Gleb S Pokrovski
email: pokrovsk@lmtg.obs-mip.fr

Jacques Roux

Jean-Louis Hazemann

Denis Testemale

An X-ray absorption spectroscopy study of argutite solubility and aqueous Ge(IV) speciation in hydrothermal fluids to 500°C and 400 bar

Keywords: germanium, X-ray Absorption Fine Structure (XAFS) spectroscopy, argutite, solubility, Ge hydroxide complexes, density model, HKF model, Ge/Si ratio

Dissolution of synthetic argutite (GeO 2 , tetragonal, rutile-like) in pure water, and local atomic structure around Ge(IV) in aqueous solution were characterized by in situ X-ray Absorption Fine Structure (XAFS) spectroscopy at the Ge K-edge using a new high temperature -high pressure cell.

XAFS transmission and fluorescence spectra were collected from germanic acid aqueous solutions of 0.02 to 0.09 mol Ge/kg H 2 O at ambient pressure and temperature, and from a 0.04 mol Ge/kg H 2 O solution at 400 bar from 20 to 450°C. Spectra at all temperatures and concentrations exhibit the 1 st shell contribution from 4±0.3 oxygen atoms at 1.75±0.01Å, consistent with a tetrahedral structure of the Ge(OH) 4 complex which is a chemical analog of Si(OH) 4 and is the dominant Ge aqueous species, in agreement with previous solubility and potentiometric measurements. The constancy of Ge(OH) 4 structural parameters over the wide temperature and fluid-density range is consistent with the strong covalent character of the Ge-(OH) bonds. A dissolution experiment on argitite in pure H 2 O was carried out at 400 bar from 200 to 500°C by monitoring the height of the Ge absorption edge of transmission spectra. The solubility of GeO 2 , derived from a classical X-ray absorption relation using the absorption height values and fluid density, increases with increasing temperature up to 400°C but decreases at 450 and 500°C, similar to that observed for quartz. The new solubility data were analyzed using both a density model and the revised HKF equation of state to better constrain Ge(OH) 4 thermodynamic properties. Calculations using these models indicate that despite strong similarities in the structure and energetics of aqueous germanic acid and silica, differences in the thermodynamic properties of germanate and silicate dissolution reactions may account for the increase of the Ge/Si ratio observed in high temperature natural fluids.

Introduction

Although in the Earth's crust most germanium is dispersed through silicate minerals due to the isomorphic substitution of Ge(IV) to the chemically similar Si(IV), germanium can be highly enriched relative to silicon in a variety of geological materials such as secondary clay minerals, sulfides, iron hydroxides, coals, and hydrothermal fluids (e.g., [START_REF] Bernstein | Germanium geochemistry and mineralogy[END_REF][START_REF] Bernstein | Germanium crystal chemistry in hematite and goethite from the Apex Mine, Utah, and some new data on germanium in aqueous solution and in stottite[END_REF]. This property makes germanium a potentially useful geochemical tracer of continental weathering intensity, hydrothermal and tectonic activity, or fluid sources (e.g., [START_REF] Froelich | The geochemistry of inorganic germanium in natural waters[END_REF][START_REF] Murnane | Germanium and silicon in rivers of the Orinoco drainage basin[END_REF][START_REF] Kurtz | Germanium-silicon fractionation in the weathering environment[END_REF]. For example, the Ge/Si atomic ratio is ~0.6×10 -6 in rivers, (1 to 3)×10 -6 in most silicate minerals, and (10 to 100)×10 -6 in high-temperature hydrothermal fluids [START_REF] Froelich | The geochemistry of inorganic germanium in natural waters[END_REF][START_REF] Kurtz | Germanium-silicon fractionation in the weathering environment[END_REF]refs therein). It is likely that such significant variations may be related to differences in aqueous speciation and/or crystal chemistry between Ge and Si. For example, it has been recently suggested that possible differences in the thermodynamic properties between Ge and Si aqueous complexes and minerals at elevated temperatures could explain the anomalously high Ge/Si ratios observed in hot natural fluids emanating from mid-ocean ridges (Pokrovski & Schott, 1998a). Thus, knowledge of Ge aqueous complexes stability (i.e., thermodynamics), structure, and Ge coordination is of importance for the quantitative use of the Ge/Si ratios to trace natural processes. At present, however, the scarcity of such information, particularly at elevated temperatures, greatly hampers the quantitative prediction of both Ge/Si ratios in hydrothermal/magmatic processes and Ge-versus-Si hydrothermal fluxes to the hydrosphere and biosphere.

Previous studies have shown that the easiness of Ge, contrary to Si, to extend its coordination from 4 to 6, is responsible for the preferential incorporation of Ge into iron hydroxide minerals [START_REF] Bernstein | Germanium crystal chemistry in hematite and goethite from the Apex Mine, Utah, and some new data on germanium in aqueous solution and in stottite[END_REF], and aqueous chelate complexes with organic ligands (Pokrovski & Schott, 1998b;[START_REF] Pokrovski | An X-ray absorption fine structure spectroscopy study of germanium-organic ligand complexes in aqueous solution[END_REF]. Nevertheless, in most of low to moderate temperature organic-poor superficial and hydrothermal waters, germanium, like silicon, is present as the neutral hydroxide complex, germanic acid, of the presumed stoichiometry Ge(OH) 4 based on the analogy with silicic acid. The knowledge of the thermodynamic properties of this species is, however, limited to 350°C (Pokrovski & Schott, 1998a), and its exact structure and coordination are not known at temperatures above ambient.

The aim of the present study is to provide new data about Ge species structure and stability in near and supercritical aqueous fluids using X-ray Absorption Spectroscopy.

Until recently, most of measurements of mineral solubilities in high-temperature/pressure (T-P) aqueous fluids are performed using batch or flow reactors which require fluid quenching after or sampling during the experiment. Thus, significant efforts are necessary to account for or avoid possible precipitation/adsorption or oxidation (depending on the chemical system) of the initial high T-P fluid during sampling or quenching procedures. To obtain species identities and stoichiometries from the measured total dissolved metal concentrations, one requires many experimental points and an accurate knowledge of the intensive parameters (e.g., pH, Eh, ligand activities) which are often poorly constrained at elevated temperatures and pressures. In the recent years, the development of high T-P spectroscopic cells (e.g., [START_REF] Bassett | Hydrothermal diamond anvil cell for XAFS studies of first-row transition elements in aqueous solution up to supercritical conditions[END_REF][START_REF] Hoffmann | New experimental developments for in situ XAFS studies of the chemical reactions under hydrothermal conditions[END_REF] and improvement of laser and X-ray sensitivities allowed the use of vibrational (Raman, UV) and X-ray Absorption spectroscopies for numerous in situ investigations of metal speciation in a variety of systems in hydrothermal fluids, most of them limited to temperatures up to ~350°C (see [START_REF] Brown | An overview of synchrotron radiation applications to low temperature geochemistry and environmental sciences[END_REF] for a review). A few studies of mineral solubilities by X-ray fluorescence and Raman scattering using diamond-anvil techniques allowing measurements to 10's kbar have recently appeared (e.g., quartz, Zotov & Keppler, 2002;AgCl, Schmidt & Rickers, 2003;SrCO 3 , Sanchez-Valle et al., 2003). However, a simultaneous in situ measurement of both species structures and mineral solubilities at near-and supercritical conditions in a single series of experiments or using a single cell configuration still remains rare.

X-ray Absorption Fine Structure (XAFS) spectroscopy provides in fact a very efficient, and, sometimes, unique way of both in situ determination of metal local structure in its complexes, and solid phase solubilities (aqueous concentrations). In this study, we used a new Xray cell allowing simultaneous acquisition of transmission and fluorescence spectra at high temperature and pressure to measure both Ge atomic environment in germanic acid aqueous solutions and the solubility of germanium oxide (GeO 2 , tetragonal, argutite,) in water to 500°C and 400 bar. The new data obtained were used to better constrain the stability and structure of Ge(IV) hydroxide complexes at supercritical conditions, and to provide useful comparisons of the geochemical behaviour of germanium and silicon in crustal fluids.

Materials and Methods

Experimental samples

Germanic acid aqueous solutions for XAFS measurements were prepared by dissolving weighted amounts of the soluble hexagonal GeO 2 polymorph (Aldrich, 99.999%) in MilliQ water at 90°C, and then were filtered through a 0.2-µm Millipore filter. The values of pH were adjusted by adding a 1M NaOH Titrisol solution and were monitored using a combination pH glass electrode. Aqueous Ge content in solutions before and after XAFS runs was analyzed by inductively coupled plasma optical emission spectroscopy (ICP-OES) and was found identical, within 1% of the value, to the initially prepared concentration. More details about solution preparation and analyses can be found in Pokrovski and Schott (1998a,b). Argutite (GeO 2 , tetragonal, rutile-like) was synthesized from commercial GeO 2 (hex) following the method of Factor and Carasso (1965) as detailed in Pokrovski and Schott (1998a).

The obtained fine powder of argutite was aged for several weeks in contact with water in a titanium autoclave at 250-300°C and saturated vapor pressure (P sat ). Ageing runs were repeated several times, followed each time by rapid quenching of the reactor, rinsing the solid and replacing the reacted solution with fresh water. This treatment was intended to remove ultra-fine particles and favor the formation of bigger argutite crystals (Pokrovski and Schott, 1998a).

Compact crystal agglomerates and crusts of argutite larger than 1 to 2 mm in size that formed on the reactor walls were selected for XAFS dissolution experiments. Their crystallinity and crystal morphology were checked by X-ray diffraction and electronic microscopy. The good crystallinity and big size of GeO 2 crystals chosen for the experiments prevent artifacts which might otherwise lead to an overestimated solubility, due to dissolution of poorly crystallized solids or the suspension of fine and porous particles in solution on the passage of the X-ray beam during XAFS measurements.

