Yawen Wang
email: yawen.wang@univ-poitiers.fr

Zahra Gohari Bajestani
email: zahra.goharibajestani@univ-lemans.fr

Jérôme Lhoste
email: jerome.lhoste@univ-lemans.fr

Sandy Auguste
email: sandy.auguste@univ-lemans.fr

Annie Hémon-Ribaud

Monique Body
email: monique.body@univ-lemans.fr

Christophe Legein
email: christophe.legein@univ-lemans.fr

Vincent Maisonneuve
email: vincent.maisonneuve@univ-lemans.fr

Amandine Guiet
email: amandine.guiet@univ-lemans.fr

Sylvette Brunet
email: sylvette.brunet@univ-poitiers.fr

The Effects of Various Parameters of the Microwave-Assisted Solvothermal Synthesis on the Specific Surface Area and Catalytic Performance of MgF2 Nanoparticles

Keywords: inorganic fluorides, nanoparticles, nanoparticle size, microwave synthesis, solvothermal route, catalytic performance, BET surface area, XRPD data, TEM data, solid-state NMR

High-specific-surface-area MgF2 was prepared by microwave-assisted solvothermal synthesis. The influences of the solvent and the magnesium precursors, and the calcination atmospheres, on the nanoparticle sizes and specific surface areas, estimated by X-Ray Powder Diffraction, N2 sorption and TEM analyses, were investigated. Nanocrystallized (~7 nm) magnesium partially hydroxylated fluorides (MgF2-x(OH)x) with significant specific surface areas between 290 and 330 m 2 •g -1 were obtained. After activation under gaseous HF, MgF2-x(OH)x catalysts underwent a large decrease of both their surface area and their hydroxide, rates as shown by their 19 F and 1 H solid-state NMR spectra. Expect for MgF2 prepared from the acetate precursor, an activity of 30-32 mmol/h•g was obtained which was about 40% higher compared with that of MgF2 prepared using Trifluoroacetate method (21.6 mmol/h•g).

Introduction

In the last few decades, numerous works have been devoted to the synthesis and characterization of metal nanofluorides due to their prospective applications in photonics, biosensing and the development of the new lubricants and high temperature superconductor devices and catalysis [1]. In particular, nanoscopic magnesium fluoride MgF2 is frequently applied in antireflective coatings [START_REF] Löbmann | Sol-Gel processing of MgF2 antireflective coatings[END_REF]- [START_REF] Scheurell | Optimisation of a Sol-Gel synthesis route for the preparation of MgF2 particles for a large scale coating process[END_REF], functional ceramics [START_REF] Nakamura | Scintillation, dosimeter and optical properties of MgF2 transparent ceramics doped with Gd3+[END_REF] and catalysis [START_REF] Kemnitz | Nanoscale metal fluorides: A new class of heterogeneous catalysts[END_REF][START_REF] Mao | Fe/Hollow nano-MgF2: A green and highly-efficient alternative to classical Cr-based catalysts for the gas-phase fluorination reaction[END_REF][START_REF] Jia | Hollownano-MgF2 supported catalysts: Highly active and stable in gas-phase dehydrofluorination of 1,1,1,3,3-pentafluoropropane[END_REF][START_REF] Kemnitz | Tailor-made MgF2-based catalysts by Sol-Gel synthesis[END_REF]. Many different synthesis approaches have been developed for the preparation of MgF2 nanosized particles, such as mechanochemical synthesis [START_REF] Dreger | An easy access to nanocrystalline alkaline earth metal fluorides-just by shaking[END_REF], sol-gel processes (TFA [11 -12] and fluorolytic [START_REF] Rywak | Sol-Gel synthesis of nanocrystalline magnesium fluoride: Its use in the preparation of MgF2 films and MgF2-SiO2 composites[END_REF][START_REF] Murata | Investigations of MgF2 optical thin films prepared from autoclaved sol[END_REF][START_REF] Murthy | Sol-Gel-Fluorination synthesis of amorphous magnesium fluoride[END_REF][START_REF] Wuttke | Novel Sol-Gel synthesis of acidic MgF2-x(OH)x materials[END_REF][START_REF] Teinz | Highly selective metal fluoride catalysts for the dehydrohalogenation of 3-chloro-1,1,1,3-tetrafluorobutane[END_REF][START_REF] Krüger | Transparent MgF2-films by Sol-Gel coating: synthesis and optical properties[END_REF]), the precipitation method [START_REF] Sevonkaev | Formation of magnesium fluoride particles of different morphologies[END_REF][START_REF] Wojciechowska | MgF2 as a non-conventional catalytic support. Surface and structure characterization[END_REF][START_REF] Lellouche | Antibiofilm activity of nanosized magnesium fluoride[END_REF][START_REF] Nandiyanto | Nanometer to submicrometer magnesium fluoride particles with controllable morphology[END_REF][START_REF] Lellouche | Improved antibacterial and antibiofilm activity of magnesium fluoride nanoparticles obtained by water-based ultrasound chemistry[END_REF], reversed micelle synthesis [START_REF] Cao | Synthesis and characterization of MgF2 and KMgF3 nanorods[END_REF][START_REF] Bas | Synthesis of amphiphilic triblock copolymers for the formation of magnesium fluoride (MgF2) nanoparticles serkan[END_REF] and hydro(solvo)thermal synthesis [START_REF] Clarenc | Synthèse et Caractérisation de Composés Fluorés pour le Piégeage de Fluorures Gazeux[END_REF][START_REF] Demourgues | About MX3 and MX2 (Mn+ = Mg2+, Al3+, Ti4+, Fe3+; Xp-= F-, O2-, OH-) nanofluorides[END_REF][START_REF] Murata | Wettability characterization of transparent MgF2 nanoparticle coatings with SiO2 binder covered with fluoroalkylsilane self-assembled monolayers[END_REF][START_REF] Ji | Analysis and research on the formative factors and properties of nano-MgF2 crystals with different morphologies[END_REF][START_REF] Pietrowski | Microwave-assisted synthesis of spherical monodispersed magnesium fluoride[END_REF]. In this last approach, the use of non-metal alkoxides precursors together with the microwave-assisted solvothermal method combines the advantages of rapid heating and the pressurized solvothermal process. This association leads to a high reaction rate and short reaction time for higher efficiency and energy savings. Furthermore, in comparison with conventional heating in a classical furnace, microwave irradiation allows one to rapidly reach a homogeneous temperature, limiting the crystalline growth and consequently increasing of the specific surface areas of the synthesized materials [START_REF] Bilecka | Microwave chemistry for inorganic nanomaterials synthesis[END_REF]. For example, MgF2 nanoparticles were prepared using a mixture of magnesium acetate, HF and isopropanol treated at 90 °C for 30 min with a specific surface area of 116 m 2 •g -1 [27] [26]. This high surface area can be explained by the microwave/precursors-solvent interaction governed by two main processes involving in the heating mechanism [START_REF] Bilecka | Microwave chemistry for inorganic nanomaterials synthesis[END_REF]. The first process results in the alignment of the dipoles or ions in the electric field inducing molecular friction: it is the case of solvents with a dipolar moment and HF solution. The second, ionic conduction, is due to the presence of ions (Mg 2+ and F -). These charged particles oscillate back and forth, collide with neighboring molecules and thus create heat. However, until now, no systematic study on the impacts of the solvent and the magnesium precursor on crystal growth to obtain a large surface area and their influences on the OH rates of MgF2-x(OH)x nanoparticles obtained via microwave-assisted solvothermal synthesis has been published. In this paper, we report such a study through XRPD, N2 sorption, TEM and 19 F and 1 H solid-state NMR investigations. Furthermore, the influences of the different treatment atmospheres on the structure and surface properties were explored, especially under HF gas since catalytic gas-phase fluorination with anhydrous HF is a crucial process with which to introduce C-F bonds into organic compounds in industry [START_REF] Wang | Fluorine in pharmaceutical industry: Fluorine-containing drugs introduced to the market in the last decade (2001-2011)[END_REF]. More particularly, the effect of the HF gas treatment was studied by solid-state NMR and by CO adsorption followed by IR spectroscopy to quantify the number and strength of the Lewis active sites. Finally, the catalytic performances of these various MgF2 nanoparticles for the gas-phase fluorination of 2-chloropyridine as the model molecule are also reported.

Experimental Part

MgF2 Nanoparticles-Catalyst Preparation

Magnesium acetate (Mg(C2H3O2)2•4H2O, Alfa Aesar, Schiltigheim, France), magnesium nitrate (Mg(NO3)2•6H2O, Alfa Aesar), magnesium carbonate hydroxide (Mg5(CO3)4(OH)2.4H2O, Acros Organics, Noisy-le-Grand Seine-Saint-Denis, France) and magnesium chloride (MgCl2•6H2O, Alfa Aesar), were employed as the starting magnesium precursors and used without any prior purification. Solvents such as i PrOH, EtOH, MeOH, EG and DMSO were used as purchased by Sigma-Aldrich (Saint Quentin Fallavier, France). Hydrofluoric acid solution (15 mmol, 27.6 mol•L -1 (HF 40%) was provided by Riedel De Haen (Paris, France).

Magnesium fluoride nanoparticles were prepared by microwaves-assisted solvothermal route using different solvents (distilled water, i PrOH, EtOH, MeOH, EG and DMSO) and different magnesium precursors: carbonate (Mg(C2H3O2)2•4H2O), nitrate (Mg(NO3)2•6H2O), carbonate (Mg5(CO3)4(OH)2•4H2O) and chloride (MgCl2•6H2O) (Figure S1).

In a typical synthesis, 0.01 mol of magnesium precursor was introduced in a Teflon ® chamber (CEM Corp., Saclay, France); reactor 2 mL of the desired solvent was added under stirring. After few mins of stirring, 0.88 mL of aqueous hydrofluoric acid "HF 40%" (15 mmol, 27.6 mol•L -1 ) with a [F]/[Mg] molar ratio equal to 2, and 8 mL of solvent, were alternately added. The reactor was placed on the microwave's carousel and connected to the temperature and pressure sensors of a MARS-5 microwave digestion system (CEM Corp., Saclay, France). The temperature was raised to 90 °C with a heating time of 5 min and was maintained for 30 min. After cooling to room temperature, the resulting product in gel form was collected and washed three times with EtOH by centrifugation, and the washed gel was dried in an oven at 80 °C. White powder of MgF2 nanoparticles was obtained. MgF2 prepared with different precursors is labelled MgF2-acetate, MgF2-carbonate, MgF2-chloride or MgF2-nitrate respectively. The effect of solvent was determined using magnesium acetate as precursor, and the effect of the magnesium precursor (acetate, carbonate, nitrate and chloride) using methanol as the solvent. The MgF2 samples prepared from various precursors in methanol were thermally treated under air flow and pure O2 at 350 °C for 2 h.

