Jean-Yves Chauleau

William Legrand

Nicolas Reyren

Davide Maccariello

Sophie Collin

Horia Popescu

Karim Bouzehouane

Vincent Cros

Nicolas Jaouen

Albert Fert²

Chirality in magnetic multilayers probed by the symmetry and the amplitude of dichroism in X-ray resonant magnetic scattering

Chirality in condensed matter is now a topic of the utmost importance because of its significant role in the understanding and mastering of a large variety of new fundamental physicals mechanisms. Versatile experimental approaches, capable to reveal easily the exact winding of order parameters are therefore essential.

Here we report X-ray resonant magnetic scattering (XRMS) as a straightforward tool to identify directly the properties of chiral magnetic systems. We show that it can straight-forwardly and unambiguously determine the main characteristics of chiral magnetic distributions: i.e. its chiral nature, the quantitative winding sense (clockwise or counter-clockwise) and its type (Néel/cycloidal or Bloch/helical). This method is model-independent, does not require a-priori knowledge of magnetic parameters and can be applied to any system with magnetic domains ranging from few nanometers (wavelength limited) to several microns. By using prototypical multilayers with tailored magnetic chiralities based on the Co|Pt interface we illustrate the strength of this method.

Chirality is central to understand many fundamental mechanisms in various domains of physics and chemistry. In condensed matter, a large variety of physical phenomena hinge on the emergence of these complex chiral windings of order parameters, their observation and subsequently their control especially in magnetism and spintransport at the nanoscale. The ability to probe the nature of these chiral magnetic textures has now become a crucial element of modern magnetism and is therefore essential to gain a deeper understanding of these mechanisms. Spin-polarized scanning tunneling microscopy (SP-STM) revealed that magnetic textures with a cycloidal configuration of the magnetization and Néel domain walls are stabilized in ultra-thin magnetic films (one or a few atomic layers) on heavy metal substrates [1] . It was realized that these magnetic textures are stabilized by Dzyaloshinskii-Moriya (DM) interaction [2,3], (∑ 𝑫 𝑖𝑗 〈𝑖𝑗〉 • 𝑺 𝑖 × 𝑺 𝑗 , with Si and Sj two neighboring spins) which is the anti-symmetric analog of the Heisenberg interaction favoring a curling magnetization textures around the DM vector 𝑫. The DM interaction requires spin-orbit coupling (SOC) and broken inversion symmetry, found either in specific crystalline structures, such as B20 materials [4], or at film interfaces [5,6].

In this letter, we demonstrate that XRMS experiments (Figure 1a) allow us to reveal the actual magnetic textures existing in ultrathin magnetic multilayers with perpendicular anisotropy and large interfacial chiral interaction. Importantly, this determination is straightforward and does not require any assumptions or careful comparison to parameter-dependent micromagnetic simulations. Moreover, the circular dichroism in XMRS enables to identify directly not only the direction but also the sense of the magnetic winding and therefore of the actual sign of DM interaction as we proved by a thorough analysis. This information has a far-reaching impact in particular for spin-orbitronics and spin-orbit torque (SOT) studies. Indeed, SOT is a recent very promising approach to move efficiently domain walls [7] and magnetic skyrmions along magnetic race-tracks and shows therefore a great potential for future spintronic devices. Yet, the detailed texture of the domain walls plays a major role in their motion [8]: the DW high speed is related to its nature (Néel or Bloch) while its direction of motion depends on its chirality [7]. Besides, DM interaction can play an important role for existing technological applications in spintronics already using ultrathin magnetic multilayers with perpendicular magnetic anisotropy such as MRAM or detectors, in which the presence and the impact of non-negligible DM interaction has been largely overlooked (see e.g. [9,10]), emphasizing thus the need to probe its consequences on magnetic textures. XRMS presents several advantages that might soon turn it to a standard way to characterize and quantify the DM interaction. First, XMRS is a non-perturbative technique contrary to the approach based on magnetic domain analysis though magnetic force microscopy (MFM) imaging or domain wall motion. Second, such study is applicable not only to metallic chiral magnets but can be extended to the substantial number of insulating magnetic systems. Third, this experiment is based on the scattering on magnetic domains so sample patterning is not required. Then, this technique is sensitive to thicknesses of only a few nanometers of total magnetic materials (either in a single film or in multilayers) that conveniently can be buried below a few nanometers of materials (e.g. capping). Finally, XMRS experiments can be extended to time resolved experiments using synchrotron [11] or free electron laser [12], which should open new horizons to the exploration of the dynamics of magnetic chirality.

Here, we perform XRMS experiments using circularly polarized x-rays on prototypical Co/Pt based multilayers which have proven to be systems of choice for the emergence of homochiral magnetic distributions and are consequently also prototypical for SOT applications [13,14]. Our magnetic multilayers have been prepared using magnetron sputtering on thermally oxidized silicon substrates (see [15] for details]. Two types of samples composed of five-fold repetition of a trilayer are considered: //[Pt(1nm)/Co(0.8nm)/Ir(1nm)]x5 and its reversedstacking counterpart, //[Ir(1nm)/Co(t)/Pt(1nm)]x5. The symbol "//" stands for the substrate and the 10-nm-thick Pt buffer. To avoid oxidation, a 3-nm-thick Pt capping is deposited on top of the multilayers. In these samples, we measure a saturation magnetization MS ≈ 1 MA/m and a large effective out-of-plane anisotropy Keff ≈ 0.1 MJ/m 3 . According to our previous studies on these systems [16], the mean DM magnitude (arising mainly from the Pt/Co interfaces but also from Co/Ir interfaces) is about 2 mJ/m² . Such DM magnitude is large enough to impose pure Néel DW texture [8], with counterclockwise (CCW) Néel DW structure in case of a thin Co layer deposited on top of Pt, and conversely a clockwise (CW) Néel DW in case of Pt is deposited on Co. Before running the XRMS experiments, magnetic domain configurations have been imaged at room temperature using (MFM) after a demagnetization process using an out-of-plane field. In Figure 1b, we display a characteristic randomly disordered magnetic stripe patterns with a mean period of about 180 ± 30 nm (see the FFT of the MFM image in the inset of Figure 1b).

XRMS experiments have been performed on the two types of multilayer stackings at the SEXTANTS beamline [17] of the SOLEIL synchrotron. They have been performed in reflectivity conditions for circularly left (CL) and right (CR) incident X-ray beam polarizations at the Co L3 edge (photon energy = 778.2 eV) using the RESOXS diffractometer [18]. The diffracted X-rays are collected on a Peltier-cooled square CCD detector covering 6.1° at the working distance of this study. Typical diffracted patterns of the domain structure are displayed in Figures 1c-e. All the images have been geometrically corrected along the Qx-direction in order to account for the projection related to the photon incidence angle θ (of 18.5° in this case). As shown in Fig. 1e, the sum of the images obtained with CR (Fig. 1c) and CL (Fig. 1d) polarized light gives rise to a clear ring-shaped diffraction pattern around the specular beam (blocked by a beamstop to avoid saturation of the CCD) in the reciprocal plane (Qx,Qy). The ring radius, labelled as qp indicates the in-plane isotropy of the domain sizes with a typical periodicity in real space 𝑝 = 2𝜋/𝑞 𝑝 . The domain size p/2 of 90 ± 9 nm agrees with the one determined by MFM (see Fig. 1b) as the Fourier transform of the MFM image can be directly compared to the XRMS sum image. The circular dichroism (CD) of the scattering signal is defined as (ICL-ICR)/( ICL+ICR), where ICL and ICR are the intensities collected by the camera for CL and CR polarizations respectively. The colored map of the diffracted CD in Fig. 1f displays two lobes, one blue and one red, indicating an opposite dichroism sign. The amplitude of the dichroism is rather large, typically 10% of the sum signal, and for sure sufficient to univocally reveal the nature of the DW texture as explained hereafter. Indeed, XRMS has been recently used to characterize magnetic bulk compound hosting skyrmions. In this case, it unambiguously determined the winding number of skyrmions lattices in Cu2OSeO3 [19,20] through the analysis of the symmetry of the scattering signal. In our work, by leveraging the dichroism in XRMS scattering signal observed with circularly polarized light, we demonstrate how it provides a simple and straightforward novel approach to identify the nature of DW texture, i.e. its character (Néel or Bloch) and the magnetic chirality. We believe that these results, that take inspiration in the study by Dürr et al. [21] of the chiral behavior of closure magnetic domains at the surface of 40 nm thick FePd layer, is of high importance given the huge recent interest for this type of magnetic multilayers with large interfacial DM interaction leading to promising applications for a new generation of spin-orbitronic devices [22].

In order to precisely analyze the dichroism in XRMS, we use the following expression of the diffracted intensity I(Q) for a scattering vector Q = kf-ki in the kinematical approximation:

𝐼(𝑸) ∝ |∑ 𝑓 𝑛 •exp(𝑖𝑸 • 𝒓 𝑛 ) 𝑛 | 2
where fn is the resonant scattering amplitude of a single ion at the rn position in the electron-dipole approximation. In case this ion carries a magnetic moment mn, different contributions to this scattering amplitude can be distinguished at resonance [23][24][25] 𝑓 𝑛 = 𝑓 0 + 𝑓 𝑚 1 + 𝑓 𝑚 2 where f0 is the anomalous charge scattering amplitude and fm 1 and fm 2 are the magnetic resonant scattering amplitudes:

𝑓 𝑚 1 ∝ -𝑖 (𝜖̂× 𝜖̂′) • 𝒎 𝑛 𝑓 𝑚 2 ∝ (𝜖̂′ • 𝒎 𝑛 )(𝜖̂• 𝒎 𝑛 )
with 𝜖̂ and 𝜖̂′ the polarization state of the incident and diffracted X-ray beam respectively. Note that while fm 1 scales with m, fm 2 scales with m 2 . Considering the extracted characteristic domain period, the magnetic diffracted intensity is mainly related to fm 1 . The diffracted intensity for a given incident beam polarization is expressed as follows [26]: 𝐼(𝑸) = Tr[𝑓 ̃𝑛 𝜌 𝑓 ̃𝑛 † ] where 𝑓 ̃𝑛 and 𝑓 ̃𝑛 † are the Fourier transform of the scattering amplitude 𝑓 𝑛 and its complex conjugate and 𝜌 is the density matrix of the incident X-ray beam. In the Stoke-Poincaré representation [25] this density matrix for a circularly left or right incident beam is expressed as follows:

