 ± 0.13	6.22 ± 0.03	4.52 ± 0.02	2.76 ± 0.01	2.34 ± 0.02	0.85 ± 0.01 265 ± 10 2702 ± 128
	K-BR-Vit-A 25.31 ± 0.51	9.92 ± 0.15	2.70 ± 0.04	3.67 ± 0.07	5.91 ± 0.27	1.85 ± 0.04	219 ± 2	1924 ± 18
	K-BR-Vit-V 21.64 ± 0.28	7.96 ± 0.05	2.47 ± 0.02	5.25 ± 0.03	3.04 ± 0.06	5.01 ± 0.04	184 ± 1	1549 ± 11
	K-BR-Vit-W 20.80 ± 0.06	7.78 ± 0.03	2.47 ± 0.01	5.88 ± 0.02	3.79 ± 0.22	6.01 ± 0.02	199 ± 3	1668 ± 7

* Silicon was only measured in one replicate of L-BR-Gui-E and L-BR-Gui-W samples.

The chemical composition of the samples is listed in

Table 2 (additional elements are reported in Table

Acknowledgments

The authors acknowledge financial support from the CNRS through the MITI interdisciplina ry programmes (PRIME 2020:ExtraMet project), the Agence Nationale de la Recherche through the RECALL project (ANR-20-CE04-0007). The thesis contract of Claire Lallemand was funded by CEPAC (Caisse d'épargne Provence Alpes Corse) through the AMIDEX foundation (Aix-Marseille University). We acknowledge the European Synchrotron Radiation Facility for provision of synchrotron radiation facilities on beamline BM30. Hamed Pourkhorsandi thanks F.R.S.-FNRS for funding. The authors also thank the ACE Partner project that funded the work of Pierre Tamba Oulare (World Bank, the Association of African Universities, the French Development Agency, the Institute of Research for Development and INRIA)

Data Availability

Data will be made available on request.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Supporting information

Supplementary data associated with this article can be found in the online version at doi:10.1016/j.jhazmat.2023.132941.


Ziming Liu

Ezio Malis

Philippe Martinet

ONE-STAGE DEEP STEREO NETWORK

Keywords: Stereo Matching, Depth Estimation, Deep Learning

Stereo matching is one of the low-level visual perception tasks. Currently, two-stage 2D-3D networks and three-stage recurrent networks dominate deep stereo matching. These methods build a cost volume with low-resolution stereo feature maps, which splits the network into a feature net and a matching net. However, the 2D feature map is not uncontrollable, and the low-resolution feature map has lost important matching information. To overcome these problems, we propose the first one-stage 2D-3D deep stereo network, named StereoOne. It has an efficient module that builds a cost volume at image resolution in real-time. The feature extraction and matching are learned in a single 3D network. According to the experiments, the new network can easily surpass the 2D-3D network baseline and it can achieve competitive performance with the state-of-the-art.

INTRODUCTION & RELATED WORKS

As one of the most important computer vision tasks, stereo matching has experienced several stages of development, including traditional algorithms (e.g., SGM [START_REF] Hirschmuller | Accurate and efficient stereo processing by semi-global matching and mutual information[END_REF]), early convolutional networks (e.g., MC-CNN [START_REF] Zbontar | Stereo matching by training a convolutional neural network to compare image patches[END_REF]), two-stage 2D-3D stereo networks (e.g., PSMNet [START_REF] Chang | Pyramid stereo matching network[END_REF]), and three-stage recurrent stereo networks [START_REF] Lipson | Raftstereo: Multilevel recurrent field transforms for stereo matching[END_REF][START_REF] Xu | Iterative geometry encoding volume for stereo matching[END_REF]. In the age of deep learning techniques, stateof-the-art stereo matching methods have been dominated by deep stereo matching networks. Among them, the most successful solutions are the two-stage 2D-3D CNN methods [START_REF] Chang | Pyramid stereo matching network[END_REF][START_REF] Gu | Cascade cost volume for high-resolution multi-view stereo and stereo matching[END_REF]. Even the newest state-of-the-art recurrent stereo networks [START_REF] Xu | Iterative geometry encoding volume for stereo matching[END_REF] highly rely on the two-stage stereo networks [START_REF] Chang | Pyramid stereo matching network[END_REF].

