25Mg Solid-State NMR of Magnesium Phosphates: High Magnetic

Article pubs.acs.org/JPCC

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Mg Solid-State NMR of Magnesium Phosphates: High Magnetic Field Experiments and Density Functional Theory Calculations

D. Laurencin,† C. Gervais,‡ H. Stork,§ S. Kram ̈ er,§ D. Massiot,∥,⊥ and F. Fayon∥,⊥,* †

Institut Charles Gerhardt de Montpellier, UMR CNRS 5253, UM2 UM1 ENSCM, CC 1701 Université de Montpellier 2, Place E. Bataillon, 34095 Montpellier Cedex 5, France ‡ Laboratoire Chimie de la Matière Condensée de Paris, UMR CNRS 7574, UPMC Université Paris 06, Collège de France, 11 place Marcelin Berthelot, 75231 Paris Cedex 05, France § Laboratoire National des Champs Magnétiques Intenses, UPR CNRS 3228, CNRS − UJF − UPS - INSA 25 rue des Martyrs, B.P. 166, 38042 Grenoble cedex 9 and 143 avenue de Rangueil, 31400 Toulouse, France ∥ CEMHTI, UPR CNRS 3079, 1D avenue de la Recherche Scientifique, 45071 Orléans Cedex 2, France ⊥ Université d’Orléans, Faculté des Sciences, Avenue du Parc Floral, 45067 Orléans Cedex 2, France S Supporting Information *

ABSTRACT: Natural-abundance 25Mg solid-state NMR data obtained using very high magnetic fields of 17.6, 20.0, and 30.0 T are reported for a series of magnesium phosphate compounds, some of which are of potential biomedical interest. The 25Mg NMR parameters have been calculated by using the DFT PAW and GIPAW methods, for both the experimental and DFT atomic position optimized structures. For most of the studied compounds, the geometry optimization step improves significantly the accuracy of the calculations and good correlations between experimental and calculated 25Mg chemical shifts and quadrupolar coupling constants were achieved showing that this approach can be used to obtain unambiguous assignments of the 25Mg resonances in more complex phosphate compounds. The possibility of recording natural abundance 25Mg NMR spectra in materials with very low Mg content is illustrated for a ∼10% Mg-substituted hydroxyapatite sample. In this case, the distribution of 25Mg quadrupolar coupling measured experimentally has been compared with values previously calculated for several structural models. The results suggest that more complex structural models must be developed to improve the understanding of the Ca/Mg substitution on the basis of 25Mg NMR data.

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INTRODUCTION

magnesium has been shown to have a significant impact on the properties of these materials. Few techniques are available to provide information about the local environment around Mg in the mineral part of biological materials, making it difficult to establish the link between its structural and biological roles. Indeed, two main spectroscopic techniques allow Mg local environments to be selectively characterized: Mg K-edge X-ray absorption spectroscopy (XAS) and 25Mg solid-state nuclear magnetic resonance (NMR). On the one hand, Mg K-edge XAS, which requires the use of synchrotron facilities equipped with soft Xray beamlines (Mg K-edge energy of 1.31 keV) can be used to probe the Mg local environment in minerals and glasses,24−28 and this technique has been recently employed to characterize several biominerals in the prospect of understanding the role of Mg in the stabilization of biogenic amorphous calcium carbonate.3 However, in complex systems containing multiple

Magnesium is one of the 10 most abundant elements in the Earth’s crust,1 where it is found in clays, sedimentary rocks, and metamorphic rocks under the form of minerals like dolomite (MgCa(CO 3 ) 2 ), epsomite (MgSO 4 ·7H 2 O), or talc (Mg3Si4O10(OH)2), to name a few. Mg-containing minerals are also present in living systems: Mg2+ cations have been found to be associated with (i) carbonates, in mixed Ca,Mg(CO3)2 phases like those present in sea urchin tests,2,3 (ii) oxalates, in minerals like glushinskite (Mg(C2O4)·2H2O), which can be produced by certain cactaceae,4,5 and (iii) phosphates, under the form of struvite stones ((NH4)MgPO 4 ·6H 2 O) 6 or as substituents in hydroxyapatite (Ca10(PO4)6(OH)2), which is the main mineral phase of bone and teeth.7−10 Magnesium has been found to play an important role in the mineral phase of bones, notably because Mg deficiency can cause bone fragility.11 Because of this, Mg is often incorporated in various inorganic biomaterials designed for bone tissue engineering, such as bioglasses, 12−17 cements,18,19 or ceramics,20−23 and the presence of traces of © 2012 American Chemical Society

Received: July 27, 2012 Revised: August 30, 2012 Published: August 30, 2012 19984

