Pierre Gras

Annabelle Baker

Christèle Combes

Christian Rey

Stéphanie Sarda

Adrian J Wright

Mark E Smith

John V Hanna

Christel Gervais

Danielle Laurencin

Christian Bonhomme
email: christian.bonhomme@upmc.fr

From crystalline to amorphous calcium pyrophosphates: a solid state Nuclear Magnetic Resonance perspective

Keywords: Crystalline calcium pyrophosphates, amorphous calcium pyrophosphates, 1 H, 31 P, 43 Ca solid state NMR, first principles GIPAW calculations

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Introduction

Crystalline calcium pyrophosphate dihydrates (CPPD, Ca 2 P 2 O 7 •2H 2 O) are among the most common forms of pathologic articular minerals: their prevalence increases with age, impacting on 17.5% of the population after the age of 80. [START_REF] Richette | An update of the epidemiology of calcium pyrophosphate dihydrate crystal deposition disease[END_REF] Although often asymptomatic, they are frequently involved or associated with acute articular arthritis such as pseudogout, and, more rarely, with chronic polyarthritis and destructive arthropathy; current treatments are mainly directed at relieving the symptoms of joint inflammation but not at inhibiting calcium pyrophosphate (CPP) formation nor at dissolving these crystals. [START_REF] Macmullan | Treatment and management of pseudogout: insights for the clinician[END_REF][START_REF] Ea | Diagnosis and clinical manifestations of calcium pyrophosphate and basic calcium phosphate crystal deposition diseases[END_REF][START_REF] Liu | Contribution of calcium-containing crystals to cartilage degradation and synovial inflammation in osteoarthritis[END_REF] CPP have been identified in vivo as two polymorphs of CPPD: 5 a triclinic form with a known structure, [START_REF] Brown | Fertilizer materials, preparation and characterization of some calcium pyrophosphates[END_REF] and a monoclinic form with a recently solved structure [START_REF] Gras | Etude Physico-chimique et structurale de pyrophosphates de calcium hydratés : application aux microcalcifications associées à l'arthrose[END_REF] (respectively denoted as t-CPPD and m-CPPD). Other crystalline forms of hydrated calcium pyrophosphates have been synthesized in vitro and characterized, including a dimorphic monoclinic tetrahydrate (CPPT: Ca 2 P 2 O 7 •4H 2 O), referred to as m-CPPT α and m-CPPT β. [START_REF] Balic-Zunic | Structure of the β form of calcium pyrophosphate tetrahydrate[END_REF][START_REF] Davis | Structure of monoclinic calcium pyrophosphate tetrahydrate[END_REF] Recently, Gras et al. [START_REF] Gras | Etude Physico-chimique et structurale de pyrophosphates de calcium hydratés : application aux microcalcifications associées à l'arthrose[END_REF] performed a systematic investigation of the synthesis of pure hydrated calcium pyrophosphates. They described the pH and temperature conditions leading to the formation of m-CPPT β, t-CPPD and m-CPPD, [START_REF] Gras | Synthesis and characterisation of hydrated calcium pyrophosphate phases of biological interest[END_REF] as well as the identification of a new monohydrated calcium pyrophosphate phase exhibiting monoclinic symmetry, referred to as m-CPPM (CPPM: Ca 2 P 2 O 7 •H 2 O), [START_REF] Gras | Crystallisation of a highly metastable hydrated calcium pyrophosphate phase[END_REF] and an unreferenced highly metastable trihydrated monoclinic calcium pyrophosphate phase derived from the structure of m-CPPT β. [START_REF] Gras | Structure of the calcium pyrophosphate monohydrate phase (Ca 2 P 2 O 7 •H 2 O): towards understanding the dehydration process in calcium pyrophosphate hydrates[END_REF] The preparation of amorphous phases of biological interest, noted a-CPP (Ca 2 P 2 O 7 •nH 2 O), has also been reported by Slater et al. [START_REF] Slater | Enhanced stability and local structure in biologically relevant amorphous materials containing pyrophosphate[END_REF] and Gras et al., [START_REF] Gras | Synthesis and characterisation of hydrated calcium pyrophosphate phases of biological interest[END_REF] and it was found that these phases are particularly stable compared to amorphous calcium orthophosphate and amorphous calcium carbonate.

Several characterizations have been performed on all the hydrated calcium pyrophosphate phases mentioned above by several approaches, including powder XRD (X Ray diffraction) and vibrational spectroscopies, providing information on the configuration of the pyrophosphate groups. [START_REF] Gras | Synthesis and characterisation of hydrated calcium pyrophosphate phases of biological interest[END_REF] It was observed that pyrophosphate ions in CPP phases have a wide range of P-O-P angles (between 123.1 and 134.1°). [START_REF] Balic-Zunic | Structure of the β form of calcium pyrophosphate tetrahydrate[END_REF][START_REF] Davis | Structure of monoclinic calcium pyrophosphate tetrahydrate[END_REF] This angle is important in understanding the relationship between the various CPP forms and their stability and transformation ability. Developing complementary tools for the characterization of hydrated calcium pyrophosphates is of particular interest, especially to understand the structure of phases like m-CPPD, for which the positioning of protons may be very difficult based exclusively on X-ray powder diffraction data, particularly considering that single crystals suitable for diffraction structure resolution are not yet available. Indeed, this phase has the highest inflammatory potential of all CPP phases, and it would be of interest to determine its structure in detail in order to understand the inflammation mechanism, which is possibly based on rupture of lysosome phospholipid membranes induced by pyrophosphate groups on the surface of the crystals. [START_REF] Mandel | The structural basis of crystal-induced membranolysis[END_REF][START_REF] Roch-Arveiller | Inflammatory reactions induced by various calcium pyrophosphate crystals[END_REF][START_REF] Swan | Evidence for a causal relationship between the structure, size, and load of calcium pyrophosphate dehydrate crystals, and attacks of pseudogout[END_REF][START_REF] Wierzbicki | Molecular dynamics simulation of crystal-induced membranolysis[END_REF] Solid state NMR is a technique which is attracting increasing attention for the study of synthetic and natural biomaterials [START_REF] Bonhomme | Recent NMR developments applied to organic-inorganic materials[END_REF] including calcium phosphate phases. [START_REF] Fayon | Evidence of nanometric-sized phosphate clusters in bioactive glasses as revealed by sold state 31 P NMR[END_REF][START_REF] Pourpoint | Calcium phosphates and hydroxyapatite: solid-state NMR experiments and first-principles calculations[END_REF][START_REF] Pourpoint | High-resolution solid state NMR experiments for the characterization of calcium phosphate biomaterials and biominerals[END_REF][START_REF] Laurencin | Magnesium incorporation into hydroxyapatite[END_REF][START_REF] Schnitzler | Investigation of alendronate-doped apatitic cements as a potential technology for the prevention of osteoporotic hip fractures: critical influence of the drug introduction mode on the in vitro cement properties[END_REF][START_REF] Despas | High-frequency impedance measurement as a relevant tool for monitoring the apatitic cement setting reaction[END_REF][START_REF] Mellier | Characterization and properties of novel gallium-doped calcium phosphate ceramics[END_REF][START_REF] Roiland | Characterization of the disordered phosphate network in CaO-P 2 O 5 glasses by 31 P solid state NMR and Raman spectroscopies[END_REF][START_REF] Roiland | Etude de l'ordre local dans les phosphates désordonnés modèles par spectroscopies RMN et Raman[END_REF] Indeed, solid state NMR can provide detailed atomic-scale information on the local structure around nuclei like 31 P, even in disordered and amorphous phases, and is therefore highly complementary to other analytical tools like XRD and IR (Infra Red) or Raman spectroscopies. NMR studies of calcium pyrophosphate phases have been very limited to date.

