Peter L Read

Hiro Yashuhiro Yamazaki

Stephen R Lewis

Paul D Williams

Kuniko Miki-Yamazaki

Joël Sommeria

Henri Didelle

Adam M Fincham

Yasuhiro H Yamazaki

Multiple jet formation in a convectively driven flow on a beta-plane

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

Introduction

The banded pattern of ammonia clouds is one of the most striking features of the atmospheres of Jupiter and Saturn. These bands are associated with multiple zonal jets of over 100 m s -1 with alternating sign against latitude [START_REF] Limaye | Jupiter: New estimates of the mean zonal flow at the cloud level[END_REF]. A similar pattern of zonation also occurs in the Earth's oceans. The dynamical origin of this banded structure remains poorly understood, but most approaches towards understanding the zonation have suggested that the pattern may originate from the anisotropy in a shallow turbulent layer of fluid due to the β effect, i.e., due to the latitudinal variation of the effective planetary vorticity [START_REF] Rhines | Waves and turbulence on a beta-plane[END_REF]. Until recently, quantitative understanding of this process has been based principally on numerical simulations of two-dimensional or geostrophic turbulence in stirred rotating fluids [START_REF] Williams | Planetary circulations: 1. Barotropic representation of Jovian and Terrestrial turbulence[END_REF], but such models are highly idealised and take little account of the vertical structure. Laboratory experiments provide an alternative means for studying these processes, though previous investigations [START_REF] Condie | A convective model for the zonal jets in the atmospheres of Jupiter and Saturn[END_REF] have been unable to access regimes at sufficiently high Reynolds number to convincingly demonstrate nonlinear zonation effects. Here we report the results of new experiments, conducted on the world's largest rotating platform, which confirm that multiple zonal jets may indeed be generated and maintained by this mechanism.

Methods

Our experiments were performed on the 14 m diameter "Coriolis" turntable in Grenoble, France. The schematic layout of our configuration is illustrated in Fig. 1. A circular cylindrical container was set on the turntable, and convective forcing was applied by gently spraying dense water from above the main fluid layer. An equivalent topographic β-effect was obtained by imposing a conical slope at the bottom of the circular container. The slope was implemented with a plasticcoated stretched fabric sheet, which could be removed for additional experiments with a flat bottom in order to compare the flow structure both with and without a topographic β-effect (apart from a weak centrifugal deformation of the free upper surface). The rotation period for most experiments was set to 40 seconds for the results to be presented herein.

Results

The horizontal velocity fields were obtained from plan view CCD images by a Correlation Imaging Velocimetry method.

In order to diagnose the anisotropy of the evolving flow, the velocity fields were decomposed into radial and zonal (i.e., azimuthal) components and mapped into (r, rθ) coordinates, where r is the radius and θ the azimuthal angle. The welldeveloped horizontal flow is dominated by eddies of various sizes, but there is also a clear indication of banded structure along the zonal direction. The temporal fluctuation of the radial profile of mean zonal flow is shown in Fig. 2a, well after the initial growth of the kinetic energy has saturated. The formation of sustained alternating jets is now evident when the topographic β effect is imposed, although there is substantial meandering of these jets during this period and occasional splitting and mergers.

Spectra

Fig. 3 shows spatial kinetic energy spectra for the two configurations. The spectra of the zonal-mean and eddy components of kinetic energy were calculated from velocity fields obtained by a high resolution camera as a function of the total wavenumber. In the sloping bottom case, there is a peak near the Rhines scale (indicated as k β ) for both the zonal and eddy components, with the peak wavenumber of the eddy energy being slightly higher than that of the zonal mean.

The spectrum matches well with a -5/3 slope at large scales and -3 at small scales, which is predicted by the theory of geostrophic and two-dimensional turbulence [START_REF] Rhines | Waves and turbulence on a beta-plane[END_REF]. Interestingly, the spectrum of the zonal mean kinetic energy at wavenumbers between 10 and 30 m -1 shows a significantly steeper decay with k, though does not quite reach the k -5 variation anticipated from the work of Huang et al. [START_REF] Williams | Planetary circulations: 1. Barotropic representation of Jovian and Terrestrial turbulence[END_REF]. The apparent near-equilibration of the jets at a scale comparable to L R would seem to indicate that we are in a regime for which bottom drag is relatively insignificant in the selection of jet scale.

Figure 1 :

 1 Figure 1: Schematic cross-section of the circular container, showing the rotating spray arm used to provide continuous convective forcing. The entire apparatus is set on a circular turntable.

  Fig. 2b shows the evolution of the zonal mean flow observed in a corresponding flat bottom experiment. The domain-filling single-cell circulation, which is most evident in this case, is presumably due at least in part to differential wind stress effects. The characteristic scale-widths of the jets are closer to the Rhines scale L R (on the order L R = π 2U/β, where U is a typical horizontal velocity scale) of 0.63 to 1.4 m, rather than to the external radius of deformation (L D ∼ √ gD/f , where f is the Coriolis parameter and D the fluid depth), which ranged from L D ∼ 4.5 m (along the inner wall) to 7.4 m (near the outer wall).

Figure 2 :Figure 3 :

 23 Figure 2: Horizontal velocity field. a, structure and fluctuation of the mean zonal velocity of the mature flow. The contour interval is 0.2 cm s -1 and the solid line denotes the contour of null velocity. b, initial development of the zonal mean flow in the flat bottom experiment. a b


T Alleau

L Lanquetin

A.-V Salsac

Use of a parametric finite-element model of the mitral valve to assess healthy and pathological valve behaviors

Keywords: mitral valve, finite element model, chordae tendineae rupture, prolapsus

Introduction

The mitral valve is the cardiac valve separating the left atrium from the left ventricle. It is composed of four elements: the anterior and posterior leaflets; the annulus which serves as insertion site in the heart muscle for the leaflets; the chordae tendineae which are attached to pillars in the ventricular wall and ensure that the very flexible leaflets remain within the ventricle; the papillary muscles which are located at the tip of the chordae tendineae and actively modify the tension acting on the leaflets. In the physiological case, the valve is open during diastole letting blood flow into the ventricle, and close during systole: the leaflets then create a hermetic seal between the two chambers preventing blood from regurgitating into the left atrium when ejected into the aorta. Mitral insufficiency is a valvular heart disease caused by a leaky mitral valve. It is the most frequent valvular pathology in Western countries after aortic narrowing upon calcification [START_REF] Singh | Prevalence and clinical determinants of mitral, tricuspid, and aortic regurgitation (the Framingham Heart Study)[END_REF]. Mitral valve scan is the gold standard to obtain geometrical information. Anatomical studies have shown that human mitral valve measures may differ among patients [START_REF] Gunnal | Study of mitral valve in human cadaveric hearts[END_REF][START_REF] Khalighi | Mitral Valve Chordae Tendineae: Topological and Geometrical Characterization[END_REF]), but generic patterns exist [START_REF] Drach | Population-Averaged Geometric Model of Mitral Valve From Patient-Specific Imaging Data[END_REF][START_REF] Lau | Mitral Valve Dynamics in Structural and Fluid-Structure Interaction Models[END_REF], which opens up the possibility to define parametric models of typical mitral valves. Several valve models have been developed in physiological conditions [START_REF] Lau | Mitral Valve Dynamics in Structural and Fluid-Structure Interaction Models[END_REF][START_REF] Kunzelman | Fluid-structure interaction models of the mitral valve: function in normal and pathological states[END_REF][START_REF] Shen | The geometric model of the human mitral valve[END_REF], but pathological conditions have been little studied. The aim of the present study is to develop a geometrical model of mitral valves in both healthy and pathological states.