XAFS spectra acquisition

XAFS spectra (including the X-ray absorption near edge structure region or XANES, and the extended X-ray absorption fine structure region or EXAFS) of aqueous solutions of germanic acid were collected in both transmission and fluorescence mode at the Ge K-edge (~11,104 eV) over the energy range 11,000-12,300 eV at undulator-based ID26 beamline [START_REF] Gauthier | The ESRF beamline ID26: X-ray absorption on ultra-dilute samples[END_REF] of the European Synchrotron Radiation Facility (ESRF, Grenoble, France). The storage ring was operated at 6 GeV with a ~200 mA current. The beam energy was selected using a Si (220) double-crystal monochromator. The beam size on the sample was focused to about 600 µm horizontal x 1000 µm vertical, thus keeping a high X-ray photon flux (~10 13 photons/s). PIN silicon diodes were employed for measuring the intensities of incident (I0) and transmitted (I1) X-ray beam. Fluorescence spectra were collected using either a Silicon photo-diode or a 13element Canberra detector (depending on Ge concentration).

Experimental solutions were placed in a high-pressure cell developed at the Laboratoire de Cristallographie (Grenoble). The present cell construction is based on previous designs operating in transmission mode [START_REF] Tamura | XAFS measurements at high temperatures and pressures[END_REF][START_REF] Soldo | Semiconductor-to-metal transition in fluid selenium at high pressure and temperature: An investigation using X-ray absorption spectroscopy[END_REF]Pokrovski et al., 2002a) and will be described in detail elsewhere (Testemale et al., submitted). Briefly, the apparatus consists of a poly-crystalline sapphire optical cell (Fig. 1a) which is inserted in a super-hightension steel vessel (Fig. 1b). The vessel has a water-cooling jacket and three Be windows for Xray passage. The cell contains a vertically oriented outer sapphire tube (internal diameter (I. D.) ~ 5 mm) with walls of ~0.2 mm in thickness and two sapphire coaxial inner rods (I. D. ~ 4.7 mm) that delimit the sample space below and above. The sample solution is placed in the gap between the two inner rods. The cell was loaded with the experimental solution under primary vacuum (~10 -3 bar) to avoid eventual air bubbles which may create fluid inhomogeneities in the sample space. The volume of the sample space is about 0.2 cm 3 . The cell has a stainless-steel flexible bellows attached to the lower end of the outer tube via a Viton seal. The bellows transmits the pressure into the tube and serves as a solution reservoir (~0.6 cm 3 ). The reservoir and the sample space are connected through a gap between the inner rod and the outer tube. The temperature in the sample space is maintained within ±0.2°C by Mo heating resistances and Pt-Pt/Rh thermocouples connected to a Eurotherm  temperature regulator. Temperature gradients through the sample space do not exceed 5°C at 500°C. The sample reservoir situated in the lower part far outside the heating zone (see Fig. 1a) always remains cool (<50°C when sample-space temperature is 500°C). Its position, below the sample chamber, prevents convection and therefore minimizes fluid circulation within the assembly, avoiding corrosion of the steel bellows and Viton seal by the hot fluid. The autoclave is pressurized by high-purity grade helium gas with low absorption constant for X-rays. Pressure in the sample space is always balanced with that of He gas through the bellows. Thus the sample thickness is kept constant at high T and P, and thin sapphire walls are never broken by stress. The present design permits operating up to 600°C and 1000 bar.

Two kinds of experiments were performed. The first one consisted of measuring XAFS transmission and fluorescence spectra of a germanic acid aqueous solution with an initial concentration of 0.04 m at 400 bar from 20 to 450°C in the absence of solid phase (Experiment 1). Up to 10 scans (of ~40 min/scan data collection time) were collected and then averaged together at each temperature point. The second type of experiment was started with pure water and argutite crystals placed at the bottom of the sample space out of the X-ray beam passage (Experiment 2). The initial solid-to-solution mass ratio was about 1:6. Dissolution was studied at 400 bar from 200°C to 500°C by monitoring the Ge absorption-edge height as a function of time in transmission mode. Fluorescence spectra were also recorded, but because of lower Ge concentrations (~ 0.02 m on average) and limited beam time, they were found to be more noisy than those of the 0.04 m Ge solution (Experiment 1). As a result, quantitative EXAFS treatment was performed on both fluorescence and transmission spectra obtained in Experiment 1, whereas transmission spectra from Experiment 2 were used for measuring GeO 2 solubility. Germanic acid aqueous solutions (0.02 -0.09 m Ge) of slightly acid to basic pH were also recorded in both fluorescence and transmission modes at ambient temperature and pressure using fused-silica capillaries (I.D. = 3 mm, wall thickness = 0.01 mm). Germanium dioxide polymorphs of well-known crystallographic structure (quartz-like and rutile-like GeO 2 ; [START_REF] Jorgensen | Compression mechanism in α-quartz structure: SiO 2 and GeO 2[END_REF][START_REF] Baur | Rutile-type compounds. IV. SiO 2 , GeO 2 and a comparison with other rutile-type structures[END_REF] which can serve as model compounds for Ge local environment, were diluted with boron nitride, carefully homogenized by grinding and shaking, pressed in pellets, and recorded similarly to the aqueous samples at ambient conditions.

Determination of solute concentration from the absorption edge height

The X-ray path length through the fluid is fixed by the geometry of the sapphire tube. As temperature increases at constant pressure, the fluid from the sample space expands into the flexible reservoir enabling changes of the fluid density. It stems from the Beer-Lambert classical X-ray absorption relation that the absorption jump over the Ge edge in such isobaric cell configuration is directly related to the amount of the absorbing species (Ge) in the fluid. Because the solvent contribution to absorption does not vary significantly over the Ge K-edge, the amplitude of the absorption edge height at given T and P (∆µ) can be written as ∆µ = ∆σ Ge l M Ge m Ge d fluid (1) where ∆σ Ge is the change of the total absorption cross-section of Ge over its K-edge (cm 2 g -1 ), l is the optical path length inside the cell (cm), M Ge is the atomic weight of germanium (0.07259 kg mol -1 ), m Ge is the molal Ge aqueous concentration (mol kg -1 of solution), and d fluid is the density of the aqueous solution (g cm -3 ) at given T and P. The absorption cross-sections for Ge were taken from the recent compilation of [START_REF] Chantler | X-Ray Form Factor, Attenuation and Scattering Tables (version 2.0)[END_REF]. These values are in close agreement, within 2-5% below and above Ge K-edge, with older databases (e.g., [START_REF] Henke | X-ray interactions: photoabsorption, scattering, transmission and reflection at E = 50-30,000 eV, Z = 1-92[END_REF][START_REF] Saloman | X-ray attenuation cross sections for energies 100 eV to 100 keV and elements Z=1 to Z=92[END_REF]. The fluid density at experimental temperature and pressure was calculated using the Pressure-Volume-Temperature (PVT) properties of pure water [START_REF] Kestin | Thermophysical properties of fluid H 2 O[END_REF] and assuming that the low concentrations of dissolved Ge and Al (m Ge < 0.04, m Al < 0.0001) do not significantly modify these properties. This assumption is supported by recent high-temperature in situ density measurements on aqueous solutions of germanic acid analogs, arsenious and arsenic acids, which show that density differences between a 0.1-m As solution and pure water do not exceed 2% to at least 350°C [START_REF] Perfetti | Mesures expérimentales volumiques et calorimétriques de l'arsenic (III) et (V) en solution à 25-350°C et 0.1-29 MPa. Applications aux systèmes naturels[END_REF]. Owing to the very low thermal expansion coefficient of sapphire, the X-ray path length inside the cell remains constant through the entire experiment. Because of the cylindrical shape of the sapphire tube and relatively large beam size in the horizontal plane (see Section 2.2) which makes difficult to align the beam exactly in the cell's vertical axis, the X-ray path inside the cell was calibrated at 30°C/400 bar prior to experiment using a germanic acid aqueous solution of precisely known concentration (0.0400±0.0005 m). Combining the absorption edge height determined for that sample with the value of ∆σ chosen above, equation (1) yielded 0.48±0.01 cm for the optical path length. This value is identical within errors to the nominal geometric inner diameter of the tube (0.50±0.01 cm), thus further supporting the validity of equation ( 1). Note that such a calibration also eliminates uncertainties associated with the choice of the absorption crosssections over Ge edge, because the measured ∆µ values are proportional to the product of l and ∆σ.

The presence of harmonics in the incident beam and nonlinear response of electronics and I0 and I1 detectors may further contribute to uncertainties associated with equation (1). The contribution of higher order harmonics from the Si( 200) monochromator crystal at the undulator beam line ID26 equipped with two mirrors does not exceed 0.1% of the transmitted intensity in the energy and I0/I1 ranges of our experiments [START_REF] Gauthier | The ESRF beamline ID26: X-ray absorption on ultra-dilute samples[END_REF]. The response of the I0 and I1 PIN silicon detectors is known to be linear within better than 0.1% at ID26 beamline. The overall linearity related to the whole set of electronic instruments and the present experimental setup was also checked at ambient conditions by measuring ∆µ values of germanic acid solutions of different concentration placed in sapphire or fused silica holders with absorption coefficients similar to that of the HT-HP cell. The absorption jump amplitude was found to be linear function of Ge concentrations within ~5% in a wide range at least from 0.01 to 0.09 m.