To the best of our knowledge, 31 P NMR has only been applied to the characterization of the crystalline α-and β-Ca 2 P 2 O 7 anhydrous phases, and of a hydrated amorphous calcium pyrophosphate of composition ~ Ca 2 P 2 O 7 •4H 2 O [START_REF] Slater | Enhanced stability and local structure in biologically relevant amorphous materials containing pyrophosphate[END_REF][START_REF] Legrand | 31 P solid state NMR study of the chemical setting process of a dual-paste injectable brushite cement[END_REF] In the latter case, the hydrolysis of the P-O-P bridge upon heat treatment was demonstrated using 1 H MAS, [START_REF] Bryce | Calcium binding environments probed by 43 Ca NMR spectroscopy[END_REF] P MAS and 1 H-31 P cross-polarisation (CP) MAS NMR experiments. With regards to [START_REF] Iuga | Population and coherence transfer induced by double frequency sweeps in half-integer quadrupolar spin systems[END_REF] Ca NMR, only the anhydrous α-Ca 2 P 2 O 7 phase has been analyzed to date, [START_REF] Gervais | New perspectives on calcium environments in inorganic materials containing calcium-oxygen bonds: a combined computational-experimental 43 Ca NMR approach[END_REF] showing that the two crystallographically-inequivalent Ca sites can be unambiguously resolved at 14.1 T. Although [START_REF] Iuga | Population and coherence transfer induced by double frequency sweeps in half-integer quadrupolar spin systems[END_REF] Ca is a more challenging nucleus than 31 P, [START_REF] Laurencin | Development of 43 Ca solid state NMR spectroscopy as a probe of local structure in inorganic and molecular materials[END_REF][START_REF] Bryce | Calcium binding environments probed by 43 Ca NMR spectroscopy[END_REF] given its quadrupolar nature, [START_REF] Van Eck | Recent advances in experimental solid state NMR methodology for half-integer spin quadrupolar nuclei[END_REF] low natural abundance (0.014 %) and small magnetic moment (leading it to be a member of the group of so-called low-γ nuclei), [START_REF] Mackenzie | Multinuclear Solid State NMR of Inorganic Materials[END_REF] recent studies have shown that it can be very sensitive to subtle changes in Ca local environments. [START_REF] Reinholdt | Synthesis and characterization of crystalline structures based on phenylboronate ligands bound to alkaline earth cations[END_REF][START_REF] Colas | H 2 O: structural study by a combined NMR, crystallography and modeling approach[END_REF][START_REF] Sene | Structural study of calcium phosphonates: a combined synchrotron synchrotron powder diffraction, solid-state NMR and first-principles calculations approach[END_REF] Finally, even more challenging isotopes like oxygen-17 which usually require isotopic enrichment have been completely neglected so far.

The purpose of this study is to demonstrate, using a combined experimental-computational approach, how solid state NMR can be used for the structural investigation of calcium pyrophosphate phases, whether hydrated or anhydrous, and whether crystalline or amorphous. For this purpose, the 31 P, [START_REF] Iuga | Population and coherence transfer induced by double frequency sweeps in half-integer quadrupolar spin systems[END_REF] Ca and 1 H MAS NMR spectra of a series of crystalline CPP phases (m-CPPD, t-CPPD, m-CPPT β and m-CPPM) are first reported, followed by those of amorphous calcium pyrophosphates. Then, we report the results of firstprinciples calculations of the NMR parameters of the crystalline calcium pyrophosphate phases, which were carried out using the Gauge-Including Projector Augmented Wave (GIPAW) approach. [START_REF] Charpentier | The PAW/GIPAW approach for computing NMR parameters: a new dimension added to NMR study of solids[END_REF][START_REF] Bonhomme | First-principles calculation of NMR parameters using the gauge including projector augmented wave method: a chemist's point of view[END_REF] The comparison between experimental and calculated NMR parameters not only validates the structural models of each compound allowing the assignment of P and Ca sites in crystalline phases, but also helps determine what atomic-scale information can be determined by solid state NMR. Interpretations of the NMR spectra of amorphous calcium pyrophosphate are given, a phase that has recently been proposed as an interesting component of bone cements. 39

Materials and methods

Syntheses

Crystalline hydrated calcium pyrophosphates m-CPPD, t-CPPD and m-CPPT β were synthesized following the methods previously published by Gras et al., [START_REF] Gras | Synthesis and characterisation of hydrated calcium pyrophosphate phases of biological interest[END_REF] by double decomposition between a potassium pyrophosphate solution and a calcium nitrate solution mixed into a buffer solution at a controlled temperature. The crystalline m-CPPM phase was prepared starting from m-CPPT β crystals and heating them at 110°C for 30 min as previously reported by Gras et al. [START_REF] Gras | Structure of the calcium pyrophosphate monohydrate phase (Ca 2 P 2 O 7 •H 2 O): towards understanding the dehydration process in calcium pyrophosphate hydrates[END_REF] The amorphous calcium pyrophosphate phases, of general formula Ca 2 P 2 O 7 .xH 2 O (with x ~ 4), [START_REF] Gras | Synthesis and characterisation of hydrated calcium pyrophosphate phases of biological interest[END_REF][START_REF] Slater | Enhanced stability and local structure in biologically relevant amorphous materials containing pyrophosphate[END_REF] were prepared using two different synthetic procedures. According to Gras,[START_REF] Gras | Synthesis and characterisation of hydrated calcium pyrophosphate phases of biological interest[END_REF] precipitation at a controlled temperature (25°C) and pH (5.8) was used (compound referred to as "sample A" thereafter). According to Slater et al. [START_REF] Slater | Enhanced stability and local structure in biologically relevant amorphous materials containing pyrophosphate[END_REF] a precipitation at room temperature without any specific control/monitoring of the pH was also performed (compound referred to as "sample B" thereafter). In the latter case, the amorphous phase was also heat treated to 140 and 220 °C, in view of further solid state NMR characterizations of the transformations under temperature.