dx.doi.org/10.1021/jp307456m | J. Phys. Chem. C 2012, 116, 19984−19995

The Journal of Physical Chemistry C

Article

distinct Mg environments, Mg K-edge XAS spectra only provide information about the average short-range structure around Mg. On the other hand, 25Mg solid-state NMR spectroscopy can allow obtaining site-specific information about the Mg local environment in ordered or disordered systems. Unfortunately, the magnetically active isotope, 25Mg, has a small gyromagnetic ratio (γ = −1.639 × 107 rad·s−1·T−1) and a low natural abundance (10.1%) leading to a relatively weak NMR receptivity. In addition, 25Mg is a spin-5/2 nucleus with a significant quadrupolar moment29 that gives rise to relatively large second-order quadrupolar broadenings in magicangle spinning (MAS) NMR powder spectra recorded at moderate magnetic fields. Because of these difficulties, 25Mg natural-abundance solid-state NMR has been limited to relatively few applications during the 90s.30−41 Thanks to instrumental and methodological developments, 25 Mg solid-state NMR has recently become more accessible and an increasing number of 25Mg NMR studies of inorganic10,42−61 and organic52,62−64 compounds have been reported during the last 10 years, as recently reviewed by Freitas and Smith.65 These works have greatly benefited from the increase in the available very high magnetic field magnets, which increase the NMR sensitivity and enhance the resolution in static and MAS spectra of half-integer quadrupolar nuclei (because the second-order quadrupolar broadening decreases with the magnetic field).66,67 Sensitivity enhancement techniques for half-integer quadrupolar nuclei68−70 and multiple-echoes acquisition methods71−73 have also been employed to increase further the signal-to-noise ratio of 25Mg NMR spectra. To use 25Mg NMR as a structural probe in complex systems with unknown structures, relationships between 25Mg NMR parameters and the local environment of magnesium were then investigated, and it was found that 25Mg NMR parameters are sensitive to the local structure around the cation.35,52,58,59 Indeed, in the case of Mg oxoanion systems, for example, it was reported that changes in the average Mg−O bond distance affect the 25Mg isotropic chemical shift, whereas small variations in the geometry of the Mg coordination polyhedron lead to strong changes in the quadrupolar coupling constant (CQ).52 It was also noticed that the number of water molecules directly coordinated to Mg2+ can affect 25Mg NMR spectra.52 However, these empirical correlations are only reliable for a specific class of compounds, because different trends are observed for different families of Mg compounds (aluminates, silicates, sulfates, carboxylates, and so on). Another way to establish links between structure and NMR data consists of calculating the NMR parameters from structural models using first-principles methods. In the case of crystalline systems, first-principles molecular calculations require the critical definition of a large cluster to mimic the crystalline structure,58 and methods employing periodic boundaries conditions are more efficient. In this context, the PAW (projector-augmented wave)74,75 and GIPAW (gauge including projector-augmented wave) methods,76 which are based on the plane-wave pseudopotential formalism of the density functional theory (DFT), have proven their efficiency for the calculations of the quadrupolar coupling and chemical shift tensors in a variety of compounds,77 and it was recently shown that these methods allow us to calculate accurately the 25 Mg solid-state NMR parameters (chemical shift and quadrupolar coupling tensors) of several inorganic magnesium compounds52,53,59 as well as some molecular organic Mg complexes.52,53

Concerning the Mg-phosphate family of compounds, only a few phases have been investigated so far by 25Mg solid-state NMR experiments: Mg 3 (PO 4 ) 2 ·8H 2 O, MgHPO 4 ·3H 2 O, NH4MgPO4.H2O, NH4MgPO4·1.2H2O, and (NH3-(CH2)nNH3)MgPO4·H2O (n = 2, 4).53,58 In all of these compounds, Mg is associated with orthophosphate anions, and no experimental or computational studies involving pyrophosphate or metaphosphate units have yet been reported, despite the fact that these may be present in Mg-containing biomaterials like bioglasses. Therefore, to determine fully how this technique can be used to characterize Mg-phosphate structures such as those commonly found in biological systems and biomaterials, it appears necessary to study a larger number of compounds. In this work, we present results of (i) 25Mg NMR experiments of a series of Mg meta-, pyro-, and ortho-phosphates (Mg(PO3)2, αMg2P2O7, β-Mg2P2O7, Mg3(PO4)2, Mg3(PO4)2·8H2O, and NH4MgPO4·6H2O), and (ii) DFT calculations of the NMR parameters for these compounds as well as for another hydroxylated magnesium phosphate phase for which 25Mg NMR data have been recently reported (MgHPO4·3H2O).53 The link between the 25Mg NMR data and structural parameters concerning the local environment of the cation is also discussed. The study is then extended to the analysis of Mg local environments in a Mg-substituted hydroxyapatite phase.

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EXPERIMENTAL SECTION Sample Preparations. Mg3(PO4)2·8H2O (97%) and NH4MgPO4·6H2O (98%) were purchased from Fluka and Alfa Aesar, respectively. The Mg3(PO4)2 sample was obtained by heating 500 mg of Mg3(PO4)2·8H2O in a Pt crucible at 600 °C for 3 h under air. After cooling, 320 mg of Mg3(PO4)2 was recovered (yield ≈ 99%). The α-Mg2P2O7 phase was prepared by heat treatment of MgHPO4·3H2O (99%, Alfa Aesar). 600 mg of MgHPO4·5H2O was heated to 1000 °C for 3 h under air in an alumina crucible. After cooling at room temperature, 380 mg of α-Mg2P2O7 was obtained (yield ≈ 99%). Attempts to prepare a pure phase of β-Mg2P2O7 by quenching a sample heated at high temperature (700 to 1000 °C) were unsuccessful (due to α−β diffuse phase transition around 70 °C). Consequently, NMR and XRD experiments on β-Mg2P2O7 were performed in situ at 80 °C. The Mg(PO3)2 sample was prepared from a stoichiometric dried powder resulting from the mixing of (NH4)2HPO4 and Mg(NO3)2 aqueous solutions. The mixture was heated to 650 °C for 12 h under air in a Pt crucible. The Mg-substituted hydroxylapatite sample (Ca10−xMgx(PO4)6(OH)2 with x = 0.9) was prepared by precipitation, as previously described.10 The purity of all samples was carefully checked by X-ray diffraction. Solid-State NMR. 25Mg solid-state NMR experiments were carried out on Bruker Avance III WB spectrometers operating at magnetic fields of 20.0 and 17.6 T (corresponding to 25Mg Larmor frequencies of 52.0 and 45.9 MHz, respectively) and a Bruker Avance I spectrometer operating at magnetic field 9.4 T (25Mg Larmor frequency of 24.5 MHz). The experiments were performed using Bruker 7 mm single-resonance and 4 mm double-resonance MAS probeheads (20.0 and 17.6 T), a 5 mm single resonance static probehead (20.0 T), and a 7 mm double-resonance MAS probehead (9.4 T). For the Mg(PO3)2, α-Mg2P2O7, β-Mg2P2O7, and Mg3(PO4)2 samples, the 25Mg central-transition (CT) static and MAS spectra were recorded using the QCPMG pulse sequence,71−73 which allows acquiring trains of whole spin echoes by applying a series of equidistant CT-selective 180° refocusing pulses. This results in enhanced 19985