Methods

Mitral valve definition

A mitral valve parametric model was created using FreeCAD software and Fortran subroutines, assuming a left-to-right symmetry and average geometrical parameter values (Table 1). It is constructed by defining points along the edges of the leaflets, which are then interpolated using b-splines.

* Corresponding author. Email: thibaut.alleau@utc.fr

The annulus of the mitral valve is defined using a planar D-shape, similarly to the Carpentier-Edwards Physio annuloplasty ring (Edwards Lifesciences). The papillary muscles tips are placed at fixed positions obtained from medical data [START_REF] Sakai | Distance between mitral anulus and papillary muscles: Anatomic study in normal human hearts[END_REF] 1 Geometrical parameters used for the model.

Model of the mitral function

The closure of the mitral valve is simulated using a structure-only finite element method with the software ADINA v9.5. The impact of the blood flow dynamics on the valve deformation is indeed negligible when the valve is closed [START_REF] Toma | Fluidstructure interaction and structural analyses using a comprehensive mitral valve model with 3D chordal structure[END_REF]. We solve for the displacement of the leaflets when subjected to a pressure profile composed of an initial linear ramp up to 0.1 s, followed by a constant plateau. The annulus and papillary muscle tips are fixed during the computation. The leaflet and chordae tendineae are assumed to be isotropic linear elastic, with Young modulus 𝐸 = 3 MPa, Poisson ratio 𝜈 = 0.45 and density 𝜌 = 10 3 kg/m 3 . The contact is accounted for implicitly with a constraint function parameter set at 10 -9 . We use a second-order implicit time integration scheme called Bathe scheme [START_REF] Noh | Performance of an implicit time integration scheme in the analysis of wave propagations[END_REF] and assume large displacements. The leaflets are discretized using 4-node 3D-shells of maximum length 8 × 10 -1 mm. The chordae tendineae are discretized using 2-node truss elements deforming in traction-only. The pathological case shown was obtained by rupturing some of the chordae tendineae attached to the anterior leaflet. It corresponds to a case where an asymmetry appears. The linear part of the problem is solved directly using LU decomposition, and the non-linear part using the Newton-Raphson algorithm with a maximum of 15 iterations. A time step of 10 -3 s is used from 0 s to 0.1 s and of 10 -2 s hereafter. In addition, an adaptive time step method is used if convergence difficulties arise, the time step being then reduced to 10 -7 s and 10 -5 s, respectively.

Results and discussion

The stress distribution is plotted in the pathological (Figure 1) and healthy (Figure 2) cases. In the pathological case, a zone of higher stress than in the healthy case forms along the annulus. The valve is also not fully closed, which is a consequence of the lack of chordae tendineae attached to the anterior leaflet. The area of passage between the two leaflets can be quantified at systole to estimate valvular regurgitation. The anterior leaflet can be seen to protrude above the annulus plane in the pathological case, while it remains under it in the healthy case. The rupture of the chordae tendineae thus leads to the appearance of prolapse, which can be more easily detected thanks to imaging techniques than valve leakage itself, and can be of use to diagnose mitral regurgitation.

Conclusions

A geometrical model of the mitral valve capable of modeling healthy and pathological mitral valves has been built. The model allows to test several mitral geometries, and to assess in each case the mitral valve function using a finite element method. The model might be of use to numerically test medical procedures on mitral valves.

Figure 1

 1 Figure 1 Stress distribution on the pathological valve at 𝑡 = 0.09 s. Red is 1 MPa and blue is 0 MPa.

Figure 2

 2 Figure 2 Stress distribution on the healthy valve at 𝑡 = 0.09 s. Red is 1 MPa and blue is 0 MPa.

  . The chordae tendineae are created as uniformly distributed chords going from the edges of the leaflets to the papillary muscle tips.

	Anterior-posterior leaflet	8.3° -5.3°
	angles
	Leaflet height	7.7 to 23.4 mm
	Leaflet thickness	0.8 mm
	Annular width	4 cm
	Annular height	3 cm
	Table

Acknowledgements

We gratefully acknowledge the support and funding from ANRT (Cifre 2017/1188).


Alleau Thibaut
email: thibaut.alleau@utc.fr

Anne-Virginie Salsac
email: a.salsac@utc.fr

Laurent Lanquetin
email: laurent.lanquetin@segula.fr

USE OF A PARAMETRIC FINITE-ELEMENT MODEL OF THE MITRAL VALVE TO ASSESS HEALTHY AND PATHOLOGICAL VALVE BEHAVIORS

The present study is focused on the mitral heart valve, which is the valve that separates the left ventricle from the left atrium. The aim is to provide a parametrical geometrical model of the valve in order to study pathological valves (e.g. suffering from cord rupture) and compare it to the physiological case. A finite element model is used to quantify how the valve defects affect the valve dynamics during closure, the internal stress distribution along the valve leaflets and the level of regurgitation.

Introduction

The mitral valve is a cardiac valve composed of four elements: the anterior and posterior leaflets, the annulus which is the structure through which the leaflets are attached to the heart muscle, the chordae tendinae which are attached to pillars in the ventricular wall and ensure that the very flexible leaflets remain within the ventricle, the papillary muscles which are located at the tip of the chordae tendinae and actively modify the tension acting on the leaflets. These four elements allow a healthy mitral valve to let blood flow from the atrium to the ventricle during diastole, and to create a hermetic seal between the two chambers during systole. This seal prevents blood from regurgitating into the left atrium when being ejected from the ventricle. Several pathologies may exist, since each of the four elements (e.g. chordae rupture) may potentially be the source of dysfunctions. Mitral insufficiency is the most frequent valvular pathology in Western countries after aortic narrowing upon calcification [START_REF] Singh | Prevalence and clinical determinants of mitral, tricuspid, and aortic regurgitation (the framingham heart study)[END_REF].