The height of the absorption-edge step (∆µ) in each EXAFS scan was determined using a standard normalization procedure implemented in the AUTOBK algorithm [START_REF] Newville | Near-edge x-ray-absorption fine structure of Pb: A comparison of theory and experiment[END_REF]. A straight line is regressed to the data in the before-edge region and subtracted from the whole spectrum. Then a quadratic polynomial is regressed to the data in some region above the edge and extrapolated back to E 0 which is the energy corresponding to the maximum of the first edge derivative. The extrapolated value of the post-edge polynomial at E 0 was taken as the absorption edge height. Spectra were processed between -200 and -30 eV before the edge and between 100 and 750 eV after the edge. Notice that using such a procedure effectively avoids the uncertainties associated with variations of ∆σ in the near-edge region (within ~50 eV above the edge, [START_REF] Chantler | Detailed tabulation of atomic form factors, photoelectric absorption and scattering cross section, and mass attenuation coefficients in the vicinity of absorption edges in the soft X-ray (Z=30-36, Z=60-89, E=0.1 keV-10 keV), addressing convergence issues of earlier work[END_REF]. Moreover, an independent background removal procedure, Cromer-Liberman normalization (CLnorm, [START_REF] Cromer | Relativistic calculations of anomalous Scattering Fractors for X-rays[END_REF] implemented in the Athena software [START_REF] Ravel | EXAFS analysis software using IFEFFIT[END_REF], was used to check the validity of ∆µ empirical determinations made by the AUTOBK algorithm. Values of ∆µ found using both CLnorm and AUTOBK approaches were identical within errors, thus confirming the validity of estimates of atomic-like background over Ge K-edge. The uncertainty on ∆µ determination, as estimated by changing fitted energy ranges or by comparing different scans for the same Ge solution concentration, vary from less than 1-2% of the total value for absorption steps greater than 0.2, to about 10-15% for absorption steps lower than 0.02. Considering together the uncertainties of temperature measurement (< ± 5°C; they mostly affect the fluid density calculations), those of X-ray path length, and nonlinearities in electronic instruments, it follows that equation ( 1) provides an absolute measure of aqueous solute concentration or mineral solubility in dilute aqueous solution (of the order of 10's millimol) with a precision better than 10% below ~300°C (where the density variations with temperature are small) and 20 to 30% at higher temperatures, for dissolved elements having Kedge energies similar to Ge at (see also Table 3).

An example of transmission XAFS scans recorded in a solubility experiment (Experiment 2) as a function of temperature at 400 bar is shown in Fig. 2. The decrease of the before-edge absorption (where germanium contribution to the absorption is small in comparison to that of water, less than ~2%) exactly follows the decrease of water density with temperature, whereas the absorption-edge height corresponds to Ge solution concentration according to equation (1).

XAFS data reduction

Data analysis was performed with the Athena and Artemis packages [START_REF] Ravel | EXAFS analysis software using IFEFFIT[END_REF] based on IFEFFIT [START_REF] Newville | IFEFFIT: interactive XAFS analysis and FEFF fitting[END_REF] and AUTOBK [START_REF] Newville | Near-edge x-ray-absorption fine structure of Pb: A comparison of theory and experiment[END_REF] programs. Details about spectra reduction can be found in elsewhere [START_REF] Pokrovski | Iron(III)-silica interactions in aqueous solution: Insights from X-ray absorption fine structure spectroscopy[END_REF][START_REF] Pokrovsky | Gallium(III) adsorption on carbonates and oxides: Xray absorption fine structure spectroscopy and surface complexation modelling[END_REF].

Spectra were normalized to the absorption edge height (see Section 2.3 above), backgroundremoved using the AUTOBK algorithm, weighted by k n , where 1≤n≤3, filtered over the k range from ~1.6 to 10-17 Å -1 (depending on signal-to-noise ratio), and Fourier-transformed (FT) using Kaiser-Bessel window with dk values of 3.0, to produce radial structure functions (RSF). To obtain structural information, fits were performed in the R-space on both real and imaginary parts of one or several FT contributions [START_REF] Newville | IFEFFIT: interactive XAFS analysis and FEFF fitting[END_REF]. This gives the identity of the backscattering atoms, Ge-neighbor distance (R) and coordination number (N), and the Debye-Waller factor (σ 2 ) for a given scattering path. In addition to these structural parameters, a nonstructural parameter, ∆E, was varied in initial fits to account for its estimate made by FEFF.

To diminish correlations between N and σ 2 , and better account for light versus heavy neighbors and multiple scattering paths (see below), fits were performed simultaneously with k-weighting of 1, 2 and 3, and the obtained values of structural parameters were averaged. Raw EXAFS spectra were also fitted in k-space with multiple shells; they produced values of structural parameters similar to those extracted from fits of filtered signals in R-space. Theoretical backscattering amplitude and phase-shift functions for Ge-O, Ge-H, and Ge-Ge single and multiple scattering paths were computed using the FEFF 8 ab initio code [START_REF] Ankudinov | Real-space multiple-scattering calculation and interpretation of x-ray-absorption near-edge structure[END_REF], using Ge(OH) 4 -(H 2 O) n model clusters. The amplitude reduction factor (S o 2 ) used in modeling of experimental samples was fixed at 0.88±0.08 as found by fitting EXAFS spectra of germanium oxides. The influence of anharmonic disorder in determining structural parameters was checked using the cumulant expansion method (e.g., [START_REF] Crozier | Amorphous and liquid systems[END_REF]. The values of third-and fourth-order cumulants (c 3 and c 4 ) found when fitting the filtered signal for the Ge 1 st coordination shell, always converged to zero within error, and, consequently, did not affect R and N values derived from fits without cumulants. The influence of possible multiple scattering (MS) events within the Ge first coordination shell was also tested using the FEFF code, assuming local T d or O h geometries around Ge, as found in the model compounds investigated.

Results

Local structure of germanium in aqueous solution

XANES spectra of the 0.04 m solution at 20 to 450°C at 400 bar and of 0.02 -0.09 m solutions at 20°C and 1 bar (not shown) exhibit very similar edge-crest energies (11,111.0±0.5 eV) and spectral shapes. The magnitude of the white line of normalized spectra for all solutions with m Ge ≤ 0.04 m recorded in both transmission and fluorescence modes were the same, suggesting the absence of self-absorption in fluorescence mode. For the most concentrated solution (0.086 m Ge), however, minor self-absorption effects were detected in the fluorescence spectrum whose white-line magnitude was lower by about 20% in comparison to the corresponding transmission spectrum. This effect was, however, found to have no influence on EXAFS structural parameters. The shape and energy position of the spectra for all aqueous samples are similar to those of quartz-like GeO 2 , thus suggesting a similar tetrahedral geometry around Ge(IV) in solution.

Normalized averaged k 2 -weighted EXAFS fluorescence spectra and their Fourier Transforms of the studied 0.04-m germanic acid aqueous solutions as a function of temperature at 400 bar in Experiment 1 are presented in Fig. 3. They are pretty similar to those for 0.02 -0.09 m solutions recorded at ambient conditions (not shown). Both low-and high-temperature spectra exhibit a 1 st shell contribution from 4±0.3 oxygens at 1.75-1.76 Å (Tables 1 and2). This is similar to the Ge-O distances and coordination numbers reported for the GeO 2 polymorph having a quartz-like structure and for numerous germanates [START_REF] Jorgensen | Compression mechanism in α-quartz structure: SiO 2 and GeO 2[END_REF]. This strongly suggests a similar tetrahedral environment for aquated Ge in solution in a wide pH (4 -12), concentration (0.02 -0.09 m) and temperature (20 -450°C) range, and is consistent with the formation of Ge(IV) hydroxide complexes (note that EXAFS is not capable of seeing hydrogen atoms in most cases). At basic pH, Ge-O distance and DW factor increase significantly in comparison with those for the slightly acid solutions (Table 1), suggesting a distortion of the GeO 4 tetrahedron. This is in excellent agreement with previous solubility, potentiometric and Raman spectroscopy studies which show that Ge aqueous speciation is dominated by the neutral Ge(OH) 4 complex at pH<9 and by the negative GeO(OH) 3 -species at higher pH [START_REF] Baes | The Hydrolysis of Cations[END_REF]Pokrovski & Schott, 1998a).

A weak 2 nd contribution apparent on the RSF spectra at ~2.3 Å (not corrected for phase shift, Fig. 3) is likely to arise from multiple scattering events within the regular GeO 4 tetrahedron. This was confirmed by FEFF simulations carried out on GeO 4 (±H 4 )±(H 2 O) n clusters. In these calculations, we adopted the S 4 symmetry for Ge(OH) 4 by analogy with silicic acid whose optimized geometry was modeled in many quantum chemical studies (e.g., [START_REF] Sefcik | Thermochemistry of silicic acid deprotonation: Comparison of gasphase and solvated DFT calculations to experiment[END_REF]; references therein). It was found that MS paths within the [GeO 4 ] cluster such as a triangular path Ge-O1-O2, an angular path Ge-O1-Ge-O2, and a linear path Ge-O1-Ge-O1 may contribute to the EXAFS signal. Their DW factors were estimated using the equation-of-motion (EM) and recursion method (RM) models incorporated in the FEFF 8 code [START_REF] Poiarkova | X-ray absorption fine structure Debye-Waller factors[END_REF][START_REF] Poiarkova | Multiple-scattering x-ray-absorption fine-structure Debye-Waller factor calculations[END_REF]. Both models yield close DW values for all MS paths of 0.005±0.002 Å 2 at 20°C which increase slightly with temperature (e.g., ~0.008 Å 2 at 450°C). It can be seen in Fig. 4 that the inclusion of these MS paths in the fit reasonably accounts for the 2 nd shell contribution observed in Ge aqueous solutions in a wide temperature range. Possible contributions of hydrogen atoms from OH-groups or oxygens from water molecules of outer hydration shells were also tested using both qualitative wavelet analyses [START_REF] Munoz | Continuous Cauchy wavelet transform analyses of EXAFS spectra: A qualitative approach[END_REF] of our EXAFS spectra (not shown), and quantitative FEFF simulations. Both approaches demonstrated that neither hydrogens nor water molecules can account for the observed nextnearest shell signal.