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sensitivity, depending on the 25Mg transverse coherence lifetime that defines the number of acquired echoes. For each sample, the delay between the 180° refocusing pulses was carefully chosen to avoid truncation of the individual echo signal, and the number of refocusing pulses was adjusted such that the full coherence decay was recorded. The processing of the QCPMG data was performed by splitting the QCPMG echo-train into individual spin−echoes and by making the Fourier transform of the sum of the individual echoes to recover a conventional powder pattern. A comparison between the QCPMG powder patterns and the QCPMG spikeletspectra obtained from the direct Fourier transform of the QCPMG echo-train71,72 is shown in the Supporting Information (SI) (Figure S1). In the case of the Mg3(PO4)2·8H2O and NH4MgPO4·6H2O samples, 25Mg CT static and MAS spectra were recorded using a Hahn echo sequence with 1H continuous-wave (CW) decoupling during acquisition (1H nutation frequencies of 26 and 42 kHz for the 7 and 4 mm probeheads). The 25Mg CT static NMR spectra of the ∼10% Mg-substituted hydroxyapatite sample were recorded using the QCPMG sequence. For this compound with low Mg content, we have used 5 (20.0 T) and 7 mm (17.6 T) single-resonance probeheads that allow studying large sample volume but without 1H decoupling during signal acquisition. For all samples except NH4MgPO4·6H2O, the durations of the 25Mg 90 and 180° CT-selective pulses were 2.5 and 5.0 μs. For NH4MgPO4·6H2O, weaker radio frequency field strengths were employed with 90° CT-selective pulse durations of 3.8 and 5.0 μs at 17.6 and 9.4 T, respectively. The recycle delay was varied between 1 and 15 s depending on the sample. All experiments were performed at room temperature, except in the case of βMg2P2O7, for which the 25Mg spectrum was recorded in situ at 80 °C, as mentioned above. Additional experimental details are given in the SI (Tables S1 and S2) 25 Mg static NMR spectra of NH4MgPO4·6H2O, α−β Mg2P2O7, and Mg(PO3)2 were also recorded at the Laboratoire National des Champs Magnétiques Intenses (LNCMI, Grenoble, France) at an ultrahigh magnetic field of 30 T, using a 24 MW resistive magnet, a home-built NMR console, and a home-built broadband NMR probe tuned to 77.78 MHz. The drift of the magnetic field was compensated using the 63Cu signal of CuCl (frequency of 336.6 MHz) as an internal lock. The poor intrinsic homogeneity of these types of magnets of typically more than 100 ppm for 5 mm sample size was improved to a value of 10 ppm by means of a passive shim unit. This device consists of a specially designed thin-walled iron cylinder, which is placed around the sample region and generates a field profile opposite to the one of resistive magnet. Therefore with our chosen sample size of 5 mm in diameter and 6 mm in length, the line broadening due to the inhomogeneity of the external field was still below 3 kHz and we were able to preserve at the same time the largest sample volume possible for sensitivity. The 25Mg spectra were recorded with a Hahn echo sequence using CT-selective 90° pulse duration of 1.5 μs and short interpulse delay of 100 to 150 μs to minimize the effect of the rapid fluctuations of the external field (in the range of up to 1 kHz and on the order of 20 ppm) on transverse coherence lifetime. Because of the presence of these fluctuations, no QCPMG sequence could be applied. The total number of transients for each spectrum recorded at 30 T using the Hahn echo sequence was about 100 times lower than in the spectra recorded at the two superconducting fields.

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Mg chemical shifts were referenced relative to a 1 M aqueous solution of MgCl2. All spectra simulations were performed using the DMFit software.78 The errors in the simulations were determined using a Monte Carlo approach: 500 data sets with added experimental noise were generated from the best fit of the experimental spectra and fitted using the same procedure. The obtained standard deviations were used to estimate the uncertainties (two times the standard deviation, corresponding to the 95% confidence limit). DFT Computations. DFT calculations of the NMR parameters were performed with the CASTEP79,80 code implemented in the Materials Studio 5.0 environment using the PAW74,75 and GIPAW76 algorithms for computing the EFG and NMR chemical-shielding tensors, respectively. The Perdew−Burke−Ernzerhof81 (PBE) functional was used for the exchange-correlation kernel. The core−valence interactions were described by ultrasoft pseudopotentials (USPPs).82 The USPPs were generated using the on-the-fly generator (OTF_USPP) included in CASTEP. For oxygen, a core radius of 1.3 Å was used with 2s and 2p valence orbitals; for magnesium, a core radius of 2.0 Å was used with 2p and 3s valence orbitals, and for phosphorus, a core radius of 1.8 Å was used with 3s and 3p valence orbitals. An energy cutoff of 600 eV was used for the plane-wave basis set expansion. The Brillouin zone was sampled using a Monkhorst-Pack grid spacing of 0.04 Å−1 (corresponding to a k-point mesh of 2 × 3 × 3 for Mg(PO3)2 and α-Mg2P2O7, 4 × 4 × 6 for β-Mg2P2O7, 3 × 3 × 5 for Mg3(PO4)2, 3 × 2 × 6 for Mg3(PO4)2·8H2O, 4 × 4 × 2 for NH4MgPO4·6H2O, and 2 × 2 × 2 for MgHPO4·3H2O). The convergence of the total energy and the calculated 25Mg shielding and EFG tensors was carefully checked. Increasing the cutoff energy and the number of k-points leads to changes smaller than 0.1 eV, 0.2 ppm, and 0.005 MHz for the total energy, 25Mg isotropic shielding, and 25Mg quadrupolar coupling constant, respectively (SI, Figure S2). For all compounds, computations of the NMR parameters were performed for both the experimental (ES) and DFT-PBE atomic position optimized (APO) structures. The APO structures were obtained by minimizing the residual forces on all atoms up to |F|max below 8 meV·Å−1, keeping symmetry constraints and fixing the cell parameters to the experimentally determined values.