Mitral valve scans obtained by magnetic resonance imaging, computed-tomography (CT-scan) or echocardiography [START_REF] Toma | Fluid-structure interaction and structural analyses using a comprehensive mitral valve model with 3d chordal structure[END_REF][START_REF] Ma | Image-based fluid-structure interaction model of the human mitral valve[END_REF][START_REF] Chnafa | Image-based large-eddy simulation in a realistic left heart[END_REF][START_REF] Votta | Mitral valve finite-element modelling from ultrasound data: a pilot study for a new approach to understand mitral function and clinical scenarios[END_REF] can be used in computational analysis to have a better understanding of the valve function and help surgeons determine patient-specific medical treatments. It is, however, difficult to extrapolate results from one patient to another. Indeed, anatomical studies have shown that human mitral valve measures differ among patients [START_REF] Gunnal | Study of mitral valve in human cadaveric hearts[END_REF][START_REF] Sakai | Distance between mitral anulus and papillary muscles: anatomic study in normal human hearts[END_REF], but some patterns, however, exist [START_REF] Drach | Population-averaged geometric model of mitral valve from patient-specific imaging data[END_REF][START_REF] Khalighi | Mitral valve chordae tendineae: topological and geometrical characterization[END_REF]. Another approach is thus to define the valve using a simplified parametric geometry. The advantage of such models is that one can vary the characteristic lengths of the valve systematically and simulate pathological conditions. Several geometrical valve models have been developed in the literature [START_REF] Lau | Mitral valve dynamics in structural and fluid-structure interaction models[END_REF][START_REF] Kunzelman | Fluid-structure interaction models of the mitral valve: function in normal and pathological states[END_REF][START_REF] Shen | The geometric model of the human mitral valve[END_REF], but pathological conditions have been little studied. The aim of the present study is to develop a geometrical model of mitral valves in both healthy and pathological states.

Material and methods

Mitral valve definition

We create a parametric model of a valve with a left-to-right symmetry using FreeCAD and Fortran subroutines (Figure 1a). It is constructed by defining points along the edge of the leaflets and using The annulus of the mitral valve is defined using a planar D-shape with a ratio 3/4 between the anteropostero and the inter-commisural diameters (Figure 1b), similarly to the Carpentier-Edwards Physio annuloplasty ring (Edwards Lifesciences). The annulus is supposed to be planar and the anteropostero diameter to be 3 cm.

The papillary muscles tips, onto which the chordae tendineae are attached, are placed at fixed positions obtained from medical data [START_REF] Sakai | Distance between mitral anulus and papillary muscles: anatomic study in normal human hearts[END_REF]. The chordae tendineae are represented as cords going from the papillary muscle tips to the border of the leaflets. Their distribution is approximately uniform along the leaflet edges.

The geometric model of the valve is exported as an IGES file. Specific python macros are used to make adjustments on the FreeCAD model, for instance to create the b-splines and isolate points along the b-splines.

Model of the mitral function

The closure of the mitral valve is simulated using a finite element method (software ADINA v9.4), modeling the displacement of the leaflets under a hydrodynamic pressure. Being little influenced by fluid-structure interactions, the valve closure can be well approximated by structure-only simulations. The leaflets are loaded under a pressure ramp corresponding to the systolic pressure evolution. The pressure ramp start at 0 s and reach its peak value at 0.1 s.

The annulus and the papillary muscle tips are fixed during computation. The leaflet material is assumed to be isotropic linear elastic, with Young modulus E = 3 MPa, Poisson ratio ν = 0.45 and density ρ = 1 kg.m -3 . The chordae tendineae are also supposed to be isotropic linear elastic but with Young modulus E = 40 MPa.

We assume large displacement and use a second-order implicit time integration scheme called Bathe scheme ( [START_REF] Bathe | Insight into an implicit time integration scheme for structural dynamics[END_REF][START_REF] Noh | Performance of an implicit time integration scheme in the analysis of wave propagations[END_REF]). An implicit contact method is used, setting the compliance factor of the constraint function to 1 × 10 -9 . Double-sided detection is activated on all the surfaces of the leaflets.

The leaflets are discretized using 4227 elements (27-node hexahedrons and 11-node tetrahedrons) of maximum length 8 × 10 -1 mm. The chordae tendineae are discretized using 457 2-node truss elements. A time step of 1 × 10 -4 s is used from 0 s to 0.1 s and of 1 × 10 -2 s hereafter until the end of the computation. In addition, an adaptative time step method is used if convergence difficulties arise, possibly reducing the time step to 1 × 10 -7 s and 1 × 10 -5 s, respectively. The linear part of the problem is solved directly using LU decomposition, and the non-linear part using the Newton-Raphson algorithm with a maximum of 15 iterations.

The pathological case shown was obtained by rupturing the chordae tendineae, attached to the anterior leaflet. This was modeled by deleting the corresponding elements in the numerical model.

Results

The stress distribution is shown in Figure 2 during valve closure. Even though the stress field remains of the same magnitude in the pathological and healthy cases, differences in distribution are observed in the center of the anterior leaflet and close to the clefts of the posterior leaflet. The orifice area projected within the annular plane is larger in the pathological case than in the healthy case. Cord rupture will indeed cause regurgitation during diastole. The lack of chordae tendineae in the pathological case also implies a larger amplitude of the anterior leaflet motion, as it is less attached to the papillary muscle than in the healthy anterior leaflet. At t = 0.09 s, the pathological anterior leaflet is nearly above the annular plane. We thus observe a mitral valve prolapse.

Conclusion

We have built a geometrical model of the mitral valve capable of modeling both healthy and pathological mitral valves. The parameters allow to test several mitral valves, and to assess in each case the mitral valve function using a finite element method. The model might be of use to numerically test medical procedure on mitral valves.

Figure 1 :

 1 Figure 1: Parametric geometrical model of mitral valve. a. Three-dimensional representation of the modeled valve. b. Geometrical definition of the mitral annulus.

Figure 2 :

 2 Figure 2: Stress distribution within the leaflet of the mitral valve during closure at times t = 0.01 s (a), 0.03 s (b), 0.05 s (c) and 0.09 s (d). Left column: healthy valve, right column: pathological valve. The units are in dyne.cm -2 (1 dyne.cm -2 = 0.1 Pa)


Dr Nicolas Clavier
email: nicolas.clavier@icsm.fr

Adel Mesbah

Stephanie Szenknect

N Dacheux

Monazite, rhabdophane, xenotime & churchite : vibrational spectroscopy of gadolinium phosphate polymorphs

Keywords: Vibrational spectroscopy of gadolinium phosphate polymorphs phosphate, rare earth elements, monazite, FTIR, Raman

published or not. The documents may come

Introduction

Rare-earth phosphate minerals with the general formula REEPO4•nH2O belong to four distinct structural types, mainly depending on their hydration content and the atomic weight of the rare-earth elements incorporated (i.e. light or heavy REE) [START_REF] Achary | Recent progress on synthesis and structural aspects of rare-earth phosphates[END_REF]. Among them, monazite LnPO4 (hexagonal, P21/n), typically crystallizing with Ln = La-Tb [START_REF] Clavier | Crystal chemistry of the monazite structure[END_REF], is probably the most widespread in nature and is therefore widely documented. Monazite constitutes one of the main ores exploited for lanthanide extraction, and naturally bears high contents in uranium and thorium (up to 15 wt.%), mainly through coupled substitutions with divalent elements such as calcium [START_REF] Qin | Incorporation of thorium in the rhabdophane structure: Synthesis and characterization of Pr1-2xCaxThxPO4•nH2O solid solutions[END_REF]. For heavy rare-earth elements, i.e. Ln = Gd-Lu, as well as for yttrium and scandium, anhydrous LnPO4 phase adopts the zircon structure type (tetragonal, I41/amd) [START_REF] Ni | Crystal-Chemistry of the Monazite and Xenotime Structures[END_REF], leading to the formation of xenotime. This latter frequently coexists with monazite within granitic and metamorphic rocks [START_REF] Forster | The chemical composition of REE-Y-Th-U-rich accessory minerals in peraluminous granites of the Erzgebirge-Fichtelgebirge region, Germany. Part II: Xenotime[END_REF].