𝜌 CL = ( 1 -𝔦 +𝔦 1 ) 𝜌 CR = ( 1 +𝔦 -𝔦 1 )
In the following, we consider two types of possible magnetic windings, i.e. helicoidal (or Bloch-like) and cycloidal (or Néel-like) depicted in Fig. 2a and 2b respectively, that are the ones expected in the multilayer systems considered in this study. From both these winding configurations, the circular dichroism of their diffraction patterns can be calculated using (𝐼 CL -𝐼 CR ) (𝐼 CL + 𝐼 CR ) ⁄ . In Fig. 2c, we present the calculated orthoradial profiles of the normalized circular dichroism for the two possible windings and for each of them for the two possible chiralities, i.e. clockwise (CW) or counterclockwise (CCW). For the case of a helicoidal winding (Blochlike), the circular dichroism is respectively maximum (for CW) and minimum (for CCW) in positions corresponding to incident beam plane of 𝜓 = 0 or 180° and vanishes for 𝜓 = 90° or 270°. On the contrary, for a cycloidal winding (Néel-like), the maximum (for CW) and minimum (for CCW) are obtained for 𝜓 = 90° and 270°, resulting in the rotation of the dichroic diffraction pattern by 90° around the specular beam. Thus, it provides a simple way to determine unambiguously the actual texture of the domain wall from the orientation of the experimentally observed dichroism. In Fig. 2d, we display the orthoradial experimental profile of the circular dichroism we obtained for the //[Ir(1)/Co(0.8)/Pt(1)]x5 multilayer measured at an incidence angle 𝜃 = 17.5°. We emphasize that this angle corresponds to the first multilayer peak where the dichroic signal is enhanced. From the comparison with the predicted profile (yellow curve in Fig. 2d), and notably the positions of the maxima and minima, we can directly assert that the magnetic winding in our Ir/Co/Pt multilayers is of Néel type. Hence, it confirms by a direct measurement and without assumptions, that the DW texture is Néel (CW or CCW) as already known for this multilayer system with additive interfacial DM interaction either indirectly through analysis of the skyrmion size and comparison with micromagnetic simulations [15] or directly through Lorentz transmission electron microscopy [27]. Other methods have already been utilized to access to the texture of the DW or skyrmions such as spin-polarized STM [1,28], scanning nitrogen-vacancies-magnetometry (NV) [29,30] or spinpolarized low-energy electron microscopy (SPLEEM) [31]. On the other hand, DM interaction has also been probed by spin wave spectroscopy techniques such as Brillouin light scattering (BLS) [32] or time-resolved Kerr microscopy [33]. Once the type of winding is determined, the chirality (CW or CCW) of the Néel texture is usually indirectly deduced, for example, from DW dynamics and micromagnetic comparison [START_REF] Vansteenkiste | [END_REF], is straight-forwardly assessed by XRMS. Indeed, from Fig. 2d, we conclude that the magnetic texture for sample //[Ir(1)/Co(0.8)/Pt(1)]x5 corresponds to a fixed CW Néel DW chirality. Finally, the global circular dichroism pattern (changing sign only twice) allows to corroborate that the overall topological winding number of the entire magnetic distribution is N=1 [19]. We notice that beyond this qualitative comparison, we observe a deviation between the measurement and the calculated curves in Fig. 2d outside the angles corresponding to maxima and minima. We attribute it to the use of the kinematical approximation in our simulation that is known not to be strictly valid in the soft x-ray range [START_REF] Authier | Int. Tables Crystallogr. Vol. B Reciprocal Space[END_REF] but this does not affect the main conclusion. In order to experimentally confirm the origin of this dichroic contrast in the diffraction maps, we compare directly in Fig. 3, two samples having the same multilayer constitution but opposite stacking: //[Ir(1)/Co(0.8)/Pt(1)]x5 (top of Fig. 3) or //[Pt(1)/Co(0.8)/Ir(1)]x5 (bottom of Fig. 3). In these two multilayers, we expect a reversed direction of DM vector as predicted from the shape of the interfacial origin of the DM interaction [5,16] in bilayers or multilayers with magnetic material in contact with heavy materials. In Fig. 3b and3e, we display the MFM images obtained after demagnetization under perpendicular field on each sample prior to the XRMS experiments. For both samples, we find a maze domain configuration, with a difference in the mean domain width (see FFT in the insets of Fig. 3b and Fig. 3e) due to some (quasi-unavoidable) non-negligible difference in the magnetic parameters of the two multilayers, such as the perpendicular magnetic anisotropy, saturation magnetization and DM interaction. However, despite these differences, it can be directly and unambiguously concluded from the dichroism XRMS diagram (Fig. 3c and3f) that both the //Ir/Co/Pt and //Pt/Co/Ir multilayers have the same pure Néel domain wall configuration but with opposite winding signs. Indeed, they both present a complete disappearance of the dichroism for 𝜓 = 0 or 180° but with a clear reversal of the sign of the dichroism. Thus, a simple XRMS map taking a few minutes (the dichroism is so large that even a single circular polarity might be enough to conclude) directly reveals that a system with Co on top of Pt has a CCW Néel DW configuration, while for Co below Pt, a CW Néel DW is found, as expected from theoretical predictions for bilayers. The result of energy minimization using micromagnetic simulations using MuMax3 code [START_REF] Vansteenkiste | [END_REF], using our film parameters, confirms opposite Néel DW spin textures in the two stackings (Fig. 3a and3d). In conclusion, we investigated the circular dichroism in the X-ray resonant magnetic scattering to determine chiral magnetic distribution, i.e. its type (Neel or Bloch) and its magnetic chirality in thin films presenting a strong DMI. In this work, we apply XRMS to the prototypical Pt/Co system, evidencing Néel type domain walls as well as their chirality depending on the stacking order. However, this method can be applied to any type of magnetic materials, either in static or in time resolved mode, and will be useful to investigate, for instance, metallic mutlilayers based on Co or Fe. Besides, further analysis associated to modelling might be performed to get some quantitative information such as DM magnitude and even anisotropies. The power of this method is its unambiguous conclusion regarding the DMI sign independently of other magnetic parameters. In a broader perspective, Circular Dichroism in x-ray scattering appears to be a unique tool for studying the type and the chirality of the magnetic phase of any magnetic material. Similar investigations could be profitably extended to different types of systems showing a non collinear magnetic ordering such as skyrmion lattices or conical/helical phases stabilized by the Dzyaloshinskii-Moriya interaction as well as more complex systems such as the recently observed antiskyrmion lattices [37].

Figure 1 :

 1 Figure 1 : a) XRMS measurement principle and experimental configuration. b) 6x6 µm 2 MFM phase image showing the out-of-plane magnetic contrast of [Ir(1)/Co(0.6)/Pt(1)]x5 multilayer with its corresponding FFT pattern (inset) evidencing a 180 ± 30nm period disordered magnetic stripe pattern . Corresponding diffracted patterns for circularly left, CL (c) and right, CR (d) polarized incident X-ray beam. e) Resulting sum image of the diffracted pattern (CL+CR), confirming that the diffraction corresponds to the magnetic domains observed by MFM. f) Normalized difference image (CL-CR/CL+CR) evidencing a pronounced circular dichroism. Note that the straight black area crossing the diffraction ring is the shadow of a beam-stop used to block the specular reflection.

Figure 2 :

 2 Figure 2 : (a) diagram of a Bloch (helicoidal) winding and of a (b) Néel (cycloidal) winding. (c) Calculated orthoradial profile of the circular dirchroism of different magnetic textures: clockwise (CW, orange) and counter-clockwise (CCW, green) Bloch (dashed) and Néel (solid) windings for an incident angle θ=17.5°. (d) Comparison with the experimental circular dichroism orthoradial profile of a [Ir(1)/Co(0.8)/Pt(1)]x5 multilayer for the same incident angle θ=17.5° (dots). Note that the red rectangles indicate the position of the beamstop.

Figure 3 :

 3 Figure 3 : Comparison of two samples with inverted stacking //[Ir(1)/Co(0.8)/Pt(1)]x5 (a-c) and //[Pt(1)/Co(0.8)/Ir(1)]x5 (d-e). The corresponding magnetization textures are obtained by micromagnetic simulations based on material parameters (a & d). (b & e) MFM images with labyrinth-shape domains and their Fourier transform in inset. (c & f) Normalized circular dichroism signal (ICL-ICR)/(ICL+ICR) measured on sample a (e) and sample b (f).The diffraction sum images are shown in inset, confirming again that the diffraction corresponds to the magnetic domains.

Ackownledgments:

SoGraph (ANR-15-GRFL-0005) and MAGicSky (European Union Grant, No. FET-634 Open-665095) are acknowledged for financial support.


Julie Aufort
email: julie.aufort@upmc.fr

Christel Gervais

Loïc Segalen

Nathalie Labourdette

Cristina Coelho-Diogo

Benoit Baptiste

Olivier Beyssac

Romain Amiot

Christophe Lécuyer

Etienne Balan

Loïc Ségalen

Benoît Baptiste

Atomic scale transformation of bone in controlled aqueous alteration experiments

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Introduction

Bones and teeth are composed of three constituents: a mineral component and a fraction of organic and water molecules [START_REF] Pasteris | Bone and tooth mineralization: why apatite?[END_REF]. The mineral component is a form of hydroxyl-deficient nanocrystalline carbonate-bearing hydroxylapatite (Ca 5 (PO 4 ) 3 (OH)) [START_REF] Elliott | Phosphates: Geochemical, Geobiological, and Material Importance[END_REF]. During biomineralisation, the stable isotope compositions of structural carbonate and phosphate groups in bioapatite record a combination of environmental features and biological processes. Carbon and oxygen isotope ratios (expressed as δ 13 C and δ 18 O values) in bioapatite reflect that of ingested food [START_REF] Deniro | Influence of diet on the distribution of carbon isotopes in animals[END_REF][START_REF] Lee-Thorp | Stable carbon isotope ratio differences between bone collagen and bone apatite, and their relationship to diet[END_REF]Cerling and Harris, 1999;[START_REF] Passey | Carbon isotope fractionation between diet, breath CO2, and bioapatite in different mammals[END_REF] and drinking water [START_REF] Longinelli | Oxygen isotopes in mammal bone phosphate: a new tool for paleohydrological and paleoclimatological research[END_REF]. They can provide information on the dietary preferences (Cerling et al., 1999) of vertebrates and on the climatic conditions that prevailed in the environment [START_REF] Fricke | Intra-tooth variations in  18 O (PO4) of mammalian tooth enamel as a record of seasonal variations in continental climate variables[END_REF][START_REF] Levin | A stable isotope aridity index for terrestrial environments[END_REF].

The stable isotope compositions of fossil remains of vertebrates are thus widely used to reconstruct past climates and past environments (e.g. [START_REF] Kohn | Stable isotope compositions of biological apatite[END_REF][START_REF] Amiot | Latitudinal temperature gradient during the Cretaceous Upper Campanian -Middle Maastrichtian: δ 18 O record of continental vertebrates[END_REF][START_REF] Kingston | Isotopic dietary reconstructions of Pliocene herbivores at Laetoli: implications for early hominin Paleoecology[END_REF][START_REF] Tütken | Early diagenesis of bone and tooth apatite in fluvial and marine settings: Constraints from combined oxygen isotope, nitrogen and REE analysis[END_REF][START_REF] Roche | Stable isotope analysis of tooth enamel carbonate of large herbivores from the Tugen Hills deposits: palaeoenvironmental context of the earliest Kenyan hominids[END_REF].

The fossilisation process involves several mechanisms that can affect the mineralogical and crystal-chemical composition of vertebrate skeletal tissues: degradation of the organic matrix, variation of the carbonate content, diagenetic enrichment of exogenous trace elements such as rare earth elements and fluorine, as well as an increase in crystallinity (e.g. [START_REF] Hedges | Bone diagenesis: an overview of processes[END_REF][START_REF] Trueman | Why do crystallinity values fail to predict the extent of diagenetic alteration of bone mineral? Palaeogeography[END_REF][START_REF] Roche | Preservation assessment of Miocene-Pliocene tooth enamel from Tugen Hills (Kenyan Rift Valley) through FTIR, chemical and stable-isotope analyses[END_REF][START_REF] Reynard | Trace elements and their isotopes in bones and teeth: Diet, environments, diagenesis, and dating of archeological and paleontological samples[END_REF][START_REF] Keenan | evaluating the consequences of diagenesis and fossilization on bioapatite lattice structure and composition[END_REF].

