Solid-State 17O NMR Spectroscopy of Hydrous Magnesium Silicates

J. Phys. Chem. C 2009, 113, 465–471

465

Solid-State 17O NMR Spectroscopy of Hydrous Magnesium Silicates: Evidence for Proton Dynamics John M. Griffin,† Stephen Wimperis,*,‡ Andrew J. Berry,§ Chris J. Pickard,| and Sharon E. Ashbrook*,† School of Chemistry and EaStCHEM, UniVersity of St Andrews, North Haugh, St Andrews KY16 9ST, U.K., Department of Chemistry and WestCHEM, UniVersity of Glasgow, Glasgow G12 8QQ, U.K., Department of Earth Sciences and Engineering, Imperial College London, South Kensington SW7 2AZ, U.K., and School of Physics and Astronomy, UniVersity of St Andrews, North Haugh, St Andrews KY16 9SS, U.K. ReceiVed: September 30, 2008; ReVised Manuscript ReceiVed: October 29, 2008

First-principles calculations of 17O quadrupolar and chemical shift NMR parameters were performed using CASTEP, a density functional theory (DFT) code, to try and interpret high-resolution 17O NMR spectra of the humite group minerals hydroxyl-chondrodite (2Mg2SiO4 · Mg(OH)2) and hydroxyl-clinohumite (4Mg2SiO4 · Mg(OH)2), which are models for the incorporation of water within the Earth’s upper mantle. The structures of these humite minerals contain two possible crystallographically inequivalent H sites with 50% occupancy. Isotropic 17O multiple-quantum magic angle spinning (MQMAS) spectra were therefore simulated using the calculated 17O NMR parameters and assuming either a static or dynamic model for the positional disorder of the H atoms. Only the dynamic disorder model provided simulated spectra that agree with experimental 17O MQMAS spectra of hydroxyl-chondrodite and hydroxyl-clinohumite. Previously published 17 O satellite-transition magic angle spinning (STMAS) spectra of these minerals showed significant dynamic line-broadenings in the isotropic frequency dimension. We were able to reproduce these line-broadenings with at least qualitative accuracy using a combination of the same dynamic model for the positional H disorder, calculated values for the change in 17O quadrupolar NMR parameters upon H exchange, and a simple analytical model for dynamic line-broadening in MAS NMR experiments. Overall, this study shows that a combination of state-of-the-art NMR methodology and first-principles calculations of NMR parameters is able to provide information on dynamic processes in solids with atomic-scale resolution that is unobtainable by any other method. Introduction For a number of years, it has been hypothesized that the Earth’s mantle may contain a vast amount of water. Indeed, it is believed that the total amount may be equivalent to, or even more than, that present on the Earth’s surface in the oceans and the atmosphere.1,2 However, the exact mechanism by which this water is stored is not well understood. It is currently thought that defect sites within the nominally anhydrous silicates prevalent in the Earth’s mantle may hold sufficient amounts of structurally bound hydrogen to account for the inner-Earth water budget.1,3-5 Structural studies of these minerals and related compounds, therefore, have important implications in a wider context for understanding the physical and chemical properties of the deep Earth. The high sensitivity of solid-state NMR to the local structural environment makes it a potentially powerful structural probe of inner-Earth materials. The natural samples available are restricted to the upper parts of the Earth’s mantle and also contain significant amounts of iron, thus requiring the prepara* To whom correspondence should be addressed. Tel: +44-1334-463779. Fax: +44-1334-463808. E-mail: [email protected] (S.E.A.), Tel: +44141-3308284. Fax: +44-141-3304888. E-mail: [email protected] (S.W.). † School of Chemistry and EaStCHEM, University of St Andrews. ‡ Department of Chemistry and WestCHEM, University of Glasgow. § Department of Earth Sciences and Engineering, Imperial College London. | School of Physics and Astronomy, University of St Andrews.

tion of synthetic analogues for NMR studies. To date, several experimental NMR studies have provided structural insight into a range of synthetic materials based on silicate minerals that are present naturally in the Earth’s mantle.6-13 However, the synthesis of many of these materials for the purpose of NMR studies can be very challenging. The low natural abundances of the NMR-active nuclei 17O (I ) 5/2) and 29Si (I ) 1/2) mean that isotopic enrichment is usually required for enhancement of the NMR signal. Furthermore, the high pressures (15-20 GPa) that are required to synthesize some phases of particular relevance to the Earth’s interior greatly restrict the amount of sample that can be produced. Thus, even with isotopic enrichment of synthetic samples, the inherently poor sensitivity can often hinder the acquisition of solid-state NMR spectra from which useful structural information can be extracted. In view of the practical and experimental difficulties associated with solid-state NMR of deep-Earth minerals, the calculation of NMR parameters from first-principles can provide a valuable complementary tool for interpreting experimental data and gaining additional structural insight. There has been much recent interest in the calculation of NMR parameters using the gauge including projector augmented wave (or GIPAW)14 approach, within planewave, pseudopotential, density functional theory (DFT) codes such as CASTEP,15 which exploit the periodicity of crystalline solids. This approach has already seen widespread application to a diverse range of materials.16-19 In the study of deep-Earth materials, we have implemented this