In comparison, related hydrated counterparts are far less present in nature. For light rareearth elements, rhabdophane LnPO4•0.667H2O (monoclinic, C2) [START_REF] Mesbah | Monoclinic Form of the Rhabdophane Compounds: REEPO4.0.667H2O[END_REF], is frequently restricted to the uppermost portion of the crust due to its metastable character regarding to monazite [START_REF] Gausse | Determination of the Solubility of Rhabdophanes LnPO4.0.667H2O (Ln = La to Dy)[END_REF].

Hence, rhabdophane is one of the main LREE carriers in bauxite, laterites and hydrothermal systems, while monazite dominates in magmatic and metamorphic silicic rocks [START_REF] Berger | Formation and composition of rhabdophane, bastnasite and hydrated thorium minerals during alteration: Implications for geochronology and low-temperature processes[END_REF]. Finally, churchite is most often reported with the ideal formulae YPO4•2H2O (monoclinic, isostructural to gypsum) and also contains variable amounts of heavy rare-earth elements such as dysprosium and erbium. It was found in association with limonite deposits, but also in laterites [START_REF] Onac | A modern, guano-related occurrence of foggite, CaAl(PO4)(OH)2•H2O and churchite-(Y), YPO4•2H2O in Cioclovina Cave, Romania[END_REF]. One must note that this mineral is still frequently called as weinschenkite even if this name was early discarded by the Commission on New Minerals and Mineral Names [START_REF] Claringbull | A Re-Examination of Churchite[END_REF].

Owing to their numerous potential applications in several fields of research, such as phosphor light emitters [START_REF] Shinde | Europium-Activated Orthophosphate Phosphors For Energy-Efficient Solid-State Lighting: A Review[END_REF], geochronometers [START_REF] Harrison | U-Th-Pb dating of phosphate minerals, Phosphates: Geochemical, Geobiological[END_REF], thermal barrier coatings [START_REF] Sudre | Monazite-based thermal barrier coatings United States Patent[END_REF] or ceramics for the storage [START_REF] Dacheux | Monazite as a promising long-term radioactive waste matrix: Benefits of high-structural flexibility and chemical durability[END_REF][START_REF] Schlenz | Monazite as a suitable actinide waste form[END_REF] or the transmutation [START_REF] Burghartz | Inert matrices for the transmutation of actinides: fabrication, thermal properties and radiation stability of ceramic materials[END_REF] of nuclear waste, REEPO4•nH2O compounds were investigated through a wide range of physico-chemical techniques of characterization. Among them, vibrational spectroscopy was frequently considered, due to its easy operation and to the intense signal provided by the vibration modes of the PO4 tetrahedra. As a matter of fact, Raman spectra were used to validate the formation of monazite-type BkPO4, CfPO4, and EsPO4, which remain up to now among the few samples prepared at a weighable scale with these heavy transuranic elements [START_REF] Hobart | Raman-Spectra of the Transplutonium Ortho-Phosphates and Trimetaphosphates[END_REF]. Raman spectroscopy was also demonstrated for long as a powerful tool in the analysis of scarce natural samples, such as REEPO4•2H2O churchite [START_REF] Frost | A vibrational spectroscopic study of the phosphate mineral churchite (REE)(PO4)•2H2O[END_REF].

Along with the studies devoted to minerals, numerous works were also undertaken on synthetic samples series. Once again, monazite-type compounds were widely investigated, most often through comparisons along the light lanthanides series (Ln = La-Gd) [START_REF] Silva | Vibrational spectra of monazite-type rare-earth orthophosphates[END_REF][START_REF] Begun | Raman-Spectra of the Rare-Earth Ortho-Phosphates[END_REF][START_REF] Heuser | Raman and infrared spectroscopy of monazite-type ceramics used for nuclear waste conditioning[END_REF] which allowed to point out a shift of the vibration modes towards the highest wavenumbers with the atomic number of the cation. Isostructural cheralite samples incorporating tetravalent actinides also present similar spectroscopic features [START_REF] Podor | Raman spectra of the actinide-bearing monazites[END_REF]. In comparison, the studies concerning the xenotime series, obtained for heavy rare earth elements (Ln = Tb -Lu) [START_REF] Begun | Raman-Spectra of the Rare-Earth Ortho-Phosphates[END_REF][START_REF] Yurchenko | Infrared and Raman-Spectra of Anhydrous Ortho-Phosphates from Tb to Lu[END_REF], appear to be more ancient and scarce. However, recent works renewed the interest for spectroscopy in this field, with some works dealing with the calculations of vibrational dynamics [START_REF] Giarola | Vibrational dynamics of YPO4 and ScPO4 single crystals: An integrated study by polarized Raman spectroscopy and first-principles calculations[END_REF] and to the behavior of xenotime samples under pressure [START_REF] Tatsi | Raman study of tetragonal TbPO4 and observation of a first-order phase transition at high pressure[END_REF]. Quite similarly, only the Assaoudi's group undertook systematic spectroscopic investigations of the hydrated rare earth phosphates, rhabdophane and churchite [START_REF] Assaoudi | Vibrational spectra and structure of rare earth orthophosphates, weinschenkite type[END_REF][START_REF] Assaaoudi | Vibrational spectra of hydrated rare earth orthophosphates[END_REF].

However, if the evolution of the vibrational spectra was studied for each REEPO4•nH2O structural type as a function of the metal center, no study compared FTIR and Raman spectra of the four polymorphs for the same cation. This lack probably arises from the difficulty to stabilize the different phases for one given lanthanide element, gadolinium being the only one possible. Indeed, if GdPO4 monazite as well as GdPO4•0.667H2O rhabdophane are well described [START_REF] Yu | Dependence of morphology and photoluminescent properties of GdPO4 : Eu 3+ nanostructures on synthesis condition[END_REF][START_REF] Terra | Preparation and characterization of lanthanum-gadolinium monazites as ceramics for radioactive waste storage[END_REF], a very limited number of synthesis protocols is available for xenotime and churchite [START_REF] Assaaoudi | Gadolinium orthophosphate weinschenkite type and phase change in rare earth orthophosphates[END_REF]. The present study then reports for the first time the direct comparison of both Raman and FTIR spectra of the four gadolinium phosphate structures and establishes connections between their crystal structure, including symmetry of PO4 groups and hydrogen bond network formed by water molecules, and their spectroscopic behavior.

Experimental

Preparation and characterization of the samples

All the samples were synthesized from GdCl3•6H2O (99%) as well as concentrated H3PO4 (85%) and HCl, all supplied by Sigma-Aldrich. In order to avoid any weighing bias due to the hygroscopic character of the gadolinium salt, this latter was first dissolved in 1M HCl.