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RESULTS AND DISCUSSION The natural-abundance 25Mg CT static and MAS spectra of the studied magnesium phosphates, recorded at different magnetic fields of 20.0, 17.6, and 9.4 T, are shown in Figures 2 and 3. Measurements at two different magnetic fields were necessary to derive unambiguously the 25Mg NMR parameters, especially for compounds containing more than one Mg crystallographic site, and recording static spectra was of importance to observe properly the 25Mg resonances with very large quadrupolar coupling constants.83 For all compounds, the observed powder patterns are characteristic of second-order quadrupolar broadening. Very satisfactory fits of the static and MAS spectra acquired at the different magnetic fields are simultaneously obtained using ideal quadrupolar lineshapes and neglecting the 25 Mg chemical shift anisotropy (CSA), which is expected to be very small.53,65 This is also supported by DFT GIPAW76 calculations of the 25Mg shielding tensors, which predicted CSA absolute values (|δCSA| = |δZZ − δISO|) ranging from 2.5 to 17 ppm in the studied compounds (SI Table S3). Because the CSA broadening increases linearly with the applied magnetic 19986



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Figure 1. Crystal structures and Mg coordination polyhedra for Mg(PO3)2, α-Mg2P2O7, β-Mg2P2O7, Mg3(PO4)2, Mg3(PO4)2·8H2O and NH4MgPO4·6H2O. Mg, P, O, H and N atoms are in blue, green, red, gray and purple, respectively. In the representation of the Mg coordination polyhedra, the O atoms are all connected to P, except when they correspond to water molecules, as explicitly indicated on the figures.

field while the second-order quadrupolar effects are scaled down,66,67 additional static experiments were performed at a much higher magnetic field of 30 T using a resistive magnet to magnify the very weak 25Mg CSA and allow its measurement. However, the presence of external field fluctuations and the remaining magnetic field inhomogeneity actually limits the achievable resolution at 30 T to 20 ppm. In the recorded spectra (see SI Figure S3), no features characteristic of CSA were observed in the spectral singularities, which suggests that the 25Mg CSA in these compounds is very weak and below 20 ppm. The 25Mg CSA was therefore neglected in all simulations of the experimental spectra. The structure of Mg(PO3)2, which is made of alternating layers of four-membered P4O13 rings and edge-sharing MgO6

octahedra, involves two crystallographically inequivalent Mg sites with the same multiplicities (Figure 1).84 As shown in Figure 2a, the 25Mg static and MAS spectra of Mg(PO3)2 exhibit two overlapping resonances with characteristic secondorder quadrupolar powder patterns and relative intensities in a 1:1 ratio, in agreement with the structure. In such case, assignment of the resonances to the Mg crystallographic sites is not straightforward. By considering the distortions of the Mg coordination polyhedral, the 25Mg resonance with the largest quadrupolar coupling constant (δiso = −2 ppm, CQ = 4.62 MHz, ηQ = 0.83) is tentatively assigned to the Mg2 site with the largest bond angle distribution and the remaining one (δiso = −10 ppm, CQ = 3.09 MHz, ηQ = 0.35) assigned to the Mg1 site. 19987



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Figure 2. Experimental (black lines) 25Mg QCPMG static and MAS NMR spectra of (a) Mg(PO3)2, (b) α-Mg2P2O7, and (c) Mg3(PO4)2 and their analytical simulations (dashed red lines).The individual Mg resonances are shown below the experimental and simulated spectra. Top: static spectra recorded at 20.0 T. Middle: static spectra recorded at 17.6 T. Bottom: MAS spectra recorded at 17.6 T with a spinning frequency of 7 kHz. The QCPMG powder patterns were obtained by splitting the QCPMG echo-trains into individual spin−echoes and making the Fourier transform of the sum of the individual echoes.

The structure of Mg3(PO4)2 consists of a 3D framework built of distorted MgO6 octahedra, MgO5 polyhedra, and nearly regular PO4 tetrahedra that are linked together by sharing corners and edges.87 The 25Mg static NMR spectra of Mg3(PO4)2 (in Figure 2c) exhibit well-defined singularities giving evidence of the presence of two overlapping secondorder powder patterns with relatively large quadrupolar coupling constants. In such cases, 25Mg MAS spectra show much more complicated shapes due to the overlap of numerous second-order broadened spinning sidebands.83 On the basis of their relative intensities that are in a 2:1 ratio, the two resonances are unambiguously assigned to the five-fold coordinated Mg1 site with a Wyckoff multiplicity 4 (δiso = 17 ppm, CQ = 7.12 MHz, ηQ = 0.24) and to the six-fold coordinated Mg2 site with a Wyckoff multiplicity 2 (δiso = −4 ppm, CQ = 5.77 MHz, ηQ = 0.43). The structure of synthetic Mg3(PO4)2·8H2O, which involves two inequivalent Mg sites, is built from isolated MgO2(H2O)4 octahedra (Mg1 site with Wyckoff multiplicity 2) and edgesharing MgO4(H2O)2 octahedra forming dimers (Mg2 site with Wyckoff multiplicity 4) linked together by PO4 tetrahedra to form layers parallel to the ac plane (Figure 1).88 The two distinct Mg environments of the structure are clearly evidenced in the 25Mg static and MAS spectra, which show two