However not all skeletal tissues exhibit the same chemical-structural characteristics. Bones consist of about 50 vol% of ~ 2 nm thick, 10-20 nm wide and 20-50 nm long apatitic nanocrystallites and a nearly equivalent volume of collagen fibrils [START_REF] Glimcher | Bone: Nature of the calcium phosphate crystals and cellular, structural, and physical chemical mechanisms in their formation[END_REF][START_REF] Pasteris | Bone and tooth mineralization: why apatite?[END_REF]. In contrast, tooth enamel is made of ~90 vol% of larger apatite crystallites and low organic matter and water content [START_REF] Legeros | Calcium phosphates in oral biology and medicine[END_REF]LeGeros, 1984, Elliott, 2002). In bones, the smaller crystal size leads to a high specific surface area, resulting in higher reactivity and solubility compared to tooth enamel [START_REF] Legeros | Calcium phosphates in oral biology and medicine[END_REF][START_REF] Berna | Solubilities of bone mineral from archaeological sites: The recrystallization window[END_REF]. Bone is thus expected to be less resistant to post-mortem alteration than the more mineralised and less porous tooth enamel [START_REF] Michel | Chemical and structural changes in Cervus elaphus tooth enamels during fossilization (Lazaret cave): a combined IR and XRD Rietveld analysis[END_REF][START_REF] Lee-Thorp | Three case studies used to reassess the reliability of fossil bone and enamel isotope signals for paleodietary studies[END_REF][START_REF] Pasteris | Experimental fluoridation of nanocrystalline apatite[END_REF]. For this reason, palaeoenvironmental reconstructions in continental environments are mainly carried out based on stable isotope analysis of fossil enamel [START_REF] Wang | A model for fossil tooth and bone diagenesis: implications for paleodiet reconstruction from stable isotopes[END_REF][START_REF] Ayliffe | The retention of primary oxygen isotope compositions of fossil elephant skeletal phosphate[END_REF]. However, fossil enamel may be scarce in certain fossilisation contexts whereas bone fossils can be retrieved in larger quantities and a few major taxa do not have any teeth, such as most birds, turtles or primitive fish. Moreover, while enamel is mineralised during childhood in mammals, bone apatite also provides dietary information about adult life stages that can be further completed by the joint stable isotope analysis of collagen, when preserved (Lee-Thorp and [START_REF] Lee-Thorp | Three case studies used to reassess the reliability of fossil bone and enamel isotope signals for paleodietary studies[END_REF][START_REF] Lee-Thorp | On isotopes and old bones[END_REF]. Furthermore, the study of bone diagenetic processes has wide implications, e.g. in archaeological contexts where preservation assessment of bones is key to bone collagen dating [START_REF] Lebon | Rapid quantification of bone collagen content by ATR-FTIR spectroscopy[END_REF] and in oceanic environments where biomineralised tissues of Devonian fish shed light on their ontogeny and taphonomy [START_REF] Chevrinais | New insights in the ontogeny and taphonomy of the Devonian acanthodian Triazeugacanthus affinis from the Miguasha fossil-Lagerstätte, Eastern Canada[END_REF].

Overall, fossil bones and teeth often display a transformation of the original apatite towards a carbonated fluorapatite. This transformation can be understood in the light of the more general processes of mineral replacement reactions through dissolution-recrystallisation at the solid/solution interface [START_REF] Putnis | Mineral replacement reactions: from macroscopic observations to microscopic mechanisms[END_REF][START_REF] Putnis | The mechanism of reequilibration of solids in the presence of a fluid phase[END_REF]Wang et al., 2013). It most likely occurs via a dissolution/recrystallization mechanism driven by the lower solubility of fluorapatite [START_REF] Kolodny | Dinosaur bones: fossils or pseudomorphs? The pitfalls of physiology reconstruction from apatitic fossils[END_REF][START_REF] Trueman | Trace elements in recent and fossil bone apatite[END_REF]. Recent study of early diagenetic processes suggested that formation of fluorine-enriched apatite can occur rapidly, within one month of burial [START_REF] Keenan | Early diagenesis and recrystallization of bone[END_REF]. Studies that have focused on the incorporation of rare earth and trace elements in fossil bone also suggest that diffusion processes pervasively affect the organo-mineral composite [START_REF] Millard | A diffusion-adsorption model of uranium uptake by archaeological bone[END_REF]Hedges, 1996, Kohn, 2008). Accordingly, the extent of diagenetic transformations can be assessed from the chemical or isotopic composition characteristics of fossils, whereas optical or scanning electron microscopic observations may fail to detect incipient transformations of apatite.

Mineralogical investigations based on vibrational FTIR or Raman spectra, and X-ray diffraction (XRD) can also bring precious information on the transformations of biomaterials.

They often rest on the estimation of crystallinity indices [START_REF] Sharp | The effect of diagenesis on oxygen isotope ratios of biogenic phosphates[END_REF][START_REF] Weiner | States of preservation of bones from prehistoric sites in the Near East: a survey[END_REF][START_REF] Person | Early diagenetic evolution of bone phosphates: a X-ray diffractometry analysis[END_REF][START_REF] Sillen | Diagenesis of bone from Border Cave: implications for the age of the Border Cave hominids[END_REF][START_REF] Sponheimer | Alteration of enamel carbonate environments during fossilization[END_REF], accounting for modifications of the size and/or structural order of apatite particles. These indices are technique-dependent and can differently reflect the natural heterogeneity of bioapatites [START_REF] Surovell | Standardizing infrared measures of bone mineral crystallinity: an experimental approach[END_REF][START_REF] Nakano | Variation in crystallinity of hydroxyapatite and the related calcium phosphates by mechanical grinding and subsequent heat treatment[END_REF]. As a result, explicit correlations are hardly identified between crystallinity indices and intake in trace elements or perturbation of the isotopic composition of fossils [START_REF] Pucéat | Can crystallinity be used to determine the degree of chemical alteration of biogenic apatites?[END_REF][START_REF] Trueman | Why do crystallinity values fail to predict the extent of diagenetic alteration of bone mineral? Palaeogeography[END_REF].

These previous studies call for in-depth analysis of the atomic scale transformations of bone when exposed to aqueous fluids. In the present contribution, artificial alteration experiments are carried out on modern bone samples in order to better specify the physico-chemical mechanisms involved in bone diagenesis. Modifications of the chemical and stable isotope (δ 13 C, δ 18 O) compositions observed on the reacted samples are interpreted under the light of the crystal-chemical transformations inferred from their vibrational spectra (ATR-FTIR, Raman), solid-state Nuclear Magnetic Resonance ( 19 F, 13 C, and 1 H NMR) spectra and X-ray diffraction (XRD) patterns. A special attention is given to the role of fluorine and to the behaviour of structural carbonate groups in the transformation mechanism.

Materials and Methods

Samples description and alteration conditions

The materials used in the following alteration experiments all come from a metapodial bone of modern ox, TH1, collected on the shores of the Bogoria Lake (Kenya). This sample presented the usual characteristics of biological bone and no evidence was found of significant alteration prior to performing the following experiments. Two types of samples were investigated to provide complementary results: bone powders allowed for a high rate of transformation and bone wafers provided spatially resolved information about the alteration process. The cortical bone was sawn into 1 to 2 mm wide and thick, and about 5 mm long wafers using a low-speed IsoMet diamond-edged saw. Bone powders were obtained with a rotary drill equipped with a diamond-tipped burr and ground with an agate mortar and pestle. These bone wafers and powders were used directly in the alteration experiments described below without any pretreatment. Either the bone wafer or bone powder (~ 600 mg) were soaked in 100 mL of solution prepared from MilliQ water (δ 18 O = -6.7 ‰ V-SMOW) for various amounts of time listed in Table 1 without stirring. The solution was then filtered to collect the powder sample while the wafer was retrieved and rinsed with MilliQ water. In both cases, samples were then left to dry overnight in an oven at 60 °C. Various alteration conditions were investigated and are described in Table 1. Following the protocol used for the experimental fluorination of modern horse tooth by [START_REF] Pasteris | Experimental fluoridation of nanocrystalline apatite[END_REF], a phosphate buffer solution (Fisher Chemical, Fisher Scientific UK, Loughborough, Leics) was used at pH 7. A phosphate-free 20 mM piperazine-N,N'-bis(2-ethanesulfonic acid) (PIPES) solution ("organic buffer") was also tested as pH 7 buffer. For alkaline conditions, 100 mL of KOH solutions at pH 9 (10 -5 M) and pH 10 (10 -4 M) were used.

For each pH condition, alteration experiments were duplicated using either a fluorine-free solution or a fluorinated solution with a 10 -2 M NaF concentration. Throughout the manuscript, each experiment is referred to by a letter, the prime symbol referring to the fluorinated sample.

Reacted samples in fluorine-free solutions will be referred to as control samples. Finally, a natural sample originating from the sedimentary phosphate deposit of Taiba, Senegal, was used as a reference sample for carbonated fluorapatite (C-Fap; [START_REF] Morin | Native Cd + in sedimentary fluorapatite[END_REF].

Analytical techniques

Fluorine content and Ca/P ratios are reported in Table 2. For each analysis, 100 mg of sample was dissolved in 5 mL of a 30% suprapure nitric acid solution for 1h at 80°C following the protocol previously used by [START_REF] Maurer | Intra-skeletal variability in trace elemental content of Precolumbian Chupicuaro human bones: the record of post-mortem alteration and a tool for palaeodietary reconstruction[END_REF]. Fluorine content was measured using a fluoride ion selective electrode (Mettler Toledo), Ca was measured by energy dispersive X-ray fluorescence (Niton XL3t Thermo Fischer scientific) and phosphorus by spectrophotometry (Milton Roy Spectronic 301 spectrometer). The estimated analytical error based on the analysis of a certified reference material (bone ash SRM 1400) expressed as RSD is 11% for F, 3% for Ca and 4% for P. ATR-FTIR spectra were recorded using a Quest ATR device and a Nicolet 6700 FTIR spectrometer. A few milligrams of pure powder samples were packed at the surface of the ATR crystal and two different spectra were recorded for each sample, using either a diamond or a Ge ATR crystal, between 400 and 4000 cm -1 by averaging 200 scans with a resolution of 1 cm -1 .

The use of a diamond (n = 2.4) ATR crystal allows the detection of relatively weak bands, such as those ascribed to structural carbonate groups, whereas Ge (n = 4) ATR is less affected by electrostatic effects and provides a better insight into the sample microscopic structure [START_REF] Aufort | Modeling the attenuated total reflectance infrared (ATR-FTIR) spectrum of apatite[END_REF][START_REF] Balan | Line-broadening and anharmonic effects in the attenuated total reflectance infrared spectra of calcite[END_REF]. All ATR spectra are reported in absorbance units A=log(I 0 /I R ) where I0 and IR are the intensities of the incident and reflected light, respectively. Detailed analysis of the ν 1 PO 4 and ν 2 CO 3 ATR-FTIR bands was performed after a baseline subtraction using the Baseline Spline procedure from Igor Wavemetrics. To evaluate the asymmetry of the ν 1 PO 4 band, the Half Width at Half Maximum on the high frequency side (HWHM) was determined by constructing a vertical line at the position of the peak maximum and measuring the width from that line to the high frequency side of the band at half maximum.