Gadolinium concentration was finally accurately determined by Inductively Coupled Plasma

Atomic Emission Spectroscopy (ICP-AES) and was always in the 0.5-1M range. GdPO4•0.667H2O rhabdophane [START_REF] Mesbah | Monoclinic Form of the Rhabdophane Compounds: REEPO4.0.667H2O[END_REF] was obtained following the protocol reported in our previous work [START_REF] Gausse | Determination of the Solubility of Rhabdophanes LnPO4.0.667H2O (Ln = La to Dy)[END_REF]. Hydrochloric solution containing gadolinium was mixed with 5M H3PO4 in a PTFE-lined vessel, an excess of 2 mol.% being considered to ensure the quantitative precipitation of the cations. The container was then transferred into an oven and left at 90°C for two weeks. The precipitate formed afterwards was recovered by centrifugation at 14000 rpm, then successively washed twice with deionized water and once with ethanol, and finally dried overnight in air at 90°C. The GdPO4 monazite counterpart was obtained by heating the former compound at 1100°C for 6 hours in air. These firing conditions were chosen in order to fully convert rhabdophane into monazite, the transition being reported around 850°C [START_REF] Jonasson | Dta Study of the Rhabdophane to Monazite Transformation in Rare-Earth (La-Dy) Phosphates[END_REF]. GdPO4•2H2O churchite was obtained through a similar protocol than that described for the preparation of rhabdophane. However, in this case, the mixture of reactants was placed in a fridge at 4°C for several months. Separation of the precipitate, as well as washing and drying steps were repeated as described above. Finally, GdPO4 xenotime was prepared after firing the churchite precursor at 1000°C for 6 hours in air [START_REF] Assaaoudi | Gadolinium orthophosphate weinschenkite type and phase change in rare earth orthophosphates[END_REF].

The nature of the various GdPO4•nH2O phases prepared was first checked by the means of powder X-ray diffraction (PXRD) using a Bruker D8 advance diffractometer equipped with a lynxeye detector and having copper radiation (λ=1.54184Å). The collected patterns confirm the formation of four different polymorphs (Figure 1), in good agreement with the structures reported in the literature for Gd-based monazite (PDF file #01-083-0657 [START_REF] Ni | Crystal-Chemistry of the Monazite and Xenotime Structures[END_REF]), xenotime (#00-062-824 [START_REF] Celebi | Hydrothermal synthesis of xenotime-type gadolinium orthophosphate[END_REF]), rhabdophane (#00-039-0232) and churchite (#00-021-0337 [START_REF] Hezel | X-Ray Powder Data and Cell Dimensions of Some Rare Earth Orthophosphates[END_REF]). Associated unit cell parameters obtained from Rietveld refinement are gathered in Table 1. As previously stated, Gd-monazite adopts a P21/n monoclinic structure. This latter is based on the widely-described nine-fold coordination of the cation which can be described as a pentagon interpenetrated by a distorted tetrahedron. These REEO9 polyhedra then form chains along the [001] direction [START_REF] Clavier | Crystal chemistry of the monazite structure[END_REF]. Within the xenotime structure, the PO4 tetrahedra share corners and edges with REEO8 polyhedra, which themselves share edges together to form chains parallel to the [100] direction. These chains are cross-linked with PO4 units by sharing corners.

The connections between monazite and xenotime structures, already described by Ni et al. [START_REF] Ni | Crystal-Chemistry of the Monazite and Xenotime Structures[END_REF],

consists in a shift of the (100) planes along with a slight rotation of the PO4 tetrahedra around

[001].

Described for long as an hexagonal structure, GdPO4•0.667H2O rhabdophane was only recently reported to crystallize in the monoclinic system in the C2 space group. The structural arrangement consists in infinite channels oriented along the [101] direction and formed by the connection of six chains. One must note that the channels contain two types of chains, depending on the coordination of the cation which can be 8 or 9 [START_REF] Mesbah | Monoclinic Form of the Rhabdophane Compounds: REEPO4.0.667H2O[END_REF].

Finally, the churchite crystallizes in the gypsum structure type in the C2/c space group of the monoclinic system [START_REF] Ivashkevich | Preparation and structure of the yttrium phosphate dihydrate YPO4•2H2O Phosphor[END_REF]. Each Gd atom is coordinated to 8 oxygen atoms, six being provided by the phosphate groups and two by water molecules, to form distorted square antiprisms. These polyhedra are separated by phosphate groups and form infinite 2D layers stacked down the b axis.

Raman spectroscopy

Raman spectra were recorded by the means of a Horiba -Jobin Yvon Aramis apparatus equipped with an edge filter and using a Nd:YAG laser (532 nm). In order to avoid any laserinduced degradation of the compound, the power was turned down by the means of optical filters to about 1-4 mW depending on the sample analyzed. The laser beam was then focused on a small fraction of powder simply deposited on a glass lamella using an Olympus BX 41 microscope. A 100 objective with a numerical aperture of 0.9, resulting in a spot size of about 1 m 2 was used. The scattered Raman light was collected in a 180° backscattering geometry and dispersed by a grating of 1800 grooves/mm after having passed a 150 µm entrance slit, resulting in a spectral resolution lower than 1 cm -1 . For each spectrum, a dwell time of 90 to 180 seconds was considered with an average of 3 scans. Before analysis, the apparatus was calibrated with a silicon wafer, using the first-order Si line at 520.7 cm -1 .

FTIR spectroscopy

FTIR spectra were recorded in the 380-4000 cm -1 range thanks to a Perkin-Elmer FTIR Spectrum 100 device. Powdered samples were deposited at the surface of an ATR crystal without any prior preparation. The spectra collected in such operating conditions exhibited a resolution lower than 2 cm -1 .

Results and discussion

General overview

The FTIR and Raman spectra recorded for the four gadolinium phosphate polymorphs are gathered in Figure 3. Band component analysis of the different data sets was carried out by the means of the Jandel Peakfit software, using pseudo-Voigt functions (Gaussian-Lorenzian ratio systematically higher than 0.7) with the minimum number of components. Correlation coefficients R 2 greater than 0.992 were usually obtained for the results reported in Table 2. All the spectra recorded for the four polymorphs could be split in three distinct zones of interest. The first one, comprised between 300 and 800 cm -1 , corresponds to the deformation modes of the PO4 tetrahedron, while stretching modes led to characteristic bands in the 900-1200 cm -1 range. If these regions are similar for the various compounds studied herein, the number of vibration bands assigned to PO4 groups differs depending on the crystal symmetry of the samples. The subsequent factor group analysis was reported by many authors for monazite [START_REF] Silva | Vibrational spectra of monazite-type rare-earth orthophosphates[END_REF][START_REF] Begun | Raman-Spectra of the Rare-Earth Ortho-Phosphates[END_REF][START_REF] Heuser | Raman and infrared spectroscopy of monazite-type ceramics used for nuclear waste conditioning[END_REF], including recent papers bringing ab initio simulations to the state of the art [START_REF] Errandonea | High-pressure structural and vibrational properties of monazite-type BiPO4, LaPO4, CePO4, and PrPO4[END_REF]. Meanwhile, some data also exists in the literature for xenotime [START_REF] Begun | Raman-Spectra of the Rare-Earth Ortho-Phosphates[END_REF] and churchite [START_REF] Assaaoudi | Vibrational spectra of hydrated rare earth orthophosphates[END_REF].