HF Activation and Catalytic Measurements

As described previously [START_REF] Astruc | High specific surface area metal fluorides as catalysts for the fluorination of 2-chloropyridine by HF[END_REF], [START_REF] Wang | Fluorine in pharmaceutical industry: Fluorine-containing drugs introduced to the market in the last decade (2001-2011)[END_REF], the activation by HF and the catalytic activity performances of the various MgF2 materials for the transformation of 2-chloropyridine (2ClPy) were measured in a fixed-bed reactor. The different MgF2 samples were diluted with 6 cm 3 of Lonza graphite (size grains between 125 and 200 µm). Firstly, the catalyst was activated in situ by HF under nitrogen (N2/HF molar ratio: 1/4) for 1 h at 350 °C (activation step). Then, 2-chloropyridine was introduced into the reactor using a syringe pump. The partial pressures of the various components were 0.806 bar for HF, 0.075 bar for 2-chloropyridine and 0.132 bar for nitrogen (HF/2ClPy/N2: 10.8/1/1.7). The organic gas products were trapped into 1,2-dichloroethane. HF and HCl were quenched in water at the outlet of the reactor. The organic components were analyzed with a Scion 456 gas-phase chromatograph (Bruker) equipped with a DB5 capillary column (inside diameter: 0.2 mm; thickness film: 1 µm; length: 30 m). The oven temperature was raised from 100 to 200 °C at a rate of 5 °C•min -1 .

The catalysts' performances were compared at iso-conversion of 2-chloropyridine lower than 25% in order to be in a differential regime. In all cases, only 2-fluoropyridine (2FPy) was observed as a reaction product and HCl as by-product. Thus, the selectivity towards 2-fluoropyridine was equal to 100% and the conversion of 2-chloropyridine corresponded to the 2-fluoropyridine yield. In these experiments, the molar balance was always higher than 90%. No thermal decomposition of 2-chloropyridine was observed.

The catalytic activity A (mmol.h -1 •g -1 ) was defined as the conversion of 2-chloropyridine multiplied by the flow of 2-chloropyridine (mol.h -1 ) and divided by the mass of catalyst. The intrinsic catalytic activity Ai (mmol h -1 •m -2 ) was calculated by taking into account the specific surface area of the catalyst after the activation step by HF. The turn over frequency, TOF (h -1 ), was calculated from the catalytic activity, A (mmol h -1 •g -1 ), divided by the number of actives sites defined as coordinately unsaturated metallic sites Qs (µmol•g -1 ) measured by CO adsorption followed by IR spectroscopy.

Pure O2 (O2 ≥ 99.5%, 200 bar, L50) and gaseous HF (cylinder of 800g) were provided by Air Liquid and the 2-chloropyridine by Sigma-Aldrich.

Characterizations

All MgF2 samples (solvent, precursors and calcination effect) were characterized by X-ray powder diffraction (XPRD), N2 sorption, scanning electronic microscopy (SEM) (JSM 6510 LV, JEOL, Croissy sur Seine, France) and transmission electron microscopy (TEM) (JEOL JEM 2100 HR, JEOL, Croissy sur Seine, France) before and after the activation step at 350 °C under HF to follow the crystallinity and the morphology evolution of the MgF2 nanoparticles. The numbers of active sites and the strengths of their Lewis acidity were titrated by CO adsorption followed by infrared.

X-ray powder diffraction (XRPD) patterns of the MgF2 nanoparticles were recorded with a PANalytical / Bragg-Brentano Empyrean diffractometer (CuK1+2 radiations) (PANalytical, Limeil Brévannes, France) equipped with the PIXcel1D detector. Data were collected in the [15-110°] 2θ scattering angle range for a total acquisition time of 3 h with a 0.499° step. The NIST standard reference material LaB6 (NIST SRM 660b) was used to take account the instrumental broadening. The XRPD pattern of LaB6 was recorded with the same data collection conditions (step and counting time) used for the analysis of MgF2 samples. XRPD patterns were refined by using Le Bail method [START_REF] Bail | Ab-Initio structure determination of LiSbWO6 by X-ray powder diffraction[END_REF] implemented in the Fullprof program [START_REF] Rodriguez-Carvajal | Recent advances in magnetic structure determination neutron powder diffraction[END_REF]. The X-ray line broadening due to the nanometric size of the sample contribution was calculated by using Thompson-Cox-Hastings pseudo-Voigt function [START_REF] Thompson | Rietveld refinement of debye-scherrer synchrotron X-ray data from Al 2 O 3[END_REF] that includes size and strain-broadening terms for both Lorentzian and gaussian components. The two parameters (Y and F) of the Lorentzian component of this function were refined to calculate the apparent crystallite size <L> with Fullprof using Langford's method [START_REF] Langford | A rapid method for analysing the breadths of diffraction and spectral lines using the Voigt function[END_REF]. The diameter DXRD of the spherical particles is related to <L> by the following formula DXRD = 4/3×<L>.

Scanning electronic microscopy (SEM) images of the powders were obtained using a JEOL microscope (JSM 6510 LV, Croissy sur Seine, France). Acceleration voltages varied between 20 and 30 kV as a function of the analyzed samples. Elementary quantitative microanalyses were performed using an Energy dispersive X-ray (EDX) OXFORD detector (AZtec software) (OXFORD Instruments, Gometz La Ville, France).

Transmission electron microscopy (TEM) study was performed on a JEOL JEM 2100 HR electron microscope (JEOL, Croissy sur Seine, France) operating at 200 kV. The samples for transmission electron microscopy investigation were prepared by ultrasonically dispersing each raw powder in ethanol, depositing a drop of the resulting suspension onto a holey carbon-coated copper grid and finally drying the grid in air. Mean diameters of the nanoparticles (DTEM) were deduced by statistical evaluation of about 100 particles using ImageJ software (https://imagej.nih.gov/ij/) [37]. For all measurements, the standard deviation was around 25%.

The specific surface areas were measured at 77 K using a TriStar II 3020 (Micrometrics, Merignac, France). The MgF2 samples were degassed under vacuum at 100 °C for 12 h prior to measurement. The specific surface areas were calculated using the Brunauer-Emmett-Teller (BET) method. For accurate determination of specific surface areas as low as 30 m 2 •g -1 , a minimum of ≈ 350 mg of powder had to be used, as the lowest surface measured using a TriStar II 3020 is around 10 m 2 in the cell.

After synthesis and calcination under air and O2 of MgF2 powders, Fourier transform infrared spectroscopy (FT-IR) spectra were collected in air at room temperature with a Bruker ALPHA FT-IR spectrometer (Bruker, Wissembourg, France) equipped with the Platinum QuickSnap ATR sampling module. The spectral resolution was 4 cm -1 in the 400-4000 cm -1 range. Twenty-five consecutive scans were averaged to obtain a single spectrum. A reference IR spectrum was collected in the same conditions with an empty cell and subtracted from specimen spectra to remove H2O(g) and CO2(g) contributions.

The CO adsorption was carried out using a ThermoNicolet NEXUS 5700 (ThermoFisher Scientific, Paris, France) spectrometer with a resolution of 2 cm -1 and 64 scans per spectrum were collected. Samples were pressed into thin pellets (10-60 mg) with diameter of 16 mm and activated in situ during one night at 350 °C under high vacuum (≈ 10 -6 bar). After cooling down the samples to room temperature, the cell was cooled down with liquid nitrogen to 100 K. A background spectrum was collected which was then subtracted from the other spectra obtained after CO adsorption. Then, successive doses of CO were introduced quantitatively, and an infrared spectrum was recorded after each adsorption until saturation. The final spectrum was recorded with 1 Torr of CO at equilibrium pressure (saturation). All spectra were normalized to an equivalent sample mass (25 mg). The quantification of the amount of CO adsorption corresponding to the titration of active Lewis acid sites Qs (µmol•g -1 ) was carried out by the integration of the total area of the IR bands at saturation between 2100 and 2200 cm -1 using the molar absorption coefficient ε of MgF2 [START_REF] Astruc | Mixed Ba1-xLaxF2+x fluoride materials as catalyst for the gas phase fluorination of 2-chloropyridine by HF[END_REF].

Thermogravimetric analyses were either performed with a TGA-TA Instruments SDT Q600 (TA, Paris, France) between 25 and 900 °C under synthetic air flow with a heating rate of 5 °C min -1 or on a Netzch STA 449 F3 (Netzch, Dardilly, France) coupled with a QMS 403 C mass spectrometer (1-200 amu mass range) under a N2/air atmosphere with a heating rate of 10 °C/min. A continuous analysis of HF, F -, H2O and HO -rates was carried out for MgF2-acetate directly after synthesis.

The elemental analysis of carbon of the metal fluorides was carried out with an elementary analyzer (NA2100 analyzer, CE instruments, Paris, France).

1 H and 19 F solid-state MAS NMR experiments were performed on a Bruker Avance III spectrometer operating at 7.0 T ( 1 H and 19 F Larmor frequencies of 300.1 and 282.4 MHz, respectively), using a 1.3 mm CP-MAS probe head. The 1 H and 19 F MAS spectra were recorded using a Hahn echo sequence with an interpulse delay equal to one rotor period. The 90° pulse lengths were set to 2.4 and 1.25 s; the recycle delays were set to 20 s and 900 s; and 8 to 192 and 32 (or 48) transients were accumulated for 1 H and 19 F, respectively. 1 H and 19 F spectra refer to TMS and CFCl3, respectively, and they were fitted by using the DMFit software (dmfit#20200306, CEMHTI -CNRS -UPR3079 , Orléans, France) [START_REF] Massiot | Modelling one-and two-dimensional solid-state NMR spectra[END_REF].

Results and Discussion

Synthesis of MgF2 Nanofluorides

MgF2 nanofluorides were synthesized via the facile and rapid microwave-assisted solvothermal method using aqueous HF (HF 40%) as the fluorinated agent. The impacts of the solvent, the magnesium precursors, the calcination atmospheres (air and O2) and the activation step by HF, on the composition, the particle size and the specific surface area are reported. Assuming a stoichiometric reaction, the reaction can be described by Equation (1) for the acetate, chloride and nitrate precursors and by Equation (2) for the carbonate magnesium precursor.

MgX2 + 2 HF  nano-MgF2 + 2 HX, (1)
Mg5(CO3)4(OH)2 + 10 HF  nano-MgF2 + 4 CO2 + 6 H2O, (2)
The impacts of the solvent dielectric properties were studied using magnesium acetate (Mg(C2H3O2)2) as the precursor. Indeed, it has been shown that the nature of the solvent significantly influences the size of the nanoparticle prepared by solvothermal synthesis [START_REF] Wuttke | Variation of Sol-Gel synthesis parameters and their consequence for the surface area and structure of magnesium fluoride[END_REF]. MeOH, H2O, i PrOH, EtOH, EG and DMSO were selected and their respective dielectric constants, dielectric losses and loss angles tan δ (tan δ = ε''/ ε' with ε', the dielectric constant and ε'', the dielectric loss) are presented in Table 1. The loss angle tan δ is a measure of reactance (resistance in a capacitor) of a molecule. A material with δ = 0 is completely transparent to microwave irradiation and tan δ is infinite for a perfectly absorbing material. Solvents with tan δ around 1 are remarkable microwave absorbers [START_REF] De La Hoz | Microwave Heating as a Tool for Sustainable Chemistry[END_REF].

MgF2 Nanofluoride's Characterization by XRPD, N2 Sorption, FT-IR and TEM.