Raman spectra were obtained using a Renishaw InVia Reflex spectrometer. The Raman instrument had been initially calibrated using a standard Neon-Argon lamp and the frequency calibration was checked and corrected daily using a silicon wafer (peak at 520 cm -1 ). A microscope was used to focus the 532 nm laser beam on a ~ 2-3 μm spot with a x 50 longworking distance objective (numerical aperture 0.45). A maximal 5 mW laser power was delivered at the sample surface, ensuring negligible thermal effects. Detailed analysis of the ν1 PO4 Raman peak was performed after a baseline subtraction using the Baseline Spline procedure from Igor wavemetrics. Spectral parameters were extracted by fitting with a Voigt function with an uncertainty on peak position and width of ±0.1 cm -1 and ±0.5 cm -1 respectively. X-Ray powder diffraction measurements were carried out on a Panalytical Empyrean diffractometer using Cu Kα radiation source (λKα1=1.540598Å, λKα2=1.544426Å) and a PIXcel3D detector. X-ray data were collected between 5° and 130° 2θ with a 0.01° 2θ step for 7 h. Cell parameters, mean coherent domain (MCD) sizes and microstrain were refined using Le Bail method as implemented in the Fullprof software [START_REF] Rodriguez-Carvajal | Recent advances in magnetic structure determination by neutron powder diffraction[END_REF]. Starting from the known cell parameters of apatite, the LeBail refinements converged rapidly. Since the peak width was significantly larger than the instrumental resolution (0.05° à 2θ= 50°), Lorentzian isotropic size (Y) and Lorentzian isotropic strain (X) parameters were refined. The two effects can be decoupled on the diagram measured over a wide angular range because the first induce a peak broadening as Y/cos whereas the second as Xtan. Then, anisotropic refinements of size parameters significantly improve the fit and the corresponding spherical harmonic coefficients are given in Table S1.

Single-pulse 19 F magic angle spinning (MAS) NMR experiments were performed on an Avance 700 Bruker spectrometer (16.3T) operating at 658.93 MHz using a 4 mm rotor at a 14 kHz spinning frequency. Cross-polarization 13 C CP MAS NMR experiments were performed on an Avance 300 Bruker spectrometer operating at a Larmor frequency of 75.51 MHz using a 7 mm rotor at a 5 kHz spinning frequency. Single-pulse 1 H MAS NMR experiments were performed on an Avance 700 Bruker spectrometer operating at 700.29 MHz using a 2.5 mm rotor at a 30 kHz spinning frequency.

Stable isotope measurements were performed on the carbonate and phosphate components of altered bone powder samples. For the carbonate component, the carbon and oxygen isotope compositions were measured (δ 13 C, δ 18 Ocarbonate). Samples weighing 800 μg were analysed on a Kiel IV device coupled to a DeltaVAdvantage IRMS. Samples were reacted under vacuum with 100% orthophosphoric acid at 70°C to generate water vapour and carbon dioxide. The resultant CO 2 was then purified in an automatic cryogenic trapping system. Measurements were normalised to the NBS 19 standard (δ 13 C = 1.95 ± 0.02 ‰ PDB and δ 18 Oc = 28.64 ± 0.07 ‰ V-SMOW; n = 3). The stable oxygen isotope ratio of carbonate in bioapatite was calculated using the temperature-dependent fractionation factor between calcite and CO2 [START_REF] Kim | Phosphoric acid fractionation factors for calcite and aragonite between 25 and 75°C: Revisited[END_REF].

Uncertainties given are calculated from measuring the samples three times. Regarding the oxygen isotope composition of the phosphate component (δ 18 Ophosphate), apatite powders were treated following the protocol described by [START_REF] Crowson | Preparation of phosphate samples for oxygen isotope analysis[END_REF] slightly modified by [START_REF] Lécuyer | Thermal excursions in the ocean at the Cretaceous-Tertiary boundary (northern Morocco): δ18O record of phosphatic fish debris Palaeogeography[END_REF]. This protocol consists in the isolation of structural phosphate in apatite as silver phosphate (Ag3PO4) crystals using acid dissolution and anion-exchange resin. After dissolution of 15 mg of powdered bone in 2 mL of 2 M HF at 25 °C for 24 h, the CaF2 residue was separated from the solution that contained the phosphate by centrifugation. This solution was then neutralised by adding 2.2 mL of 2 M KOH. Then, 2.5 mL of Amberlite™ anion-exchange resin was added to the solution to separate the PO4 3-ions. The solution was removed after 24 h and the resin was eluted with 27.5 mL of 0.5 M NH4NO3 for 4 h. A volume of 0.5 mL of NH4OH and 15 mL of an ammoniacal solution of AgNO3 were then added and the samples were placed in a thermostated bath at 70°C for 7 h, allowing the precipitation of Ag3PO4 crystals. Oxygen isotope compositions were measured using a VarioPYROcube TM elemental analyser (EA) interfaced in continuous flow (CF) mode to an Isoprime TM isotopic ratio mass spectrometer hosted by the Laboratoire de Géologie de Lyon (Université Claude Bernard). For each sample, five aliquots of ~300 μg of silver phosphate were mixed with the same amount of pure graphite powder in silver foil capsules and pyrolysis was performed at 1450 °C. Measurements were calibrated against the NBS120c standard whose value was fixed at 21.7 ‰ (V-SMOW) according to [START_REF] Lécuyer | Thermal excursions in the ocean at the Cretaceous-Tertiary boundary (northern Morocco): δ18O record of phosphatic fish debris Palaeogeography[END_REF] and the NBS127 (barium sulfate, BaSO4: δ 18 O = 9.3 ‰ (V-SMOW); [START_REF] Hut | Consultants'group meeting on stable isotope reference samples for geochemical and hydrological investigations[END_REF]. NBS120c standards that were converted into silver phosphate from each chemistry batch have a mean δ 18 Op value of 21.70 ± 0.51 ‰ (n = 5).

Results

Chemical composition of bone samples

Fluorine content of the unaltered bone TH1 and control samples is about 0.2 wt% (Table 2).

Fluorinated bone powders at 70°C contain 2.0 -2.5 wt.% fluorine whereas the bone powder fluorinated at 20°C (C') contains only 1.6 wt.% fluorine. The Ca/P molar ratio of the unaltered bone is 1.57, consistent with the range of values found in bone (Sillen andLeGeros, 1991, Kourkoumelis et al., 2012) and slightly below the 1.67 value for end-member hydroxylapatite.

All altered bone powders have higher Ca/P molar ratios ranging from 1.64 to 1.86, values typically found in archaeological and fossil bones [START_REF] Reiche | A multi-analytical study of bone diagenesis: the Neolithic site of Bercy (Paris, France)[END_REF]. No significant variation in Ca/P molar ratio is observed from control to fluorinated samples but samples that reacted with phosphate buffered solutions display lower Ca/P ratios than the others.

Oxygen and carbon isotopic compositions

Oxygen and carbon isotope compositions, i.e. δ 18 Ocarbonate, δ 18 Ophosphate, and δ 13 C, of altered bone powder samples are reported in Table 2. Only minor deviation from the original oxygen isotope composition of structural carbonate in the non-altered bone (36.31 ‰ V-SMOW) is observed in bone powders altered in a phosphate buffer, with δ 18 Ocarbonate values ranging from 35.2 to 37.4 ‰ (V-SMOW). In contrast, bone powders altered in alkaline conditions exhibit lower δ 18 Ocarbonate values, ranging from 32.8 to 34.1 ‰ (V-SMOW). The situation is reversed when considering oxygen phosphate isotope compositions. The δ 18 Ophosphate of samples altered in a phosphate buffer range between 20.5 and 22.7 ‰. These values are significantly lower than the initial TH1 value (25.8 ‰). Considering that inorganic oxygen exchange of phosphate groups is a very slow process [START_REF] Lécuyer | Oxygen isotope exchange between dissolved phosphate and water at temperatures ≤135°C: Inorganic versus biological fractionations[END_REF][START_REF] Sharp | The effect of diagenesis on oxygen isotope ratios of biogenic phosphates[END_REF]Zazzo et al., 2004a), this suggests incorporation of phosphate species from the phosphate buffer, which displays a lighter oxygen isotopic composition (12.6 ‰ V-SMOW). Other samples, altered in alkaline conditions and organic buffer, display values ranging from 26.3 to 27.1 ‰ (V-SMOW) close to that of the starting material (25.8‰). Based on isotopic compositions, it is thus possible to distinguish two groups: bone powders altered in a phosphate buffer and bone powders altered in all other conditions. This is most apparent when comparing oxygen isotope composition of phosphate, δ 18 Ophosphate, with carbonate, δ 18 Ocarbonate (Fig 1a). While oxygen isotope compositions of samples altered in alkaline conditions or in the organic buffer fall close to the δ 18 Ocarbonateδ 18 Ophosphate correlation line for bioapatites (e.g. [START_REF] Lécuyer | Oxygen isotope fractionation between apatite-bound carbonate and water determined from controlled experiments with synthetic apatites precipitated at 10-37°C[END_REF], samples altered in the phosphate buffer deviate due to significantly lower δ 18 Ophosphate values. Importantly, the type of buffer used has more influence on the isotopic composition than the presence or absence of fluoride. Indeed, isotopic compositions do not vary significantly from non-fluorinated samples to their fluorinated counterparts. Regarding carbon isotope compositions (Fig 1b), samples altered in a phosphate buffered condition also show overall ~0.5-0.8 ‰ lower δ 13 C values than other samples, regardless of the presence or absence of fluorine.

X-ray diffraction

XRD patterns show apatite as the only crystalline phase present in altered bone powders (Figure S1). Variations in cell parameters indicate a systematic decrease in the lattice parameter a from control to fluorinated bone powders (Table 3). The a cell parameter of the original unaltered bone sample TH1 is 9.417 Å. Values of a cell parameter in samples fluorinated at 70°C are systematically lower and range between 9.392 and 9.378 Å. An intermediate value is obtained for the sample fluorinated at 20°C (9.403 Å), consistent with its lower fluorine content and closer to that of the original TH1 sample (9.417 Å). The process of soaking bone powders in solution leads to a significant decrease of the strain parameter and all altered samples display smaller mean coherent domain (MCD) sizes in both [020] and [003] directions than the unaltered bone, TH1 (Table 3). Moderately larger MCD sizes are observed in fluorinated samples compared to control samples (Table 3).

Vibrational spectroscopic study of bone samples

ATR-FTIR spectrum of bone samples

Both diamond and Ge ATR-FTIR spectra of modern bone (Figure 2, Figure S2) display the characteristic absorption bands ascribed to the internal vibrations of apatite phosphate groups, to the structural carbonate incorporated at the A and B sites (hydroxyl and phosphate sites, respectively) of apatite structure and to the amide bands related to the collagen matrix (e.g. [START_REF] Elliott | Phosphates: Geochemical, Geobiological, and Material Importance[END_REF][START_REF] Chadefaux | Curve-fitting micro-ATR-FTIR studies of the amide I and II bands of type I collagen in archaeological bone materials[END_REF]. Intense bands observed between 550 and 600 cm -1 and between 1010 and 1090 cm -1 are related to the ν4 PO4 bending and ν3 PO4 stretching modes of the structural phosphate groups respectively, while the weaker band at ~960 cm -1 is related to the ν1 PO4 stretching mode. As previously observed by [START_REF] Aufort | Modeling the attenuated total reflectance infrared (ATR-FTIR) spectrum of apatite[END_REF], the line shape and particularly the width of the strong ν4 and ν3 PO4 bands is affected by macroscopic electrostatic effects, i.e. related to electrostatic interactions between apatite particles and therefore depending on porosity, grain size and shapes of particles. In contrast, the position and line shape of weaker and narrower bands, such as the ν 1 PO 4 band, are less affected by these electrostatic effects and are thus expected to provide a better insight into the short-range order of the crystal structure [START_REF] Balan | Line-broadening effects in the powder infrared spectrum of apatite[END_REF][START_REF] Aufort | Modeling the attenuated total reflectance infrared (ATR-FTIR) spectrum of apatite[END_REF][START_REF] Aufort | Macroscopic electrostatic effects in ATR-FTIR spectra of modern and archaeological bones[END_REF][START_REF] Aufort | Assessing bone transformation in late Miocene and Plio-Pleistocene deposits of Kenya and South Africa[END_REF]. However, the overlap of the ν 1 PO 4 band with the stronger ν3 PO4 band in the diamond ATR spectrum significantly affects the line shape of the ν 1 PO 4 band. In Ge ATR-FTIR spectra, the overlap between ν 1 and ν 3 PO 4 bands is less pronounced. Information related to the structural order of altered samples was thus extracted from the comparison of ν 1 PO 4 Ge ATR-FTIR bands after baseline subtraction (Figure S3).