The two-stage methods were proposed in [START_REF] Kendall | End-to-end learning of geometry and context for deep stereo regression[END_REF] and [START_REF] Chang | Pyramid stereo matching network[END_REF]. The original two-stage stereo networks consist of a 2D feature extraction network and a 3D matching network. Since then, many methods have been proposed based on this two-stage architecture, such as [START_REF] Gu | Cascade cost volume for high-resolution multi-view stereo and stereo matching[END_REF] and [START_REF] Guo | Group-wise correlation stereo network[END_REF].

More recently, three-stage recurrent stereo networks have achieved state-of-the-art accuracy performance [START_REF] Xu | Iterative geometry encoding volume for stereo matching[END_REF][START_REF] Lipson | Raftstereo: Multilevel recurrent field transforms for stereo matching[END_REF][START_REF] Li | Practical stereo matching via cascaded recurrent network with adaptive correlation[END_REF]. These methods perform well on high-resolution stereo images, but their inference speed is affected by the timeconsuming design of recurrent GRU units. Recurrent stereo networks are also based on the two-stage stereo network [START_REF] Xu | Iterative geometry encoding volume for stereo matching[END_REF].

The previous methods build the cost volume on the lowresolution feature maps. The important matching information has been lost because the stereo matching is performed at a low-resolution. This is an primary problem for the 2D-3D networks [START_REF] Chang | Pyramid stereo matching network[END_REF] or recurrent networks [START_REF] Li | Practical stereo matching via cascaded recurrent network with adaptive correlation[END_REF]. Besides the spatial resolution, the disparity resolution in cost volume also affects the stereo matching.

In addition, the stereo 2D feature maps are not optimal in the previous methods [START_REF] Chang | Pyramid stereo matching network[END_REF][START_REF] Zhang | Adaptive unimodal cost volume filtering for deep stereo matching[END_REF]. The 2D-3D network methods optimize the feature network and the matching network by minimizing the loss between the ground truth disparity and the prediction. The optimization goal is to minimizing the matching cost, instead of extracting high-quality feature maps. There are some methods [START_REF] Zhang | Adaptive unimodal cost volume filtering for deep stereo matching[END_REF] have shown that the extracted 2D feature maps are not suitable to build a single peak cost volume. They propose a constraint loss after the 2D feature network to reduce this effect.

Instead, if the stereo cost volume is built at the raw image resolution and the feature extraction and the feature matching are learned in one 3D network, the matching information lost can be reduced and the conflict of the optimal goal between the feature network and the matching network can be avoided.

In this paper, we propose the first one-stage 3D stereo network, namely StereoOne. StereoOne build the stereo cost volume on the raw stereo images with a new image volume module. We propose an efficient and real-time volume generation methods which is much faster than the previous methods [START_REF] Chang | Pyramid stereo matching network[END_REF][START_REF] Li | Practical stereo matching via cascaded recurrent network with adaptive correlation[END_REF]. Furthermore, we introduce general 3D network [START_REF] Carreira | Quo vadis, action recognition? a new model and the kinetics dataset[END_REF][START_REF] Feichtenhofer | Slowfast networks for video recognition[END_REF] to learn the feature extraction and matching.

Furthermore, a disparity dense-sparse network is introduced to maintain a high-resolution disparity in the cost volume. On the one hand, the disparity-dense network is lowcost for high-resolution disparity. On another hand, the densesparse design is easier to process different disparity range scales of different samples.

This paper is organized as follows: In Section 1, we introduce the background and motivation for our proposed onestage stereo matching network. In Section 2, we describe the details of the proposed StereoOne. In Section 3, we present our experimental results on popular stereo matching benchmarks. Finally, we conclude our work and discuss future research directions in Section 4.