XRPD confirmed the rutile type crystal structure of MgF2 (space group P42/mnm (n°136), 20513-ICSD) independently of the solvent used (Figure 1). Among all samples, MgF2 nanoparticles prepared in MeOH, i PrOH, EtOH and DMSO solvents presented the highest specific surface areas (SBET) of between 325 and 345 m 2 •g -1 (Table 2), related to the lower particle diameters between 4 and 6 nm, determined by Le Bail refinement from the XRPD pattern (DXRD). Those highest specific surface areas can be explained by the high tan δ values for those solvents (Table 1). The lowest specific surface area measured for the sample prepared in H2O corresponds to the formation of particles of larger size (8-11 nm). This phenomenon can be explained by the lower tan δ value of H2O. In the case of MgF2-EG, the specific surface area is surprisingly low despite the small nanoparticle size (6-7 nm) and the highest tan δ (tan δ = 1.349). This result could be related to the presence of EG residue on the nanoparticle's surface evidenced by the FT-IR analysis; the EG absorption bands [START_REF] Krishnan | Raman and infrared spectra of ethylene glycol[END_REF] at 1050 cm -1 (ν(C-O) stretching)) and at 950 cm -1 (ν(C-C) stretching) could be observed (Figure S2). EG might be embedded in the NPs and have a negative effect on the NP's surface. To conclude, as the reaction yields for DMSO and EtOH were very low (less than 50%), MeOH was selected as an optimized solvent for the synthesis of MgF2 nanoparticles with high specific surface areas and the smallest particle size, as demonstrated in the case of nanostructured -AlF3-x(OH)x [START_REF] Lhoste | Microwave-assisted synthesis, characterization, and hydrogen adsorption of nanostructured -AlF3-x[END_REF]. For all spectra, the two bands observed at 3393 cm -1 and 1598 cm -1 correspond to hydroxyl groups of H2O and EtOH molecules adsorbed on the surfaces of the nanoparticles.

Table 2. Impacts of the solvent on the specific surface areas (SBET) and particle diameters determined by XRPD (DXRD) of the nanoparticles of MgF2 and yield of the synthesis.

Solvent

SBET (m Regarding the influences of the magnesium precursors on the MgF2 nanoparticle features, four magnesium precursors (magnesium acetate, carbonate, chloride and nitrate) were selected. Transparent MgF2 gels were obtained except for MgF2-carbonate, for which an opaque white gel was observed (Figure S3). The MgF2 nanoparticles' purity was first controlled by XRPD analysis, and XRPD profile refinements confirm the rutile type crystal structure of MgF2 (space group P42/mnm (n°136), 20513-ICSD) independently of the precursor used (Figure S4).

The purity was also confirmed by the FT-IR analyses, as illustrated in Figure S5. All spectra show a strong adsorption band at 460 cm -1 corresponding to the stretching vibration ν of the Mg-F bond and two bands centered at 1600 and 3700 cm -1 assigned to the bending vibration δ and the stretching vibration ν of water molecules [START_REF] Ji | Analysis and research on the formative factors and properties of nano-MgF2 crystals with different morphologies[END_REF]. In the case of MgF2-nitrate, two extra bands emerged at 1400 cm -1 and 1350 cm -1 corresponding to nitrate residue (ν stretching) at the particle surface. The low carbon amount analyzed by elemental analysis (<3%) confirmed also the bright white color of the MgF2 nanoparticle powders (Figure S6). High specific surface areas (SBET), ranging from 237 m 2 •g -1 to 372 m 2 •g -1 , were obtained for the four MgF2 samples (Table 3). Before any thermal treatment, all isotherms belonged to type IV according to IUPAC classification, i.e., the type characteristic of mesoporous materials (Figure 2a). The isotherms measured for MgF2 nanoparticles prepared from acetate, chloride and nitrate magnesium precursors are similar to the hysteresis loop of type H2 [START_REF] Rouquerol | Texture Des Matériaux Divisés -Taille de Pores Des Matériaux Nanoporeux Par Adsorption d'azote Cet[END_REF]- [START_REF] Rouquerol | Texture des matériaux divisés-aire spécifique des matériaux pulvérulents ou nanoporeux[END_REF]. Such pore structures can be regarded as intergranular porosity. Surprisingly, a different shape for the hysteresis loop was observed for MgF2-carbonate. This shape tends to be similar to the H3 type observed for aggregates. The size, morphology and structure of the particles were characterized by TEM (Figure 3), thereby revealing that the MgF2 nanoparticles were irregularly shaped with average crystallite sizes of 5 to 10 nm, consistent with those obtained from XRPD Le Bail refinements (Table 4, results of a refinement are given as an example in Table S1). Selected area electron diffraction (SAED, Figure S7) performed on TEM confirmed also the crystallinity of the MgF2 nanoparticles, as all rings of the SAED patterns were well indexed to the crystal planes (110), (011), ( 111) and (121) of the rutile type MgF2 structure. No lattice fringe could be observed at high resolution, as MgF2 nanoparticles were not stable at high magnification under the electron beam as it induced the departure of the water molecules. Among these four pure MgF2 samples, MgF2 nanoparticles prepared from magnesium acetate precursor exhibited the highest specific surface areas (SBET) (372 m 2 •g -1 , Table 2) related to the lower particle diameters of between 4 and 5 nm, determined by Le Bail refinement form the XRPD pattern (DXRD).

Carbonate Acetate

To probe the thermal stability of the particles synthesized from different precursors, thermal treatments were performed under air and under O2, at 350 °C for 2 h. The temperature of 350 °C was chosen, as it is the temperature of the fluorination reaction of 2-chloropyridine. A drop of specific surface area for all samples was observed after the calcination in air and in O2 (Table 3), and a significant change in the hysteresis loop was induced (Figure 2b,c). Indeed, after calcination in air, the specific surface areas were around 60-70 m 2 •g -1 except for the sample prepared using magnesium chloride as a precursor (47 m 2 •g -1 ). Differences were more pronounced after the calcination under O2, for which the lower specific surface areas were observed for the samples prepared using acetate and chloride magnesium precursors and the highest for those prepared using nitrate and carbonate magnesium precursors. Except for MgF2-carbonate (D ≈ 9 nm), this decrease corresponds to a nanoparticle growth induced by the thermal calcination in air and in O2 (DXRD and DTEM ≈ 15-20 nm, Table 4). Despite the stability of the rutile structure, a decrease of the specific surface area was also observed after the activation by HF under operating conditions (350 °C) of the catalytic fluorination of 2-chloropyridine. In fact, whatever the magnesium precursors used, similar specific surface areas were observed after the activation step by HF of the as-synthesized samples and after the calcination step under air and under O2. This demonstrates that the calcination step did not stabilize the MgF2 samples and is not crucial before the activation step by HF gas. Except for the sample prepared with magnesium acetate as the precursor (33 m 2 •g -1 ), the microwave-assisted solvothermal method using MeOH as solvent allowed us to obtain higher-specific-surface-area MgF2 catalysts (50-60 m 2 •g -1 ) after the activation step by HF (Figure 4, Figure 5 and Figure S8) in comparison with MgF2 prepared from commercial magnesium oxide (16 m 2 •g -1 ) or carbon-free MgF2 prepared by using TFA method (33 m 2 •g -1 ) [START_REF] Astruc | High specific surface area metal fluorides as catalysts for the fluorination of 2-chloropyridine by HF[END_REF].

MgF2 Nanofluoride's Characterization by 19 F and 1 H Solid-State MAS NMR

The structural investigations were completed by 19 chloride and nitrate precursors. For the rutile type crystal structure of MgF2 involving a single F crystallographic site [START_REF] Baur | Rutile-type compounds. V. refinement of MnO2 and MgF2[END_REF], a single 19 F NMR line is observed on its spectrum [ 47 ] . The 19 F spectra of the samples before activation show a main line with a maximum at a similar isotropic chemical shift value (δiso ~ -197.7 ppm) but also a shoulder towards higher δiso values, and even, distinctly, a second contribution at around -185 ppm (Figure 6, fits and results of these fits given in Figure S9 and Table S2). The spectra of the samples after activation show far less pronounced shoulders (Figure S10) but remain asymmetrical (three contributions with close δiso are necessary to reconstruct them perfectly, (Figure 7; fits and results of these fits are given in Figure S11, Figure S12 and Table S3)). Moreover, compared with the 19 F NMR line of a MgF2 microcrystalline sample [START_REF] Clavier | Synthèse, caractérisations et évaluation de l'activité bactéricide de composés inorganiques à base de cuivre[END_REF], these lines are broader (line widths of 876, 930, 1000, 853 and 795 Hz for samples prepared from acetate, carbonate, chloride and nitrate precursors and micro crystalline, respectively). The broadening mirrors chemical shift distributions related to disorder around fluorine atoms due to the high specific surface area and partial hydroxylation. The shoulders or contributions at higher 19 F δiso values are due to partial hydroxylation. The increase of the 19 F δiso value with the hydroxide content, i.e., the number of hydroxide groups in the environment of the fluoride ion in hydroxyfluorides, is a well-known phenomenon which has been observed in magnesium hydroxyfluorides (up to 40 ppm) [START_REF] Prescott | New magnesium oxide fluorides with hydroxy groups as catalysts for michael additions[END_REF]. Nevertheless, due to the very large number of different environments of the fluoride ions in magnesium partially hydroxylated fluorides, MgF2-x(OH)x, the assignment of the additional lines seems to be unrealistic. Indeed, the environment of the site of the fluoride ion in MgF2 consists of three magnesium ions and eleven fluoride ions at four different distances (between 2.58 and 3.35 Å, Table S4) [START_REF] Baur | Rutile-type compounds. V. refinement of MnO2 and MgF2[END_REF]. Then, depending on the positions occupied by the anions, there are several inequivalent FMg3F11-y(OH)y 6-(0 ≤ y ≤ 11) environments for each of the twelve y values. In any case, the proportion of fluoride ions in environments free of hydroxide ions (FMg3F11) can be roughly estimated within the range 35% to 50% for the samples before activation (Table S2) and is superior to 80% for the samples after activation (Table S3). The rates of -OH groups can be estimated by assuming a random distribution of OH -and F -ions at anionic sites (Table S5). Only rates ranging from 6% to 9% (0.12 ≤ x ≤ 0.18) for the samples before activation and below 2% (x < 0.04) for the samples after activation satisfy such proportions of FMg3F11 environment. The rates of -OH groups were therefore low in the as-prepared samples and very low after HF treatment, in agreement with Wuttke et al. regarding MgF2-x(OH)x samples prepared by fluorolytic sol-gel synthesis [START_REF] Wuttke | Novel Sol-Gel synthesis of acidic MgF2-x(OH)x materials[END_REF]. In detail, for samples prepared from chloride and nitrate precursors which show similar spectra and the narrowest shoulders, similar OH rates around 6% are expected, substantially lower than those of the samples prepared from acetate and carbonate precursors, for which OH rates of 8% and 9% were respectively estimated. For the latter two samples, it should be noted that the formation of bonds between magnesium atoms on the surfaces of the nanoparticles and residual acetate and carbonate ions acting as ligands is likely and that the effect of such ligands on the 19 F δiso values is expected to be similar to that of -OH groups; -OH group rates are potentially the sum of rates of -OH and -OCOCH3 or -OCO2 groups. Finally, for the as-prepared MgF2-x(OH)x samples, it appears that specific surface areas and -OH group rates are not independent. Even if the sample with the highest -OH group rate did not have the largest surface area, a trend was observed with the two samples with the smallest (largest) surface areas and the smallest (largest) OH rates. After activation, whatever the precursor used, i.e., whatever the OH rate of the MgF2-x(OH)x samples, similar OH rates below 2% are likely. Surprisingly, at first glance, the widths of the main 19 F NMR lines and the areas are not classified in the same order. The narrowest main line was even observed for the sample prepared from nitrate precursor, which had the largest specific surface area, but this is consistent with the greatest relative intensity of the lines attributed exclusively to FMg3F11 environments.