Characterization

General characterization

XRD measurements were performed using a Seifert XRD-3000TT diffractometer with a Cu Kα radiation (Cu Kα 1 λ = 1.54060 Å and Cu Kα 2 λ = 1.54443 Å), and equipped with a graphite monochromator. The XRD patterns were obtained between 2 and 70° (2θ) with a step size of 0.02° and a scan step time of 16 s at 298 K. The corresponding XRD powder patterns can be found in supporting information (Figure S1). The other characterization performed on the crystalline and amorphous synthesized phases, using notably vibrational spectroscopies, can be found in previous publications. [START_REF] Gras | Synthesis and characterisation of hydrated calcium pyrophosphate phases of biological interest[END_REF][START_REF] Slater | Enhanced stability and local structure in biologically relevant amorphous materials containing pyrophosphate[END_REF] 2.2.2 31 P solid state NMR All 31 P MAS NMR data were recorded at 14.1 T using a VNMRS-600 (600 MHz 1 H frequency) spectrometer operating at a 31 P Larmor frequency of 242.81 MHz, using a Varian 3.2 mm HXY T3 MAS probe. MAS frequencies ranging from ~ 2.8 to 10 kHz were used in order to extract the chemical shift anisotropy (CSA) parameters. Experiments were performed using a set of saturation 31 P pulses, followed by a delay of 128 s, and a 90° excitation pulse of 2.5 µs. Spinal-64 [START_REF] Richette | An update of the epidemiology of calcium pyrophosphate dihydrate crystal deposition disease[END_REF] H decoupling (100 kHz RF) was applied during acquisition. [START_REF] Fung | An improved broadband decoupling sequence for liquid crystals and solids[END_REF] A total of 4 transients were acquired for each spectrum. The 31 P chemical shifts were referenced to Si 5 O(PO 4 ) 6 as a secondary reference (at -44.0 ppm with respect to an 85% H 3 PO 4 solution). [START_REF] Lejeune | Studies of silicophosphate derivatives by 31 P → 29 Si CP MAS NMR[END_REF] Temperature regulation was used during the experiments, to ensure that the temperature inside the rotor was ~ 10 °C. Prior to all experiments, the magic angle was carefully set in order to obtain the best [START_REF] Bryce | Calcium binding environments probed by 43 Ca NMR spectroscopy[END_REF] P MAS resolution, avoiding the reintroduction of any CSA or dipolar interaction which would broaden the spectra.

43 Ca solid state NMR

Natural abundance [START_REF] Iuga | Population and coherence transfer induced by double frequency sweeps in half-integer quadrupolar spin systems[END_REF] Ca MAS NMR data were acquired at 14.1 and 20.0 T using Varian VNMR-600 (600 MHz 1 H frequency) and Bruker Avance III-850 (850 MHz 1 H frequency) spectrometers operating at [START_REF] Iuga | Population and coherence transfer induced by double frequency sweeps in half-integer quadrupolar spin systems[END_REF] Ca Larmor frequencies of 40.37 and 57.22 MHz, respectively. All [START_REF] Iuga | Population and coherence transfer induced by double frequency sweeps in half-integer quadrupolar spin systems[END_REF] Ca chemical shifts were referenced at 0 ppm to a 1 mol.L -1 aqueous solution of CaCl 2 . [START_REF] Gervais | New perspectives on calcium environments in inorganic materials containing calcium-oxygen bonds: a combined computational-experimental 43 Ca NMR approach[END_REF][START_REF] Laurencin | Development of 43 Ca solid state NMR spectroscopy as a probe of local structure in inorganic and molecular materials[END_REF] The 14.1 T experiments were performed using a Varian 7.5 mm HXY MAS probe enabling MAS frequencies of 5 to 6 kHz, and the temperature was regulated at ~ 12°C throughout each measurement. The Double Frequency Sweep (DFS) [START_REF] Kentgens | Advantages of double frequency sweeps in static, MAS and MQMAS NMR of spins I = 3/2 nuclei[END_REF][START_REF] Iuga | Population and coherence transfer induced by double frequency sweeps in half-integer quadrupolar spin systems[END_REF] signal-enhancement scheme was applied for sensitivity enhancement prior to a selective 3.2 µs 90° solid pulse for the central transition. DFS parameters were optimized using [START_REF] Iuga | Population and coherence transfer induced by double frequency sweeps in half-integer quadrupolar spin systems[END_REF] Ca-enriched CaHPO 4 , with a convergence sweep from 300 to 70 kHz (duration ~ 5.5 ms; RF ~ 8 kHz), leading to an enhancement factor of ~ 2. Only m-CPPT β was recorded using a 9.5 mm Varian HX (for reasons unrelated to the nature of the sample); the spinning rate was set to 4 kHz, and the acquisition parameters for the DFS and excitation pulses were optimized in a similar fashion as described above.

At 850 MHz, a low-γ 7 mm Bruker MAS probe was used, spinning at 5 kHz. A RAPT (rotor-assisted population transfer) [START_REF] Yao | Sensitivity enhancement of the central transition NMR signal of quadrupolar nuclei under magic-angle spinning[END_REF] enhancement scheme was applied prior to a 1.7 µs 90° solid pulse selective for the central transition. The RAPT pulses were first optimized on [START_REF] Iuga | Population and coherence transfer induced by double frequency sweeps in half-integer quadrupolar spin systems[END_REF] Ca-enriched CaHPO 4 , with an offset of 150 kHz (RF ~ 9 kHz), leading to an enhancement factor of ~ 2.

Details of the recycle delays, number of transients acquired, and total experimental times needed for each sample at both fields can be found in Table S1 (in supplementary information).

1 H solid state NMR

Calculations of NMR parameters

The first principles calculations based on the GIPAW 48 method were performed within Kohn-Sham DFT (Density Functional Theory) using the QUANTUM-ESPRESSO code. [START_REF] Giannozzi | QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials[END_REF] The crystalline structure is described as an infinite periodic system using periodic boundary conditions. The NMR calculations were performed as follows: for hydrated phases, proton positions geometry optimization was carried out, starting from the published experimental structures of t-CPPD 50 , m-CPPT β 51 and m-CPPD,7 allowing the positions of protons to relax using the VASP (Vienna Ab Initio Simulation Package) code. [START_REF] Kresse | Ab-initio molecular-dynamics for liquid-metals[END_REF] In the case of m-CPPM, [START_REF] Gras | Structure of the calcium pyrophosphate monohydrate phase (Ca 2 P 2 O 7 •H 2 O): towards understanding the dehydration process in calcium pyrophosphate hydrates[END_REF] all atomic positions were relaxed to obtain a better agreement with the experimental data (see later in the text). The 1 H-relaxed structures are named "Rel H" hereafter, and the fully relaxed structure of m-CPPM is referred to as "Rel tot". The α-Ca 2 P 2 O 7 53 structure was calculated without further relaxation. For NMR calculations, the PBE generalized gradient approximation [START_REF] Perdew | Generalized Gradient Approximation Made Simple[END_REF] was used and the valence electrons were described by norm conserving pseudopotentials [START_REF] Troullier | Efficient pseudopotentials for plane-wave calculations[END_REF] in the Kleinman-Bylander form. [START_REF] Kleinman | Efficacious form for model pseudopotentials[END_REF] The wave functions were expanded on a plane wave basis set with a kinetic energy cut-off of 80 Ry. The integral over the first Brillouin zone was performed using a Monkhorst-