Note that a systematic decrease in the intensity of amide bands is observed in the ATR-FTIR spectra of all altered bone samples compared to that of unaltered bone. This decrease reflects the degradation of collagen and is more significant in samples altered in a phosphate buffer at 70°C (D and D') and in the sample fluorinated at pH 9 (F'), for which the amide I band is hardly visible on the ATR-FTIR spectra (Figure S2). The ν1 PO4 Ge ATR-FTIR band is located at ~960 cm -1 in modern ox bone TH1 and at ~966 cm -1 in the carbonated fluorapatite (C-Fap) sample. It is well modeled by a large and dominantly Gaussian signal in TH1 while it displays a pronounced Lorentzian shape in C-Fap.

The ν1 PO4 Ge ATR-FTIR band is systematically shifted towards higher frequencies in all bone powder samples altered with fluorine compared to their non-fluorinated counterparts (Figure 3). This shift towards higher vibrational frequencies is consistent with the unit cell volume contraction typically associated with fluoride ion incorporation in the apatite channel sites. All bone powders altered with fluorine at 70°C (D', E', F', G') display a shift of + 2.0 -2.5 cm -1 compared to their respective non-fluorinated counterparts (Table 4). This shift is less pronounced (+ 0.8 cm -1 ) for the bone powder altered in a phosphate buffer at 20°C (C+NaF). This is consistent with the lower fluorine content (1.6 %) measured in this sample (Table 2) than in bones altered at 70°C (2.0-2.5%). Indeed, the increase in ν1 PO4 Ge ATR-FTIR frequency correlates with the increase in fluorine content (Figure S4a). In contrast, the Full Width at Half Maximum (FWHM) of the ν1 PO4 band is not directly correlated with fluoride ion incorporation. Overall, no significant narrowing of the band is observed from nonfluorinated to fluorinated samples (Table 4). The line shape asymmetry was assessed by comparing the Half Width at Half Maximum (HWHM) on the high frequency side of the band to the corresponding full width (FWHM), which is systematically lower in fluorinated samples (Table 4). The asymmetry parameter, defined as 1 -2(𝐻𝑊𝐻𝑀 𝐹𝑊𝐻𝑀 ⁄ ) increases with increasing frequency of the ν1 PO4 band (Figure S4b). The infrared splitting factor (IRSF;

Weiner and Bar-Yosef, 1990) determined from the ν4 PO4 bands on the Ge ATR-FTIR spectra is also broadly correlated to frequency of the ν 1 PO 4 band (Figure S5).

Phosphate stretching bands in Raman spectra

Complementary information on the fluorine incorporation and structural order of the sample can also be obtained from Raman spectroscopy. An upward shift (+1 cm -1 ) in the band position of ν1 PO4 stretch and a decrease (-1 cm -1 ) in FWHM was observed in the wafer sample altered in NaF for 1 week at 20 °C (Experiment A; Figure 4a). These observations are in agreement A more pronounced upward shift (+2.5 cm -1 ) in the ν1 PO4 band position and decrease (-4 cm -1 ) in FWHM was observed in the bone powder sample altered with NaF 10 -2 M for 3 weeks at 20 °C compared to the control sample (Experiment C; Figure 4b). For both samples, Raman spectra were collected on various grains to check the homogeneity, reproducibility and significance of the variations observed in both peak position and FWHM. The longer duration of the experiment and the larger interface between powder and solution can account for the more important variations in Raman spectral features observed in Figure 4b compared to Figure 4a. Spectral parameters, i.e. position of the phosphate peak, FWHM and asymmetry parameter, of the other altered bone powder samples are reported in Table 4.

Concerning the bone wafers soaked in the organic buffer for 3 weeks at 70°C (experiment H), an upward shift (+ 3 cm -1 ) in the ν1 PO4 band position and a decrease (~ -4 cm -1 ) in FWHM was observed in the bone wafer altered with NaF 10 -2 M compared to the control wafer (Figure 4c, Table S2). For both samples, Raman spectra were collected on a transect surface, obtained by cutting perpendicular to the largest face of the wafer to obtain a cross-section in which only the outer edges of the transect have been in direct contact with the solution. Raman spectra were collected at various spots along the transect surface, from the edges to the centre, to provide spatial information on the incorporation of fluorine. Compared to spectra recorded on various grains of the bone powder (Figure S4b), a greater heterogeneity in peak positions and FWHM, ranging 959.7 -960.6 cm -1 and 17.1 -13.0 cm -1 and 962.9 -963.8 cm -1 and 12.5-9.3 cm -1 for the control and fluorinated samples respectively, is observed between spectra collected at various spots on the transects. However, no regular trend was observed from the edges to the core of the wafer. The whole transect is thus affected by fluorination, with some spatial variations, suggesting fluoride diffusion through the bulk wafer, i.e. at the millimetre scale.

A decrease in Raman FWHM is systematically observed in samples reacted with fluorinated solutions. Raman spectroscopy thus confirms the results obtained with ν 1 PO 4 Ge ATR-FTIR bands and attests of the higher degree of crystalline order in artificially fluorinated samples.

Note that Raman asymmetry parameters are about twice lower than their Ge ATR-FTIR counterparts (Table 4).

3.4.2 Environment of structural carbonate groups inferred from the ν2 CO3 band in ATR-

FTIR spectra

Regarding structural carbonate groups, diamond ATR-FTIR bands related to the ν2 out-ofplane bending mode of CO3 2-groups in bone powder samples are observed at 879-881 cm -1 for A sites and 871-873 cm -1 for B sites (Figure 5a). The broad band centred at ~860-865 cm -1 , resulting in a significant asymmetry towards low wavenumbers, is ascribed to labile carbonate groups [START_REF] Rey | Non-apatitic environments in bone mineral: FT-IR detection, biological properties and changes in several disease states[END_REF][START_REF] Michel | Chemical and structural changes in Cervus elaphus tooth enamels during fossilization (Lazaret cave): a combined IR and XRD Rietveld analysis[END_REF]. After normalization of the intensity using the ν4 PO 4 band, all altered bone samples exhibit a lower carbonate content than the original TH1 sample. Furthermore, the ν2 CO3 band intensity decreases from non-fluorinated to fluorinated bone samples. Bone powders altered with fluorine in alkaline conditions (F', G') or at neutral pH in an organic buffer (E') display an additional signal at 865 cm -1 . This signal matches that observed in the reference sedimentary carbonated fluorapatite (Figure 5b), i.e. a narrow peak observed at ~865 cm -1 . It has been ascribed to a clumped (CO3 2-, F -) defect substituting for the phosphate group in the apatite structure and has also been observed in fossil teeth from the East African Rift [START_REF] Yi | A carbonate-fluoride defect model for carbonate-rich fluorapatite[END_REF][START_REF] Yi | Probing atomic scale transformation of fossil enamel using FTIR and NMR spectroscopy: A case study from the Tugen Hills (Rift Gregory, Kenya)[END_REF]. In contrast, no signal corresponding to this clumped (CO3 2- , F -) defect is observed in bone powders altered with fluorine in a phosphate buffer (C', D').

The clumped defect signal in the bone powder sample fluorinated in an organic buffer (E') is less intense (by ~2/3) than in bone powders fluorinated in alkaline conditions (F', G'; Figure 5b). Note that there is no significant variation in A/B carbonate ratios between non-fluorinated samples and their fluorinated counterparts, regardless of whether the clumped (CO3 2-, F -) defect is formed or not.

Ge ATR-FTIR spectra of non-fluorinated bone powders, normalised using the ν4 PO4 band intensity, are reported in Figure S6a. Although displaying a lower signal/noise ratio, Ge ATR-FTIR spectra of bone powders soaked in a phosphate buffer (C, D, C', D') reveal the presence of a weak and broad signal below the ν 2 CO 3 band on its high frequency side, at ~890 cm -1

(Figure S6a andS6b). This spectral feature could not be observed in the matching diamond ATR-FTIR spectra, due to the strong overlap with the electrostatically broadened ν 3 PO 4 band.

This signal is accompanied by a decrease in carbonate content compared to the other samples. [START_REF] Apfelbaum | A FTIR study of carbonate in synthetic apatites[END_REF] observed a similar spectral feature in FTIR spectra of synthetic carbonated apatites with low carbonate contents and ascribed it to HPO4 2-ions. Indeed, the P-OH stretching mode of HPO4 2-absorbs in the same spectral region as the CO3 bending mode as pointed out by [START_REF] Arends | HPO 4 2content in enamel and artificial carious lesions[END_REF] who assessed the contribution of HPO4 2-ions to the ν 2 CO 3 signal in healthy and pathologic enamel. [START_REF] Wopenka | A mineralogical perspective on the apatite in bone[END_REF] also reported on the presence of an additional weak Raman peak around 900 cm -1 in calcium phosphate phases containing HPO 4 2-ions. The presence of HPO 4 2-ions is thus inferred in samples reacted with phosphate buffered solutions. The 19 F MAS NMR spectra of bones altered with fluorine display a main signal at ~ -102 ppm ascribed to F -ions incorporated in the channel sites of the apatite structure (Figure 7). This signal is broader in bone samples (FWHM of 6.1 ppm at 20°C and 3.7-4.1 ppm at 70°C) than in the reference sedimentary carbonated fluorapatite (1.8 ppm). A less intense signal is observed in sedimentary carbonated fluorapatite at -88 ppm and corresponds to the clumped (CO 3 2-, F -) defect substituting for the phosphate group in the structure of carbonated fluorapatite [START_REF] Yi | A carbonate-fluoride defect model for carbonate-rich fluorapatite[END_REF]. Due to the low 14 kHz spinning frequency of the rotor in this experiment, the chemical shift anisotropy distributes an important contribution of the fluorine signal into the spinning side bands. For this reason, two spinning side bands are represented on each side of the isotropic signal to better assess the presence or absence of clumped defect in the altered samples. Bone powders altered with fluorine in alkaline conditions (F', G') display the signal at -88 ppm while samples altered in a phosphate buffer (C', D') do not, which is consistent with the observations made on the ν2 CO3 band of diamond ATR-FTIR spectra. 19 F NMR spectra of F' and G' suggest that the proportion of fluoride ions incorporated in the channel sites is far greater than that incorporated in the clumped defect, with the area of the clumped defect signal representing about 1% of the total 19 F NMR spectrum area in both samples. Unlike the ν 2 CO 3 band, no defect signal could be observed in the sample altered in the organic buffer (E'). As signal could explain why the latter is not visible in the 19 F MAS NMR spectrum of E'.