The 1 H solid-state MAS NMR spectra of the four as-prepared samples (Figure 6; fits and results of these fits in Figure S13 and Table S6) and after HF activation (Figure 7; fits and results of these fits in Figure S14 and Table S7) present one main broad contribution with δiso values maximally ranging from 5.0 to 5.8 ppm, assigned to absorbed H2O molecules and a smaller contribution with δiso values maximally ranging from 1.0 to 1.4 ppm, assigned to Mg3-OH environments [START_REF] Sideris | Mg/Al ordering in layered double hydroxides revealed by multinuclear NMR spectroscopy[END_REF]. However, the spectra of the samples before and after treatment are clearly differentiated by several characteristics, the most significant being the larger relative intensity of the contribution assigned to Mg3-OH environments after activation, largely offset by the large decrease of the intensity of the NMR spectra. This decrease is explained by a decrease of the amounts of adsorbed H2O molecules, related to the decrease of the surfaces of the nanoparticles, leading, despite a large number of scans, to rather low signal to noise ratios and confirming that, after activation, the amounts of residual -OH groups are small. The 1 H NMR contributions are broadened by distributions in the chemical shifts reflecting heterogeneity of the local hydrogen environment. As for 19 F, after activation, it was for the sample prepared from the nitrate precursor, that the broadening was the least, despite its higher specific surface area. Lastly, the 1 H spectrum of the sample prepared from acetate precursor shows a line at 2.1 ppm (Table S6) which can be assigned to protons from residual -OCOCH3 group, probably bonded to magnesium atoms on the surfaces of the nanoparticles.

Properties of the Active Sites Characterized by Adsorption of CO as a Probe Molecule Followed by IR Spectroscopy

Finally, after the activation step by HF which led to the effective catalyst, the properties of the active sites (quantities and strength of Lewis acidity) involved in Cl/F exchanges were characterized by adsorption of CO as a probe molecule followed by IR spectroscopy. CO is a suitable probe molecule for the characterization of Lewis acidity because the (CO) frequency is very sensitive to the local cationic environment. After CO adsorption, this band shifts more or less depending on the strength of Lewis acidity: the stronger the Lewis acidity, the higher the shift. On the different studied catalysts, CO was adsorbed on under-coordinated metal sites of metal fluorides which were the Lewis acid sites. The change of the strength of Lewis acidity between each catalyst was practically studied. It is also important to note that CO can also be adsorbed on Bronsted acid sites. In the present work, no Bronsted acid sites were detected.

As reported in Figure 8, no difference of wave numbers (2170 cm -1 ) was noticed for the samples corresponding to similar low Lewis acidity strengths for all unsaturated metallic sites. Regarding the quantification (Table 5), it is difficult to establish a trend given the uncertainties. The number of sites appears to be constant except for three samples for which the values are higher. These experiments were reproduced and the results confirmed. The adsorption of several CO molecules on the same site may be suggested as reported by Wuttke et al. [START_REF] Wuttke | Infrared investigation of the acid and basic properties of a Sol-Gel prepared MgF2[END_REF]. The formation of complexes between CO and metallic centers may be also considered. On the other hand, the concentration of sites Csites was constant (1.8-2.0 µmol•m -2 ) whatever the precursor used except after the treatment in air.

Catalytic Performances

The performances of the various MgF2 samples were measured for the transformation of 2-chloropyridine at 350 °C under atmospheric pressure (Table 6). All MgF2 catalysts are active for the fluorination of 2-chloropyridine with a selectivity towards 2-fluoropyridine of 100%. Expect for MgF2 prepared from the acetate precursor, an activity of 30-32 mmol•h -1 •g -1 was obtained, which was about 40% higher than that of MgF2 prepared using TFA method (21.6 mmol•h -1 •g -1 ) [START_REF] Astruc | High specific surface area metal fluorides as catalysts for the fluorination of 2-chloropyridine by HF[END_REF]. This gain of activity was due to the increase of the specific surface area (from 33 m 2 •g -1 to 48 m 2 •g -1 ). Indeed, in both cases, the activity per square meter was around 0.7 mmol•h -1 •g -1 . The lower activity of the MgF2 prepared from the acetate precursor could be explained from the different thermal behaviors of the as-synthesized MgF2 nanoparticles (Figure S15). For all, a first weight loss of ≈20% related to the departure of residual solvent and HF and -OH group was observed. Table 6. Impacts of the precursors and of the treatment in air and in O2 of different MgF2 samples after HF activation on the transformation of 2-chloropyridine (T=350 °C, HF/2chloropyridine/N2: 7/1/1.7, isoconversion around 30%). A: Activity for the transformation of 2-chloropyridine: (a) mmol.h -1 •g -1 ; (b) mmol.h -1 •m -2 ; TOF (turn over frequency, h -1 ): A/Qsites with A (activity, mmol•h -1 •g -1 ); and Qsites (µmol•g -1 ), the amount of CO adsorbed followed by FT-IR. Estimated relative uncertainty: 15%. In the case of MgF2-acetate, a supplementary weight loss was clearly detected at higher temperatures. In order to get more information, MS-TGA analysis was performed on this sample (Figure S16). It confirmed the release of H2O or -OH groups (m/z 18), F -groups (m/z 19) and CH3 + groups between 110 °C and 150 °C. The CH3 + group came from acetic acid formed during the reaction between acetate precursor and HF. The second CH3 + peak observed at 440 °C was probably due to acetate groups strongly coordinated to the metal ions at the surface, as confirmed by 19 F NMR. These remaining acetate groups could block the active sites lowering the catalyst activity. Regarding the activity per square meter, no difference of activity (0.7-0.8 mmol•m 2 •g -1 ) was noticed according to the similar specific areas, nanoparticle sizes and morphologies of the different MgF2 samples after HF treatment. Finally, the activity per site (TOF defined as A/Qsites ratio) was in general the same, whatever the magnesium precursor, except for three samples for which the TOF was lower (around 200 h -1 instead 350 h -1 ). This corresponded also to an abnormally high CO adsorption.

Sample-

Acetate

Carbonate

Conclusion

In this work, various parameters involved in the synthesis of MgF2 by microwave-assisted solvothermal synthesis were investigated. Methanol as a solvent provided significant yields, small nanoparticle size and the highest specific surface area. Whatever the magnesium precursors, hydroxylated magnesium fluoride MgF2-x(OH)x compounds with OH rates probably ranging from 6% to 9% (0.12 ≤ x ≤ 0.18) and with large specific surfaces ranging from 237 m 2 •g -1 to 372 m 2 •g -1 (from magnesium acetate precursor) were obtained. All were strongly impacted by the HF activation step, during which significant decreases of both the specific surface area, ranging from 28 m 2 •g -1 to 59 m 2 •g -1 , and the OH rates (below 2%) were highlighted. Despite this drop of the specific surface area, microwave-assisted solvothermal synthesis using non-alkoxide precursors allows the rapid, straightforward and cheap preparation of scalable MgF2 catalysts for the fluorination of 2-chloropyridine with a higher activity (40%) compared with that of MgF2 prepared using the TFA method.

Supplementary Materials:

The following are available online at www.mdpi.com/xxx/s1. Figure S1: Representation of microwaves assisted synthesis of MgF2 nanoparticles. Figure S2: FT-IR spectra of MgF2 powders synthetized using H2O, i PrOH, EtOH, EG and DMSO as solvent. Figure S3: Pictures of the as-synthesized MgF2 nanoparticles as gel after the washing procedure and before drying to obtain a white powder. Figure S4: Le Bail refinements of MgF2 nanoparticles prepared from (a) acetate, (b) carbonate, (c) chloride and (d) nitrate magnesium precursors. Vertical markers give the Bragg peak positions of the crystalline structure of MgF2 (space group P42/mnm (n°136)). Figure S5(: FT-IR spectra of MgF2 nanoparticles prepared from acetate, carbonate, chloride and nitrate magnesium precursors and using MeOH as solvent.

Figure 1 .

 1 Figure 1. XRPD patterns of MgF2 nanoparticles prepared by microwaves-assisted solvothermal synthesis using H2O, i PrOH, EtOH, EG or DMSO as solvent.

Figure 2 .

 2 Figure 2. N2 adsorption and desorption isotherms of (a) as-synthesized, (b) calcined under air (350 °C, 2 h) and (c) calcined under O2 (350 °C, 2 h) MgF2 prepared from acetate, carbonate, chloride and nitrate magnesium precursors.

Figure 3 .

 3 Figure 3. TEM of MgF2 nanoparticles prepared from acetate (a), carbonate (b), chloride (c) and nitrate (d) magnesium precursors.

Figure 4 .

 4 Figure 4. TEM of as-synthesized (a,b) and calcined in O2 (c,d) MgF2 prepared from acetate and nitrate magnesium precursors, after the HF activation step.

Figure 5 .

 5 Figure 5. N2 adsorption and desorption isotherms of (a) as-synthesized; (b) calcined in air and (c) calcined in O2 MgF2 prepared from acetate, carbonate, chloride and nitrate magnesium precursors, after HF activation.

  F and 1 H solid-state MAS NMR studies before and after the activation step by HF for MgF2 samples prepared from acetate, carbonate,

Figure 6 .

 6 Figure6.19 F and 1 H (in the inset on the left) solid-state MAS (64 kHz and 60 kHz, respectively) NMR spectra of MgF2 samples prepared from (a) acetate, (b) carbonate, (c) chloride and (d) nitrate magnesium precursors, before the HF activation step and for19 F of (e) a micro crystalline sample of MgF2. The isotropic lines of the19 F spectra are expanded in the inset on the right. The star symbols on the19 F spectra indicate the spinning sidebands.

Figure 7 .

 7 Figure 7. 19 F and 1 H (in the inset on the left) solid-state MAS (64 kHz and 60 kHz, respectively) NMR spectra of MgF2 samples prepared from (a) acetate, (b) carbonate, (c) chloride and (d) nitrate magnesium precursors, after the HF activation step. The isotropic lines of the 19 F spectra are expanded in the inset on the right and compared with that of (e) a micro crystalline sample of MgF2 recorded under the same conditions. The star symbols on the 19 F spectra indicate the spinning sidebands. The dot symbols on the 19 F spectra of (d) indicate fluoride impurities.

Figure 8 .

 8 Figure 8. CO adsorption followed by FT-IR over as-synthesized MgF2 prepared from acetate, carbonate, chloride and nitrate magnesium precursors after the HF activation step.