The low-temperature phase of the magnesium pyrophosphate, α-Mg2P2O7, contains two inequivalent Mg sites: a sixfold coordinated Mg site and a five-fold coordinated Mg site, with the same Wickoff multiplicities.85 In the structure, the edge-sharing MgO6 and MgO5 polyhedra form sheets parallel to the ab plane, and the bent P2O7 units lie between these sheets (Figure 1).85 The obtained 25Mg NMR spectra clearly show two distinct second-order quadrupolar lineshapes with relative intensities in a 1:1 ratio (Figure 2b). The resonance with a very broad static powder pattern (which splits into numerous overlapping spinning sidebands in the MAS spectrum) is assigned to the distorted MgO5 environment (δiso = 6 ppm, CQ = 12.45 MHz, ηQ = 0.06), and the remaining one with a smaller quadrupolar coupling constant (δiso = −11 ppm, CQ = 4.05 MHz, ηQ = 0.92) is assigned to the more symmetric MgO6 site. The structure of the high-temperature phase β-Mg2P2O7 (α−β phase transition around 70 °C) is in many respects similar to that of α-Mg2P2O7, except that it involves a single six-fold coordinated Mg site and that the P2O7 groups standing between the sheets of MgO6 octahedra are linear (Figure 1).86 As expected, a single resonance (δiso = −6 ppm, CQ = 8.88 MHz, ηQ = 0.07) is observed in the static spectrum recorded in situ at 80 °C (Figure 3a). 19988



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Figure 3. (a) Experimental 25Mg QCPMG static NMR spectrum (17.6 T) of β-Mg2P2O7 recorded at 80 °C (black lines) and its best fit (dashed red line). (b) Experimental 25Mg NMR spectra of Mg3(PO4)2·8H2O recorded using a Hahn echo sequence with 1H decoupling and their best fits (dashed red line). The individual Mg resonances are shown below the experimental and simulated spectra. Top: static at 20.0 T, middle: static at 17.6 T, bottom: MAS at 17.6 T with a spinning frequency of 14 kHz. (c) Experimental 25Mg MAS NMR spectra (spinning frequency of 7 kHz) of NH4MgPO4·6H2O recorded at 17.6 (top) and 9.4 T (bottom) using a Hahn echo sequence with 1H decoupling, and their analytical simulations (dashed red lines).

compounds) seems to be a more pertinent structural indicator than the isotropic chemical shift. To obtain structural information from solid-state NMR parameters, relationships between chemical shifts or quadrupolar coupling constants and simple structural parameters have been deeply investigated.90 For the most commonly observed nuclei in crystalline and disordered inorganic materials (i.e., 29Si, 27Al, 17O, 31P, and so on), numerous empirical correlations between the isotropic chemical shift and structural parameters, like coordination number, average bond length, bond angles, electronegativity of the ligands, or number and nature of second neighbors, for example, have been proposed.90 In the case of magnesium, early studies of minerals31,35,38 have shown that the Mg coordination number has a strong effect on the 25Mg isotropic chemical shift (δiso) and that decreasing the Mg coordination number leads to higher δiso values. This trend is also clearly observed here in the case of the Mg phosphates, the 25Mg δiso values of MgO5 sites being higher than those of MgO6 environments (Figure 4). More recently, the relationship between the 25Mg isotropic chemical shift and the average Mg−O bond length was investigated.52 Indeed, a correlation between the 25Mg δiso and the mean Mg−O distance was reported for sulfates, nitrates, aluminates, and titanates, but this correlation could not be

resonances with very different second-order quadrupolar coupling broadening (Figure 3b). According to their relative intensities, the intense narrow resonance is assigned to the Mg2 site (δiso = 2 ppm, CQ = 1.42 MHz, ηQ = 0.51), whereas the broad resonance of weaker intensity is assigned to Mg1 (δiso = 6 ppm, CQ = 6.65 MHz, ηQ = 0). The 25Mg isotropic chemical shifts and quadrupolar parameters measured for this compound are in good agreement with previously reported values.53 The structure of NH4MgPO4·6H2O (struvite), which is one of the most common biominerals found in human calculi,6 involves a single Mg site coordinated by six water molecules in a distorted octahedron linked to NH4 groups and PO4 tetrahedra by hydrogen bonds.89 As shown in Figure 3c, a single resonance (δiso = 1 ppm, CQ = 3.56 MHz, ηQ = 0.34) is observed in the 1H-decoupled 25Mg MAS NMR spectra recorded at two different magnetic fields in agreement with structural data. Overall, from this experimental study and previously published works,53,58 it appears in this stage that for the various Mg environments found in crystalline phosphates the range of 25Mg δiso extends over ∼30 ppm with CQ values ranging from 1 to ∼13 MHz. Considering this relatively weak 25 Mg isotropic chemical shift range, the quadrupolar coupling constant CQ (which exhibits large variations in the studied 19989



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Figure 4. Evolution of the 25Mg isotropic chemical shift (δiso) as a function of the average Mg−O bond length for the five- and six-fold coordinated Mg sites in phosphates (red triangle). Data for other inorganic compounds for which assignment of the Mg resonances was unambiguous are also shown (open circle).

observed for other inorganics like silicates or for organic compounds.52 In the present case of phosphates, the 25Mg isotropic chemical shift globally decreases as the average Mg−O bond distance increases (Figure 4), in agreement with the trends reported so far for inorganic compounds. However, considering 25Mg NMR data of other inorganic compounds for which the resonance assignment was unambiguous (i.e., Mg(OH)2, MgCO3, MgTiO3, Mg2SiO4, α-MgSO4, β-MgSO4, MgSO4·7H2O, MgWO4, MgMoO4, Mg(NO3)2·6H2O, and αMg2V2O7),52,53 it is clear that the variations of 25Mg δiso are not only driven by changes of the mean Mg−O bond length and that the effect of next-nearest neighbors must be taken into account. The quadrupolar coupling parameters, which are related to the principal components of the electric field gradient (EFG) tensor originating from the deformation of the electronic density around the nucleus, can also provide structural insight. For several nuclei, correlations between the quadrupolar coupling constant (CQ) and the longitudinal strain |α| or shear strain |ψ| parameters have been proposed,90 suggesting that EFGs are dominated by local effects. These two parameters, introduced by Ghose and Tsang91 to quantify the distortion of coordination polyhedra, are defined as |α | =