1 H MAS NMR spectra of altered bones display a signal at 0 ppm corresponding to the hydroxyl groups located in the channel sites, aliphatic signals between 1 and 2 ppm associated with the organic matrix of the bone and a large signal at ~5 ppm related to adsorbed water (Figure S7). In the unaltered bone, TH1, channel hydroxyl groups are not observed because of their low concentration [START_REF] Pasteris | Lack of OH in nanocrystalline apatite as a function of degree of atomic order: implications for bone and biomaterials[END_REF]Cho et al., 2013) 5). A stoichiometric hydroxylapatite contains about 3.4 wt.% of OH groups but due to a high proportion of vacancies at anionic sites in bones, less than half of OH sites are typically filled with OH groups [START_REF] Loong | Evidence of hydroxyl ion deficiency in bone apatites: an inelastic neutron scattering study[END_REF], with estimations in the literature ranging from substantial depletion (e.g. 20 % of the expected amount in [START_REF] Cho | Detection of hydroxyl ions in bone mineral by solidstate NMR spectroscopy[END_REF] to near absence of OH groups (e.g. [START_REF] Pasteris | Lack of OH in nanocrystalline apatite as a function of degree of atomic order: implications for bone and biomaterials[END_REF]. Even if all channel sites were occupied by OH groups in the control bone samples, percentages of remaining OH groups after fluorination would not exceed 0.4 wt. %. This is consistent with the high fluorine contents measured in the fluorinated samples, ranging between 1.6 and 2.5 wt%. Note that the maximum fluorine amount that can be incorporated in the channel sites of apatite is 3.8 wt%, therefore not all channel sites are occupied by F -nor OH - ions in the fluorinated bone samples investigated here.

Discussion

Evidence of secondary apatite formation

All reacted samples display significant changes of the chemical, isotopic and structural properties of apatite with respect to the original bone. In line with previous observation by [START_REF] Pasteris | Experimental fluoridation of nanocrystalline apatite[END_REF], these changes can be interpreted as resulting from the partial dissolution of primary biogenic material and formation of a secondary apatite. In fact, a systematic occurrence of fluoride ions in apatite channel sites of samples reacted with fluorinated solutions is attested by their 19 F NMR spectra and can be inferred from the upward shift in ATR-FTIR and Raman ν1 PO4 band positions and correlated decrease of a cellparameter (Tables 3 and4; Figure S8). Based on the study of [START_REF] Brenan | Kinetics of fluorine, chlorine and hydroxyl exchange in fluorapatite[END_REF], solid-state diffusion of fluorine in the crystallites is not expected to be an efficient process in the range of alteration conditions investigated here, e.g. 3 weeks at 20 and 70°C, even though the defective nature of biologic apatite might facilitate chemical diffusion with respect to well-crystallised samples. Several observations also reveal significant changes pointing to the formation of a secondary phase. These changes include the observation of HPO4 2-groups and modification of 18 Ophosphate value in the samples reacted with phosphate buffered solutions, as well as the formation of the (CO3 2-, F -) defect in some of the reacted samples. However, the lack of extensive narrowing of ν1 PO4 bands and 19 F NMR signals in altered bone samples also suggests that dissolution and reprecipitation of a new phase is an incomplete process.

Based on these considerations, the ν1 PO4 Ge ATR-FTIR bands were fitted using a twocomponent model. One of the component is a Gaussian function, whose position and width were kept fixed to that of the unaltered bone TH1. The second component is described by a Lorentzian function whose position was kept fixed to that of the reference carbonated fluorapatite sample in fluorinated samples and was let free in non-fluorinated samples (Figure 3). Assuming that extinction coefficients for the ν1 PO4 band are similar in both phases, it is expected that the relative proportion of these two spectroscopic contributions match the fraction of PO4 groups occurring in the primary and secondary apatite. Thus, it should reflect the relative molar proportions of both phases. In fluorinated samples, percentages of the secondary phase are about 60 % in samples altered at 70°C (D', E', F', G') and 30% in the sample altered at 20°C. In non-fluorinated samples, the second component is observed at 962.7-963.5 cm -1 and accounts for 19 to 57 % of the total ν1 PO4 Ge ATR band. Consistently, the frequency of the ν1 PO 4 band reported as a function of the fraction of secondary apatite broadly defines two distinct linear trends depending on the presence or absence of fluorine (Figure 8). For fluorinated samples, the linear trend points to the frequency of the reference carbonated fluorapatite whereas for the other samples it points to a frequency slightly above that of hydroxylapatite (962.9 cm -1 , from [START_REF] Balan | Line-broadening effects in the powder infrared spectrum of apatite[END_REF][START_REF] Aufort | Modeling the attenuated total reflectance infrared (ATR-FTIR) spectrum of apatite[END_REF]. For fluorinated samples, the F concentration reported as a function of secondary apatite fraction also supports a mixing model involving the starting material and newly formed fluorapatite displaying an almost fulloccupancy of the apatite channel sites by fluorine. Almost full channel occupancy in the secondary phase is also consistent with the corresponding very weak OH signal observed in the 1 H NMR spectra.

This set of observations supports the precipitation of a secondary phase induced by a partial dissolution of the original bioapatite in all reacted bone samples. It is noteworthy that the secondary apatite can consist in fluorapatite or hydroxylapatite, depending on the composition of the altering aqueous solution. Accordingly, fluorine does not appear to be a key element driving the transformation of bone apatite. However, fluorinated samples tend to display a larger proportion of secondary apatite, suggesting a higher rate of transformation. A higher precipitation rate of fluorapatite is expected due to its lower solubility and corresponding larger chemical affinity of the precipitation reaction compared to that of hydroxylapatite [START_REF] Elliott | Phosphates: Geochemical, Geobiological, and Material Importance[END_REF]. In both instances, the driving force of the transformation is likely the solubility difference between the secondary phase and the more soluble bioapatite. While in the fluorinated samples the formation of carbonated fluorapatite is driven by its lower solubility compared to that of bioapatite [START_REF] Kolodny | Dinosaur bones: fossils or pseudomorphs? The pitfalls of physiology reconstruction from apatitic fossils[END_REF][START_REF] Trueman | Trace elements in recent and fossil bone apatite[END_REF], the replacement of bioapatite by a less carbonated and more hydroxylapatite-rich phase in the case of bones samples altered without fluorine, could be driven by the lower solubility of hydroxylapatite compared to that of carbonated bioapatite [START_REF] Berna | Solubilities of bone mineral from archaeological sites: The recrystallization window[END_REF]). Another feature emerging from the present series of experiments is an apparent maximum advancement of the transformation reaction, with a fraction of secondary apatite limited at ~60%. Note that an estimate of the fraction of secondary fluorapatite can also be inferred from the fluorine content measured in the fluorinated bone powders. Indeed, by considering that pure fluorapatite contains 3.77 wt.% F, the fluorinated samples with F contents ranging from 2.0 to 2.5 wt.% should consist of about 48 to 61 % of fluorapatite, which supports the findings from the ν1 PO4 band decomposition.

The limited range of transformation, irrespective of the alteration conditions, suggests that the secondary phase could have a protecting role against their further transformation. Thus, it is likely that the formation of secondary apatite occurs at the surface of initial grains. The degradation degree of the collagen matrix, inferred from amide bands in ATR-FTIR spectra and the signals ascribed to carboxylic functions and aliphatic carbons in 13 C NMR spectra, does not seem to affect the advancement of the apatite transformation.

Carbonate incorporation in secondary apatite

The oxygen and carbon isotopic compositions of structural carbonate groups from fossil apatites are important proxies for palaeo-environmental reconstructions. The behaviour of carbonate groups during aqueous alteration of teeth and bones thus deserves a special attention.

In the present study, the overall decrease in the ν 2 CO 3 band intensity of reacted samples, suggests that the secondary apatite phase is depleted in carbonate compared to the initial material. However, several observations also indicate that it is not carbonate-free.

In the fluorinated samples, the (CO3 2-, F -) defect is readily identified from its specific vibrational and NMR spectroscopic properties. Such atomic-scale modification of the environment of carbonate groups substituted for phosphate groups is a strong indication of their incorporation during the precipitation of the secondary apatite from the solution. In an ion-byion attachment model of crystal growth, incorporation at the B-site involves a competition between PO4 and CO3 groups. A high concentration of phosphate in solution is thus expected to inhibit carbonate incorporation at the B-site, precluding the formation of the clumped defect in phosphate buffered solutions.

In the absence of (CO3 2-, F -) defect, the ν2CO3 band reveals little modification of the carbonate environment or A-type to B-type ratio, which could suggest that only structural carbonate groups initially present in the bone apatite are preserved in these reacted samples.

However, the oxygen and carbon isotopic compositions of structural carbonates contradict this interpretation. The lower δ 13 C values of bones altered in a phosphate buffer (C, C', D, D') suggest incorporation of organic carbon, characterised by lower 13 C/ 12 C ratios (typically ~ -20 ‰, [START_REF] Lee-Thorp | Stable carbon isotope ratio differences between bone collagen and bone apatite, and their relationship to diet[END_REF][START_REF] Koch | Isotopic reconstruction of past continental environments[END_REF] than apatite structural carbonate, likely originating from the degradation of the collagen matrix. This is consistent with the significant loss of the signal corresponding to carboxylic functions observed in 13 C NMR for D and D' samples. The oxygen isotopic composition also reveals system opening. Samples tend to display a broad negative correlation as a function of secondary apatite fraction. Contrary to phosphate, oxygen exchange between carbonate in solution and water molecules occurs rapidly (Wang andCerling, 1994, Lécuyer et al., 1999;[START_REF] Geisler | Real-time monitoring of the overall exchange of oxygen isotopes between aqueous CO3 2and H2O by Raman spectroscopy[END_REF]. Consequently, the variation of the δ 18 O carbonate values combined with almost constant δ 13 C in samples altered in alkaline or organic buffer conditions, where the relative preservation of the organic matrix limits the incorporation of lighter organic carbon, could reflect a partial re-incorporation of carbonate during the transformation of apatite via dissolution and reprecipation from solution. It is noteworthy that the carbon and oxygen isotope compositions of structural carbonates in samples altered in alkaline conditions display similar variations irrespective of the presence or absence of fluorine, suggesting re-incorporation of carbonate groups in similar quantities. [START_REF] Rogers | X-ray diffraction of the effects of heat treatment on bone mineral microstructure[END_REF][START_REF] Pucéat | Can crystallinity be used to determine the degree of chemical alteration of biogenic apatites?[END_REF][START_REF] Trueman | Why do crystallinity values fail to predict the extent of diagenetic alteration of bone mineral? Palaeogeography[END_REF][START_REF] Thompson | The application of a new method of Fourier Transform Infrared spectroscopy to the analysis of burned bone[END_REF]. In the present study, a special attention was given to the use of ν1 PO4 Ge ATR-FTIR band to infer the degree of transformation of reacted samples. In previous studies (e.g. [START_REF] Pasteris | Experimental fluoridation of nanocrystalline apatite[END_REF][START_REF] Pucéat | Can crystallinity be used to determine the degree of chemical alteration of biogenic apatites?[END_REF], the ν1 PO4 bands observed in Raman spectroscopy were also used to infer the structural state of experimentally or naturally altered biogenic apatite samples. It is thus relevant to compare the information obtained from IR and Raman spectroscopy using closely related vibrational modes. We note, however, that in crystalline apatite the intense ν1 PO4 signal observed in the Raman spectrum is related to a A irreducible representation. It differs from the vibrational mode belonging to a E irreducible representation and corresponding to the weak ν1 PO4 signal of the IR spectrum [START_REF] Leroy | Polarized micro-Raman study of fluorapatite single crystals[END_REF][START_REF] Ulian | Effect of mechanical stress on the Raman and infrared bands of hydroxylapatite: A quantum mechanical first principle study[END_REF]. Both types of vibrational modes however display very close frequencies. In the present study, the position of the ν1 PO4 Ge ATR-FTIR band correlates well with that of the Raman ν1 PO4 (Figure 9a), both spectroscopies showing the same extent of frequency shift from non-fluorinated to fluorinated bone samples. However, Raman and Ge ATR-FTIR FWHM do not correlate well (Figure 9b). Indeed, the ν1 PO4 Raman peaks are narrower and more symmetric than their Ge ATR-FTIR counterparts, the Raman asymmetry parameters being about half that of ATR-FTIR peaks (Figure 9c). This difference could be related to the observation that the Raman intensity is more strongly affected by structural distortions than the infrared one [START_REF] Ulian | Effect of mechanical stress on the Raman and infrared bands of hydroxylapatite: A quantum mechanical first principle study[END_REF]. As a consequence, the smaller carbonate content of secondary apatite might lead to an increase in its Raman scattering efficiency, leading to an overexpression of its contribution in the Raman spectra. Correspondingly, the ν1 PO4 Raman peaks appear as narrower and more symmetric than their infrared counterparts do. These observations illustrate how the physical processes involved in related but different probing techniques can affect the determination of sample structural order.