  Figure S6: Pictures of MgF2 nanoparticles powders prepared from different precursors. Figure S7: SAED patterns of MgF2 nanoparticles prepared from (a) acetate, (b) carbonate, (c) chloride and (d) nitrate precursors.

  Figure S8: Nanoparticle sizes of MgF2 after HF treatment measured from TEM images.

  FigureS9:19 F MAS (64 kHz) experimental (blue line) and fitted (dashed red line) NMR spectra of the MgF2 samples prepared from (a) acetate, (b) carbonate, (c) chloride and (d) nitrate precursors, before HF activation. FigureS10: Isotropic lines of the19 F MAS experimental spectra of the MgF2 samples prepared from acetate, carbonate, chloride and nitrate

Table 1 .

 1 Dielectric constants (ε'), dielectric losses (ε'') and loss tangents (tan δ = ε''/ε') of the various solvents (MeOH, H2O, i PrOH, EtOH, EG and DMSO) .

	Solvent	ε'	ε''	tan δ
	MeOH	34.0	21.5	0.632
	H2O	80.4	9.9	0.123
	i PrOH	18.3	14.6	0.798
	EtOH	24.3	22.9	0.942
	EG	37.0	49.9	1.349
	DMSO	45.0	37.1	0.824

  2

Table 3 .

 3 Impacts of the magnesium precursors (acetate, carbonate, chloride, nitrate) and of the treatments (air, O2) on the specific surface areas (SBET, m 2 •g -1 ) of the MgF2 samples, before and after HF activation.

	-Sample		Acetate	Carbonate	Chloride	Nitrate
	As-synthesized	Before HF After HF	372 33	327 49	237 47	240 59
	Air	Before HF	62	71	47	63

Table 4 .

 4 Impacts of the precursors and of the treatments in air and in O2 on the MgF2 nanoparticle diameters, determined by XRPD (DXRD, nm) and TEM (DTEM, nm), before and after HF activation.

	-Sample	Acetate DXRD DTEM	Carbonate DXRD DTEM	Chloride DXRD DTEM	Nitrate DXRD DTEM
	As-synthesized	Before HF After HF	4 35	5 36	4 19	5 21	8 19	5 2	7 27	5 28
	Air	Before HF After HF	14 33	--	9 15	--	15 28	--	14 27	--
	O2	Before HF After HF	20 27	21 28	9 16	--	16 25	--	14 24	16 27

  ). Estimated relative uncertainty: 5%.

	Sample-	Acetate Qsites Csites	Carbonate Qsites Csites	Chloride Qsites Csites	Nitrate Qsites Csites
	As-synthesized	64	1.9	87	1.8	177	2.4	106	1.8
	Air	87	3.1	156	3.2	79	2.3	90	2.8
	O2	68	2.1	151	1.8	78	1.7	96	2.0

(http://creativecommons.org/licenses/by/4.0/).

Acknowledgments: Yawen Wang thanks the University of Poitiers for a PhD grant. The authors wish to thank François Metz and Eric Perin from Solvay St Fons France for their fruitful discussions. The authors greatly acknowledge the platforms "Diffusion et Diffraction des Rayons-X" and "Electronic Microscopy" of IMMM.

Conflicts of Interest:

The authors declare no conflict of interest.


Emmanuel Lizé

Marc Rébillat

Nazih Mechbal

Christian Bolzmacher

Spatial integration of baseline-free damage detection algorithms based on dual-PZT for the structural health monitoring of anisotropic composite aeronautic structures

The focus is put here on the Structural Health Monitoring (SHM) of composite aeronautic structure using Lamb waves emitted and recorded with piezoelectric transducers (PZT). Conventional algorithms perform Lamb waves acquisition in the healthy state of the structure (referred to as the "baseline") and then compare incoming data from an unknown state with this one to detect, locate, classify and quantify any potential damage. The acquisition, storage, and update of the initially recorded baseline database constitute a severe drawback of such algorithms. Indeed, the structure under study as well as the environment may vary during its operational life without the appearance of any damage and thus the initial baseline may not be relevant at any instant where damage monitoring is needed. In order to circumvent this drawback, "baselinefree" method (such as the instantaneous baseline [BI] and rupture of reciprocity [RR]) have been developed. Moreover, the use of dual-PZT, i.e. concentric PZT made of a ring and a disk lying on the same ceramic, has been shown as attractive for baselinefree purposes. However, now that several algorithms based on dual-PZT are available, no study dealing with the spatial integration of the results provided by these algorithms have been reported in the literature. It is thus proposed in this paper to investigate strategies for the spatial integration of common baseline-free methods (namely BI and RR) on an experimental case of damage on a highly anisotropic composite plate. Results illustrate the decomposition of Lamb wave modes in signals measured via dual PZTs as well as the proposed spatial integration strategies for these methods.

INTRODUCTION

Monitoring in real-time and autonomously the health state of structures is of high interest in the industry, and more specifically for the aeronautic and civil engineering applications fields. Such a process is referred to as Structural Health Monitoring (SHM) [START_REF] Nichols | Encyclopedia of Structural Health Monitoring[END_REF][START_REF] Staszewski | Health Monitoring of Aerospace Structures: Smart Sensor Technologies and Signal Processing[END_REF]. To achieve this goal, these structures become "smart" in the sense that they are equipped with sensors, actuators and artificial intelligence that allow them to state regarding their own health. One can compare such smart structures with the human body which, thanks to its various senses and nerves, can know if it has been hurt and where. The SHM process is classically decomposed into four steps: damage detection, damage localization, damage classification and damage quantification.

Damage detection using Lamb waves is one of the most common methods for the SHM of aeronautic composite structures. Among all the methods employed to trigger and catch Lamb waves, the use of piezoelectric transducer (PZT) is one of the cheapest and easiest-to-settle. The common approach is based on the comparison of signals recorded on a "pristine" structure -the baseline -against those obtained on a possibly damaged structure. The resulting signal strongly depends on the structure's mechanical and geometrical properties as well as environmental conditions. Some solutions have been proposed to compensate for the effect of temperature [START_REF] Fendzi | A general Bayesian framework for ellipse-based and hyperbola-based damage localization in anisotropic composite plates[END_REF][START_REF] Zheng | Sensor Self-Diagnostics for Piezoelectric Transducers Operating in Harsh Temperature Environments[END_REF] or to extend baseline data to a wider range of environmental conditions [START_REF] Liu | Robust ultrasonic damage detection under complex environmental conditions using singular value decomposition[END_REF][START_REF] Hajrya | Principal component analysis and perturbation theory based robust damage detection of multifunctional aircraft structure[END_REF]. This drawback of existing methods has also fed the interest for "baseline-free" methods. "Baselinefree" is here an abusive word (see Axiom II in [START_REF] Nichols | Encyclopedia of Structural Health Monitoring[END_REF]) since data, models, or physical assumptions are always needed to decide whether a structure is damaged or not. This expression thus refers here to methods where a baseline of signals recorded from the pristine condition of the monitored structure is not mandatory for damage detection.

Lamb wave excitation in composite aeronautic structures generates simultaneously at least two propagating modes having different physical properties (velocity, wave number, etc…). Those symmetric and antisymmetric Lamb wave modes are very useful for SHM as they convey complementary information when interacting with damages [START_REF] Hajrya | Principal component analysis and perturbation theory based robust damage detection of multifunctional aircraft structure[END_REF]. Dual PZTs are made of a concentric ring and disc. Both parts can be used as actuators and sensors bringing more signal combinations than conventional PZTs and allow for the isolation of the first antisymmetric or symmetric mode [START_REF] Su | Identification of Damage Using Lamb Waves[END_REF][START_REF] Yeum | Delamination detection in a composite plate using a dual piezoelectric transducer network[END_REF]. With dual PZTs, damage can then be detected in a "baselinefree" manner by using the damage-introduced mode conversion and attenuation of the propagating waves. The theoretical aspect justifying the use of those transducers for "baseline-free" SHM is well developed in and experiments [START_REF] Su | Identification of Damage Using Lamb Waves[END_REF].

Svral "baseline-free" methods, where mode decomposition based on dual PZT have been proposed. The "instantaneous baseline" (BI) method is based on a transducer network with paths having the same dimensions and orientations. Instead of comparing signals obtained at a random condition with a pristine baseline, signals are compared instantaneously between paths even under varying environmental conditions [START_REF] Yeum | Lamb wave mode decomposition using concentric ring and circular piezoelectric transducers[END_REF][START_REF] Lim | Reference-free damage detection, localization, and quantification in composites[END_REF][START_REF] An | Instantaneous crack detection under varying temperature and static loading conditions[END_REF]. Drawbacks are that examined paths must have identical PZT positioning and bonding and that reflection of elastic waves from boundaries must be avoided. In the "reciprocity principle" (RR) method, two signals obtained from both possible directions of a given path is directly compared. Its drawbacks are that the implemented PZTs must be identically bonded to the structure, and that damages located far from the investigated path are difficult to detect [START_REF] Anton | Reference-free damage detection using instantaneous baseline measurements[END_REF].

However, even if these "baseline-free" algorithms based on dual-PZT are available, no study dealing with the spatial integration of the results provided by these algorithms have been reported in the literature. Drawing on previous works of the authors [START_REF] Sohn | Development of dual PZT transducers for reference-free crack detection in thin plate structures[END_REF], it is thus proposed in this paper to investigate strategies for the spatial integration of common baseline-free methods (namely BI, RR) on an experimental case of damage on a highly anisotropic composite plate. The outline of the paper is as follows: in section 2 the structure under study mounted with dual PZTs is presented. The two proposed baseline-free damage detection approaches are described in section 3. Then in section 4, four methods dedicated to the computation of a damage localization map from the previously computed damage indexes are investigated. Results are presented, analyzed and discussed in section 5.

STRUCTURE UNDER STUDY

The structure under study is a CFRP plate, with plies having [0° 90°] stacking and properties as shown in Figure 1. This plate is equipped with 7 dual-PZTs produced by NOLIAC (NCE51 material). The delamination-type damage is introduced into samples in a calibrated way using Laser Shock Wave Testing (LWST) and more particularly symmetrical laser shock configuration. LSWT is chosen as an alternative to conventional damage generation techniques such as conventional impacts and Teflon inserts since it allows for a better calibration of damage in type, depth and size. In the present case a 20 mm diameter damage has been created by cumulating damages produced by successive and close LASER shocks. The delamination control has been carried out using standard C-Scan and results demonstrate that the CFRP plate is indeed damaged as the required position. However, a visual inspection of the plate surface does not allow to detect any damage.