Solubility of argutite in high-temperature solution and thermodynamic properties of Ge(OH) 4 (aq)

All XAFS scans for a Ge aqueous solution of 0.040-m initial concentration recorded in the X-ray cell at 400 bar from 30 to 450°C show similar absorption-edge heights at each given temperature. Germanium molal concentrations calculated from these data using equation ( 1) are reported in Table 3. These concentrations (~0.040±0.005 m) are identical within errors to the initial concentration at all temperatures, thus demonstrating that neither oxide precipitation nor reaction with the sapphire cell walls occurred during the experiment. The absence of Ge-oxide precipitation in the sample space at high temperature and in the colder parts of the cell from solutions supersaturated with respect to argutite (see Table 3), is consistent with the extremely slow nucleation kinetics for this mineral observed in previous work (Pokrovski & Schott, 1998a).

Moreover, the good match between experimental and nominal Ge concentration within less than 10% over a wide temperature-density range implies that the uncertainties associated with the choice of the absorption cross section, estimation of atomic-like background and fluid densities are correctly accounted for at high temperature. This provides a further support for the use of a classical absorption relation (equation 1) for absolute determination of solute concentrations at extreme conditions.

The evolution of transmission XAFS spectra and Ge absorption edge height with temperature and time for consecutive scans during the argutite dissolution experiment 2 is shown in Fig. 2 and 5, respectively. It can be seen that steady state values for the absorption-edge height at 300, 350, 400, 450 and 500°C are attained within an hour after each temperature rise.

Germanium steady-state concentrations derived from the edge height values using Eqn (1) are reported in Table 3 and compared with other available data in Fig. 6. Our concentrations are in excellent agreement with those previously obtained below 350°C using batch-reactor experiments with solid:solution ratios ranging from 1:3 to 1:300 and run durations from a few days to several months (Pokrovski & Schott, 1998a). Moreover, similar Ge concentrations are obtained at 400°C both on heating and cooling (see Fig. 5) demonstrating the reversibility of the dissolution reaction. These findings strongly suggest that the solid-solution equilibrium was attained in our XAS experiment at ≥ 300°C. Based on the results of our XAFS analysis and previous solubility and potentiometric work (Pokrovski & Schott, 1998a;references therein) which demonstrate the formation of Ge(OH) 4 °(aq) at acid to neutral pH, the following reaction was adopted to describe the solubility of GeO 2 in water in a wide range of temperature and pressure:

GeO 2 (tetr

) + 2 H 2 O = Ge(OH) 4 °(aq) (2)
The equilibrium constants K(2) of reaction (2), were generated from the available data on argutite solubility obtained in the present work from 300 to 500°C at 400 bar, and in previous studies at temperatures from 25 to 350°C and pressures from P sat to 1 kbar (see Fig. 6). These data show that GeO 2 solubility increases with increasing temperature up to 400°C in agreement with the previous HKF model predictions based on data obtained up to 350°C (see Pokrovski & Schott, 1998a), but decreases above 400°C, which is not predicted by the existing model. It should be emphasized that the solvation Born coefficient, ω, which accounts for the contribution of solute-solvent electrostatic interactions to the Gibbs free energy of an aqueous species in the HKF model, could not be reliably estimated in that study owing to the minor changes in this term in dense aqueous fluids below 300-350°C. In contrast, this term which is dependent on the solvent dielectric constant, becomes very sensitive to the evolution of solubility patterns and heat capacity and volume values of aqueous species in low-density solution near and above the critical point (e.g., [START_REF] Plyasunov | Correlation strategy for determining the parameters of the revised Helgeson-Kirkham-Flowers model for aqueous nonelectrolytes[END_REF]. Consequently, the solubility decrease at 450 and 500°C and 400 bar measured in our study is likely due to the significant drop of both water dielectric constant and density at such conditions. These new solubility data allow a far better constraining of the HKF equation-of-state parameters for aquated Ge in supercritical fluids. The values of the heat-capacity coefficients, c 1 and c 2 , and the Born parameter, ω, were refined by regression of all available log K(2) values using UT-HEL computer code (Shvarov, 1993) consistent with the revised HKF equation of state [START_REF] Tanger | Calculation of the thermodynamic and transport properties of aqueous species at high pressures and temperatures: Revised equations of state for the standard partial molal properties of ions and electrolytes[END_REF]. Details about this procedure can be found in Pokrovski & Schott (1998a). In this regression, the basic thermodynamic properties (∆ f G°2 98 , S°2 98 , V°2 98 ) and other HKF coefficients for Ge(OH) 4 (aq)

were taken from Pokrovski & Schott (1998a) and kept constant because their variation was found to have negligible effect on the log K(2) values above 350°C. The refined HKF coefficients of Ge(OH) 4 (aq) are reported in Table 4, and the values of log K(2) calculated using these data are shown by the dashed line in Fig. 6. The Born parameter found in our study for Ge(OH) 4 °(aq) (ωx10 5 = 0.09 cal/mol) is close to those of chemically similar neutral hydroxide species like Si(OH) 4 (0.13, [START_REF] Walther | Calculation of the thermodynamic properties of aqueous silica and the solubility of quartz and its polymorphs at high pressures and temperatures[END_REF], As(OH) 3 (0.07, [START_REF] Perfetti | Mesures expérimentales volumiques et calorimétriques de l'arsenic (III) et (V) en solution à 25-350°C et 0.1-29 MPa. Applications aux systèmes naturels[END_REF], B(OH) 3 (0.06, [START_REF] Plyasunov | Correlation strategy for determining the parameters of the revised Helgeson-Kirkham-Flowers model for aqueous nonelectrolytes[END_REF], Sb(OH) 3 (0.05, Zotov et al., 2003) retrieved from either direct heat capacity and volume measurements or solubility data over wide temperature-pressure ranges. A positive value of ω accounts for the drop of solubility observed for argutite and quartz and the similar shape of the heat capacity patterns of neutral hydroxide species in low-density near-critical fluids (e.g., see Fig. 7).

An alternative approach to the HKF equation of state for predicting mineral solubilities and thermodynamic properties of solutes is the density model [START_REF] Mesmer | Thermodynamics of aqueous association and ionization reactions at high temperatures and pressures[END_REF][START_REF] Anderson | The density model for estimation of thermodynamic parameters of reactions at high temperature and pressure[END_REF][START_REF] Manning | The solubility of quartz in H 2 O in the lower crust and upper mantle[END_REF] which treats the solvation contribution in terms of fluid density instead of dielectric constant. In this study, we attempted to describe GeO 2 solubility as a function of temperature using a simplest three-parameter equation [START_REF] Mesmer | Thermodynamics of aqueous association and ionization reactions at high temperatures and pressures[END_REF]:

log K = A + B / T + E . (log 10 d H2O ) (3)
where A, B, and E are constants independent of temperature and pressure, T is temperature in Kelvin, and d H2O is the water density (in g cm -3 ). It can be seen in Fig. 6 (solid line) that such a simple equation fits satisfactorily the whole set of experimental data from 20 to 500°C. Although regressions involving additional terms like [C/T 2 ], [D/T 3 ] and/or [F (log d H2O )/T], which where used to describe the water dissociation reaction [START_REF] Mesmer | Thermodynamics of aqueous association and ionization reactions at high temperatures and pressures[END_REF] and quartz solubility [START_REF] Manning | The solubility of quartz in H 2 O in the lower crust and upper mantle[END_REF] in a much wider T-P range (to 900°C and 10 kbar), yielded visually better fits, these models were less stable and exhibit both large uncertainties and strong correlations on the regression parameters, and thus judged statistically inadequate. Consequently, taking into account the relatively limited T and P range of our data, we decided to use equation (3) when deriving thermodynamic functions for reaction (2). The regression parameters A, B, and E together with their corresponding uncertainties are reported in Table 4. Differentiation of equation ( 3) over temperature at constant pressure yields enthalpy, entropy and isobaric heat capacity values for reaction (2) (see [START_REF] Mesmer | Thermodynamics of aqueous association and ionization reactions at high temperatures and pressures[END_REF][START_REF] Anderson | The density model for estimation of thermodynamic parameters of reactions at high temperature and pressure[END_REF] for details). The thermodynamic properties of aqueous Ge(OH) 4 ° were then calculated using these functions and the corresponding values for GeO 2 (tetr) and H 2 O taken from Pokrovski & Schott (1998a) and [START_REF] Kestin | Thermophysical properties of fluid H 2 O[END_REF], respectively.

It can be seen in Table 4 that the thermodynamic properties of Ge(OH) 4 (aq) generated in this study using both density and HKF models are similar within errors. Both equations of state account properly for the argutite solubility maximum measured in this study at 400°C (Fig. 6)

and have very similar shapes outside the experimental range, exhibiting a weak solubility minimum at ~480°C (Figs. 6 & 7) and ~570°C (not shown) for the density and HKF models, respectively. The argutite solubility pattern is very similar to that documented for quartz on the basis of extensive solubility measurements (e.g., [START_REF] Walther | Calculation of the thermodynamic properties of aqueous silica and the solubility of quartz and its polymorphs at high pressures and temperatures[END_REF]Manning, 1994 and references therein). At low pressures (< 500 bar), quartz solubility shows a similar well pronounced maximum near 400°C, and a weaker minimum at ~500°C. These features disappear at pressures above 1000 bar. The solubility shape predicted by the HKF and density models for both quartz and GeO 2 can be easily explained by the relative changes in solvation versus nonsolvation contributions to the aqueous species free energy as a function of dielectric constant or water density. In dense aqueous solution below 350°C (d H2O >0.5-0.6 g cm -3 ), the solvation term E . (log 10 d H2O ) of equation ( 3), accounting mostly for the interactions between Ge(OH) 4 and water molecules, is almost constant whereas the nonsolvation term B/T, accounting for the properties of the species itself, changes significantly with temperature owing to the increasing thermal motion. At temperatures and pressures near the critical point of water, the solvation term exhibits strong changes because of the dramatic drop of the fluid density at these conditions (Fig. 8). This explains the observed solubility decrease for most solutes near the critical point. Far above the critical point (> 450°C) at low pressures (<500 bar), the fluid density becomes very weak (<0.1 g cm -3 ), and its evolution with temperature again very slow. As a result, the increasing thermal motion of species destabilizes the weak hydration shell and thus prevails over the solvation contribution. This explains the weak minimum of the solubility around 500°C at low pressures. At higher pressures (>600-800 bar), however, the solvation term evolves more gradually thus following the slower changes of the density as a function of temperature (Fig. 8).