∑ ln i

|ψ | =

li l0

∑ |tan(θi − θ0)| i

Figure 5. Evolution of the 25Mg quadrupolar coupling constant (CQ) as a function of the longitudinal strain |α| (a) and shear strain |ψ| (b) parameters for the five-fold and six-fold coordinated Mg sites in phosphates (red triangle). Data for other inorganic compounds (MgO6 sites) for which assignment of the Mg resonances was unambiguous are also shown (open circle). Error bars are within the symbols.

mentioned above, which all exhibit only six-fold coordinated Mg sites, were also represented in these plots. Whereas it is observed that the 25Mg quadrupolar coupling constants globally increase with both the longitudinal and shear strains, no clear correlation can be established. Similar trends were also observed by considering other structural parameters, such as the quadratic elongation92 and the bond angle variance which also provide quantitative measure of distortion in coordination polyhedra (SI Figure S4). In agreement with previous work,52,59 this suggests that such relationships relating the 25 Mg quadrupolar coupling constant to the Mg local environment are not yet clear-cut, meaning that the assignment of 25 Mg NMR resonances may actually be erroneous when considering only geometrical features. Therefore, in this stage, simple empirical relationships between the Mg local environment and 25Mg isotropic chemical shift or quadrupolar coupling constant cannot be applied for obtaining accurate structural information in phosphates, or for resonance assignment purposes in compounds containing multiple Mg sites. In such situations, the approach to use to relate experimental solid-state NMR observations to structural information consists

(1)

(2)

where li and l0 are the individual and ideal bond lengths and θi and θ0 the individual and ideal bond angles, the ideal bond length and bond angle being derived from the perfect coordination polyhedron having the same volume as the coordination polyhedron under consideration. The variations of the 25Mg CQ values in magnesium phosphates as a function of the longitudinal and shear strain parameters are shown in Figure 5. (For the five-fold coordinated Mg site, a trigonal bipyramid was considered to be the perfect coordination polyhedron.) The values for the 11 other inorganic compounds 19990



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Table 1. Experimental 25Mg Isotropic Chemical Shifts and Quadrupolar Parameters (CQ, ηQ) of the Magnesium Phosphatesa ICSD codeb

compound Mg(PO3)2

4280

site

δisoExp (ppm)

Mg1

−10(1)

Mg2 α-Mg2P2O7

15326

ηQExp

3.09(4)

0.35(2)

4.62(6)

Mg1

−11(1)

4.05(4)

0.92(2)

Mg2

6(3)

12.45(4)

0.06(4)

22328

Mg1

−6(1)

8.88(2)

0.07(2)

Mg3(PO4)2

31005

Mg1

17(2)

7.12(2)

0.24(2)

202099

NH4MgPO4·6H2O MgHPO4·3H2O

60626 31281

Mg2

−4(2)

5.77(6)

0.43(2)

Mg1

6(2)

6.65(4)

0.00(2)

Mg2

2(1)

1.42(2)

0.51(4)

Mg1

1(1)

3.56(2)

0.34(2)

Mg1

−6.3(2)

e

2.5(1)

e

σisoCalc (ppm)

0.83(2)

β-Mg2P2O7

Mg3(PO4)2·8H2O

a

−2(2)

|CQ|Exp (MHz)c

0.05(5)

e

ES APO ES APO ES APO ES APO ES APO ES APO ES APO ES APO ES APO ES APO ES APO

568.8 568.7 558.1 557.9 571.8 571.0 560.1 559.2 564.2 569.8 548.4 546.8 573.3 571.7 552.1 552.5 559.1 560.4 559.8 562.4 569.2 569.5

δisoCalc (ppm) −6.1d 3.7d −8.2d 2.5d −7.1d 13.8d −8.9d 8.6d 1.4d −0.4d −6.9d

CQCalc (MHz)

ηQCalc

3.81 3.63 −5.48 −5.94 −4.32 −4.48 13.83 13.34 12.77 10.95 7.87 7.85 −7.09 −6.12 −11.45 −5.04 −0.37 3.03 4.39 4.97 2.68 −2.58

0.32 0.39 0.80 0.73 0.89 0.88 0.06 0.09 0.16 0.01 0.50 0.30 0.50 0.48 0.23 0.32 0.88 0.16 0.28 0.37 0.27 0.54

25

DFT-calculated Mg isotropic shielding constant and quadrupolar parameters for both experimental (ES) and DFT-PBE atomic position optimized (APO) structures. The quadrupolar coupling constant (CQ) and asymmetry parameter (ηQ) are defined as CQ = (eQVzz)/h and ηQ = (VYY − VXX)/VZZ, with Vii being the principal components of the EFG tensor defined in the sequence |VZZ| ≥ |VXX| ≥ |VYY|. The quadrupolar moment (Q) of 25Mg was taken from ref 29. bFIZ-NIST Inorganic Crystal Structure Database Version 2011/2. cOnly the absolute value of CQ can be determined from solid-state NMR powder spectra. dCalculated δiso values are deduced from the linear regression (δiso= −0.91σiso + 513) obtained for the APO structures. eExperimental values from ref 53.