METHOD

In this section, we describe the details of the proposed 3D stereo network, namely StereoOne. The structure comparison is shown in Fig. 1.

An Efficient Image Volume Module

As the cost volume V is built by enumerating all aligned stereo images of different disparities.

V = ([L, f(R) P x +d ] c , ..., ) D-1 d=0 (1)
Where [L, R] c is the concatenating of left image L and right image R on the channel dimension. P x is the x direction image coordinate. f(.) P x +d is the d pixels image horizontal shift.

The previous methods use two ways to build cost volume: image warping [START_REF] Li | Practical stereo matching via cascaded recurrent network with adaptive correlation[END_REF][START_REF] Zhang | Adaptive unimodal cost volume filtering for deep stereo matching[END_REF] or looping-index [START_REF] Chang | Pyramid stereo matching network[END_REF], as Eq. 2. With the index tensors, we can easily obtain the aligned right image f(R) in one step (e.g. using torch.gather in pytorch). This process is shown in Fig. 2.

Warping : V = [L, W 3D (R) (P x +d) D-1 d=0 ,P y ] c Looping -index : V = ([L, R[:, 0 : W -d]] c f or d ∈ [0, D)) (2) Where W 3D is a 3D image warping. R[:, 0 : W -d]
Finally, the raw cost volume is generated by concatenating them V = [L, R] c . Our method avoid the time-consuming loop operation, and be much faster than the previous on both CPU and GPU devices.

3D Network

Overall

In StereoOne, the raw cost volume is built on raw stereo images. StereoOne network introduces a general 3D network to process this image volume. In this way, the 3D network not only learns the stereo features but also learns the feature matching in one network. StereoOne is based on a general 3D network, which makes it to be flexible and easier to be deployed. Specifically, the 3D network is an encoder-decoder structure. For the encoder part, the general 3D encoder networks [START_REF] Carreira | Quo vadis, action recognition? a new model and the kinetics dataset[END_REF][START_REF] Feichtenhofer | Slowfast networks for video recognition[END_REF] can be used. For the decoder part, we designed a 3D feature pyramid network (FPN) based on 2D FPN [START_REF] Lin | Feature pyramid networks for object detection[END_REF]. In the 3D FPN, feature maps of four stages are mapped to the same channel size with FPN lateral connection layers, which is a 3D convolution layer (kernel = (1, 1, 1), stride = (1, 1, 1)). Then, these feature maps are summed from the top The error results on the online benchmark ::::::::: KITTI2012, :::::::::: KITTI2015. The error metrics are described in benchmarks.

to the bottom. Each feature map is upsampled ×2 size. Finally, the bottom feature are mapped to channel = 1. Same as the previous, with the learned cost volume, a soft Argmin disparity prediction layer is used following the previous stereo networks [START_REF] Kendall | End-to-end learning of geometry and context for deep stereo regression[END_REF][START_REF] Chang | Pyramid stereo matching network[END_REF].

Furthermore, because the different images have different disparity ranges, we propose a disparity dense-sparse encoder network and a dense-sparse fusing module to learn a better stereo cost volume.

Disparity Dense-sparse Encoder

Disp-Dense Branch: The dense disparity branch maintains a high disparity resolution, it focuses on learning the matching information. It has a shallow feature dimension to reduce the computation cost, usually 1/8 of the sparse disparity branch.

Disp-Sparse Branch: In contrast, the sparse branch focuses on learning the image's spatial information and extracting better features. Each pixel on the predicted disparity map is not independent, the spatial context information is important for the disparity prediction, especially the homogeneous area [START_REF] Mahdi | Boosting monocular depth estimation models to high-resolution via contentadaptive multi-resolution merging[END_REF]. Therefore, the sparse disparity branch keeps a higher channel dimension but a low disparity resolution to learn abundant image spatial information.