This renders the solubility curve smoother, without pronounced inflections (see Fig. 7). A similar reasoning can be used in the case of the HKF equation, because the dielectric constant of water, which is involved in the solvation terms of the model, exhibits a similar T-P pattern as the density (Fig. 8; [START_REF] Tanger | Calculation of the thermodynamic and transport properties of aqueous species at high pressures and temperatures: Revised equations of state for the standard partial molal properties of ions and electrolytes[END_REF].

Argutite solubilities predicted by both models at, for example, 700°C differ by less than 0.4 log unit at 400 bar, and ~0.25 log unit at 1000 bar, thus demonstrating the remarkable agreement of estimations at such extreme conditions made by the simplest density equation (3) involving only three adjustable parameters and by more complex HKF model which was usually considered inappropriate at densities lower than 0.3 g cm -3 in the absence of experimental data (e.g., [START_REF] Shock | Calculation of the thermodynamic properties of aqueous species at high pressures and temperatures: effective ionic radii, dissociation constants, and standard partial molal properties to 1000°C and 5 kbar[END_REF][START_REF] O'connell | Infinite dilution partial molar volumes of aqueous solutes over wide ranges of conditions[END_REF][START_REF] Schulte | The temperature dependence of the standard-state thermodynamic properties of aqueous nonelectrolytes[END_REF]. The thermodynamic parameters derived in this study allow more rigorous prediction of GeO 2 solubility and Ge(OH) 4 stability beyond the T-P range covered by experiments.

Discussion

Evolution of the local Ge(IV) structure in high-temperature crustal fluids

The EXAFS and XANES spectra of Ge(IV) aqueous solutions do not show conspicuous modifications in a wide range of temperature (20-500°C) and concentration (0.01-0.09 m), suggesting that the Ge(OH) 4 structure is likely to be similar in both high-density aqueous solution and low-density supercritical fluid (0.2 g cm -3 ≤ density ≤ 1.0 g cm -3 , see Tables 2 and3). The tetrahedral geometry of the Ge(OH) 4 molecule shows no detectable changes, at least in the studied temperature and density range, as demonstrated by the low DW factor (~0.0015 Å 2 ) and the persistence with increasing temperature of the small MS contributions arising from the GeO 4 cluster. Similar but less symmetrical and more polar hydroxide complexes, such as As(OH) 3 °(aq) having a pyramidal-like geometry, also show small changes of static and thermal disorder, but may in addition exhibit an increase of the O-As-O angle with increasing temperature [START_REF] Testemale | Structural and electronic evolution of the As(OH) 3 molecule in high temperature aqueous solutions: An x-ray absorption investigation[END_REF]. The Ge-O distances change only very little with increasing temperature (in the limit of 0.01 Å from 20 to 450°C). This behavior is similar to that of other strongly-bound (OH)/O aqueous complexes like arsenite (As(OH) 3 °, Pokrovski et al., 2002a;[START_REF] Testemale | Structural and electronic evolution of the As(OH) 3 molecule in high temperature aqueous solutions: An x-ray absorption investigation[END_REF] [START_REF] Hoffmann | An infrared and X-ray absorption study of the structure and equilibrium of chromate, bichromate, and dichromate in high-temperature aqueous solutions[END_REF] which also show only minor changes in the metal-oxygen distances (within 0.01 Å) and DW factors in a wide temperature range. Hydrated mono-and divalent and some large trivalent cations (e.g., Rb + , Ag + , Sr 2+ , Yb 3+ , [START_REF] Fulton | Rubidium ion hydration in ambient and supercritical water[END_REF][START_REF] Seward | An X-ray absorption (EXAFS) spectroscopic study of aquated Ag in hydrothermal solutions to 350°C[END_REF][START_REF] Poiarkova | X-ray absorption fine structure Debye-Waller factors[END_REF][START_REF] Mayanovic | The structure of Yb 3+ aquo ion and chloro complexes in aqueous solutions at up to 500°C and 270 MPa[END_REF] [START_REF] Mayanovic | Hydrogen bond breaking in aqueous solutions near the critical point[END_REF][START_REF] Simonet | X-ray absorption spectroscopy of ionic association in aqueous solutions of zinc bromide from normal to critical conditions[END_REF] demonstrate, in contrast, partial loss of the 1 st water hydration shell and significant shortening of the hydration shell radius and metal-ligand bond length with increasing temperature, typically about 0.05-0.10 Å in the range 25-300°C. These changes are in agreement with the temperature evolution of solvent hydrogen bonding, and solvent-solute interactions including such factors as dielectric saturation and solvent compressibility (e.g., [START_REF] Shock | Calculation of the thermodynamic properties of aqueous species at high pressures and temperatures: effective ionic radii, dissociation constants, and standard partial molal properties to 1000°C and 5 kbar[END_REF][START_REF] Oelkers | An EXAFS spectroscopic study of aqueous antimony(III)-chloride complexation at temperatures from 25 to 250[END_REF]. More covalent metal complexes (e.g., Cu I Cl/Br, [START_REF] Fulton | An X-ray absorption fine structure study of copper(I) chloride coordination structure in water to 325°C[END_REF]; [START_REF] Sherman | Speciation of tin (Sn 2+ and Sn 4+ ) in aqueous Cl solutions from 25 to 350°C: an in situ EXAFS study[END_REF], and some +2 and +3 cations (e.g., Ni 2+ , Hoffmann et al., 1999; In 3+ , Seward et al., 2000; Y 3+ , Ragnarsdottir et al., 1998) exhibit only minor changes of metal-chloride and metal-oxygen distances with increasing temperature. This may be explained by the covalent character of such complexes and the strong electrostriction of the hydration shell around a small strongly charged cation [START_REF] Seward | Indium(III) chloride complexing and solvation in hydrothermal solutions to 350°C: an EXAFS study[END_REF]. Thus, the constancy of the Ge-O bond length and low DW factor over the wide temperature and density range implies that due to a strong covalent character of the Ge-oxygen bonds [START_REF] Pauling | The Nature of the Chemical Bond[END_REF], the increasing thermal vibration with temperature has no significant effect on the inter-atomic distances and the structure of the Ge first atomic shell.

Sn II Cl 3 - , Sn II Cl 4 2- ,
It should be noticed, however, that minor modifications in the symmetry, orientation or angles of Ge-O-H bonds might be induced by outer-sphere water molecules linked to the Ge(OH) 4 complex via hydrogen bonds. For example, molecular dynamics calculations of solvated orthosilicic acid [START_REF] Rustad | A molecular dymanics study of solvated orthosilicic acid and orthosilicate anion using parameterized potentials[END_REF] indicate a diffuse hydration shell of O at ~4 Å around Si consisting of 9 to 18 water molecules. By analogy, a similar hydration shell may be expected to exist around aqueous germanium in solution. However, its detection by XAFS spectroscopy, which is very sensitive to disorder, is likely to be difficult. Despite this limitation of XAFS spectroscopy, it can be inferred from this study that changes in the structure of Ge(OH) 4 solvation environment with temperature are responsible for the observed germanium oxide solubility pattern which is largely controlled by the evolution of water density (or dielectric constant) at near-and supercritical temperatures. More studies that combine quantum chemical approaches and different spectroscopic methods would be necessary to quantitatively relate the solvation structures of solutes with the observed evolution of their solubilities as function of macroscopic parameters (density, dielectric constant, temperature).

Comparison with silica

The new structural and thermodynamic data obtained for the dominant Ge(OH) 4 species allow quantitative comparisons of the behavior of aqueous Ge and Si in high-temperature natural waters. It should be noticed that the exact structure of silicic acid in high T-P fluids is not yet firmly established. Available quartz solubility experiments in the H 2 O-Ar/CO 2 systems in which water activity was varied by adding inert Ar or CO 2 [START_REF] Walther | The dielectric constant approach to speciation and ion pairing at high temperature and pressure[END_REF]refs therein) indicate that aqueous SiO 2 is solvated by about 2 water molecules. Raman spectroscopy measurements on silicic acid at high T-P demonstrate Si-OH vibrations (Zotov & Keppler, 2002) which likely imply a Si(OH) 4 stoichiometry. These data are corroborated by quantum chemical calculations on silicic acid in gaseous and aqueous phase at ambient conditions [START_REF] Rustad | A molecular dymanics study of solvated orthosilicic acid and orthosilicate anion using parameterized potentials[END_REF][START_REF] Sefcik | Thermochemistry of silicic acid deprotonation: Comparison of gasphase and solvated DFT calculations to experiment[END_REF]. Our study on the chemically similar Ge(OH) 4 provides an additional support to these data, suggesting that silica is likely to form a similar tetra-hydroxide complex over wide temperature and pressure ranges. The similarity of Si-and Ge(IV)-water interaction energetics with increasing temperature is further supported by comparing the solubilities of quartz and argutite and partial molal isobaric heat capacities of silicic and germanic acids (Fig. 7). The solubility curves plotted in Fig. 7a were calculated using equation

(3) generated in this study (Table 4) for GeO 2 and the density equation of [START_REF] Manning | The solubility of quartz in H 2 O in the lower crust and upper mantle[END_REF] for SiO 2 . The uncertainties for quartz solubility predictions to 600°C and 1000 bar with Manning's equation do not exceed 0.05 log units; those for argutite are expected to be within 0.3 log units (see Section 4.1). It can be seen in Fig. 7a that both minerals exhibit similar solubility patterns in water. The evolution of Si(OH) 4 and Ge(OH) 4 heat capacities obtained respectively by differentiation of Manning's relationship and equation (3) from this study is also very close (Fig. 7b). Their magnitude and evolution with temperature are typical of electrolytes (e.g., [START_REF] Sedlbauer | A new equation of state for correlation and prediction of standard molal thermodynamic properties of aqueous species at high temperatures and pressures[END_REF]refs therein) and hydroxide aqueous complexes of metalloids like B(OH) 3 [START_REF] Hnedkovsky | Volumes and heat capacities of H 3 BO 3 (aq) at temperatures from 298.15 K to 705 K and at pressures to 35 MPa[END_REF], H 3 PO 4 [START_REF] Sharygin | Apparent molar heat capacities of aqueous solutions of phosphoric acid and sulfur dioxide from 303 to 623 K and a pressure of 28 MPa[END_REF], and H 3 As V O 4 and As III (OH) 3 [START_REF] Perfetti | Mesures expérimentales volumiques et calorimétriques de l'arsenic (III) et (V) en solution à 25-350°C et 0.1-29 MPa. Applications aux systèmes naturels[END_REF].