BASELINE FREE METHODS UNDER STUDY

Two « baseline-free » methods are here investigated using the damage index computed on the previously described structure under study.

a. Reciprocity principle

This method has originally been implemented with dual-PZTs for crack detection within aluminum structures and with standard PZT elements in a composite structure. Its extension to composite structures equipped with dual PZTs allows to study the impact of delamination on each mode. In this case, the two signals at the basis of the damage indexes computation are et (the index depicts the chosen actuating/sensing part of the dual-PZTs [disk, ring, entire], and the index refers to the dual PZTs actuator sensor configuration). This method can naturally be used by considering isolated and modes and in these cases, the signals used for damage index computations are denoted and or and which correspond to symmetric and antisymmetric mode contributions extracted from the previous signals.

b. Instantaneous baseline

This method is the most mature one and the most widely used. Isolation of and modes within this method should allow to improve damage detection in several situations. For this method, the experimental signals used for damage index computation corresponds to the signal recorded one path and to the reference signal which is the average signal overall comparable paths. Comparable paths existing on the structure under study are depicted in the following Figure . This method can naturally be used by considering isolated and modes and in these cases, the signals used for damage index computation correspond to symmetric and antisymmetric mode contributions extracted from the previously defined signals.

DAMAGE LOCALIZATION MAPS COMPUTATION

Four methods dedicated to the computation of damage localization map from the previously computed damage indexes are here investigated. They are denoted as "PATH, PZT, PIXEL, and CLUSTER". These methods constitute various potential ways to integrate damage indexes over the surface of the structure under study. The "PATH" approach relies on paths comparison over the whole structure. For the structure under study, containing 7 dual-PZTs, 42 paths can be defined for which a damage index is computed. The "PZT" approach relies on the computation of one damage index per PZT by considering the average damage index over all the paths including that PZT. As the structure under study contains 7 PZT, 7 of such damage indexes can be computed that represent the damage state in the vicinity of each dual-PZT. Areas associated with each dual-PZTs have been obtained through a Voronoi partitioning algorithm. Within the "PIXEL" approach the structure under study is divided arbitrarily in square zones, denoted as "PIXELs", according to the experimenter choice. One PIXEL stands for a zone delimited by this mesh. For each PIXEL, the computed damage index (DI) value corresponds to the mean of the DI values related to paths that cross that PIXEL divided by the number of such paths. For the structure under study, square PIXELs of side size of 20 mm have been retained and thus 336 PIXELs have been defined. Within the CLUSTER approach, a CLUSTER denotes an area delimited by PZT elements, as shown in Figure 4. One DI is computed for each CLUSTER by considering the DIs over the paths crossing the CLUSTER. The structure under study has been divided in 6 of such CLUSTERs as shown above.

RESULTS

Examples of results obtained when applying the previously defined baseline-free methods with the various spatial integration procedures and by making use of either S0 or A0 modes are presented. In Figure 5, results for the reciprocity method, using the S0 mode and spatially integrated using the PZT approach are presented. From this figure, it can be seen that DIs do not vary largely over the various PZT. Furthermore, the maximum DI value is reached for PZT 6, which is neighboring PZT 7 corresponding to the PZT closest to the damaged area. That combination of methods (reciprocity rupture / S0 mode / PZT approach) is thus not really successful in the present example. In Figure 6, results for the instantaneous baseline method, using the S0 mode and spatially integrated using the CLUSTER approach are presented. From this figure, damage indexes again do not vary largely over the various CLUSTERs. Furthermore, the maximum damage index value is reached for CLUSTER (4/6/7), which is neighboring CLUSTER (4/5/7) which contains the damaged area. Again, that combination of methods (instantaneous baseline / S0 mode / CLUSTER approach) is not really successful in the present example. In Figure 7, results for the reciprocity rupture method, using the A0 mode and spatially integrated using the PATH approach are presented. From this figure, it can be observed that DIs vary largely over the various PATHs. Furthermore, the maximum damage index value is reached for several PATHs crossing, or very close to the damaged area. That combination of methods (reciprocity rupture / A0 mode / PATH approach) is here successful in the present example. In Figure 8, results for the reciprocity rupture method, using the A0 mode and spatially integrated using the PIXEL approach are presented. From this figure, it can be observed that damage indexes again vary largely over the various PATHs. Furthermore, the maximum damage index value is reached for several PIXELs containing, or very close to the damaged area. That combination of methods (reciprocity rupture / A0 mode / PIXEL approach) is here again successful in the present example.

CONCLUSION

In order to circumvent the drawback of standard SHM methods, F"baseline-free" method (such as the instantaneous baseline (BI) and rupture of reciprocity (RR)) have been developed. The use of dual-PZT, i.e. concentric PZT made of a ring and a disk lying on the same ceramic, has also been shown as attractive for baseline-free purposes. This paper deals with the spatial integration of the results provided by these algorithms. Four strategies for the spatial integration of common baseline-free methods (namely BI and RR) are illustrated on an experimental case of damage on a highly anisotropic composite plate. Results illustrate that the proposed spatial integration strategies for these methods may be relevant in practice.

Figure 1 :

 1 Figure 1 : a) Dimensions of the [0° 90°] CFRP plate and dual-PZTs positions. . Dimensions of dual-PZTs.

Figure 2 :

 2 Figure 2: C-Scan of the damaged plate after multiple LASER Shocks. Visual inspection of the plate does not allow distinguishing the damaged area. Damage indexes, or features, are then computed on the basis of the experimental signals (5 cycle sinusoidal tone burst modulated by a Hanning window at an amplitude of 10 V and a central frequency = 50 ) after denoising. A damage index corresponding to the different between the maximum amplitude of the envelope of the two compared signals is computed for each path of the structure.

Figure 3 :

 3 Figure 3: Comparable paths for the instantaneous baseline method

Figure 4 :

 4 Figure 4: Tested strategies for damage indexes integration over the structures under study.

Figure 5 :

 5 Figure 5: Reciprocity rupture method for the S0 mode integrated with the PZT approach

Figure 6 :

 6 Figure 6: Instantaneous baseline method for the S0 mode integrated with the CLUSTER approach

Figure 7 :

 7 Figure 7: Reciprocity rupture method for the A0 mode integrated with the PATH approach

Figure 8 :

 8 Figure 8: Reciprocity rupture method for the A0 mode integrated with the PIXEL approach


domain: chim phys

text:
Virginie Simonet

Francoise Damay

Sylvie Ferlay

Andrew Cea

Catalin Maxim

Cyrille Train

Magnetic Investigation of an Atypical Three-Dimensional Bimetallic Oxalate-Based Magnet

Detailed magnetic measurements and powder neutron diffraction studies have been performed on a three-dimensional (3D) oxalate-based metal-organic framework (NH 4 ) 5 [Mn 2 Cr 3 (ox

. The thermal variations of the magnetic susceptibilitiy measured via field-cooled and zero-field-cooled procedures are compatible with an antiferromagnetic spin organization in the presence of some single-ion anisotropy. This is supported by the metamagnetic behavior observed at 0.7 T in the magnetization curve at 2 K. Temperature-dependent neutron diffraction experiments have been performed between 2.5 and 300 K on the powdered sample. The structural part of the neutron diffraction pattern matches with the C2/c space group found by single-crystal X-ray diffraction. Below 6 K, the long-range magnetic ordering leads to the observation of a single magnetic peak at 0.386 Å -1 . The refinement of the neutron diffractogram allows to propose a magnetic structure where the magnetic moments of the manganese(II) and chromium(III) ions are noncollinear with a maximum angle of almost 70°. In agreement with an orbital analysis, the coupling between these magnetic moments bridged in a bis(bidentate) oxalate ligand is mainly ferromagnetic whereas it is mainly antiferromagnetic for metal ions bridged in a monodentate-bidentate mode.

■ INTRODUCTION

Along the years, oxalate-based networks have been demonstrated to be a versatile platform toward multifunctional molecular magnets. [START_REF] Cleḿent | Polyfunctional Two-(2D) and Three-(3D) Dimensional Oxalate Bridged Bimetallic-based Magnets[END_REF] This is related to the ability of the negatively charged bimetallic oxalate-based networks to welcome a wide variety of (functional) cations and to the possibility to synthesize oxalate-based compounds in optically active forms. [START_REF] Gruselle | Oxalate-based Optically Active Multifunctional Magnets[END_REF] Recently, in particular, to develop protonic conduction in these materials, [START_REF] Sadakiyo | Rational Designs for Highly Proton-Conductive Metal-Organic Frameworks[END_REF][START_REF] Pardo | High Proton Conduction in a Chiral Ferromagnetic Metal-Organic Quartz-like Framework[END_REF] cations enabling hydrogen bonds were introduced in oxalate-based magnets. [START_REF] Sadakiyo | Rational Designs for Highly Proton-Conductive Metal-Organic Frameworks[END_REF][START_REF] Pardo | High Proton Conduction in a Chiral Ferromagnetic Metal-Organic Quartz-like Framework[END_REF][START_REF] Pardo | Topological Versatility of Oxalate-Based Bimetallic One-Dimensional (1D) Compounds with Ammonium Cations[END_REF][START_REF] Maxim | Atypical Stoichiometry for a 3D Bimetallic Oxalate-Based Long-range Ordered Magnet Exhibiting High Proton Conductivity[END_REF][START_REF] Maxim | Dialkyl substituted monoamidinium-templated oxalate-based non centro-symmetric 2D compounds[END_REF] These weak intermolecular interactions, that compete with the coordination bonds of the bimetallic oxalate network, have deeply enlarged the structural landscape of these materials, which was dominated by the two-dimensional (2D) (6,3) and threedimensional (3D) (10,3) coordination networks discovered in the 90s. [START_REF] Gruselle | Oxalate-based Optically Active Multifunctional Magnets[END_REF][START_REF] Tamaki | Syntheses and magnetic properties of mixed-metal assemblies {NBu 4 [MCr(C 2 O 4 ) 3 ]} x (NBu 4 + = tetra(n-butyl)ammonium ion; ox 2-= oxalate ion; M = Mn 2+ , Fe 2+ , Co 2+ , Ni 2+ , Cu 2+ , Zn 2+ )[END_REF][START_REF] Decurtins | A Concept for the Synthesis of 3-Dimensional Homoand Bimetallic Oxalate-Bridged Networks [M 2 (ox) 3 ] n . Structural, Moessbauer, and Magnetic Studies in the Field of Molecular-Based Magnets[END_REF] Such H-bond active cations have sometimes limited the dimensionality of the formed coordination architectures [START_REF] Maxim | Binuclear heterometallic M(III)-Mn(II) (M = Fe, Cr) oxalate-bridged complexes associated with a bisamidinium dication: a structural and magnetic study[END_REF][START_REF] Maxim | The odd association of a C3h trisamidinium cation and tosylate anion with a series of linear oxalate-bridged trinuclear heterometallic complexes[END_REF] or induced atypical 2D and 3D structures. [START_REF] Pardo | High Proton Conduction in a Chiral Ferromagnetic Metal-Organic Quartz-like Framework[END_REF][START_REF] Maxim | Atypical Stoichiometry for a 3D Bimetallic Oxalate-Based Long-range Ordered Magnet Exhibiting High Proton Conductivity[END_REF][START_REF] Maxim | Dialkyl substituted monoamidinium-templated oxalate-based non centro-symmetric 2D compounds[END_REF][START_REF] Coronado | Heptacoordinated Mn II in oxalate-based bimetallic 2D magnets: synthesis and characterisation of [Mn(L) 6 ][Mn-(CH 3 OH)M III (ox) 3 ] 2 (M III = Cr, Rh; ox = oxalate dianion; L = H 2 O, CH 3 OH)[END_REF][START_REF] Pardo | Multiferroics by rational design: implementing ferroelectricity in molecule-based magnets[END_REF] In these latter compounds, the metallic ions are indeed coordinated from 2 to 5 bridging oxalate ligands. This is in line with the numerous coordination modes of the oxalate anion: nonbridging, monodentate-bidentate as well as bis(bidentate) bridging modes. [START_REF] Serezhkin | Crystal-Chemical Role of Oxalate Ions[END_REF] This structural versatility strongly influences the magnetic exchange interactions between the metallic ions toward original magnetic behaviors. [START_REF] Maxim | Atypical Stoichiometry for a 3D Bimetallic Oxalate-Based Long-range Ordered Magnet Exhibiting High Proton Conductivity[END_REF][START_REF] Coronado | Heptacoordinated Mn II in oxalate-based bimetallic 2D magnets: synthesis and characterisation of [Mn(L) 6 ][Mn-(CH 3 OH)M III (ox) 3 ] 2 (M III = Cr, Rh; ox = oxalate dianion; L = H 2 O, CH 3 OH)[END_REF] In this contribution, this specificity brought by the use of different template cations is further demonstrated by the thorough exploration of the magnetic behavior of (NH 4 ) 5 [Mn 2 Cr 3 (ox) 9 ]•10H 2 O: [START_REF] Maxim | Atypical Stoichiometry for a 3D Bimetallic Oxalate-Based Long-range Ordered Magnet Exhibiting High Proton Conductivity[END_REF] it is investigated by detailed macroscopic magnetization measurements and its magnetic structure is determined by neutron diffraction.