The Feature Connection From the Dense to the Sparse: To better fuse dense-sparse information, the dense feature will be fused into the sparse feature at the stage 1, 2, 3 of the encoder (four stages structure). We only use single-direction connection according to the previous deep learning networks [START_REF] Feichtenhofer | Slowfast networks for video recognition[END_REF][START_REF] Lin | Feature pyramid networks for object detection[END_REF]. The single-direction connection has a similar performance as the bi-direction connection but has a lower computation cost.

The Dense-Sparse Fusing Module To fuse the two volumes of the disparity dense and sparse branches, we explore different ways to fuse dense and sparse cost volumes. (i) Concatenate them across the disparity dimension. Then use a linear layer to transform the disparity resolution to the original. (ii) Add up the two cost volumes. Firstly transform them into the original disparity resolution, then add up two volumes. (iii) Concatenate them across the channel dimension. Firstly up-sample them to the original disparity resolution, then concatenate them in the channel, and finally transform it with a linear layer. With the experiments, the third module has the best performance.

EXPERIMENTS

The Comparison with the State-of-the-art Methods

Method

Error(EPE) Speed(FPS) FLOPS PSMNet [START_REF] Chang | Pyramid stereo matching network[END_REF] 0.98 9 1.02T Cascade-PSM [START_REF] Gu | Cascade cost volume for high-resolution multi-view stereo and stereo matching[END_REF] 0.93 23 1.37T Cascade-Gwc [START_REF] Gu | Cascade cost volume for high-resolution multi-view stereo and stereo matching[END_REF] 0.81 19 1.49T AcfNet [START_REF] Zhang | Adaptive unimodal cost volume filtering for deep stereo matching[END_REF] 0.87 9 1.02T CREStereo [START_REF] Li | Practical stereo matching via cascaded recurrent network with adaptive correlation[END_REF] 0.78 5 2.27T † Ours(ResNet18 [START_REF] Carreira | Quo vadis, action recognition? a new model and the kinetics dataset[END_REF][START_REF] Feichtenhofer | Slowfast networks for video recognition[END_REF] We compare the StereoOne with the other methods on three benchmarks: the large-scale SceneFlow data, KITTI2012, 2015 Stereo data. Firstly, as the Tab 2 shows, the StereoOne achieves the lowest error compared with most recent methods.

Then we report the results on KITTI 2012, 2015 stereo data as Tab. 1. It suggests that StereoOne can achieve competitive results with state-of-the-art methods on real-world data. As shown in Tab. 3, we compare three methods. The proposed efficient volume method achieves much fastest inference speed and keep a low memory cost. Compared with the simple looping-index operation or 3D image-warping operation, the proposed module is ×66 and ×34 faster than them on 2080Ti GPU. The results suggest that our method has robust performance on different devices.

The Disparity Distribution

Fig. 3: The results on different disparity distributions on SceneFlow dataset. The two-stage network is PSMNet [START_REF] Chang | Pyramid stereo matching network[END_REF]. Every pixel error is used to measure the predictions. Further, we compare the results on different disparity distributions for the one-stage 3D and two-stage 2D-3D stereo networks. Fig. 3 suggests that StereoOne with disparity dense-sparse branches can solve the problem of different disparity distribution as we claim, especially for high disparities.

Disparity Resolution

In this part, we explore different disparity resolutions for the dense and sparse branches. We use 6, 12, 24 for the sparse branch, 48, 96, 192 for the dense branch. The error results are shown in Fig. 4. Overall, the result is better with high disparity resolution. This demonstrates the disparity-dense and sparse structure. The result of 192 also suggests that the dense/sparse ratio should not be too large.

Dense-Sparse Fusing Module

To fuse the dense and sparse cost volume efficiently, we conduct experiments of three kinds of modules as described in Sec. 2.2.2. The results as recorded in Tab. 4. The Channelconcatenating has the lowest errors on every-pixel-error, 3pixels-error, and D11 error metrics.