Despite these significant similarities in the structure and thermodynamics of aqueous Ge and Si interactions with high-temperature fluids, the absolute values of germanate and silicate dissolution products and their evolution with temperature may be different. This was demonstrated by Pokrovski & Schott (1998a) who showed, for example, that the Ge/Si ratio in a fluid in equilibrium with a Ge-bearing wollastonite increases with increasing temperature. This may be responsible for the elevated values of the Ge/Si ratio measured in high-temperature fluids emanating from the oceanic ridges (e.g., [START_REF] Arnorsson | Germanium in Icelandic geothermal systems[END_REF][START_REF] Froelich | The geochemistry of inorganic germanium in natural waters[END_REF]. The results of the present study support this hypothesis since they confirm the thermodynamic values of aqueous germanic acid derived in previous studies. It should be noticed however that more data on the thermodynamic properties of germanates, analogs of natural silicates, are required to model rigorously the Ge/Si ratios in high-temperature crustal fluids.

Concluding remarks

Solubility of argutite (GeO 2 , tetr) and local atomic structure around Ge in aqueous solution were obtained to 500°C by in situ XAFS spectroscopy in a single series of measurements using a new X-ray optical cell. The structural parameters (N Ge-O = 4.0±0.3, R Ge-O = 1.75±0.01 Å, σ 2 = 0.0015±0.0005 Å 2 ) of the dominant aqueous germanium complex, Ge(OH) 4 °(aq), show very little changes in a wide temperature-density range (20-500°C, 1.1-0.2 g cm -3 ). By analogy, it can be surmised that the structure of the chemically similar aqueous silicic acid, Si(OH) 4 °(aq), is likely to remain the same in high-temperature crustal fluids.

The evolution of argutite solubility in water as a function of temperature was found to be very similar to that of quartz, further supporting the structural similarities of Ge and Si main aqueous species. A simple 3-parameter density model was found to account for the measured (awarded to G.S.P.) and a grant from the french program GDR "Transmet". We are grateful to the ESRF scientific committee for providing beam time and access to the synchrotron facility.

We are indebted to Laurent Alvarez and Thomas Neisius for their assistance during XAFS measurements at ID 26 beamline of the ESRF, and to Olivier Geaymond and Jean-Jacques Menthonnex for their help in the X-ray cell installation and running. John Rehr and Bruce Ravel are thanked for their advice on the FEFF and horae software installation and use. Pierre

Pokrovski and Anastassia Borissova are acknowledged for their assistance in manuscript preparation. The constructive comments of the Editor, David Rickard, and two anonymous reviewers significantly improved the article's presentation. Zotov, A.V., Shikina, N.D., Akinfiev, N.N., 2003. Thermodynamic properties of the Sb(III) hydroxide complex Sb(OH) 3 (aq) at hydrothermal conditions. Geochim. Cosmochim. Acta 67, 1821-1836. Zotov, N., Keppler, H., 2002. Silica speciation in aqueous fluids at high pressures and temperatures. Chem. Geol. 184, 71-82. Each spectrum corresponds to the last scan recorded at the given temperature in the solubility experiment (see also Fig. 5). The decrease of the before-edge absorption with increasing temperature exactly follows the corresponding decrease of water density, whereas the absorption-edge height is a measure of Ge concentration in solution. 4.

Figure Captions

Fig. 7

Comparison of the solubilities of quartz (dashed line) and argutite (solid line) in pure water (A), and the partial molal heat capacities of germanic and silicic acids (B) as a function of temperature at indicated pressures. The curves for Ge and Si were generated using respectively, equation (3) with the parameters from Table 4, and the density equation reported by [START_REF] Manning | The solubility of quartz in H 2 O in the lower crust and upper mantle[END_REF].

Fig. 8 Water density (A) and dielectric constant (B) as a function of temperature at indicated pressures calculated according to [START_REF] Kestin | Thermophysical properties of fluid H 2 O[END_REF]. The dramatic changes in the density and dielectric constant patterns between 400 and 500°C at low pressure account for the particular solubility shapes observed for quartz and argutite (see text). Concentrations are expressed in mol/kg of solution (m); R = germanium-oxygen mean distance, N = Ge-O coordination number, σ 2 = squared Debye-Waller factor (DW, relative to σ 2 = 0 adopted in the calculation of reference amplitude and phase functions by FEFF8); ∆E = nonstructural parameter accounting for phase shift between experimental spectrum and FEFF calculation; R-factor defines goodness of the total fit in R-space as described in FEFFIT [START_REF] Newville | IFEFFIT: interactive XAFS analysis and FEFF fitting[END_REF]. For all samples the fitted R-range was 1.1-3.0 Å (not corrected for phase shift). The following multiple scattering paths within the GeO 4 tetrahedron as calculated using FEFF8 (see text) were included in all fits: triangular Ge-O1-O2 (R ms =3.19 Å, degeneracy=12); angular Ge-O1-Ge-O2 (R ms =3.51 Å, degeneracy=12); and linear Ge-O1-Ge-O1 (R ms =3.51 Å, degeneracy=4). a The X-ray beam optical path inside the cell was calibrated to 0.48±0.01 cm using Eqn (1), Ge initial concentration of 0.0400±0.0005mol, density of pure water at 30°C, 400 bar, and change of germanium total absorption cross-section over Ge K-edge of 174.9 cm 2 g -1 [START_REF] Chantler | X-Ray Form Factor, Attenuation and Scattering Tables (version 2.0)[END_REF]. Uncertainties on the values of m Ge and log K(2) stem mostly from those associated with the determination of the absorption edge height, X-ray path length, and water density (corresponding to a temperature variation of ±5°C in the sample chamber, see text). b not measured. a Gibbs free energies and enthalpies of minerals and aqueous species are represented as apparent standard molal Gibbs free energies (∆G°P ,T )

and enthalpies (∆H°P ,T ) of formation from the elements at the subscripted pressure (P) and temperature (T) [START_REF] Tanger | Calculation of the thermodynamic and transport properties of aqueous species at high pressures and temperatures: Revised equations of state for the standard partial molal properties of ions and electrolytes[END_REF]. The reference states for the elements (for which ∆G°1 bar,298K (∆H°1 bar,298K ) = 0) in the system Ge-O-H are elemental germanium, Ge, O 2 , ideal gas, and H 2 , ideal gas. The standard states for the solid phases and H 2 O are unit activity for the pure phase at all temperatures and pressures. For aqueous species, the reference state convention corresponds to unit activity coefficient for a hypothetical one molal solution whose behavior is ideal. Aqueous species concentrations are expressed in molal units (mol/kg H 2 O). Activity coefficients of neutral aqueous species were assumed to be unity. b Pokrovski & Schott (1998a).

Table 4

-

  GeO 2 solubilities in the 20-500°C temperature range. The argutite solubility predictions beyond the experimental T-P range using the density model are in reasonable agreement with those made by the HKF equation of state refined on the basis of the new data obtained in this study. GeO 2 solubility pattern predicted using both models reflects changes in the solvation term (solutesolvent interactions) which closely follows the evolution of the fluid density and dielectric constant.Despite the similarities of Ge and Si aqueous complex energetics and structure, differences in the thermodynamic properties between silicates and germanates may lead to the observed increase of Ge/Si ratio in high-temperature natural fluids as suggested by previous work. However, more thermodynamic data on these minerals and those on the structural position of Ge in natural silicates are required to rigorously use the Ge/Si fluid ratio for tracing hightemperature hydrothermal/magmatic processes.XAFS spectroscopy can be used for direct in situ measurement of both solubilities and local atomic structure of metals in high-temperature crustal fluids. Our novel approach, based on a classical X-ray absorption relation coupled with knowledge of the fluid density, provides an absolute measure of metal concentration in solution. Work is currently in progress to extend such measurements on solid-liquid and liquid-vapor equilibria for other metals (e.g., Sb, Au, Cu) over magmatic-hydrothermal conditions (~few kbars, 600-800°C) using an improved X-ray cell design.Acknowledgements: This work was supported by a CNRS grant "ATI Jeunes Chercheurs 2001"

Fig. 1

 1 Fig. 1 Scheme of the X-ray optical cell (A) and high T-P reactor (B) used for XAFS measurements in this study.

Fig. 2

 2 Fig. 2 Raw XAFS transmission spectra at Ge K-edge of aqueous solutions in contact with crystalline argutite (GeO 2 , tetr) at 400 bar and indicated temperatures (Experiment 2, see text).

Fig. 3

 3 Fig. 3 Normalized k 2 -weighted fluorescence EXAFS spectra of a 0.04-m germanic acid aqueous solution at 400 bar and stated temperature obtained in Experiment 1, and their corresponding Fourier Transform magnitudes (not corrected for phase shift). The vertical lines indicate the position of the 1 st atomic shell around Ge composed of four oxygens in a tetrahedral arrangement, and multiple scattering contributions within the GeO 4 tetrahedron.

Fig. 4

 4 Fig. 4 Experimental spectra (solid lines) and FEFF fits (dots) for selected germanic acid solutions at conditions indicated in the Figure. EXAFS spectra weighted by k 2 (A & C) and their corresponding Fourier Transform Magnitudes (B & D).