Pack
η Q = (V yy -V xx )/V zz .
Absolute shielding tensors were obtained. To fix the [START_REF] Iuga | Population and coherence transfer induced by double frequency sweeps in half-integer quadrupolar spin systems[END_REF] Ca scale, the calculated δ iso (isotropic chemical shift) for a series of reference compounds were compared to experimental values 29 so that the average sum of experimental and calculated shifts coincide. Moreover, it should be noted that for the C Q ( 43 Ca) calculation, an updated quadrupole moment of -44.4 mb was used, as recently recommended by Bryce et al. [START_REF] Burgess | Alkaline-Earth Metal Carboxylates Characterized by 43 Ca and 87 Sr Solid-State NMR: Impact of Metal-Amine Bonding[END_REF] In the case of [START_REF] Bryce | Calcium binding environments probed by 43 Ca NMR spectroscopy[END_REF] P and 1 H, external referencing with respect to crystalline berlinite 58 (δ iso = -24.5 ppm) [START_REF] Xue | Determination of J coupling constants between spin-1/2 and quadrupolar nuclei in inorganic solids from spin echo and refocused INEPT experiments: a case study on AlPO 4 berlinite[END_REF] for [START_REF] Bryce | Calcium binding environments probed by 43 Ca NMR spectroscopy[END_REF]

Results and discussion

31 P MAS NMR

31

P MAS NMR spectroscopy is the most used NMR approach for the study of calcium phosphate and pyrophosphate phases, because phosphorus-31 is a highly sensitive NMR isotope (100% natural abundance, I = ½, high receptivity). In the particular case of hydrated calcium pyrophosphate phases, four NMR interactions have to be considered, namely the CSA, the heteronuclear 31 P-1 H and homonuclear 31 P-31 P dipolar interactions, and the 2 J P-P coupling. Under fast MAS and 1 H decoupling, the corresponding anisotropies are averaged efficiently leading to the determination of δ iso ( 31 P). Usually, the 2 J P-P couplings are not detected directly, although they can be revealed and measured using 2D (two dimensional) MAS experiments. [START_REF] Roiland | Characterization of the disordered phosphate network in CaO-P 2 O 5 glasses by 31 P solid state NMR and Raman spectroscopies[END_REF][START_REF] Florian | 2 J Si-O-Si scalar spin-spin coupling in the solid state: crystalline and glassy wollastonite CaSiO 3[END_REF] The number of isotropic lines is thus directly related to the number of inequivalent P sites in the asymmetric unit of a given structure. (average value ~ -7.7 ppm), in agreement with data already published in the literature. [START_REF] Slater | Enhanced stability and local structure in biologically relevant amorphous materials containing pyrophosphate[END_REF][START_REF] Legrand | 31 P solid state NMR study of the chemical setting process of a dual-paste injectable brushite cement[END_REF] Concerning δ CSA , the observed range is ~ 59 to 86 ppm, and the average value for all sites is ~ 77 ppm. The average values of δ iso ( 31 P) and δ CSA are fully compatible with the data obtained for a-CPP. In the case of a-CPP (Figure 1), a minor resonance centered at ~ 0 ppm is observed. As suggested by Slater et al., [START_REF] Slater | Enhanced stability and local structure in biologically relevant amorphous materials containing pyrophosphate[END_REF] such a contribution can be safely assigned to PO 4 3or HPO 4 2-moieties, caused by the presence of traces of orthophosphates in the precursors used to prepare CPP phases, and/or resulting from the partial hydrolysis of pyrophosphates under ageing. [START_REF] Gras | Synthesis and characterisation of hydrated calcium pyrophosphate phases of biological interest[END_REF][START_REF] Slater | Enhanced stability and local structure in biologically relevant amorphous materials containing pyrophosphate[END_REF] As a matter of fact, the relative intensity of this particular resonance was found to increase with time (see supporting information, Figure S3).

Studying calcium pyrophosphates represents a challenge in terms of first principles calculations of 31 P chemical shifts, as the experimental resonances are closely separated (~ 1 ppm in the case of t-CPPD, see Table 1). The accuracy of the GIPAW method applied to [START_REF] Bryce | Calcium binding environments probed by 43 Ca NMR spectroscopy[END_REF] P has been reviewed previously. [START_REF] Bonhomme | New perspectives in the PAW/GIPAW approach: J P-O-Si coupling constants, antisymmetric parts of shift tensors and NQR predictions[END_REF] Generally, the precision of such calculations depends explicitly on the accuracy of the corresponding structural data (obtained mainly by means of X-ray and/or neutron diffraction), [START_REF] Bonhomme | First-principles calculation of NMR parameters using the gauge including projector augmented wave method: a chemist's point of view[END_REF] which means that the NMR data can act as constraints for the further refinement of a crystallographic structure. In the case of α-Ca 2 P 2 O 7 , t-CPPD and m-CPPT β, good agreement is obtained between the experimental and calculated values both in terms of δ iso ( 31 P) and δ CSA . We notice that the calculated isotropic value for P1 in m-CPPT β is underestimated. Nevertheless, P1 and P2 can unequivocally be assigned.

The case of m-CPPD is an interesting one as it demonstrates the importance of proton relaxation. Indeed, starting from the published structure, [START_REF] Gras | Synthesis and characterisation of hydrated calcium pyrophosphate phases of biological interest[END_REF] the assignment of P1 and P2 is not straightforward, because when assigning the sites based on the relative values of δ iso ( 31 P), there is a contradiction with the relative order of the δ CSA values (and vice versa). In contrast, starting from the m-CPPD relaxed structure (Rel H in Table 1, see section 2.3), the relative orders of δ iso ( 31 P) and δ CSA are correctly described by the GIPAW calculations. This point emphasizes the crucial importance of the H positions in the starting structure, in agreement with recent studies in the literature. [START_REF] Bonhomme | First-principles calculation of NMR parameters using the gauge including projector augmented wave method: a chemist's point of view[END_REF][START_REF] Gervais | First principles calculations of phenylphosphinic acid C 6 H 4 HPO(OH): assignments, orientations of tensors by local field experiments and effect of molecular motion[END_REF] Moreover, we note that for m-CPPD, both P sites have similar proximities to protons (~ 2.7 to 2.8 Å), meaning that cross-polarization experiments cannot be used to distinguish them based on differences of CP dipolar dynamics. Finally, in the case of m-CPPM, even after relaxation of all atomic positions, the agreement with the experimental values remains poor but nonetheless allows a relatively safe assignment of the P1 and P2 sites since the relative order of the δ iso ( 31 P) and δ CSA values is consistent.