Details and Datasets

To evaluate the performance of StereoOne, we use the largescale dataset Scene Flow [START_REF] Mayer | A large dataset to train convolutional networks for disparity, optical flow, and scene flow estimation[END_REF] and KITTI 2012/2015 benchmarks [START_REF] Menze | Object scene flow for autonomous vehicles[END_REF]. In the experiments on Scene Flow datasets, we use Lion optimizer with 1e-4 learning rate, and the optimizer uses gradient clip norm with L2 norm, the max norm is 35 for 48k iterations. For the experiments on KITTI, a AdamW optimizer with learning rate 2e-4 is used for 20k iterations. The gradient clip norm is also used. The batch size is 8 on two GPUs for both of them.

CONCLUSION

By reviewing the previous stereo networks, we analyzed the limitations of the previous. To realize the excellent disparity prediction, we propose the first one-stage 3D stereo network. In this paper, we use the simple ResNet [START_REF] Carreira | Quo vadis, action recognition? a new model and the kinetics dataset[END_REF] structure, more advanced network structures can be explored in the future.

Fig. 1 :

 1 Fig.1: The structure of two-stage 2D-3D stereo networks[START_REF] Kendall | End-to-end learning of geometry and context for deep stereo regression[END_REF][START_REF] Chang | Pyramid stereo matching network[END_REF], three-stage recurrent stereo network[START_REF] Lipson | Raftstereo: Multilevel recurrent field transforms for stereo matching[END_REF][START_REF] Li | Practical stereo matching via cascaded recurrent network with adaptive correlation[END_REF][START_REF] Xu | Iterative geometry encoding volume for stereo matching[END_REF], one-stage 3D stereo network (single branch) and one-stage 3D stereo network (dense-sparse).

Fig. 2 :

 2 Fig. 2: The efficient image volume index on disparity and image width dimension.

Fig. 4 :Table 4 :

 44 Fig. 4: The predicted disparity EPE errors with different disparity resolution /D.

Table 1 :

 1

	Method	Out-Noc%	KITTI2012(3pixel Error) Out-All/%	Avg-All/px	KITTI2015 D1-fg
	PSMNet 2018	8.36	10.18	1.6	4.62
	ACVNet 2022	7.03	8.67	1.5	3.07
	AcfNet 2020	6.93	8.52	1.9	3.80
	CoEX 2021	6.83	8.63	1.4	3.41
	SegStereo 2018	6.35	8.06	1.3	4.07
	CREStereo 2022	6.27	7.27	1.4	2.86
	GANet 2019	6.22	7.92	1.3	3.46
	HITNet 2021	5.91	7.54	1.2	3.20
	LEAStereo 2020	5.35	6.50	1.2	2.91
	CFNet 2023	5.96	7.29	1.3	3.56
	CroCo-Stereo 2023	-	-	-	2.65
	Ours 2023	4.99	6.50	1.2	2.62

Table 2 :

 2 The comparison with other methods on Scene Flow data test set. The model code is from the official release, all experiments use the same optimizer. Device: Nvidia A40 GPU. †: disparity dense-sparse network. ⋆: single branch.

  3.2. The Ablation Studies3.2.1. Image Volume Module

	Device	Method time/ms memory/M
	A40GPU	Warping	323	14,154
	A40GPU	Looping	421	4,938
	A40GPU	Ours	18	7,244
	2080TiGPU Warping	678	9,422
	2080TiGPU Looping	1318	4,814
	2080TiGPU	Ours	20	7,118
	CPU	Warping	2181	5,068
	CPU	Looping	221	5,060
	CPU	Ours	204	5,066

Table 3 :

 3 The performance of different volume generation methods. GPU capability: A40(8.6), 2080Ti(7.5), CPU: AMD EPYC 7413 24-Core.

D1: Percentage of stereo disparity outliers in first frame

Acknowledgments

This work was funded by 3IA Côte d'Azur. The experiments use OPAL computing cluster of INRIA and UCA.