Fig. 5

 5 Fig. 5 Evolution of the absorption-edge height of aqueous Ge as a function of time and temperature in an argutite dissolution run (Experiment 2). Each symbol corresponds to a XAFS scan. Arrows indicate temperature changes during the experiment; dashed lines linking the symbols at a given temperature are drawn to guide the eye. Error bars correspond to the symbol size.

Fig. 6

 6 Fig. 6 Logarithm of GeO 2 (tetr) dissolution constant (reaction 2) as a function of temperature at indicated pressures. The symbols were generated from measurements performed in this work (Table 3, Experiment 2) and previous studies. The curves represent regressions of all experimental points with the density model and the revised HKF equation of state using the parameters given in Table4.

Figure 1 .

 1 Figure1.Pokrovski et al., chemge2525_revised

Figure 2 .Figure 3 .

 23 Figure 1

Figure 4 .

 4 Figure3

Figure 5 .Figure 6 .Figure 7 .Figure 8 .

 5678 Figure 4

Table 1 .

 1 Structural parameters of germanium atomic environment obtained from fitting Ge K-edge EXAFS spectra of germanic acid aqueous solutions recorded at ambient temperature and pressure.

	solution	fitted k-range	scatterer	N (atoms)	R (Å)	σ 2 (Å 2 )	∆E (eV)	R-factor
	composition	Å -1
	0.020 m H 4 GeO 4	1.6-17.0	oxygen	4.3	1.753	0.0017	10.4	0.010
	pH = 4.5
	0.040 m H 4 GeO 4	1.6-13.0	oxygen	4.1	1.750	0.0014	10.4	0.009
	pH = 4.3
	0.086 m H 4 GeO 4	1.6-12.0	oxygen	3.8	1.749	0.0012	10.3	0.012
	pH = 4.1
	0.020 m H 4 GeO 4	1.6-16.0	oxygen	4.1	1.761	0.0026	11.0	0.010
	pH = 11.7
	error of EXAFS fit			±0.3	±0.004	±30%	±1.0

Table 1

 1

Table 2 .

 2 Structural parameters of Ge(IV) atomic environment obtained from fitting Ge K-edge EXAFS spectra of a

	0.04-m germanic acid aqueous solution as a function of temperature at 400 bar (Experiment 1)	a .
	T °C	fluid density	fitted k-range	scatterer	N (atoms)	R (Å)	σ 2 (Å 2 )	∆E (eV)	R-factor
		g cm -3	Å -1
	30	1.013	1.6-11.0	oxygen	3.8	1.748	0.0010	10.3	0.013
	100	0.976	1.6-10.0	oxygen	3.8	1.751	0.0010	10.2	0.015
	200	0.891	1.6-10.0	oxygen	3.9	1.749	0.0014	9.9	0.015
	300	0.765	1.6-10.0	oxygen	4.1	1.746	0.0020	9.8	0.038
	350	0.672	1.6-13.1	oxygen	4.2	1.749	0.0020	9.8	0.010
	400	0.523	1.6-13.1	oxygen	4.2	1.752	0.0018	10.1	0.010
	450	0.271	1.6-12.0	oxygen	4.0	1.749	0.0020	10.1	0.020
	Error of
	EXAFS				±0.4	±0.007	±50%	±1.5
	fit

a See footnotes of Table

1

.

Table 2 Table 3 .

 23 Germanium aqueous concentrations in equilibrium with argutite derived from the edge height of X-ray absorption spectra at Ge K-edge, and the logarithm of the equilibrium constant for reaction (2) as a function of temperature at 400 bar.

			Experiment 1				Experiment 2
			0.04m Ge(OH) 4 -H 2 O				GeO 2 (tetr) -H 2 O
	T °C	fluid density g cm -3	edge height Absorption	mol/kg m Ge	edge height Absorption	mol/kg m Ge	log 10 K(2) T, 400bar
	30	1.013	0.249	0.0400	a	---	b	---	---
	100	0.976	0.244	0.041±0.001	---		---	---
	200	0.891	0.212	0.039±0.001	---		---	---
	300	0.764	0.186	0.040±0.002	0.076	0.016±0.002	-1.80±0.07
	350	0.672	0.151	0.037±0.002	0.100	0.024±0.003	-1.62±0.05
	400	0.523	0.133	0.041±0.002	0.110	0.034±0.003	-1.47±0.05
	450	0.271	0.072	0.043±0.005	0.048	0.029±0.004	-1.54±0.10
	500	0.178	---	---		0.017	0.016±0.005	-1.80±0.15

Table 3 Table 4 .

 34 Standard molal thermodynamic properties at 25°C and 1 bar for Ge(OH) 4 (aq), coefficients of equation (3), and parameters of the revised HKF model retrieved in this study.


Marek Kurdej

Julien Moras

Véronique Cherfaoui

Philippe Bonnifait

Map-aided Fusion Using Evidential Grids for Mobile Perception in Urban Environment

published or not. The documents may come

Introduction

Autonomous driving has been an important challenge in recent years. Navigation and precise localisation aside, environment perception is an important on-board system of a self-driven vehicle. The level of difficulty in autonomous driving increases in urban environments, where a good scene understanding makes the perception subsystem crucial. There are several reasons that make cities a demanding environment. Poor satellite visibility deteriorates the precision of GPS positioning. Vehicle trajectories are hard to predict due to high variation in speed and direction. Also, the sheer number of mobile objects poses a problem, e.g. for tracking algorithms.

On the other hand, more and more detailed and precise geographic databases become available. This source of information has not been well examined yet, hence our approach of incorporating prior knowledge from digital maps in order to improve perception scheme. A substantial amount of research has focused on the mapping problem for autonomous vehicles, e.g. Simultaneous Localisation and Mapping (SLAM) approach, but the use of maps for perception is still understudied.

Marek Kurdej e-mail: marek.kurdej@hds.utc.fr • Véronique Cherfaoui • Julien Moras • Philippe Bonnifait UMR CNRS 6599 Heudiasyc, University of Technology of Compiègne, France 1

In this article, we propose a data fusion method based on Dempster-Shafer theory [START_REF] Shafer | A Mathematical Theory of Evidence[END_REF] taking into account meta-knowledge obtained from a digital map. We show the advantage of including prior knowledge into an embedded perception system of an autonomous car. The vehicle environment is modelled by 2D occupancy grids proposed in [START_REF] Elfes | Using Occupancy Grids for Mobile Robot Perception and Navigation[END_REF]. This paper describes a robust and unified approach to a variety of problems in spatial representation using the theory of probability. The theory of evidence was not combined with occupancy grids until recently to build environment maps for robot perception [START_REF] Pagac | An evidential approach to map-building for autonomous vehicles[END_REF]. Only recent works take advantage of the theory of evidence in the context of mobile perception [START_REF] Moras | Credibilist Occupancy Grids for Vehicle Perception in Dynamic Environments[END_REF]. Some works use 3D city model as a source of prior knowledge for localisation and vision-based perception [START_REF] Cappelle | Virtual 3D City Model for Navigation in Urban Areas[END_REF], whereas our method uses maps for scene understanding.

This article is organised as follows. In section 2, we describe the details of the method. Section 3 presents the results and section 4 concludes the paper.

Multi-grid fusion approach

This section presents the proposed perception schemes. The grid construction method is described in section 2.2 and all data processing steps are detailed in section 2.4. Figure 1 presents a general overview of our approach.

Heterogeneous data sources

There are three sources in our perception system: vehicle pose, lidar range scanner point cloud and vector maps. The vehicle pose comes from the Applanix system based on a GPS, an odometer and an IMU. The system is supposed to provide precise and integral positioning. Our main source of information about the environment is an IBEO Alaska XT lidar able to provide a cloud of about 800 points 10 times per second. The digital maps that we use were provided by the French National Geographic Institute (IGN) and contain 3D building models as well as the road surface.

We also performed successful tests with freely available OpenStreetMap project 2D maps [START_REF]OpenStreetMap project[END_REF], but here we limited the use to building data. We assume the maps to be precise and accurate.

Occupancy grids

An occupancy grid models the world using a tessellated representation of spatial information. In general, it is a multidimensional spatial lattice with cells storing some stochastic information. In our case, each cell representing a box (a part of environment) X ×Y where X = [x -, x + ], Y = [y -, y + ] stores a mass function.

• ScanGrid (SG) construction: In order to process the lidar data, an evidential occupancy grid is computed when a new scan arrives, this grid is called ScanGrid. Each cell of this grid stores a mass function on the frame of discernment (FOD) Ω SG = {F, O}, where F refers to the free space and O -to the occupied space. The basic belief assignment, which reflects the sensor model, is described in [START_REF] Moras | Credibilist Occupancy Grids for Vehicle Perception in Dynamic Environments[END_REF]. • MapGrid (MG): To store the results of information fusion, an occupancy grid MG has been introduced with a FOD Ω MG = {F, C, N, S, V }. Respective classes represent: free space F, mapped infrastructure (buildings) C, non-mapped infrastructure N, temporarily stopped objects S and mobile (moving) V objects. Ω MG is a common frame used for information fusion. By using MG as a cumulative information storage, we are not obliged to aggregate preceding ScanGrids. • PriorGrid (PG) context representation: PG allows us to perform a contextual information fusion incorporating some meta-knowledge about the environment. This grid uses the same frame of discernment Ω MG as MG. The grid is obtained by projection of map data, buildings and roads, onto a 2D grid with global coordinates.