The geometric parameters of pyrophosphate ions (especially the P-O-P angle) have been used to explain the spectroscopic characteristics of vibrational spectra and correlations between band frequencies and geometric parameters have been described. [START_REF] Lazarev | Vibrational Spectra and Structure of Silicates, translated from the Russian by GD Archard[END_REF][START_REF] Cruickshank | The role of 3d-orbitals in π-bonds between (a) silicon, phosphorus, sulphur, or chlorine and (b) oxygen or nitrogen[END_REF][START_REF] Rulmont | Vibrational spectroscopy of phosphate: Some general correlations between structure and spectra[END_REF] Given the variety of geometries of the different pyrophosphate anions in the crystal structures investigated here (Figure 2), several tests were performed to evaluate the influence of these parameters on the δ iso ( 31 P) and δ CSA . Using the IVTON program, [START_REF] Zunic | IVTON -a program for the calculation of geometrical aspects of crystal structures and some crystal chemical applications[END_REF] geometric parameters were calculated, including P-O-P angles for the pyrophosphate units or, for each PO 4 tetrahedron, P-O distances, sphere radius, linear eccentricity, linear sphericity, volume distortion, volume eccentricity, volume sphericity, sphere volume, polyhedron volume, average bond distance, standard deviation of the bond distances, barycentre-centroid distance, difference in average distance centroid-barycentre, atom projection on barycentre-centroid vector and difference in average distance atom-centroid. No direct correlations were found between these geometric parameters and the δ iso ( 31 P) or δ CSA values (data not shown). The lack of correlation could be due to other effects related to the local environment of the pyrophosphates, including hydrogen bonding on pyrophosphate oxygen atoms. From an experimental perspective, 2 J(P-O-P) may also be more relevant parameters to determine, [START_REF] Florian | 2 J Si-O-Si scalar spin-spin coupling in the solid state: crystalline and glassy wollastonite CaSiO 3[END_REF][START_REF] Bonhomme | New perspectives in the PAW/GIPAW approach: J P-O-Si coupling constants, antisymmetric parts of shift tensors and NQR predictions[END_REF] as they might give additional insight on the P-O-P angles in each structure; however, these have not been measured to date.

The spectrum of a-CPP is characterized by a broadening of the unique resonance corresponding to a distribution of δ iso ( 31 P). Such a distribution is related to variations of P-O bond lengths and P-O-P angles, and also to a distribution in the relative proximity of neighbouring Ca 2+ cations and water molecules in these more disordered structures.

Interestingly, the 31 P MAS NMR spectrum is not sensitive to the synthetic protocol used for the preparation of the amorphous phase (see Figure S4).

43 Ca MAS NMR

The natural abundance [START_REF] Iuga | Population and coherence transfer induced by double frequency sweeps in half-integer quadrupolar spin systems[END_REF] Ca MAS NMR spectra of the crystalline phases were recorded at two different magnetic fields, in order to better constrain the quadrupolar parameters C Q and η Q extracted (Figures 3 andS5). Indeed, for [START_REF] Iuga | Population and coherence transfer induced by double frequency sweeps in half-integer quadrupolar spin systems[END_REF] Ca, 1D experiments at a single magnetic field are generally insufficient to extract these parameters. [START_REF] Laurencin | Development of 43 Ca solid state NMR spectroscopy as a probe of local structure in inorganic and molecular materials[END_REF] Moreover, given that high magnetic fields, large volume rotors and rather long experimental times (see Table S1) are usually essential for natural abundance [START_REF] Iuga | Population and coherence transfer induced by double frequency sweeps in half-integer quadrupolar spin systems[END_REF] Ca MAS NMR, [START_REF] Gervais | New perspectives on calcium environments in inorganic materials containing calcium-oxygen bonds: a combined computational-experimental 43 Ca NMR approach[END_REF][START_REF] Laurencin | Development of 43 Ca solid state NMR spectroscopy as a probe of local structure in inorganic and molecular materials[END_REF][START_REF] Colas | H 2 O: structural study by a combined NMR, crystallography and modeling approach[END_REF][START_REF] Sene | Structural study of calcium phosphonates: a combined synchrotron synchrotron powder diffraction, solid-state NMR and first-principles calculations approach[END_REF] the use of the 2D MQ (Multiple Quantum) MAS approaches can be excluded from a practical point of view.

As shown in Figure 3, the [START_REF] Iuga | Population and coherence transfer induced by double frequency sweeps in half-integer quadrupolar spin systems[END_REF] Ca isotropic chemical shift is sensitive enough to readily distinguish the various CPP forms both in terms of δ iso ( 43 Ca) and C Q ( 43 Ca). The [START_REF] Iuga | Population and coherence transfer induced by double frequency sweeps in half-integer quadrupolar spin systems[END_REF] Ca MAS NMR spectra were fitted using pure second-order quadrupolar lineshapes [START_REF] Massiot | Modelling one-and two-dimensional solid-state NMR spectra[END_REF] (see Table 2 and As a first attempt to correlate [START_REF] Iuga | Population and coherence transfer induced by double frequency sweeps in half-integer quadrupolar spin systems[END_REF] Ca NMR parameters to the local environment of calcium in these materials, the calculated δ iso ( 43 Ca) was plotted as a function of the average Ca-O bond distance (see Figure 4 and Table S2). δ iso ( 43 Ca) globally decreases as the average Ca-O bond distance increases, in agreement with the different trends reported so far for other inorganic compounds of different oxygen-bonded families. [START_REF] Gervais | New perspectives on calcium environments in inorganic materials containing calcium-oxygen bonds: a combined computational-experimental 43 Ca NMR approach[END_REF][START_REF] Laurencin | Development of 43 Ca solid state NMR spectroscopy as a probe of local structure in inorganic and molecular materials[END_REF] Interestingly, by looking more specifically at the different Ca local environments in the structures and analyzing in more detail the nature and number of the oxygen-bonded ligands coordinated to Ca, a better analysis could be proposed. Indeed, depending on the structures, the Ca 2+ can be between 6-and 8-coordinated, and the ligands can be either only O atoms belonging to pyrophosphates, or to water molecules. As shown in Figure 4, the nature of the oxygenated ligand (pyrophosphate or water) does not appear to have a big influence, but when separating the Ca sites according to their coordination number, different zones can be clearly distinguished, depending on whether the Ca is 6-, 7-or 8-coordinated. This shows that the two main parameters which appear to govern the δ iso ( 43 Ca) in the case of calcium pyrophosphates are the average Ca…O bond distance and the coordination number around the Ca. Finally, we note that similar trends were also observed using experimental δ iso ( 43 Ca) values, rather than the calculated ones.