slightly higher correlation coefficient (|CQexp| = 0.91|CQAPO| − 0.17, R2 = 0.91). For the APO structures, the three calculated principal components of the EFG tensor are very close to experimental values (|Viiexp| = 0.89|ViiAPO| − 0.01, R2 = 0.93, Figure 6b), leading also to a better agreement between experimental and calculated asymmetry parameter ηQ. Similarly, the geometry optimization step gives rise to an improved correlation between the 25Mg isotropic chemical shifts (δiso) and calculated 25Mg isotropic shielding (σiso). For the APO structures, a relatively good correlation between experimental δiso and calculated σiso values is obtained (R2 = 0.84)

of computing the NMR parameters from structural models using first-principles methods. For this purpose, the PAW74,75 and GIPAW76 methods, which employ the DFT plane-wave pseudopotential formalism, have proven to allow accurate and efficient calculations of the quadrupolar coupling and chemical shift tensors for a wide range of crystalline systems77 including magnesium compounds.52,53,59 Therefore, we have carried out DFT-PBE PAW and GIPAW calculations of the NMR parameters for the six studied magnesium phosphate compounds. The NMR parameters of MgHPO4·3H2O, for which experimental data are available in the literature,53 were also calculated. Calculations were performed for both the ES and the DFT-PBE APO structures for which complete relaxation of the atomic forces was allowed keeping symmetry constraints and fixing the cell parameters to the experimentally determined values. Results of the calculations for the ES and APO structures are summarized in Table 1 together with the experimental values. As shown in Figures 6 and 7, the 25Mg NMR parameters calculated for both the ES and APO structures reproduce nicely the observed experimental trends and fully confirm the proposed resonance assignment. It should be noted that for most of the studied compounds the accuracy of the computed parameters is improved on APO structures. This is clearly illustrated in Figure 6a, where the 25Mg quadrupolar coupling constants calculated for the ES structures are significantly overestimated with respect to experimental CQ value, as indicated by the slope of the calculated linear regression (|CQexp| = 0.70|CQES| + 0.78, R2 = 0.90). This discrepancy between experimental and calculated CQ values is partially solved after geometry optimization of the structures: the slope of the linear regression is much closer to 1 with a

δiso = −0.91σiso + 513

(3)

Taking into account the uncertainties on experimental δiso values (typically from 1 to 3 ppm depending on the extent of the second-order quadrupolar broadening in 25Mg spectra), this correlation is in very good agreement with the relationship recently reported for other inorganic magnesium compounds (δiso= −0.93σiso + 528).53 By applying eq 3 to the 25Mg σiso values calculated for the APO structures, an rms deviation between experimental and “calculated” 25Mg δiso values of 3 ppm is obtained. Considering that the 25Mg isotropic chemical shift covers a range of ∼30 ppm for the magnesium phosphates, this suggests that this equation can be used to predict the 25Mg δiso from the PBE-DFT GIPAW calculations with a quite acceptable accuracy. It should be noted that in the studied compounds, the distinction between Mg sites having close “calculated” isotropic chemical values can be made easily on the basis of the calculated quadrupolar coupling parameters. Therefore, PAW and GIPAW calculations using APO structures can be used to obtain unambiguous assignments of the 25Mg 19991



Article

Figure 7. Experimental 25Mg isotropic chemical shift (δiso) as a function of the isotropic shielding (σiso) calculated for the ES (black open triangles) and APO (red open circles) structures. The black and red dashed lines are the corresponding calculated linear regressions (δiso= −0.90σiso + 508 with R2 = 0.77 for the ES structures and δiso = −0.91σiso + 513 with R2 = 0.83 for the APO structures).

sample recorded at magnetic fields of 17.6 and 20.0 T. Despite the very large number of transient acquired (total experimental time of ∼83 h for each spectrum) and large sample volume studied (see the Experimental Section), the signal-to-noise ratio of the obtained spectra still remains relatively weak. Nevertheless, it is clear that the signal observed for this sample exhibits an asymmetric line shape with a tail on the lowfrequency side, which is characteristic of a distribution of the 25 Mg quadrupolar parameters and thus of the Mg environments. This observation is also consistent with the 25Mg MAS spectrum (5 kHz spinning frequency) previously recorded at a magnetic field of 19.6 T, which also shows the asymmetric line shape typical of disordered materials.10 The best fits of the static spectra recorded at two fields were obtained using the Gaussian isotropic model (GIM, d = 5 case of the Czjzek distribution),98 in which the distribution of the EFG is assumed to correspond to a statistical disorder.99,100 The 25Mg average quadrupolar coupling constant, asymmetry parameter, and isotropic chemical shift determined from the line shape simulations are CQ = 4.5 MHz, ηQ = 0.63, and δISO = 3 ppm. Recently, the incorporation of Mg in the crystallographic Ca(I) or Ca(II) positions of the hydroxyapatite lattice was investigated using a combination of DFT and interatomic potential computations.10 For some of the obtained structural models (which are based on an ordered configuration of the hydroxyl groups in the half-occupied 4e Wyckoff position of the structure), the 25Mg NMR parameters have been calculated using PAW and GIPAW methods.10 For the interatomic potential optimized structural models (1 × 2 × 2 supercell) of a Ca9.75Mg0.25(PO4)6(OH)2 phase, the calculated quadrupolar coupling constants were about 7.5 and 8.6 MHz upon incorporation of Mg in the Ca(I) and Ca(II) sites of hydroxyapatite, respectively.10 Whereas the CQ values calculated for these structural models fall into the broad CQ distribution determined from the simulation of the experimental 25Mg NMR spectra, it is clear that they do not correspond to the average value of the distribution, which also contains much smaller CQ values. The discrepancy between experimental and calculated 25Mg quadrupolar coupling

Figure 6. (a) Calculated 25Mg quadrupolar coupling constant CQ for the experimental (ES, open black triangles) and DFT-PBE atomic position optimized (APO, open red circles) structures versus experimental values. The dashed black (|CQexp| = 0.70 |CQES| + 0.78, R2 = 0.90) and dashed red (|CQexp| = 0.91 |CQAPO| − 0.17, R2 = 0.91) lines are the corresponding linear regressions. (b) Principal components of the EFG tensor (Vii) calculated for the APO structures versus experimental values. The dashed line is the obtained linear regression (|Viiexp| = 0.89 |ViiAPO| − 0.01, R2 = 0.93). In panels a and b, only absolute values were considered because the sign of CQ cannot be determined from NMR powder spectra. Error bars for experimental data are within the symbols.