We define two sets of polygons defining the 2D position of buildings and road surface by, respectively,

B = b i = x 1 x 2 . . . x m i y 1 y 2 . . . y m i , i ∈ [0, n B ] and R = r i = x 1 x 2 . . . x m i y 1 y 2 . . . y m i , i ∈ [0, n R ] , B ∩R = / 0.
Then, we attribute the mass to each cell {X,Y } of the PriorGrid in the following way:

We note that B = {C}, R = {F, S, V }, T = {F, N, S, V } for convenience and readability only. A denotes all other strict subsets of Ω . These aliases characterise the meta-information inferred from geographic maps. For instance, on the road surface R, we encourage the existence of free space F as well as stopped S and moving V objects. Analogically, building information B fosters mass transfer to C. Lastly, T denotes the intermediate area, e.g. pavements, where mobile and stationary objects as well as small urban infrastructure can be present. Note that neither buildings nor roads are present, so we exclude existence of mapped infrastructure C, but we cannot omit other classes. Also, we define a level of con-fidence β for each map source, possibly different for each context. Let x = x -+x + 2 , ỹ = y -+y + 2 .

m PG {X,Y }(B) = β B if ( x, ỹ) ∈ b i 0 otherwise ∀i ∈ [0, n B ] m PG {X,Y }(R) = β R if ( x, ỹ) ∈ r i 0 otherwise ∀i ∈ [0, n R ] m PG {X,Y }(T ) = 0 if ( x, ỹ) ∈ b i ∨ ( x, ỹ) ∈ r j β T otherwise ∀i ∈ [0, n B ], ∀ j ∈ [0, n R ] m PG {X,Y }(Ω ) =      1 -β B if ( x, ỹ) ∈ b i 1 -β R if ( x, ỹ) ∈ r i 1 -β T otherwise ∀i ∈ [0, n B ], ∀ j ∈ [0, n R ] m PG {X,Y }(A) = 0 ∀A Ω and A / ∈ {B, R, T } (1)

Incorporating prior knowledge

The frame of discernment Ω SG used in SG is distinct from Ω MG , so in order to enable the fusion of SG and MG we define a refining r SG : 2 Ω SG → 2 Ω MG such that r SG ({F}) = {F}, r SG ({O}) = {C, N, S,V }, r SG (A) = θ ∈A r SG (θ ). The refined mass function can be expressed as m

Ω MG SG (r SG (A)) = m Ω SG SG (A) , ∀A ⊆ Ω SG .
Then, Dempster's rule is applied in order to exploit the prior information included in PriorGrid:

m Ω MG SG,t = m Ω MG SG,t ⊕ m Ω MG PG (2)

Temporal fusion

Computing conflict masses

We use the idea from [START_REF] Moras | Moving Objects Detection by Conflict Analysis in Evidential Grids[END_REF] to distinguish between two types of conflict, which arise from the fact that the environment is dynamic. We denote / 0 FO the conflict induced when a free cell in MG is fused with an occupied cell in SG. Similarly, / 0 OF indicates the conflicted caused by an occupied cell in MG fused with a free cell in SG. In an error-free case, these conflicts represent, respectively, the disappearance and the appearance of an object. Conflict masses are calculated using the formu-

las: m MG,t ( / 0 OF ) = m MG,t-1 (O) • m SG,t (F), m MG,t ( / 0 FO ) = m MG,t-1 (F) • m SG,t (O), where m(O) = ∑ A m(A), ∀A ⊆ {C, N, S,V }.

MapGrid specialisation using a counter

Mobile object detection is an important issue in dynamic environments. We propose the introduction of a counter ζ in each cell in order to include temporal information on the cell occupancy. For this purpose, incrementation and decrementation steps δ inc ∈ [0, 1], δ dec ∈ [0, 1], as well as threshold values γ O , γ / 0 have been defined.

ζ (t) = min 1, ζ (t-1) + δ inc if m MG (O) ≥ γ O and m MG ( / 0 FO ) + m MG ( / 0 OF ) ≤ γ / 0 ζ (t) = max 0, ζ (t-1) -δ dec if m MG ( / 0 FO ) + m MG ( / 0 OF ) > γ / 0
Otherwise ζ (t) rests unchanged. Using ζ values, we impose a specialisation of mass functions in MG using the equation:

m MG,t (A) = S(A, B) • m MG,t (B) (3)
where specialisation matrix S(•, •) is defined as:

S(A\ {V } , A) = ζ ∀A ⊆ Ω MG and {V } ∈ A S(A, A) = 1 -ζ ∀A ⊆ Ω MG and {V } ∈ A S(A, A) = 1 ∀A ⊆ Ω MG and {V } / ∈ A S(•, •) = 0 otherwise (4)

Fusion rule

An important part of the method consists in fusing a discounted and specialized MG (see section 2.5 and preceding paragraph) with a SG combined with prior knowledge (see section 2.3).

m MG,t = α m MG,t-1 m SG,t (5)
The fusion rule is a modified Yager's rule [START_REF] Yager | On the Dempster-Shafer framework and new combination rules[END_REF] adapted to mobile object detection. There are of course many different rules that could be used, but in order to distinguish between moving and stationary objects some modifications had to be included. These modifications consist in transferring the mass corresponding to a newly appeared object / 0 FO to the class of moving objects V as described by the equation 6. Symbol ∩ denotes the conjunctive fusion rule.

(m 1 m 2 ) (A) = (m 1 ∩ m 2 ) (A) ∀A Ω ∧ A = V (m 1 m 2 ) (V ) = (m 1 ∩ m 2 ) (V ) + (m 1 ∩ m 2 ) ( / 0 FO ) (m 1 m 2 ) (Ω ) = (m 1 ∩ m 2 ) (Ω ) + (m 1 ∩ m 2 ) ( / 0 OF ) (m 1 m 2 ) ( / 0 FO ) = 0 (m 1 m 2 ) ( / 0 OF ) = 0 (6)
All the above steps allow us to construct a MapGrid containing reach information on the environment state, including the knowledge on mobile and static objects.

Contextual discounting

Information discounting allows to forget information which is no longer valid. Discounting parameter α serves to model the speed with which information becomes obsolete. Thanks to the contextual discounting [START_REF] Mercier | Refined modeling of sensor reliability in the belief function framework using contextual discounting[END_REF], we make use of more detailed information regarding the confidence we have in the source in various contexts. We noticed that different pieces of information become obsolete with different speed. Hence, the coarsening used is Θ = θ static , θ dynamic , θ f ree , with θ static = {C, N}, θ dynamic = {S,V }, θ f ree = {F}, and discount rates α = α static , α dynamic , α f ree . We assign higher discount rates (lower confidence) to rapidly changing contexts such as free space, stopped and moving objects, and lower rates to the static context. The discounted mass function is obtained by the disjunctive combination of the input mass function m MG and mass functions for each element of the partition Θ . α m MG,t = m MG,t ∪ m static ∪ m dynamic ∪ m f ree [START_REF] Pagac | An evidential approach to map-building for autonomous vehicles[END_REF] where each mass function m l (l = static, dynamic, free) is defined by m l (θ l ) = α l , m l ( / 0) = 1α l , m l (A) = 0, ∀A ⊆ Ω ∧ A / ∈ { / 0, θ l }.

3 Results

Setup

The data set used for our experiments was acquired in cooperation with IGN in Paris. The overall length of the trajectory was about 3 km. The size of the grid cell in the occupancy grids was set to 0.5 m, which is sufficient to model a complex environment with mobile objects. The discount rates α describing the speed of information becoming obsolete were defined empirically, but they can be learnt from data, as proposed in [START_REF] Mercier | Refined modeling of sensor reliability in the belief function framework using contextual discounting[END_REF]. We have defined the map confidence factor β by ourselves, but ideally, it should be given by the map provider. β describes data currentness (age), errors introduced by geometry simplification and spatial discretisation. β can also be used to depict the localisation accuracy. Other parameters, such as counter steps δ inc , δ dec and thresholds γ O , γ / 0 used for mobile object detection determine the sensitiveness of mobile object detection and were set by manual tuning.

(b) (a) (c) (d)

Impact of prior knowledge

The results for a particular instant of the approach tested on real-world data are presented on figure 2. The visualisation of the MG has been obtained by calculating the pignistic probability of each class [START_REF] Smets | Decision making in the tbm : the necessity of the pignistic transformation[END_REF]. The presented scene contains two cars (only one is visible in the camera image) going in the direction opposite to the test vehicle and a bus parked on the road edge. Bus and car positions are marked on the grids by green and red boxes, respectively. The test vehicle position is shown as a blue box. Different classes of Ω MG are represented by different colours: F -white, C, N -blue, S -green and V -red. PG on figure 2(b) shows the position of the road space (white) and buildings (blue).

The principal advantage gained by using map knowledge is richer information on the detected objects. A clear difference between a moving object (red, car) and a stopped one (green, bus) is visible. Also, stopped objects are distinct from infrastructure when prior map information is available (cf. figures 2(c) and 2(d). In addition, thanks to the prior knowledge, stationary objects (cyan) such as infras-tructure are distinguished from stopped objects on the road. Grids make noticeable the effect of discounting, as information on the environment behind the vehicle is being forgotten. On the other hand, the parked bus is still in evidence despite being occluded by the passing car.

Conclusion and perspectives

A new mobile perception scheme based on prior map knowledge has been introduced. Geographic information is exploited to reduce the number of possible hypotheses delivered by an exteroceptive source. A modified fusion rule taking into account the existence of mobile objects has been defined. Furthermore, the variation in information lifetime has been modelled by the introduction of contextual discounting. In the future, we anticipate removing the hypothesis that the map is accurate. This approach will entail considerable work on creating appropriate error models for the data source. Moreover, we envision differentiating the free space class into two complementary classes to distinguish navigable and non-navigable space. This will be a step towards the use of our approach in autonomous navigation. Another perspective is the use of reference data to validate the results, choose the most appropriate fusion rule and learn algorithm parameters. We envision using map information to predict object movements. It rests also a future work to exploit fully the 3D map information.

Fig. 1

 1 Fig. 1 Method overview (lidar: laser scanner, Applanix: inertial measurement unit).

Fig. 2

 2 Fig. 2 (a) Scene. (b) PG. (c) MG without prior information. (d) MG with prior map knowledge.

Acknowledgements This work has been supported by ANR (French National Agency) CityVIP project under grant ANR-07_TSFA-013-01.