■ EXPERIMENTAL SECTION General Details. (NH 4 ) 5 [Mn 2 Cr 3 (ox) 9 ]•10H 2 O polycrystalline sample has been synthesized according to the reported procedure. [START_REF] Maxim | Atypical Stoichiometry for a 3D Bimetallic Oxalate-Based Long-range Ordered Magnet Exhibiting High Proton Conductivity[END_REF] The IR spectra were recorded on a Nicolet iS50 FT-IR spectrometer as KBr pellets in the 4000-250 cm -1 region. The powder X-ray diffraction patterns were collected at room temperature on a Philips PW-1050 goniometer using the Bragg-Brentano configuration and Mn-filtered Fe Kα radiation. The quality of the samples was checked by IR spectroscopy and powder X-ray diffraction, comparing the experimental data with the published ones. [START_REF] Maxim | Atypical Stoichiometry for a 3D Bimetallic Oxalate-Based Long-range Ordered Magnet Exhibiting High Proton Conductivity[END_REF] Magnetic Studies. Magnetization measurements versus temperature (2-300 K) were performed on powdered samples using a SQUID magnetometer (Quantum Design MPMS-XL), applying magnetic fields between 10 -3 and 10 -1 T. Both fieldcooled (FC) and zero-field-cooled (ZFC) procedures were used, with the measurements being performed while increasing the temperature after cooling with or without magnetic field, respectively. Isothermal magnetization versus field up to 7 T was recorded at 2 K. All data were corrected for the contribution of the sample holder and the diamagnetism of the samples estimated from Pascal's constants. [START_REF] Pascal | Magnetochemical studies[END_REF] Neutron Diffraction. The neutron diffraction experiments were performed at the Laboratoire León Brillouin (CEA Saclay) using the G4.1 powder neutron diffractometer equipped with a multidetector of 800 cells. The powder sample was set in a cylindrical vanadium container and cooled down in a cryostat. Diffraction patterns were recorded at λ = 2.426 Å in the 6-85.9°2θ range, at different temperatures between 2.5 and 300 K. The analysis of the diffraction patterns was performed at different temperatures using the FullProf software. 16 The lattice parameters were refined to match the exact experimental peak positions. Combined with a symmetry analysis performed using the Basireps software of the FullProf Suite, this enables to obtain a model for the magnetic structure of the compound below T N .

■ RESULTS AND DISCUSSIONS

The magnetic properties of (NH 4 ) 5 [Mn 2 Cr 3 (ox) 9 ]•10H 2 O have been studied starting from the preliminarily published investigations, where a magnetic ordering temperature T N was observed at 6.0 K. [START_REF] Maxim | Atypical Stoichiometry for a 3D Bimetallic Oxalate-Based Long-range Ordered Magnet Exhibiting High Proton Conductivity[END_REF] In our previous work, the magnetic susceptibility was found to be compatible with a global antiferromagnetic (AF) long-range magnetic order (LRMO) involving dominant ferromagnetic (F) interactions. This apparently puzzling situation was tentatively explained by a magnetostructural analysis: in the (ab) planes, all the oxalate ligands are in a bis(bidentate) bridging mode (Figure 1b) which is believed, by comparison with the situation encountered in classical (2D) (6,3) 8 and three-dimensional (3D) (10,3) 17 networks, to promote F exchange interactions between the spin bearers, leading to the formation of ferromagnetically ordered planes. In the (bc) planes (Figure 1c), along the b axis, bis(bidentate) bridging oxalate ligands are retrieved (black sticks in Figure 1c) whereas along the c axis, the oxalate ligands adopt a bidentate-monodentate mode (gray sticks in Figure 1c) which is believed, by comparison with a published case of a rather asymmetrical oxalate bridge, [START_REF] Coronado | Heptacoordinated Mn II in oxalate-based bimetallic 2D magnets: synthesis and characterisation of [Mn(L) 6 ][Mn-(CH 3 OH)M III (ox) 3 ] 2 (M III = Cr, Rh; ox = oxalate dianion; L = H 2 O, CH 3 OH)[END_REF] to convey AF exchange interaction. Accordingly, this interaction should induce an antiparallel orientation of the magnetization borne by adjacent (ab) planes leading to an overall AF LRMO.

To confirm this assumption with robust experimental proofs, detailed macroscopic magnetometric studies are combined with neutron diffraction experiments allowing a microscopic insight into the LRMO.

Magnetometric Studies. The magnetization of (NH 4 ) 5 [Mn 2 Cr 3 (ox) 9 ]•10H 2 O has been measured starting from 2 K up above the ordering temperature after cooling the sample with (FC) and without (ZFC) applying an external magnetic field. For both measuring modes, there is a clear-cut change in the thermal variations of the magnetization (Figure 2a): upon temperature increase, the FC (respectively ZFC) curve decreases (respectively increases) rapidly. At 6 K, they merge and above this temperature, they decrease simultaneously at a much slower rate. This abrupt change in the thermal variations of the magnetization is a clear confirmation of the onset of an LRMO at 6 K. The difference between the FC and ZFC measurements can be related to different processes: spin glass transition, selection of magnetic domains accompanying the onset of a ferromagnetic LRMO, contribution of the magnetic moments associated with magnetic domain walls or defects for an AF LRMO in the presence of some anisotropy. The latter can be either due to single-ion anisotropy or to anisotropic interaction. The FC curves were measured in fields varying between 0.001 and 0.08 T (Figure 2a). When increasing the field, the reduced magnetization M/ H below the ordering temperature is gradually overcome by the antiferromagnetic susceptibility, indicating that the compound is essentially an antiferromagnet.

The magnetization versus field in the ordered phase is shown in Figure 3. It saturates around 18 μ B after a metamagnetic process occurring around 0.7 T best seen in the derivative of the magnetization (Figure 3). This indicates a spin reorientation under magnetic field, overcoming an anisotropy barrier, toward a ferromagnetic state compatible with a full saturation of 2 Mn(II) (2 × 5 μ B with g = 2) and 3 Cr(III) (3 × 3 μ B with g = 2) per formula unit.

Altogether, the magnetization studies indicate the onset of an AF LRMO influenced by an extra phenomenon that can be single-ion zero-field splitting (ZFS) or anisotropy of the exchange interaction induced by antisymmetric exchange interaction. A distinction between these two possibilities can be provided by the microscopic vision brought about by neutron scattering experiments.

Neutron Diffraction Study. Powder neutron diffraction (PND) patterns of (NH 4 ) 5 [Mn 2 Cr 3 (ox) 9 ]•10H 2 O have been recorded between 2.5 and 300 K. The neutron diffraction patterns are composed of thin peaks, indicating a good crystallinity of the sample. Figure 4 shows the experimental pattern at 300 K together with a profile matching fit performed using the C2/c space group observed by single-crystal X-ray diffraction. [START_REF] Maxim | Atypical Stoichiometry for a 3D Bimetallic Oxalate-Based Long-range Ordered Magnet Exhibiting High Proton Conductivity[END_REF] ). [START_REF] Maxim | Atypical Stoichiometry for a 3D Bimetallic Oxalate-Based Long-range Ordered Magnet Exhibiting High Proton Conductivity[END_REF] The temperature evolution of the structural parameters was deduced from the profile matching performed using the diffractograms recorded while lowering the temperature (Figure 5). No structural phase transition is observed between room temperature and 2.5 K. Down to the magnetic ordering temperature, a compression of the a and c by less than 1% and, to a lesser extent, b (0.17%) lattice parameters is observed. The monoclinic angle β first decreases by 0.3°down to 200 K before increasing by 0.15°down to T N . It should be noted that, given the good crystallinity of the sample, the high incoherent background due to the large number of hydrogens decreased the signal-to-noise ratio but did not prevent a precise determination of the lattice parameters. The indeterminate positions of the hydrogen atoms in the compound prevented however a complete Rietveld refinement of the atomic positions in the neutron diffractograms.

When lowering the temperature through the ordering temperature, no extra peaks appear on the neutron diffraction pattern. However, the evolution of the intensity is particularly visible for the peak at 2θ = 8.6°(Miller's indices (001)), as observed in the inset of Figure 4. The thermal studies show that the intensity of this peak increases below 6 K attesting a magnetic transition, in accordance with the temperature found by magnetometry (Figure 2). The increase of the peak intensity is related to the superposition of the magnetic contribution, induced by the long-range ordering of the magnetic moments of Mn(II) and Cr(III) ions, on top of the structural contribution. To isolate the magnetic contribution from the neutron diffraction pattern, the difference between the experimental patterns at 2.5 K, below T N , and 7 K, above T N , was calculated (Figure 6). Strikingly, only one peak is clearly visible in the magnetic diffractogram. It can be indexed in the same space group as the nuclear contribution in agreement with a propagation vector K = 0. Based on a careful use of group theory, this unique peak allows to get useful information about the magnetic structure. There are four irreducible representations, Γ 1 to Γ 4 , in the group of the wave vector (equal to the C2/c space group). For a second-order transition, a magnetic structure corresponding to one of these representations should be stabilized, the same for all coupled Mn(II) and Cr(III) magnetic moments. For each representation, the Fourier components corresponding to the 8f Wyckoff position associated with one Cr(III) site and to the 4e Wyckoff position associated with one Cr(III) site and two Mn(II) sites are reported in Table 1.