The high sensitivity of δ iso ( 43 Ca) towards its local environment shows that it is a highly relevant tool of investigation of the structure of a-CPP at the atomic scale. In Figure 5, the high field [START_REF] Iuga | Population and coherence transfer induced by double frequency sweeps in half-integer quadrupolar spin systems[END_REF] Ca MAS NMR spectrum of an a-CPP phase is presented (sample B -see section 2.1). The rather symmetrical lineshape observed covers the range of all resonances observed for the crystalline CPP phases, and is more specifically centered around the resonances of m-CPPT β, in agreement with elemental analyses which suggests the presence of an average of 4 water molecules. [START_REF] Slater | Enhanced stability and local structure in biologically relevant amorphous materials containing pyrophosphate[END_REF] Nonetheless, at this stage, no chemical shift and/or quadrupolar distribution could be extracted for a-CPP.

High field [START_REF] Iuga | Population and coherence transfer induced by double frequency sweeps in half-integer quadrupolar spin systems[END_REF] Ca NMR was actually found to be a highly relevant tool of analysis of other related a-CPP phases. Indeed, depending on the synthetic protocol (control or not of the pH during the precipitation of a-CPP), [START_REF] Iuga | Population and coherence transfer induced by double frequency sweeps in half-integer quadrupolar spin systems[END_REF] Ca MAS NMR spectra presented subtle differences (see Figure S6 for the comparison of samples A and B), showing that the structures of these materials actually slightly differ, despite the similarities in the 31 P MAS NMR data (see Figure S4). Finally, it is worth noting that the effect of heat-treatment of a-CPP could also be followed by [START_REF] Iuga | Population and coherence transfer induced by double frequency sweeps in half-integer quadrupolar spin systems[END_REF] Ca MAS NMR (Figure S7). Indeed, despite rather symmetrical lineshapes at 20.0 T, a broadening of the signal was clearly observed after having heated the a-CPP phase at 220 °C, indicating an increase of the distribution of the [START_REF] Iuga | Population and coherence transfer induced by double frequency sweeps in half-integer quadrupolar spin systems[END_REF] Ca NMR parameters, possibly due to the formation of hydrogen-phosphate anions within the material, as previously evidenced by [START_REF] Richette | An update of the epidemiology of calcium pyrophosphate dihydrate crystal deposition disease[END_REF] H and 31 P MAS NMR. [START_REF] Slater | Enhanced stability and local structure in biologically relevant amorphous materials containing pyrophosphate[END_REF] All in all, [START_REF] Iuga | Population and coherence transfer induced by double frequency sweeps in half-integer quadrupolar spin systems[END_REF] Ca NMR appears as a valuable tool for investigation of hydrated calcium pyrophosphates, which would deserve to be looked into more systematically, as it can provide complementary information about their structure at the atomic scale.

1 H MAS NMR

1 H MAS NMR spectra were recorded using homonuclear decoupling (DUMBO) during acquisition (Figure 6). Despite the use of advanced decoupling techniques, it was not possible to fully resolve the different 1 H resonances related to inequivalent water molecules in the structures. For all crystalline structures an average value of ~ 5-6 ppm was observed. Such a range of isotropic chemical shifts is compatible with those obtained for protons involved in H-bond networks. [START_REF] Fayon | Evidence of nanometric-sized phosphate clusters in bioactive glasses as revealed by sold state 31 P NMR[END_REF] A comparison with GIPAW calculated 1 H chemical shifts (Table S3) is also presented in Figure 6 for t-CPPD, m-CPPD, m-CPPM and m-CPPT β. As already stated in the 31 P discussion, the scatter of the calculated values is more pronounced in the case of m-CPPD.

This observation tends to suggest that it should be possible to improve the positioning of the protons in the structure using the 1 H chemical shifts as constraints.

The 1 H MAS spectra of a-CPP phases prepared according to different synthetic procedures were found to exhibit distinct signatures. While only one main asymmetric signal was observed for the sample prepared by simple precipitation (sample B), two distinct resonances were visible when the pH of the precipitating solution was controlled (sample A).

This observation shows that differences in the atomic-scale structure of both amorphous compounds exist, as already suggested by [START_REF] Iuga | Population and coherence transfer induced by double frequency sweeps in half-integer quadrupolar spin systems[END_REF] Ca MAS NMR. More specifically, the 1 H NMR spectrum of the a-CPP phase called sample B resembles that of m-CPPT β, while additional 1 H local environments are observed in sample A, which could be similar to those observed in m-CPPM, given the similarity in 1 H chemical shifts. Thus, it appears that despite the fact that the water content in both phases is very similar, [START_REF] Gras | Synthesis and characterisation of hydrated calcium pyrophosphate phases of biological interest[END_REF][START_REF] Slater | Enhanced stability and local structure in biologically relevant amorphous materials containing pyrophosphate[END_REF] the H-bond network of the water molecules within these amorphous phases depends on the synthetic protocol. A more systematic investigation of the 1 H NMR spectra of amorphous calcium pyrophosphates precipitated at different pH values may therefore shed light on the structural variability of these materials at the atomic scale, by providing information which is not necessarily accessible from more commonly used techniques such as IR spectroscopy. Low temperature experiments (down to ~ 100 K) would also be of high interest for a more detailed comparison of experiment and GIPAW computed parameters. Indeed, water molecules must experience intrinsic dynamics in the various structures (at least at room temperature), as demonstrated by the relative lack of resolution of the 1 H MAS spectra. It follows that the 1 H isotropic chemical shifts observed at room temperature correspond to averages. Freezing local dynamics would lead to determine "static" isotropic chemical shifts which could be compared safely to GIPAW predictions and act therefore as pertinent constraints for structure refinement.

Conclusion

In this contribution, several hydrated calcium pyrophosphate phases (both crystalline and amorphous) were characterized by multinuclear MAS NMR. It was demonstrated that 31 P and [START_REF] Iuga | Population and coherence transfer induced by double frequency sweeps in half-integer quadrupolar spin systems[END_REF] Ca MAS NMR spectroscopies are suitable for the clear distinction of the various phases.

Even in the case of amorphous samples, subtle variations of the resonance lines were observed by [START_REF] Iuga | Population and coherence transfer induced by double frequency sweeps in half-integer quadrupolar spin systems[END_REF] Ca MAS NMR depending on the synthetic protocol and heat treatment temperature. Moreover, 1 H NMR was found to be informative about differences in the H-bond networks within these phases.