resonances in complex phosphates having multiple Mg sites. With this in mind, we have computed, after a geometryoptimization step, the 25Mg NMR parameters of three other Mg-phosphates (Mg3(PO4)2·22H2O − (I), Mg3(PO4)2·22H2O − (II), and Mg7(PO4)2(OH)8) containing several distinct Mg sites (SI Table S4).93−95 Therefore, such calculations of the 25Mg isotropic chemical shift and quadrupolar coupling parameters, which can be performed for various structural models, appear to be a method of choice allowing a better understanding of the structural role of Mg in materials of biological interest such as Mg-substituted hydroxyapatite9,10 and octacalcium phosphate,96 or Mgcontaining bioglasses.12,14−17,97 It should be noted that these materials have a relatively low Mg content, which makes challenging the characterization of the Mg environments using natural-abundance 25Mg solid-state NMR. This is illustrated in Figure 8 which shows the natural-abundance 25Mg static QCPMG spectra of a ∼10% Mg-substituted hydroxyapatite 19992



Article

Figure 8. (a) Experimental natural-abundance 25Mg static QCPMG spectra of the Ca9.1Mg0.9(PO4)6(OH)2 sample recorded at magnetic fields of 17.6 and 20.0 T (black lines) and their simulations (red lines). (b) Distribution of the quadrupolar coupling parameters (CQ, ηQ) determined from the simulations of the experimental spectra.

improves significantly the accuracy of the calculations, and good correlations between experimental and calculated 25Mg chemical shifts and quadrupolar coupling constants were obtained, showing that PAW and GIPAW calculations using APO structures can be used to obtain unambiguous assignments of the 25Mg resonances in complex phosphates having multiple Mg sites. Finally, the possibility of recording natural abundance 25Mg NMR spectra in materials with very low Mgcontent has been illustrated for a ∼10% Mg-substituted hydroxyapatite sample. In this case, the measured distribution of CQ was compared with values previously calculated for several structural models. The results suggest that more complex structural models must be developed to improve the understanding of the Ca/Mg substitution on the basis of 25Mg NMR data.

parameters for this sample could be explained considering that: (i) the 25Mg NMR parameters were calculated so far for structural models in which the Mg content is lower than in the sample studied experimentally (such low-substitution models do not account for the whole distribution of Mg environments expected between the different inequivalent Ca sites), (ii) more refined structural models should be developed by taking into account a possible disordered arrangement of the hydroxyl ions within a column or the presence of structural water molecules inside the apatite lattice (as evidenced from 1H MAS NMR spectra10), and (iii) the average 25Mg CQ values and the span of the CQ distribution determined experimentally at natural abundance are likely underestimated because broader components of weaker intensities could hardly be evidenced in spectra with low signal-to-noise ratio. As a result, it appears that both the development of more complex structural models and the use of 25Mg-enriched samples, which would allow recording more reliable experimental data, are necessary to account for the preferential incorporation of Mg in the Ca(II) site of the hydroxyapatite structure previously evidenced from43Ca solidsate NMR.10

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ASSOCIATED CONTENT

S Supporting Information *

Comparison between the Fourier transforms of the QCPMG echo-trains (spikelet-spectra) and the Fourier transforms of the sum of the individual QCPMG echoes. Experimental parameters used to record the 25Mg solid-state NMR spectra. Evolution of the total energy, 25Mg isotropic shielding and quadrupolar coupling constant for β-Mg2P2O7 as a function of the cutoff energy for the plane-wave basis set expansion and the Monkhorst-Pack grid spacing. GIPAW-calculated 25Mg chemical shift anisotropy and quadrupolar coupling parameters for the studied compounds. 25Mg ultrahigh field (30 T) static NMR spectra of Mg(PO3)2, α-Mg2P2O7, and NH4MgPO4·6H2O. Variation of the 25Mg quadrupolar coupling constant as a function of the quadratic elongation and bond angle variance of the Mg coordination polyhedra. Calculated 25 Mg isotropic shielding constant and quadrupolar parameters for both the experimental (ES) and DFT-PBE atomic position optimized (APO) structures of Mg3(PO4)2·22H2O − (I), Mg3(PO4)2·22H2O − (II), and Mg7(PO4)2(OH)8. This material is available free of charge via the Internet at http:// pubs.acs.org.

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CONCLUSIONS In this work, we have recorded at high magnetic fields of 17.6, 20.0, and 30.0 T natural-abundance 25Mg solid-state NMR spectra of several previously unreported magnesium phosphate compounds with known structures. The combination of high magnetic fields and sensitivity enhancement methods allowed 25 Mg NMR spectra with good signal-to-noise ratio to be obtained and the distinct Mg environments in compounds containing multiple Mg sites to be evidenced. The link between the 25Mg NMR data and several local structural parameters has been investigated, and it was found that empirical relationships between such parameters and 25Mg isotropic chemical shift or quadrupolar coupling constant cannot be applied for obtaining accurate structural information. The 25Mg NMR parameters have also been calculated using the DFT PAW and GIPAW methods for both the ES and APO structures. For most of the studied compounds, the DFT geometry-optimization step 19993



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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support from the TGIR RMN THC FR3050 is gratefully acknowledged. The work performed at a magnetic field of 30 T in LNCMI (Grenoble, France) has been supported by EuroMagNET II under the EU contract number 228043. All computations presented in this work have been carried out at the “Centre de Calcul Scientifique en Région Centre” facility (CCRS − Orléans, France) under the CASCIMODOT program. D.L. thanks the seventh European Framework Program for a Marie Curie ERG (# 239206).

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25Mg Solid-State NMR of Magnesium Phosphates: High Magnetic

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