A Rietveld refinement of the magnetic diffractogram based on each of the four magnetic models was attempted by varying the components of the magnetic moments in agreement with the symmetry constraints. Nonetheless, due to the lack of structural refinement necessary to determine a global scaling factor, the determination of the absolute values of the magnetic moments was not possible. We therefore fixed the amplitude of the magnetic moments of the Mn(II) to 5 μ B since the orbital angular momentum is expected to be close to zero. The magnetic moments of Cr(III) were also constrained to be equal for both sites. Representation Γ 4 was the only one yielding one dominant peak with a refined magnetic moments of 2.9 ± 0.5 μ B for Cr(III), compatible with the measured saturated magnetization at 2.5 K (Figure 6 and Table 2 for the magnetic moment components). For this calculation, we also constrained the Cr magnetic moments on the 8f site to lie in the ac plane since it did not improve the fit to allow them to acquire a component along the b axis. Note that imposing a zero c component of the magnetic moments yields an unrealistically small value of the Cr magnetic moment (1.7 μ B ). The calculation of the whole magnetic diffractogram shows that other magnetic peaks are expected with much lower intensities that are, in the present case, below the noise level. Attempts to measure PND on deuterated samples did not improve this situation. Although certainly not univocal due to the large noise in the data preventing to measure the small peaks beyond the (001) one in the magnetic diffractogram (Figure 6), the main features of the magnetic structure seem quite robust, in particular, concerning the sign of the magnetic couplings.

The refinement of the magnetic neutron data corresponds to a complex organization of the magnetic moments of the Mn(II) and Cr(III) ions (Figure 7). The Cr and Mn magnetic moments have a main component along the a axis and a smaller one along the c axis, as shown in (a), leading to an antiferromagnetic structure with noncollinear magnetic moments. In this model, there are three different angles between the ferromagnetically coupled Cr and Mn magnetic moments of 11, 44, and 69°, respectively. The magnetic structure is then made of ferromagnetic sheets in the (ab) planes (Figure 7b), antiferromagnetically coupled along the c axis (Figure 7c).

■ DISCUSSION

While comparing Figures 1 and7, an univocal relation between the bridging modes (bis(bidentate) vs monodentate-bidentate) and the nature of the isotropic exchange interaction (ferromagnetic vs antiferromagnetic) is clearly evidenced for (NH 4 ) 5 [Mn 2 Cr 3 (ox) 9 ]•10H 2 O. The magnetic structure refinement nicely confirms the robustness of the magnetostructural analysis. [START_REF] Maxim | Atypical Stoichiometry for a 3D Bimetallic Oxalate-Based Long-range Ordered Magnet Exhibiting High Proton Conductivity[END_REF] Note also that the magnetic structure corresponding to the Γ 4 irreducible representation does not allow any ferromagnetism, where all components of the magnetic moments for a given metal ion are compensated. On the other hand, it is compatible with a noncollinear arrangement of the magnetic moments on the different sites, especially those borne by the two metallic ions, both for the F and AF isotropic exchange interaction observed in the (ab) planes and along the c axis respectively. Given the rather low ZFS expected for chromium(III) and manganese(II) ions, this canting might rather originate from anisotropic interactions such as antisymmetric exchange interaction, which can occur locally through the moderate (bis(bidentate) mode) to strong (monodentate-bidentate mode) asymmetry of the oxalates bridges, despite the overall centrosymmetric character of the compound space group.

The present study shows the complementarity of neutron diffraction with more widespread magnetometry studies. It brings a fine comprehension of the intrinsically complex magnetic structures of molecule-based magnets related to their low global and local symmetries. [START_REF] Ressouche | Investigating molecular magnetism with polarized neutrons[END_REF][START_REF] Gillon | Spin Densities in a Ferromagnetic Bimetallic Chain Compound: Polarized Neutron Diffraction and DFT Calculations[END_REF][START_REF] Gillon | Neutron Diffraction and Theoretical DFT Studies of Two Dimensional Molecular-Based Magnet K 2[END_REF][START_REF] Nuttall | The Magnetic Structures of the Layer Ferri-magnets P(C 6 D 5 ) 4 M II Fe(C 2 O 4 ) 3 (M II = Mn, Fe)[END_REF][START_REF] Pointillart | Are optically active three-dimensional oxalate-based ferromagnets good candidates for the observation of X-rays Magnetochiral dichroism? A neutron diffraction study[END_REF] Nonetheless, it has not been extensively used for the study of these compounds for essentially two reasons: (i) the need of nearly centimeter-scale single crystals or (ii) for studies on powder, the belief that fully deuterated samples together with the corresponding synthetic difficulties are unavoidable to obtain valuable results. As exemplified here, the improvement of the neutron sources and detectors has partly lifted these drawbacks.

■ CONCLUDING REMARKS

The long-range magnetic ordering of an atypical centrosymmetric 2D oxalate-based magnet (NH 4 ) 5 [Mn 2 Cr 3 (ox) 9 ]• 10H 2 O has been thoroughly studied by combining macroscopic magnetization measurements and microscopic neutron diffraction studies. This complementary approach has proven its efficiency. It indeed led to a successful determination, constrained by symmetry considerations, of the magnetic order of this coordination compound and a direct probe of the nature of its magnetic interactions. This analysis allows to take a further step forward and to predict other symmetry-allowed properties. For instance, the magnetic point group is 2′/m (magnetic space group P2′/c) resulting from the loss of the -2.6 ± 0.5 (0.0000) 0 (0.2911) 1.0 ± 0.9 (0.2500) Mn(4e) -4.9 ± 0.2 (0.0000) 0 (0.4495) 0.7 ± 1.0 (0.2500) Mn(4e) -4.1 ± 0.6 (0.0000) 0 (0.6946) 2.7 ± 0.9 (0.2500) inversion center combined with time reversal in the magnetic arrangement. This authorizes a linear magnetoelectric tensor, which has a nondiagonal form with nonequal off-diagonal terms as in MnPS 3 . [START_REF] Ressouche | Magnetoelectric MnPS3 as a candidate for ferrotoroidicity[END_REF] It means that an electric polarization is allowed by symmetry to be induced perpendicular to the magnetic field generating it and vice versa for a ferromagnetic contribution induced by an electric field. This special form of the magnetoelectric tensor is associated with ferrotoroidicity 24 establishing (NH 4 ) 5 [Mn 2 Cr 3 (ox) 9 ]•10H 2 O (ox 2-= C 2 O 4 2-) as a potential multifuntionnal molecular magnet.

■ AUTHOR INFORMATION

Corresponding Author *E-mail: cyrille.train@lncmi.cnrs.fr.

Figure 1 .

 1 Figure 1. Projection of the bimetallic network in the (a) ac plane, (b) ab plane, and (c) bc plane. The manganese and chromium ions are represented in magenta and green, respectively. The black and gray lines represent the oxalate bridges in a bis(bidentate) and monodentatebidentate bridging modes, respectively (adapted from ref 6 ).

Figure 2 .

 2 Figure 2. For (NH 4 ) 5 [Mn 2 Cr 3 (ox) 9 ]•10H 2 O: (a) Magnetization versus temperature measured through a field-cooled (FC) procedure (filled symbols) and zero-field-cooled procedure (ZFC) (empty symbols) in a magnetic field of 10 -3 T. (b) Field-cooled measurements in various magnetic fields. The magnetic ordering temperature occurs just below 6 K when the curves depart from each other.

  All the peaks, except the one around 2θ = 20.5°, are perfectly indexed, and the refined lattice parameters for the unit cell are: a = 8.845(1) Å, b = 35.454(4) Å, c = 16.265(2) Å, α = 90°, β = 93.395(7)°, γ = 90°, and V = 5084(1) Å 3 . Note that the additional peak is not indexed even in lower symmetry subgroups, indicating that it must be extrinsic. The structural parameters found by PND are in good agreement with those determined from single-crystal X-ray diffraction at 173 K (a = 8.8345(1) Å, b = 35.591(4) Å, c = 16.246(2) Å, α = 90°, β = 93.437(6)°, γ = 90°, and V = 5098.8(1) Å 3

Figure 3 .

 3 Figure 3. Magnetization of (NH 4 ) 5 [Mn 2 Cr 3 (ox) 9 ]•10H 2 O versus field at 2.5 K (blue dots). The derivative is also shown (dotted line and right axis) evidencing a metamagnetic process from the maximum at 0.7 T.

Figure 4 .

 4 Figure 4. (a) Experimental neutron diffraction pattern (red circles) of a polycrystalline powder of (NH 4 ) 5 [Mn 2 Cr 3 (ox) 9 ]•10H 2 O at T = 300 K, superimposed with the profile matching plot (black line), the difference (blue line), and the Bragg positions (green ticks). The agreement Bragg Rfactor and χ 2 are equal to 0.255 and 2.08, respectively. (b) Thermal variation of the measured integrated intensity of the (001) diffraction peak observed for 2θ = 8.6°for (NH 4 ) 5 [Mn 2 Cr 3 (ox) 9 ]•10H 2 O.

Figure 5 .

 5 Figure 5. Thermal evolution of the structural parameters (unit cell lattice lengths and monoclinic angle) of (NH 4 ) 5 [Mn 2 Cr 3 (ox) 9 ]•10H 2 O extracted from profile matching of the neutron diffractograms. The vertical dotted lines show T N . When not visible, the standard error bars are smaller than the size of the symbols.

Figure 6 .

 6 Figure 6. Difference (red circles) between the diffraction patterns for (NH 4 ) 5 [Mn 2 Cr 3 (ox) 9 ]•10H 2 O measured at 2.5 and 7 K, superimposed with the calculated magnetic model corresponding to the irreducible representation Γ 4 (black continuous line) as described in the text. The blue line is the difference between the measured and calculated magnetic diffractograms. The magnetic R-factor and χ 2 are equal to 46.6 and 19.3, respectively. These high values reflect the low statistics.

Figure 7 .

 7 Figure 7. Magnetic structure of (NH 4 ) 5 [Mn 2 Cr 3 (ox) 9 ]•10H 2 O deduced from PND. (a) Projection in the (ac) plane. (b) Top: projection in the (ab) plane with a ferromagnetic slice for c within [0, 0.5]. (c) Slice in the (bc) plane showing the ferromagnetic (green) and antiferromagnetic (red) exchange interactions. The colored boxes represent the antiferromagnetic stacking of ferromagnetic sheets.

Table 2 .

 2 Refined Components of the Magnetic Moments for the Four Different Sites in the Γ 4 Irreducible Representation

	site	m x (x)	m y (y)	m z (z)
	Cr(8f)	-2.4 ± 0.5 (0.3164)	0 (0.0728)	-1.7 ± 0.6 (0.4353)
	Cr(4e)

calculated magnetic diffractograms. The magnetic R-factor and χ 2 are equal to 46.6 and 19.3, respectively. These high values reflect the low statistics.Table 1. Fourier Components of the Four Irreducible Representations for both Wyckoff Sites 8f (1 Cr Site) and 4e (1 Cr Site and 2 Mn Sites) Corresponding to the Magnetic Structure of (NH 4 ) 5 [Mn 2 Cr 3 (ox) 9 ]•10H 2 O

Author Contributions

The manuscript was written through contributions of all authors. All authors have given to the final version of the manuscript.

Notes

The authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

The authors are grateful to E. Suard and C. Ritter for their help in the attempts to measure the samples by neutron diffraction at Institut Laue-Langevin. The French National Research Agency (ANR) is acknowledged for financial support through Monafer (ANR-18-CE09-0032) projects.