All crystalline structures were then studied in the context of NMR crystallography, using GIPAW as a theoretical bridge between experimental and computed data. All in all, a fairly good agreement was observed for the three studied nuclei, provided that a relaxation of the structures (focusing especially on proton positions) was carried out. Nonetheless, discrepancies remained for the hydrated phases, which may be due to the fact that NMR calculations do not take into account any temperature/local motion effects. Previous studies have indeed shown that these factors could induce significant differences between experimental and computational data. [START_REF] Bonhomme | First-principles calculation of NMR parameters using the gauge including projector augmented wave method: a chemist's point of view[END_REF] a-CPP phases, important structural features have been derived from multinuclear solid state NMR analyses. First of all, the 31 P MAS spectra are rather insensitive to the synthetic protocols: it demonstrates that the 31 P NMR parameters are mostly determined by the local geometry of the P 2 7 4-species (angle, bond lengths) and not by the localization of the calcium cations and the water molecules. This is clearly not the case when considering [START_REF] Iuga | Population and coherence transfer induced by double frequency sweeps in half-integer quadrupolar spin systems[END_REF] Ca and 1 H parameters. In particular, 1 H MAS spectra seem suitable to distinguish local environments comparable to those observed in m-CPPT β and m-CPPM crystalline phases, though contents in water molecules are comparable from one sample to another one.

Slater et al. [START_REF] Slater | Enhanced stability and local structure in biologically relevant amorphous materials containing pyrophosphate[END_REF] already pointed out structural similarity between m-CPPT β and a-CPP by pair distribution functions (PDF) analysis. This structural similarity was furthermore linked to comparable behavior regarding hydrolysis reactions. Thus it has been observed that m-CPPT β, m-CPPM and a-CPP are hydrolyzed at high temperature but this is not the case for t-CPPD and m-CPPD samples. [START_REF] Gras | Synthesis and characterisation of hydrated calcium pyrophosphate phases of biological interest[END_REF][START_REF] Gras | Structure of the calcium pyrophosphate monohydrate phase (Ca 2 P 2 O 7 •H 2 O): towards understanding the dehydration process in calcium pyrophosphate hydrates[END_REF] Based on the elemental composition of the amorphous calcium pyrophosphate phases, and on the structural information gathered here by 1 H, [START_REF] Iuga | Population and coherence transfer induced by double frequency sweeps in half-integer quadrupolar spin systems[END_REF] Ca and 31 P MAS NMR, realistic structural models for these amorphous phases are currently being developed. Following the pioneering approach initiated by Charpentier [START_REF] Charpentier | The PAW/GIPAW approach for computing NMR parameters: a new dimension added to NMR study of solids[END_REF] and very recent results presented by the same author, [START_REF] Gambuzzi | Calcium environment in silicate and aluminosilicate glasses probed by 43Ca MQMAS NMR experiments and MD-GIPAW calculations[END_REF] the idea is to compare the calculated NMR values for computational models of this material with the experimental ones, in order to propose a realistic model. This study will be presented in a forthcoming publication.

Finally, the contribution of this study in structural refinement of poorly known hydrated CPP phases is a first step towards the understanding of in vivo phenomena related to osteoarthritis: structureinflammatory response relationships, potential precursor phase formation and evolution, role of trace elements in CPP crystal formation occurring in associated diseases like hypomagnesaemia, [START_REF] Jones | Diseases associated with Calcium Pyrophosphate Deposition disease[END_REF] Wilson's disease (copper excess) [START_REF] Mcclure | Calcium pyrophosphate dihydrate deposition in the intervertebral discs in a case of Wilson's disease[END_REF] and haemochromatosis (iron excess). [START_REF] Wright | Calcium pyrophosphate crystal deposition is not always ' wear and tear ' or aging[END_REF] In addition, some applications of CPP compounds in the biomaterial field can be envisioned. 39 All other lines correspond to spinning sidebands from which CSA parameters can be extracted. In the case of a-CPP, the minor component at δ iso ~ 0 ppm is assigned to orthophosphate species (see main text). MAS rotation frequency: between 4 and 6 kHz. For details on the relaxation delay and number of scans for each sample, see Table S1. The fitting of the different MAS NMR spectra can be found in Figure S5. S2.

- S3).

a-CPP (sample A)

Table 1: Experimental and calculated 31 P chemical shift tensor (CSA) data for m-CPPD, m-CPPM, t-CPPD, m-CPPT β. The definitions of δ CSA and η CSA are given in the experimental section. In the case of m-CPPD, results obtained before and after relaxation of the proton positions ("Rel H") are presented. In order to validate the combined experimental/computational approach, both sets of data were added for α-Ca 2 P 2 O 7 (anhydrous phase). The maximum error on experimental δ iso values was estimated to 0.15 ppm. given in the experimental section. In the case of m-CPPD, results obtained before and after relaxation of the proton positions (Rel H) are presented. The spectra from which the experimental values were determined are shown in Figure S5, together with their simulation.

δ
Errors were estimated to ~2-3 ppm on δ iso and ~ 0.2-0.4 MHz on C Q , except for the m-CPPM phase for which the fitting was performed at only one magnetic field (thus leading to larger errors). Calcium Pyrophosphates (CPP)

δ

1 H

 1 NMR spectra were recorded on a Varian VNMRS 600 MHz (14.1 T) NMR spectrometer at frequency of 599.82 MHz, using a 3.2 mm Varian T3 HXY MAS probe.Windowed-DUMBO (Decoupling Using Mind-Boggling Optimization)45,46,47 1 H MAS experiments were carried out at a spinning speed of 10 kHz. A glycine sample was used for the optimization of the DUMBO experiment. The radio-frequency (RF) field strength was 100 kHz, the duration of one DUMBO element 34.4 µs, and the observation window 0.8 µs. 20 transients were acquired, with recycle delays ranging from 4 to 16 s (depending on the sample). The 1 H chemical shifts were referenced externally to adamantane, used as a secondary reference (at 1.8 ppm with respect to tetramethylsilane, TMS). Temperature regulation was used during the experiments, to ensure that the temperature inside the rotor was ~ 10° C.

  2×2×2 k-point grid. The principal components V xx , V yy , and V zz of the electric field gradient (EFG) tensor defined with |V zz | ≥ |V xx | ≥ |V yy | were obtained by diagonalisation of the tensor. The quadrupolar interaction was then characterized by the quadrupolar coupling constant C Q and the asymmetry parameter η Q , which are defined as C Q = eQV zz /h and

31 P

 31 MAS NMR spectra were recorded for m-CPPT β, m-CPPD, t-CPPD and m-CPPM and are shown in Figure1(fast and slow MAS NMR spectra). At slow spinning frequency, numerous spinning sidebands are observed: their simulation by a CSA model 62 leads to the determination of the CSA parameters δ CSA and η CSA (as defined in the Materials and Methods section). Here, it is explicitly assumed that residual 31 P-31 P homonuclear dipolar couplings can be safely ignored in the simulations as they are much smaller (in Hz) than CSA effects.All simulations of the 31 P MAS NMR spectra are presented in FigureS2. As expected from the crystal structures, two distinct 31 P resonances are observed for each compound. For all spectra, the relative intensity of the two resonances differs from the expected 1:1 ratio, because the measurements were performed only for the purpose of determining the 31 P NMR parameters δ iso , δ CSA and η CSA , and thus in conditions which do not necessarily ensure full relaxation of the different 31 P resonances. The observed range for δ iso ( 31 P) is ~ -12 to -5 ppm

Figure

  Figure S5). The spectra are clearly in agreement with the presence of two inequivalent Ca sites, Ca1 and Ca2, as observed in the corresponding crystallographic structures. For the different crystal structures obtained for the CPP phases, experimental δ iso ( 43 Ca) were found to vary between ~ 7 and ~ 33 ppm, while experimental C Q ( 43 Ca) between ~ 1.8 and ~ 4.5 MHz.