However, it has to be reconsidered for rhabdophane due to the recent description of its structure as monoclinic (C2 space group) instead of the hexagonal P6222 [START_REF] Mesbah | Monoclinic Form of the Rhabdophane Compounds: REEPO4.0.667H2O[END_REF]. Up to date, factor group analysis is then presented in Table 3. In parallel, the vibration bands assigned to the water molecules can be found between 1500 and 1700 cm -1 (bending) and around 3600 cm -1 (stretching). The results corresponding to these three different regions, i.e. to stretching and bending modes of phosphate entities, then to structural water vibrations, will be discussed in the following sections.

Phosphate stretching modes

The stretching modes of the PO4 groups are observed in the Raman spectra gathered in Figure 4. In this zone (900-1200 cm -1 ), the symmetric vibration, frequently labelled as 1, appears to be located on a very small wavenumber range for the four crystal structures considered, i.e. at 977, 984, 987 and 994 cm -1 for churchite, xenotime, monazite and rhabdophane, respectively. On this basis, the wavenumber assigned to the s(PO4) vibrations can be hardly used to accurately discriminate the various polymorphs even if some differences can be underlined concerning the number of band components. Indeed, monazite and churchite led to a single vibration band, while shoulders can be observed for xenotime (991 cm -1 , i.e. at higher wavenumber than the main vibration band) and rhabdophane (985 cm -1 , i.e. at lower wavenumber).

On the other hand, the vibrations associated to the antisymmetric stretching mode (3) located above 1040 cm -1 are generally of lower intensity. Nevertheless, they present significant differences depending on the sample considered, particularly concerning the position of the main vibration band. Indeed, the wavenumber of the band with the maximal intensity varies from 1048 cm -1 for xenotime to 1058, 1071 and 1108 cm -1 for churchite, monazite and rhabdophane, respectively. Even if no clear correlation can be established between the P-O distance in the different structures and the 3 wavenumber, the lowest wavenumbers were measured for xenotime and churchite. In both these structural type, gadolinium is eight-fold coordinated, while its coordination is 9 for rhabdophane and monazite. This lower coordination state results in shorter Gd-O distances, then in longest P-O lengths, in good agreement with the position of the PO4 stretching bands in the spectra. One must also note that if only one antisymmetric vibration band is observed for rhabdophane and churchite, several smaller vibration bands were detected for monazite and xenotime. Particularly, the existence of three bands of weak intensity at around 1000, 1040, and 1090 cm -1 for GdPO4 monazite, that was already evidenced by Begun et al. and also observed for the other members of the LnPO4 series [START_REF] Begun | Raman-Spectra of the Rare-Earth Ortho-Phosphates[END_REF], can be considered as a characteristic feature for this structural type. Compared to Raman ones, the FTIR spectra (Figure 5) recorded for the four samples appear much more convoluted. Indeed, a wide massif was systematically recorded between 800 and 1200 cm -1 , which makes it difficult to unambiguously discriminate the components assigned to symmetric and antisymmetric stretching vibration modes. Nevertheless, a sharp band can be observed for rhabdophane (at 972 cm -1 ) and monazite (at 960 cm -1 ). It could be assigned to the 1 symmetrical stretching mode. Also, these values are in good agreement with that recently reported by Heuser et al. [START_REF] Heuser | Raman and infrared spectroscopy of monazite-type ceramics used for nuclear waste conditioning[END_REF]. For xenotime and churchite, the resolution of the spectra collected was probably lowered by the crystallization state. Also, it might arise from the presence of bands related to forbidden vibration modes. Nevertheless, a simple first-basis approach could be considered in this case by assigning all the vibration bands above 1000 cm - 1 to antisymmetric stretching vibration modes (3). Finally, one must note that a specific vibration mode related to water molecules can be observed for churchite at 732 cm -1 . It will be discussed in the dedicated section.

Phosphate deformation modes

The Raman spectral zone corresponding to the bending modes of the PO4 groups is mainly characterized by the presence of an intense band around 470-480 cm -1 (Figure 6) and assigned to the symmetric vibration (frequently labelled as 2). As already noted by Silva et al., this mode occurs systematically as a broad band, regardless of any splitting of the degeneracy [START_REF] Silva | Vibrational spectra of monazite-type rare-earth orthophosphates[END_REF]. The position of this vibration mode appears to be weakly dependent on the structural type considered, with monazite, rhabdophane and xenotime features occurring on a 10 cm -1 range.

More specifically, churchite is characterized by the very low intensity of the 2 mode. For this sample, the most intense band occurs at around 360 cm -1 , i.e. just above the wavenumber domain usually assigned to external vibration modes. Nevertheless, it was systematically correlated to phosphate internal modes in the literature [START_REF] Assaoudi | Vibrational spectra and structure of rare earth orthophosphates, weinschenkite type[END_REF][START_REF] Assaaoudi | Vibrational spectra of hydrated rare earth orthophosphates[END_REF]. On the FTIR spectra, the 2 vibration mode of the PO4 units was observed for monazite, rhabdophane and churchite, even if it appears frequently as a shoulder. For the two hydrated compounds, the existence of the 2 band confirms the C2 site symmetry proposed from crystal structure. On the contrary, the D2d Raman spectra recorded in the 400-800 cm -1 range for gadolinium based rhabdophane and monazite and between 300 and 700 cm -1 for gadolinium based churchite and monazite.

At higher wavenumber, i.e. typically between 500 and 700 cm -1 , the antisymmetric bending modes (4) mostly generate intense vibration bands in the FTIR spectra, which result in some large massifs. For rhabdophane, churchite, and xenotime, two main bands were detected at around 520-540 cm -1 and 620-640 cm -1 , while monazite exhibited more complex features between 500 and 600 cm -1 , which were sometimes depicted as the succession of two doublets (538/570 then 585/623 cm -1 ) [START_REF] Kijkowska | X-Ray diffraction and IR-absorption characteristics of lanthanide orthophosphates obtained by crystallisation from phosphoric acid solution[END_REF]. On the other hand, Raman spectra often present a collection of several low-intensity bands, which wavenumbers match with that of FTIR vibrations. These latter then do not follow the geometry selection rules and probably come from the presence of solid defects. However, the structure of these additional bands can be considered as characteristic of a given structural type. Particularly, the various publications dealing with monazite-type samples systematically report bands at about 540, 580 and 600 cm -1 [START_REF] Silva | Vibrational spectra of monazite-type rare-earth orthophosphates[END_REF]. The same applies for the quadruplet recorded between 557 and 586 cm -1 for xenotime. FTIR spectra recorded in the 400-700 cm -1 range for GdPO4•nH2O rhabdophane, monazite, churchite and monazite.