Implications for fossilisation processes

This work has implications regarding bone diagenetic processes and stable isotopes analysis of fossil bioapatite. Our results are consistent with the observations that the relative importance of dissolution/recrystallisation processes during diagenesis, not only depends on the bone microstructure but also on the physical-chemical conditions prevailing in the fossilisation environments [START_REF] Berna | Solubilities of bone mineral from archaeological sites: The recrystallization window[END_REF][START_REF] Pfretzschner | Fossilization of Haversian bone in aquatic environments[END_REF][START_REF] Trueman | Mineralogical and compositional changes in bones exposed on soil surfaces in Amboseli National Park, Kenya: diagenetic mechanisms and the role of sediment pore fluids[END_REF], Zazzo et al., 2004b). As far as palaeoenvironmental reconstructions based on stable isotope analysis of bioapatites are concerned, the nature of ionic species in percolating fluids in contact with fossils could be key parameters driving the preservation or alteration of isotopic compositions.

Importantly, dissolution-recrystallisation of bone can occur in a fluorine-free environment to form secondary carbonated hydroxylapatite. This suggests that other factors drive the transformation of bone, such as the reactivity of a disordered surface layer on bone crystallites (e.g. Wang et al., 2013) and a high carbonate content [START_REF] Hankermeyer | Dissolution rates of carbonated hydroxyapatite in hydrochloric acid[END_REF]. The fact that alteration of the original bioapatite is possible without a significant variation of the A-type to B-type carbonate ratio points to a limit of single-analytical approaches in assessing bone diagenesis. In addition, it does not exclude possible reincrodorporation of carbonate into the structure, which makes the assessment of isotopic compositions preservation more complex.

This could explain why several studies reported that indicators of diagenesis indicated little about isotope alteration (e.g. [START_REF] Trueman | Why do crystallinity values fail to predict the extent of diagenetic alteration of bone mineral? Palaeogeography[END_REF].

The dissolution-recrystallization process of bone is incomplete with a maximum fraction of secondary apatite limited to ~60 %. It is thus suggested that partial transformation of bone occurs even at a nanometric scale with partial dissolution-recrystallisation of individual crystallites (Figure 10). However, it is noteworthy that the chemical changes observed between the primary and secondary phases are not compatible with the premise of Ostwald ripening process even though this mechanism has been proposed to account for dissolution of smaller crystallites and formation of larger crystals [START_REF] Ayliffe | The retention of primary oxygen isotope compositions of fossil elephant skeletal phosphate[END_REF]. The formation of a secondary phase and the lack of increase in MCD size in altered bones observed in this study points primarily to a chemically driven transformation rather than a surface driven ripening process.

Compared to modern unaltered bone, artificially fluorinated bone samples in organic buffers or in alkaline conditions show similar transformations as fossils: degradation of organic content, increase in crystallinity (e.g. increase in IRSF values), formation of carbonated fluorapatite (i.e.

clumped defect at B-site). In fossil enamel from late Tertiary continental environments, such a transformation of bioapatite to carbonated fluorapatite has been shown to occur via a dissolution-recrystallisation process, with extensive alteration of the carbonate environment [START_REF] Yi | Probing atomic scale transformation of fossil enamel using FTIR and NMR spectroscopy: A case study from the Tugen Hills (Rift Gregory, Kenya)[END_REF]. The relative preservation of the chemical and structural environment of the carbonate groups in altered bone powders is consistent with a subtler transformation mechanism, compatible with a partial dissolution-recrystallisation process operating at nanometer-size scale.

Compared to actual fossilisation environments, the alteration experiments conducted here on modern bone samples have been performed in a closed system and can be expected to become chemically self-buffered fairly quickly. In comparison, actual fossilisation environments rather lead to an open-system behaviour where the bone material is slowly altered by the repeated passage of new aqueous fluids over geological times. However, atomic scale transformation of fossil bones from late Miocene deposits of Kenya and Plio-Pleistocene deposits of South Africa also points to a partial dissolution-recrystallization process (Aufort et al., 2019). This could indicate that, also in nature, a closing of the system could occur after a certain amount of time. Accordingly, fossil bones could record the physical-chemical conditions prevailing in their early fossilisation environments. This points to a key role of the secondary phase formation as a limiting factor of the transformation process and begs the question of its potential protective role against total dissolution of the primary bioapatite.

Finally, this work illustrates that bone diagenesis cannot be summed up using only one crystallinity parameter and underlines the need to use multiple analytical approaches to depict a more complete picture of the extent of diagenetic alteration in bone. Furthermore, this shows that the combination of site-specific isotopic compositions measurements with atomic scaleprobing spectroscopies is an effective way of deciphering dissolution-recrystallisation pathways in bone.

Conclusions

This study provides a quantitative assessment of the mineralogical transformations at the atomic scale and stable isotopic changes during in vitro alteration experiments of bone bioapatite.

Partial dissolution of the biogenic apatite and recrystallization of a carbonate-bearing secondary apatite was observed in all bone samples altered in aqueous solutions at 20 and 70°C. This transformation occurs irrespective of the presence or absence of fluorine in solution and leads to the formation of carbonate-bearing fluorapatite or carbonate-bearing hydroxylapatite

respectively. An ATR-FTIR based estimate of this transformation revealed that the fraction of newly formed secondary apatite was limited to about 60%. This result could point to a protective role of the secondary apatite against total dissolution of the primary bioapatite. On a more general note, this work also contributes to the debate surrounding the passivation capacity of secondary phases (e.g. [START_REF] Velbel | Formation of protective surface layers during silicate-mineral weathering under well-leached, oxidizing conditions[END_REF][START_REF] Daval | Influence of amorphous silica layer formation on the dissolution rate of olivine at 90°C and elevated pCO2[END_REF][START_REF] Daval | Linking nm-scale measurements of the anisotropy of silicate surface reactivity to macroscopic dissolution rate laws: New insights based on diopside[END_REF][START_REF] Sissmann | The deleterious effect of secondary phases on olivine carbonation yield: Insight from time-resolved aqueous-fluid sampling and FIB-TEM characterization[END_REF][START_REF] Harrison | Influence of surface passivation and water content on mineral reactions in unsaturated porous media: Implications for brucite carbonation and CO2 squestration[END_REF], relevant to a variety of geochemical contexts involving mineral replacement reactions through dissolution-recrystallization processes at the solid/solution interface. 4 Parameters obtained from the ν1 PO4 band in Ge ATR-FTIR spectra. In addition to the Full Width at Half Maximum (FWHM), we calculated the Half Width at Half Maximum (HWHM) on the high frequency side, the low frequency side exhibiting a pronounced asymmetry. The asymmetry parameter is then defined as 1 -2(𝐻𝑊𝐻𝑀 𝐹𝑊𝐻𝑀 ⁄

). An asymmetry parameter equal to zero corresponds to a perfectly symmetrical band, an increase in the parameter corresponds to an increase in asymmetry. The IR Splitting Factor (IRSF) was calculated from the ν4 PO4 Ge ATR-FTIR band, according to [START_REF] Weiner | States of preservation of bones from prehistoric sites in the Near East: a survey[END_REF]. Parameters related to the Raman ν1 PO4 peak, i.e. position, FWHM and asymmetry, are also reported. For a 4 x 20 x 30 nm 3 crystallite size, a maximum fraction of secondary carbonated apatite of 60 % corresponds to a ~1 nm thick layer. It is proposed that partial dissolution-recrystallization of bone occurs at the nanometre scale at the surface of each individual crystallite to account for the apparent maximal fraction of secondary phase and the lack of increase in MCD size. Note that the representation is not to scale.

  3.4.2. Structural order probed by phosphate vibrational modes in ATR-FTIR and Raman spectra 3.4.2.1. Phosphate stretching bands in ATR-FTIR spectra

  with the results of fluorination experiments carried out by[START_REF] Pasteris | Experimental fluoridation of nanocrystalline apatite[END_REF] on dentine under similar conditions and indicate fluorine incorporation in the structure. This is consistent with the similar weaker resistance to alteration of both bone and dentine relative to enamel due to smaller crystallite sizes. No further peak position shift and decrease in FWHM were observed with increased NaF concentration (1 M), as previously observed by[START_REF] Pasteris | Experimental fluoridation of nanocrystalline apatite[END_REF], and further fluorination experiments were carried out with 10 -2 M NaF solutions.

3. 5 .

 5 Nuclear Magnetic Resonance spectroscopy of bone samples The 13 C CP MAS NMR spectrum of modern bone displays two components related to Atype (~168 ppm) and B-type (~170 ppm) carbonate substitutions, a component at ~173-175 ppm related to the carboxylic acids from amino acids in the organic matrix, as well as numerous signals between 10 and 80 ppm corresponding to organic functions that are enhanced by the Cross-Polarisation sequence (Figure 6a). The 13 C CP MAS NMR spectra of bone powders altered in an organic buffer (experiments E, E') and non-fluorinated alkaline solution (F) display a moderate decrease in the signals ascribed to the organic matrix compared to the 13 C CP MAS NMR spectrum of unaltered bone. In contrast, spectra of bone powders altered in a phosphate buffer (experiments D, D') and in fluorinated alkaline solution (F') reveal a significant degradation of the organic matrix, which is almost total in the D' sample. Note that the lower signal-to-noise ratio in this sample indicates a less effective cross-polarisation between 1 H and 13 C nuclei due to a lower amount of protons. Regarding the chemical environment of the carbonate groups, all 13 C spectra display predominantly B-type signals at ~170 ppm, which is consistent with the predominant nature of the B-type substitution in bioapatites (Figure 6b).

  observed in Fig 5, the intensity of the clumped defect in the ν2 CO3 diamond ATR-FTIR band is lower for E' than in F' and G'. Furthermore, the broadness and position (-82.2 ppm) of the first spinning side band on the low ppm side may hinder the NMR signal of the clumped defect in E'. The overlap between this spinning side band and a predictably weak clumped defect 19 F

  and significant overlap of their NMR signal with aliphatic signals from the organic matrix. The contribution of aliphatic signals is reduced in artificially altered bone powders, in agreement with the degradation of the organic component observed in their respective 13 C NMR spectra. All samples altered with fluorine display a weaker OH channel signal, consistent with an occupation of channel sites by OH -and F -ions. A semi quantitative estimation of the fraction of OH -groups replaced by F -ions can be obtained by matching the baseline due to the organic component of the control sample and its counterpart altered with fluorine. The OH signal is then fitted by a Gaussian function for the control sample and a Gaussian of identical width and position is used to fit the OH signal of the sample altered with fluorine. In the artificially fluorinated samples, OH channel signals range from 4 to 12 % of that observed in non-fluorinated samples (Table

4. 3 .