Figure 1 :

 1 Figure 1: 31 P MAS NMR spectra (decoupled from 1 H during the acquisition time) of t-CPPD, m-CPPD, m-CPPT β, m-CPPM and a-CPP (sample A) (14.1 T, 242.81 MHz, spinal 64 1 H decoupling, relaxation delay: 128 s, number of scans: 4, regulation of the temperature: 10 °C, saturation pulses on the 31 P channel before the first 90° pulse). MAS rotation frequency: 10.0 kHz (left) and ~ 2.8 to 5.0 kHz (right). For the slow MAS spectra, the exact rotation frequency, ν r , is specified in Figure S2 for each sample. For each spectrum, the arrow indicates the region of the isotropic resonances (two in general, except in the case of a-CPP).

Figure 2 : 7 Figure 3 :

 273 Figure 2: Configuration of the pyrophosphate anions in the crystalline CPP phases studied (as shown along two different viewing directions). O and P atoms are in red and grey, respectively.

Figure 4 :

 4 Figure 4: Correlation between the computed 43 Ca isotropic chemical shifts and the mean Ca…O bond distance in m-CPPD, t-CPPD, m-CPPT β, m-CPPM and α-Ca 2 P 2 O 7 , depending on the Ca coordination number (CN) and the number of water molecules in the coordination sphere. The values are taken from TableS2.

Figure 5 :Figure 6 : 1 H

 561 Figure 5: Natural abundance 43 Ca MAS NMR spectra of a-CPP (sample B -see section 2.1), t-CPPD, m-CPPD and m-CPPT β [20.0 T, ν 0 ( 43 Ca) = 57.22 MHz; for relaxation delay and number of scans: see TableS1]. MAS rotation frequency: 5 kHz. Comparison between the[START_REF] Iuga | Population and coherence transfer induced by double frequency sweeps in half-integer quadrupolar spin systems[END_REF] Ca MAS spectra of samples A and B are presented in FigureS6.

Table 2 :

 2 Experimental and calculated[START_REF] Iuga | Population and coherence transfer induced by double frequency sweeps in half-integer quadrupolar spin systems[END_REF] Ca chemical shift and quadrupolar parameters for α-Ca 2 P 2 O 7 , m-CPPD, t-CPPD, m-CPPT β and m-CPPM. The definitions of C Q and η Q are

			iso (ppm)		δ CSA (ppm)	η CSA
			Exp	Calc	Exp	Calc	Exp	Calc
	α-Ca 2 P 2 O 7	P1	-7.70	-9.38	59.4	65.58	0.62	0.53
		P2	-10.00 -10.39 66.9	76.49	0.38	0.36
	m-CPPD	P1	-9.70	-8.66	82.6	59.55	0.34	0.70
		P2	-5.90	-6.44	72.5	97.70	0.41	0.24
	m-CPPD	P1	-5.90	-7.42	72.5	61.59	0.41	0.60
	Rel H	P2	-9.70	-7.80	82.6	96.17	0.34	0.18
	t-CPPD	P1	-5.94	-5.22	76.6	79.95	0.56	0.57
	Rel H	P2	-4.97	-4.58	75.6	79.28	0.27	0.26
	m-CPPT β	P1	-9.31	-15.80 84.5	85.16	0.21	0.11
	Rel H	P2	-7.33	-6.90	71.6	78.50	0.41	0.54
	m-CPPM	P1	-11.27 -3.4	64.0	68.78	0.80	0.70
		P2	-7.34	-0.2	85.7	93.66	0.48	0.56
	a-CPP	P	-6.7		78.2		0.80

  For α-Ca 2 P 2 O 7 , the calculated values reported here differ from those previously published,[START_REF] Gervais | New perspectives on calcium environments in inorganic materials containing calcium-oxygen bonds: a combined computational-experimental 43 Ca NMR approach[END_REF] due to the difference in computational code used (PARATEC vs Quantum Espresso). For α-Ca 2 P 2 O 7 , only the quadrupolar parameter P Q had been reported.[START_REF] Gervais | New perspectives on calcium environments in inorganic materials containing calcium-oxygen bonds: a combined computational-experimental 43 Ca NMR approach[END_REF]

				iso (ppm)		C Q (MHz)	η Q
				Exp	Calc	Exp	Calc*	Exp	Calc
	α-Ca 2 P 2 O 7	a	Ca1	-18.0	-22.1	2.5 b	1.84	b	0.61
			Ca2	12.0	6.4	2.8 b	-2.13	b	0.51
	m-CPPD		Ca1	14.0	12.5	1.9	2.12	0.6	0.93
			Ca2	29.0	18.0	2.0	0.85	0.6	0.74
	m-CPPD		Ca1	14.0	14.9	1.9	1.96	0.6	0.96
	Rel H		Ca2	29.0	17.6	2.0	-0.84	0.6	0.99
	t-CPPD		Ca1	14.5	13.8	3.4	-3.11	0.3	0.42
	Rel H		Ca2	12.0	12.0	2.7	-2.47	0.5	0.14
	m-CPPT β	Ca1	11.0	11.9	1.8	1.57	0.6	0.43
	Rel H		Ca2	7.5	11.4	2.1	2.36	0.6	0.67
	m-CPPM		Ca1	33.0	15.2	2.6	-1.42	0.7	0.38
	Rel tot		Ca2	20.0	5.3	4.5	-3.64	0.4	0.55

a b * the sign of C Q cannot be determined by solid state NMR experiments at room temperature.

Acknowledgements

The French/UK CNRS PICS project QMAT is acknowledged. D. Laurencin and M. E. Smith thank the Royal Society for funding collaborative research (Warwick-Montpellier JP090313 partnership). The UK 850 MHz solid-state NMR Facility used in this research was funded by EPSRC and BBSRC, as well as the University of Warwick including via part funding through Birmingham Science City Advanced Materials Projects 1 and 2 supported by Advantage West Midlands (AWM) and the European Regional Development Fund (ERDF).

We thank Dr Dinu Iuga for his help at the 850 MHz Facility. NMR spectroscopic calculations were performed on the IDRIS supercomputer centre of the CNRS (Project: 091461). Finally, the authors thank the French Agence Nationale de la Recherche (CAPYROSIS project -