Water molecules

The spectral zones associated to the vibrations of water molecules, i.e. bending modes typically between 1500 and 1600 cm -1 and stretching modes above 3000 cm -1 , were particularly probed for GdPO4•0.667H2O rhabdophane and GdPO4•2H2O churchite samples, which are well known to be hydrated compounds (Figure 8). One must note that a characteristic water rocking mode can also be observed for churchite on the FTIR spectra as a broad band at around 730 cm -1 [START_REF] Assaaoudi | Vibrational spectra of hydrated rare earth orthophosphates[END_REF]. Also, even if xenotime sometimes showed some weak intensity bands in the regions mentioned above, it was more likely correlated to absorbed water due to the powder's small grain size (thus to an important number of surface adsorption sites), and the existence of structural water molecule in the structure was ruled out.

Whether regarding FTIR or Raman spectra, the characteristic features of water molecules appear to be strongly different between churchite and rhabdophane. For the FTIRactive bending modes, churchite presents two distinct bands at 1630 and 1705 cm -1 with small shoulders at lower wavenumbers (i.e. 1610 and 1690 cm -1 ) which can be assigned to forbidden vibration modes, while rhabdophane exhibits only strong vibration band at 1615 cm -1 with a shoulder at 1630 cm -1 . A similar behavior was observed for stretching modes, since more complex signals were systematically recorded for churchite. As a matter of fact, rhabdophane only presented one main vibration at around 3500 cm -1 both in Raman and FTIR spectra, which is accompanied by smaller shoulders. On the other hand, churchite is characterized by large massifs in the 3000-4000 cm -1 region, which are systematically composed by three components or more.

Figure 8.

Raman spectra in the 2500-4000 cm -1 range and FTIR spectra in the 1500-1800 cm -1 and 2500-4000 cm -1 regions, recorded for gadolinium rhabdophane, monazite, churchite and monazite.

Such differences can be easily correlated to the crystal structure of the two compounds.

Indeed, churchite bears two non-equivalent water molecules in its structure, one being strongly attached to the PO4 network and the other more loosely bound in the interlayer space [START_REF] Ivashkevich | Preparation and structure of the yttrium phosphate dihydrate YPO4•2H2O Phosphor[END_REF][START_REF] Kohlmann | Structure of a Y1-x(Gd,Dy,Er)xPO4•2H2O Microcrystal Using Synchrotron-Radiation[END_REF].

On this basis, the bending band observed at higher wavenumber (i.e. around 1700 cm -1 ) should correspond to the longest bond distance, then to the less strongly coordinated water molecule.

A similar assignment was already made for isostructural CaSO4•2H2O gypsum, for which the second band (1685 cm -1 ) was found to progressively disappear upon dehydration while the first one (1620 cm -1 ) remained present in the final CaSO4•0.5H2O spectra [START_REF] Putnis | In situ IR Spectroscopic and Thermogravimetric Study of the Dehydration of Gypsum[END_REF]. Moreover, the wavenumber of the stretching modes observed on the FTIR spectra can be used to evaluate the d(H In the case of rhabdophane, the recently revised structure includes four non-equivalent water molecules [START_REF] Mesbah | Monoclinic Form of the Rhabdophane Compounds: REEPO4.0.667H2O[END_REF]. Nevertheless, all of them take part to the coordination of the metal center, resulting in a close set of M-Ow bond distances. As a consequence, both Raman and FTIR spectra present strongly overlapping bands in the 3000-4000 cm -1 range. The narrowing of the stretching vibration bands can also be associated to the decrease of the hydration content of the GdPO4 sample compared to churchite. Indeed, it led to the weakening of the hydrogen bonding which generally tends to broaden the signal in this region [START_REF] Mandal | Anion water in gypsum (CaSO4•2H2O) and hemihydrate (CaSO4•0.5H2O)[END_REF]. Similarly, the existence of only one bending mode at 1615 cm -1 could be correlated to the quasi-equivalent nature of the water molecules in the rhabdophane structure. Also, as in the case of churchite, a parallel can be drawn with hydrated forms of gypsum. Indeed, [START_REF] Fritz | CaSeO4.0.625H2O -water channel occupation in a bassanite related structure[END_REF] but without investigating the typical wavenumber range of water molecules vibration. In these conditions, the FTIR and Raman data collected in this study for GdPO4•0.667H2O rhabdophane can be considered as a potential firstbasis approach to forecast the spectral characteristics of water in these compounds.

Discussion

The comparison of the vibrational spectra of LnPO4•nH2O lanthanide phosphate polymorphs was undertaken for the first time using a single metal cation, i.e. gadolinium. Even if the assignment of the various vibration modes was reported for long in the literature for several monazite, rhabdophane, churchite and xenotime type samples, this direct comparison can be used to propose some guidelines to quickly discriminate the different structural types.

First, whereas the symmetrical stretching vibrations of the phosphate tetrahedra usually led to the more intense vibration bands, they appeared to have very close wavenumbers. Also, their resolution is strongly dependent on the crystallization state of the samples, which can bias their analysis, particularly for natural samples. On this basis, their examination should be discarded to unambiguously identify the sample.

Conversely, the identification of water vibration modes seems to be the more rapid way to identify the crystal structure of any LnPO4•nH2O sample. Indeed, the existence of welldefined vibration bands in the 1500-1600 cm -1 range of the FTIR spectra, related to the (H2O) modes, attests of the existence of structural water in the sample. Here, bending modes are to be preferred, as the spectral region associated to stretching vibration modes could also show some large bands in the presence of adsorbed water. Thereafter, the number of (H2O) modes easily lead to identify the structure, churchite being associated to two bands, while rhabdophane only exhibits one single signal in this region.

For anhydrous samples adopting the xenotime or monazite structures, the main difference in the spectral signature probably comes from the vibrations associated to the phosphate bending modes. In the FTIR spectra, the s(PO4) mode (2) is inactive for the tetragonal xenotime, while it led to one vibration band for the monoclinic monazite.

Nevertheless, the corresponding signal is frequently merged into a large massif gathering both symmetric and anti-symmetric modes, which can hampers its identification. Then, we suggest to use the Raman data in this case. Indeed, xenotime presents only one intense 2 band, while two signals are detected for monazite, the second band located at about 430 cm -1 being almost as intense.

Based on these recommendations, a schematic methodology is proposed in Figure 9 to rapidly discriminate the four gadolinium phosphate polymorphs. Once again, it demonstrates the complementarity of FTIR and Raman spectroscopies, which have to be used together to unambiguously assign one of the four polymorphs. Also, as the method is mainly based on the number of vibration bands observed, it could be easily applied to any chemical system, including pure parent compounds or solid solutions involving several metal cations. In these conditions, it appears suitable for field investigations, particularly in the domain of geochemistry where monazite, rhabdophane, churchite and xenotime have already dragged a significant attention.

Conclusion

Gadolinium phosphates with monazite, rhabdophane, churchite, and xenotime structures were analyzed by vibrational spectroscopy (FTIR and Raman), leading to the first direct comparison of LnPO4•nH2O polymorphs for a single metal cation. General overview led to split the spectra into three zones, corresponding to the bending and the stretching vibration modes of phosphate tetrahedra and to the vibration modes of water molecules. For all the samples studied, the wavenumbers associated to s(PO4) bands were found to be very close, and can be hardly used to discriminate the various structural type, despite of their important intensities. Conversely, phosphate bending modes were found to be more informative.