 3 Comparison of infrared and Raman spectroscopy in the determination of apatite structural order Structural changes of fossil apatite are often characterized by crystallinity indices obtained from infrared spectroscopy, Raman spectroscopy or X-ray diffraction. Although usually displaying similar trends, these indices are often poorly correlated because they differ in physical nature

Figure 1 a

 1 Figure 1 a. δ 18 Ocarbonate of the unaltered and artificially altered bone samples reported against their δ 18 Ophosphate values and compared with the linear correlation derived by Lécuyer et al. (2010) from compiled data of δ 18 O values of both carbonate and phosphate from modern mammals (solid line) and with the linear correlation derived by Zazzo et al. (2004b) from modern hippopotamuses. b. δ 13 C values of the unaltered and artificially altered bones. Red and blue circles correspond to non-fluorinated and fluorinated bone samples respectively.

Figure 2

 2 Figure2Diamond and Ge ATR FTIR spectra of the modern ox bone used in all alteration experiments, TH1. For better comparison, spectra are shifted vertically and the intensity of the Ge ATR spectrum was multiplied by the factor three.

Figure 3

 3 Figure 3 ν1 PO4 Ge ATR-FTIR bands (black line) of non-fluorinated and fluorinated bone samples in different buffers and pH conditions (Experiments C, D,E, F, G) compared to the unaltered bone material (TH1) and to sedimentary carbonated fluorapatite. Fits (red line) of the ν1 PO4 band in altered bones Ge ATR-FTIR spectra were achieved using two components: a Gaussian signal whose position and width was kept fixed to that of the unaltered bone TH1 (orange line) and a Lorentzian signal whose position was kept fixed in fluorinated samples and free in non-fluorinated samples (green line). Parameters of the fits are reported in Table6. Percentages of the second component are indicated on the right-hand side of the figure.

Figure 4 a.

 4 Figure4a. Raman spectra of the ν1 PO4 band in unaltered bone wafer and in bone wafer altered with 10 -2 M NaF in a phosphate buffer solution for 1 weeks at 20°C (Experiment A). b. Raman spectra of the ν1 PO4 band in unaltered bone powder and in bone powder altered with 10 -2 M NaF in a phosphate buffer solution for 3 weeks at 20°C (Experiment C). c. Raman spectra of the ν1 PO4 band collected at various loci on a transect of bone wafer altered with and without 10 -2 M NaF in an organic buffer solution for 3 weeks at 70°C (Experiment H). The vertical dashed line is guide for the eye.

Figure 5 a

 5 Figure 5 a. ν2 CO3 diamond ATR-FTIR bands of non-fluorinated and fluorinated bone samples in different buffers and pH conditions (Experiments C, D, E, F, G) compared to unaltered bone TH1 and sedimentary carbonated fluorapatite C-Fap. All spectra are normalised based on the ν4 PO4 band intensity. b. ν2CO3 diamond ATR-FTIR band ascribed to the clumped defect in E', F' and G', obtained by subtracting the ν2CO3 band of the non-fluorinated sample from the ν2CO3 band of the fluorinated sample diamond ATR-FTIR spectra compared to the ν2CO3 band of carbonated fluorapatite. Peak areas are 0.09, 0.13 and 0.16 respectively. Subtracted spectra were normalised on the A and B components of the ν2 CO3 band.

Figure 6 a

 6 Figure 6 a. 13 C CP MAS NMR spectra of the unaltered bone, bones artificially altered with and without fluoride and 13 C MAS NMR spectrum of sedimentary carbonated fluorapatite. Signals comprised between 10 and 80 ppm correspond to organic carbon from the collagen matrix. b. Enlargement of the 140-200 ppm region of the 13 C CP MAS NMR spectra. Vertical dashed lines indicate the 13 C NMR positions of A-site and B-site carbonate signals. The component at ~173-175 ppm relates to the carboxylic acids from amino acids in the organic matrix. A vertical arrow is used to show the decrease in the latter component in the bone samples exhibiting a significant decrease in the organic fraction.

Figure 7

 7 Figure 7 19 F MAS NMR spectra of the bone samples altered with fluorine and sedimentary carbonated fluorapatite. Spectra are centred on the isotropic signal of the fluoride ions incorporated in the channels at -102 ppm with two spinning side bands on each side. The 19 F position of the clumped defect is indicated by a vertical dashed line.

Figure 8

 8 Figure 8 Evolution of (a) fluoride content, (b) ν1 PO4 Ge ATR-FTIR band frequency, (c) δ 18 Ocarbonate and (d) δ 13 C as a function of the percentage of secondary apatite. Dashed lines are guide for the eye.

Figure 9

 9 Figure 9 Comparison of ATR-FTIR Ge and Raman ν1 PO4 band position (a), FWHM (b) and asymmetry parameters (c).

Figure 10

 10 Figure 10Hypothetical schematic representation of bone crystallites before and after dissolutionrecrystallisation in the presence or absence of fluoride in the alteration solution. For a 4 x 20 x 30 nm 3 crystallite size, a maximum fraction of secondary carbonated apatite of 60 % corresponds to a ~1 nm thick layer. It is proposed that partial dissolution-recrystallization of bone occurs at the nanometre scale at the surface of each individual crystallite to account for the apparent maximal fraction of secondary phase and the lack of increase in MCD size. Note that the representation is not to scale.

Table 1

 1 Alteration conditions of bone wafers and powders. For each experiment, the prime symbol refers to the fluorinated bone sample.

	Exp.	Sample	Duration Temperature (°C) pH	Solution	[NaF]
		type
	A	Wafer	1 week	20	7	Phosphate -
	A'	"	"	"	"	"	10 -2 M
	C	Powder	3 weeks 20	7	Phosphate -
	C'	"	"	"	"	"	10 -2 M
	D	Powder	3 weeks 70	7	Phosphate -
	D'	"	"	"	"	"	10 -2 M
	E	Powder	3 weeks 70	7	PIPES	-
	E'	"	"	"	"	"	10 -2 M
	F	Powder	3 weeks 70	9	KOH	-
	F'	"	"	"	"	"	10 -2 M
	G	Powder	3 weeks 70	10	KOH	-
	G'	"	"	"	"	"	10 -2 M
	H	Wafer	3 weeks 70	7	PIPES	-
	H'	"	"	"	"	"	10 -2 M

Table 2

 2 Fluorine content, Ca/P molar ratio and isotopic composition of unaltered, control and fluorinated bones.

	Sample	F (%)	Ca/P	δ 13 C (‰PDB)	δ 18 Ocarbonate	δ 18 Ophosphate
						(‰VSMOW)	(‰VSMOW)
	TH1	0.20	1.57	-6.41 ± 0.20		36.31 ± 0.14	25.80 ± 0.39
	C	0.23	1.66	-7.06 ± 0.02		36.19 ± 0.68	21.61 ± 0.81
	C'	1.6	1.64	-7.22 ± 0.09		37.42 ± 0.02	22.65 ± 0.25
	D	0.23	1.70	-7.27 ± 0.04		35.17 ± 0.19	21.18 ± 0.14
	D'	2.0	1.72	-6.97 ± 0.02		36.88 ± 0.15	20.45 ± 0.13
	E	0.24	1.79	-6.38 ± 0.01		33.95 ± 0.30	26.49 ± 0.17
	E'	2.5	1.81	-6.50 ± 0.01		35.29 ± 0.27	26.38 ± 0.56
	F	0.26	1.84	-6.50 ± 0.07		34.05 ± 0.19	26.94 ± 0.61
	F'	2.2	1.82	-6.42 ± 0.01		33.15 ± 0.12	26.81 ± 0.42
	G	0.24	1.86	-6.43 ± 0.01		33.55 ± 0.36	26.28 ± 0.38
	G'	2.1	1.84	-6.52 ± 0.12		32.83 ± 0.23	27.03 ± 0.40
	Table 3 Lattice parameters (P63/m), average apparent size and strain from Le Bail fits of
	XRD data
	Sample	a (Å)	c (Å)	Volume (Å) Crystallite size (Å) Average microstrain
					[002]		[030]	(anisotropy)
	TH1	9.4173 (6) 6.8756 (5) 528.07 (6)	776.53	126.90 85.91 (0.094)
	C'	9.4035 (3) 6.8870 (3) 527.40 (3)	308.31	114.45 31.62 (0.079)
	D	9.4219 (2) 6.8867 (3) 529.44 (3)	397.58	115.30 33.74 (0.055)
	D'	9.3916 (2) 6.8848 (2) 525.90 (2)	427.53	140.90 25.28 (0.062)
	E	9.4155 (2) 6.8892 (3) 528.91 (3)	319.27	117.25 24.11 (0.073)
	E'	9.3826 (2) 6.8879 (2) 525.13 (2)	548.21	146.92 25.41 (0.040)
	F	9.4133 (3) 6.8913 (3) 528.84 (4)	441.28	120.53 39.39 (0.043)

Table 5

 5 Parameters of the fit of the OH signal in 1 H NMR spectra of control and fluorinated bones.

	Sample	Amplitude (a.u.) Position (ppm) Width (ppm) %remainingOHsignal
	C	2.07	-0.034	0.53
	C'	0.23	-0.034	0.53	12
	D	4.43	-0.063	0.45
	D'	0.37	-0.063	0.45	8
	E	3.49	-0.028	0.32
	E'	0.14	-0.028	0.32	4
	F	1.01	-0.018	0.36
	F'	0.09	-0.018	0.36

Table 6

 6 Parameters of multi-component fits of ν1PO4 Ge ATR-FTIR bands. It is expected that the relative proportion of the Lorentzian component reflects that of the structural phosphate groups belonging to the recrystallised secondary apatite and that the fraction corresponding to the Gaussian component reflects that of the structural phosphate groups belonging to the primary bioapatite.

	Sample	"TH1-like" Gaussian signal		Secondary Lorentzian contribution
		ω (cm -1 )	Width	Area (%)	ω (cm -1 )	FWHM	Area (%)
	TH1	960.6	8.755	100	-	-	-
	C	960.6	8.755	80.9 ± 3.9	962.7	7.901	19.1 ± 2.4
	C'	960.6	8.755	70.6 ± 3.1	966.1	8.000	29.4 ± 2.5
	D	960.6	8.755	70.5 ± 8.5	963.5	10.553	29.5 ± 7.2
	D'	960.6	8.755	43.2 ± 1.2	966.1	9.530	56.8 ± 2.0
	E	960.6	8.755	60.9 ± 6.3	962.9	7.025	39.1 ± 5.6
	E'	960.6	8.755	41.4 ± 1.9	966.1	7.971	58.6 ± 2.9
	F	960.6	8.755	47.3 ± 7.5	963.4	8.566	52.7 ± 9.0
	F'	960.6	8.755	43.1 ± 2.7	966.1	7.585	56.9 ± 4.1
	G	960.6	8.755	43.3 ± 4.4	963.4	11.748	56.7 ± 6.1
	G'	960.6	8.755	38.5 ± 3.0	966.1	7.603	61.5 ± 4.4
	C-FAp	-	-	-	966.1	5.357	100

Acknowledgements

Support by the IMPMC spectroscopy and X-ray diffraction platforms is acknowledged. This work was supported by French state funds within the framework of the Cluster of Excellence MATISSE led by Sorbonne Universités and within the INTERRVIE action of the 2017 CNRS-INSU TelluS program. The French Région Ile-de-France-SESAME programme is acknowledged for financial support (700MHz). We thank two anonymous reviewers for their thoughtful comments.