Particularly, the number of bands observed on the Raman spectra can differentiate monazite from xenotime, provided that the presence of water molecules was previously ruled out. For hydrated samples, i.e. rhabdophane and churchite, the (H2O) modes were found to be welldefined in FTIR spectra, and attested of the structural character of the water molecules.

Moreover, the number of bands observed can once again be used to identify the structure of the GdPO4•nH2O sample.

The comparison of the vibrational spectroscopy data led to propose a simple methodology to rapidly discriminate the four LnPO4•nH2O polymorphs, which could be applied during field investigations, for example in the domain of geochemistry.

Figure 1 .

 1 Figure 1. XRD patterns obtained for the four gadolinium phosphate samples.

Figure 2 .

 2 Figure 2. View of the structure of : a) GdPO4.0.667 rhabdophane (along the [101] direction; b) GdPO4 monazite ([100] direction); c) GdPO4•2H2O churchite ([001] direction); d) GdPO4 xenotime ([001] direction).

Figure 3 .

 3 Figure 3.FTIR and Raman spectra recorded for the four gadolinium phosphate polymorphs : rhabdophane, monazite, churchite and monazite.

Figure 4 .

 4 Figure 4. Raman spectra recorded in the 900-1200 cm -1 domain for gadolinium-bearing rhabdophane, monazite, churchite and monazite.

Figure 5 .

 5 Figure 5. FTIR spectra recorded in the 700-1300 cm -1 range for gadolinium bearing rhabdophane, monazite, churchite and monazite.

  the phosphate groups in the xenotime structure leads the symmetrical bending vibration to be absent on the FTIR spectra[START_REF] Heuser | Raman and infrared spectroscopy of monazite-type ceramics used for nuclear waste conditioning[END_REF].

Figure 6 .

 6 Figure 6.Raman spectra recorded in the 400-800 cm -1 range for gadolinium based rhabdophane and monazite and between 300 and 700 cm -1 for gadolinium based churchite and monazite.

  Figure 7.FTIR spectra recorded in the 400-700 cm -1 range for GdPO4•nH2O rhabdophane, monazite, churchite and monazite.

Figure 9 .

 9 Figure 9.Schematic methodology for the discrimination of lanthanide phosphate polymorphs through vibrational spectroscopy.

Table 1 .

 1 Unit cell parameters determined for GdPO4•nH2O samples.

		a (Å)	b (Å)	c (Å)	β (°)	V (Å 3 )
	Rhabdophane	28.0273(2)	6.9262(1)	11.9914(1)	115.17(1)	2106.67(4)
	Monazite	6.6515(1)	6.8446(1)	6.3340(2)	104.02(1)	279.77(1)
	Churchite	6.2102(1)	15.1104(2) 5.6162(1)	114.95(1)	477.81(2)
	Xenotime	6.9612(7)		6.1026(10)		295.73(9)

Table 2 .

 2 Assignment of the vibration bands observed on the FTIR and Raman spectra recorded for the four gadolinium phosphate polymorphs: rhabdophane, monazite, churchite and monazite. Bands indicated into parenthesis are shoulders.

	Band	Rhabdophane	Monazite	Churchite	Xenotime
	assignment	FTIR Raman FTIR Raman FTIR Raman FTIR Raman
	(H2O)	3535	3540			3365	3380
		3475	3470			3132	(3280)
		3350	(3330)			(2870)	3210
						(2360)	3125
	(H2O)	(1630)				1705
		1615				(1690)
						1630
						(1610)
	as(PO4)	1070	1106	1137	1092	1052	1058	1117	1057
		1027		1103	1071			1085	1046
		1001		(1070)	1042			1045	1013
				1022	1004
	s(PO4)	972	994	995	987	995	977	988	991
		(930)	985	960		(943)		928	984
				(933)		(878)		(870)
	
	as(PO4)	620	634	(642)	632	(649)	(634)	636	646
		576	585	623	598	630	560	(616)	586
		538	547	585	577	521		578	574
				570	(567)			566	567
				538	539			549	557
								523
								(513)
	s(PO4)	(506)	471	492	476	(493)	497		481
		(646)	429		428	(458)	(483)
	
	Lattice				404		362		364
	modes								346
									332

Table 3 .

 3 Correlation of free PO4 ion and the corresponding factor groups of gadolinium phosphate polymorphs.

		Free ion	Site symmetry	Factor group symmetry
		Td	C1	C2h
		A1		9 Ag
	Monazite	E 2 F2	9 A	9 Bg 9 Au 9 Bu
		Td	D2d	D4h
	Xenotime	A1 E 2 F2	2 A1 B1 2 B2 2 E	2 A1g 1 A1u 2 A2u 2 B1g B2g 2 B2u 2 Eg 2 Eu
		Td	C1	C2
	Rhabd.	A1 E 2 F2	9 A	5 A 4 B
		Td	C2	C2h
				5 Ag
	Churchite	A1 E 2 F2	5 A 4 B	4 Bg 5 Au 4 Bu

  •••O) bond lengths in the hydrogen bond network thanks to the empirical relation established by Libowitzky from mineral samples (including silicates and phosphates)[START_REF] Libowitzky | Correlation of O-H stretching frequencies and O-H•••O hydrogen bond lengths in minerals[END_REF].Based on the three band components at 2870, 3132 and 3365 cm -1 , distances of about 1.67, , and 1.89 Å, respectively, were obtained, which are in the same range of magnitude than those reported by Frost et al. for natural samples of Y-churchite[START_REF] Frost | Raman spectroscopic study of the phosphate mineral churchite-(Y) YPO4•2H2O[END_REF].

	1.76
					3210		Churchite				1630			Churchite					3132		Churchite
				3280	3125					1705
																			3365			2870
				3380
												1690		1610
	)
	Intensity (counts.s -1		3540	3470			Rhabdophane	Absorbance (%)			1630	1615	Rhabdophane	Absorbance (%)		3535 3475		Rhabdophane
																					3350
					3330
	4000	3800	3600	3400	3200	3000	2800	2600	1800	1750	1700	1650	1600	1550	1500	4000	3800	3600	3400	3200	3000	2800	2600
				Raman shift (cm -1 )					Wavenumber (cm -1 )							Wavenumber (cm -1 )

  Mesbah et al. already stressed out the isostructural character of CaSO4•0.625H2O and rhabdophane, as well as that of CaSO4•0.5H2O with the hexagonal LnPO4•0.5H2O [42]. Nevertheless, if numerous studies were undertaken concerning the vibrational characterization of dehydrate and hemihydrate gypsum, no reference spectra seems to exist, to our knowledge, for CaSO4•0.625H2O. Only Fritz et al. reported a Raman spectra for the selenite counterpart CaSeO4•0.625H2O

Acknowledgements

The authors would like to thank Clémence Gausse, Danwen Qin and Mariano Sandate Dominguez for their help during the synthesis of the gadolinium phosphate polymorphs.