10.1021/jp808651x CCC: $40.75  2009 American Chemical Society Published on Web 12/05/2008

466 J. Phys. Chem. C, Vol. 113, No. 1, 2009 approach for the calculation of 29Si and 17O NMR parameters in three polymorphs of Mg2SiO4, which is the principal compositional component to a depth of 660 km, namely forsterite (R-Mg2SiO4), wadsleyite (β-Mg2SiO4), and ringwoodite (γ-Mg2SiO4).20 This provided confirmation of NMR parameters extracted from experimental spectra as well as an unambiguous resonance assignment. More recently, the same approach was applied to the polymorphs of MgSiO3, the second most abundant chemical phase, where calculations led to the reassignment of previously obtained experimental spectra and enabled the further investigation of empirical correlations between NMR parameters and local structure.13 However, applications of GIPAW calculations to the study of deep-Earth materials have so far been limited to anhydrous silicate polymorphs. For insight into mechanisms of water incorporation in these materials, it is desirable to study hydrous silicates that have been suggested as models for hydrogenbearing defect sites within the anhydrous bulk. However, the increased complexity of these materials can lead to computational complications. First, the larger unit cells required to describe the crystal structures fully lead to increased calculation times and more demanding computational hardware requirements. A second, and perhaps more pertinent, consideration is that of the disorder and even dynamics that may be expected to be present within hydrous materials. While the success of the GIPAW approach has, to a large extent, been due to the efficient way in which the periodic nature of rigid crystalline systems is exploited, this property also presents intrinsic difficulties for directly modeling systems that display nonperiodic or nonrigid characteristics such as site occupancy disorder and/or dynamic exchange within the crystal structure. Nevertheless, with experimental data and suitable motional models, it can be feasible to utilize computational approaches to gain a more detailed insight into the structure and dynamic processes in such systems. In this work, we demonstrate this approach for two members of the hydroxyl-humite group, a series of minerals that provide possible models for the encapsulation of water at defect sites within forsterite.21 Specifically, we compare NMR spectra that have been simulated with calculated NMR parameters with existing 17O multiple-quantum (MQ)MAS NMR22 and satellitetransition (ST)MAS NMR23,24 experimental results,10,25 to gain insight into the structure, order, and dynamics within hydroxylchondrodite (2Mg2SiO4 · Mg(OH)2) and hydroxyl-clinohumite (4Mg2SiO4 · Mg(OH)2). (For simplicity, these minerals are hereafter referred to simply as chondrodite and clinohumite.) The calculated results are found to reproduce well the 17O MQMAS NMR experimental data, and further analysis leads to a better understanding of the peak broadenings observed in the 17O STMAS NMR spectra. For clinohumite, the calculations also suggest a refinement of a previous assignment of the experimental 17O NMR spectra. Experimental and Computational Details Full experimental details for the 17O MQMAS and STMAS spectra reproduced in this work are given in refs 10 and 25. Spectra were acquired at a magnetic field strength of B0 ) 9.4 T (17O Larmor frequency ν0 ) 54.2 MHz). Powdered chondrodite and clinohumite (35% enriched in 17O) were packed in 4 mm rotors, and MAS rates in the range of 7.5 to 8 kHz were used. Calculations of NMR parameters were carried out using the CASTEP15 density functional theory code, employing the gauge including projector augmented wave (GIPAW)14 algorithm,

Griffin et al. which allows the reconstruction of the all-electron wave function in the presence of a magnetic field. The generalized gradient approximation (GGA) PBE26 functional was employed, and core-valence interactions were described by ultrasoft pseudopotentials.27 A planewave energy cutoff of 50 Ry (680 eV) was used, and integrals over the Brillouin zone were performed using a k-point spacing of 0.05 Å-1. Atomic positions and unit-cell parameters were obtained from experimental neutron diffraction crystal structures;28,29 however, prior to calculation of the NMR parameters full geometry optimizations were performed within the CASTEP program (also using a cutoff energy of 50 Ry and k-point spacing of 0.05 Å-1), with both the lattice parameters and internal atomic coordinates allowed to vary. Calculations were performed on the EaStCHEM Research Computing Facility, which consists of 136 AMD Opteron processing cores, partly connected by Infinipath high speed interconnects. Calculation times typically ranged from 5 to 12 processor hours using 4 cores. Calculations generate the absolute shielding tensor (σ) and electric field gradient (EFG) tensor (V) in the crystal frame. From these, the isotropic chemical shift, δiso, is given by -(σiso - σref), where σiso, the isotropic shielding, is (1/3) Tr{σ}. A reference shielding, σref, of 249.8 ppm was used for 17O. This was determined by minimizing the differences between experimental and calculated isotropic shifts from a range of silicate materials both from this work and previous work.12 The magnitude (CQ ) eQVZZ/h) and asymmetry (ηQ ) (VXX - VYY)/ VZZ) of the quadrupolar interaction are generated from the principal components of the EFG tensor. A quadrupole moment, eQ, of -25.6 mB was used for 17O. Although the sign of CQ is often difficult to determine experimentally, the signs of calculated CQ values are included in our tabulated data. Using the chemical shift and quadrupolar NMR parameters obtained from the calculations, 17O MQMAS (mI ) +3/2 T -3/2) and STMAS (mI ) (1/2 T (3/2) isotropic NMR shifts, δ1, can then (using the shift conventions outlined in refs 24 and 30) be calculated:

δ1 )

17 32 δ + δ 31 iso 93 Q

(1)

where δiso is the isotropic chemical shift and δQ is the secondorder quadrupolar shift parameter (in ppm) for spin I ) 5/2, given by

δQ )

(75CQ)2(1 + η2Q ⁄ 3) ν20

(2)

Results and Discussion Hydroxyl-Humite Minerals. Hydroxyl-humite take the general form nMg2SiO4 · Mg(OH)2. The structure may be described simplistically as n forsterite-like layers that alternate with layers of brucite (Mg(OH)2). The structures of forsterite (Mg2SiO4), chondrodite (n ) 2), and clinohumite (n ) 4) are shown schematically in Figure 1, with the three, five, and nine crystallographically inequivalent oxygen species labeled. The hydroxyl oxygens are O5 in chondrodite and O9 in clinohumite. Diffraction studies for chondrodite and clinohumite have revealed two distinct H sites for each hydroxyl group,28,29,31 denoted H1 and H2 (part a of Figure 2). The hydroxyl protons (or alternatively deuterons) are shared among H1 and H2 with a 50% average occupancy of each site. Adjacent H1 sites are separated by a distance of only 1 Å, meaning that simultaneous occupancy of two such H1 sites is a highly unstable configuration. Thus, if an H1 site is occupied, the proton of the nearest hydroxyl neighbor must occupy the H2 site. However, if an

Hydrous Magnesium Silicates

Figure 1. Crystal structures of (a) forsterite Mg2SiO4, (b) hydroxylchondrodite 2Mg2SiO4 · Mg(OH)2, and (c) hydroxyl-clinohumite, 4Mg2SiO4 · Mg(OH)2. Oxygen and magnesium atoms are shown in red and green respectively, with shading indicating height within the crystal structure. SiO4 groups are represented by blue tetrahedra. Unit cells are denoted by dashed lines, and oxygen atoms are numbered in accordance with the crystallographic literature.

H2 site is occupied, the nearest H neighbor can (in principle) occupy H1 or H2. Within a single unit cell (and maintaining a 50% occupancy over this small scale) this would lead, therefore, to four possible combinations of hydroxyl group arrangements, which are represented for the case of chondrodite in part b of Figure 2. Chondrodite and clinohumite have already been the focus of an experimental solid-state NMR study, where 29Si MAS NMR and 17O three-quantum and five-quantum MAS NMR experiments were used to resolve and assign 29Si and 17O sites.10 While distinct silicate oxygen species, which are all nonbridging, could be resolved by MQMAS, in a subsequent 17O STMAS NMR study of the same materials, considerable broadening of some of the spectral resonances was observed in the isotropic (δ1) dimension.25 It was shown that this originates from dynamic processes within the solid that cause changes in the first-order quadrupolar splitting, which interferes with the ability of MAS to average this interaction efficiently in the experiment.25,32 This effect is not observed in MQMAS NMR experiments because, unlike satellite transitions, multiple-quantum transitions are unaffected to first-order by the quadrupolar interaction. Whereas an exact mechanism for the dynamics observed in chondrodite and clinohumite has not been determined, it was postulated that the hydroxyl protons may undergo exchange between the H1 and H2 sites, that is, a dynamic rather than a static disorder.25 Proton occupancy of either site results in structures with very similar energies,33 and the two H sites show larger isotropic displacement parameters in diffraction experiments, suggesting more significant motion relative to other

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Figure 2. Views of the crystal structure of hydroxyl-chondrodite showing (a) the two possible proton positions H1 and H2 that are associated with each hydroxyl group and (b) the four possible hydroxyl group proton arrangements that are possible within a single unit cell.

atoms in the structure. While this suggestion does not involve movement of the nonprotonated oxygen atoms themselves, such changes in the local environment will produce a modulation of the 17O EFG and, hence, of the quadrupolar coupling as well as of the 17O chemical shift parameters. To investigate the nature of the disorder in these materials, CASTEP calculations of NMR parameters were performed for both chondrodite and clinohumite and repeated for each of the four possible hydroxyl group arrangements. Thus, for each material, four sets of 17O NMR parameters were obtained, which were then compared with the experimental 17O MQMAS and STMAS NMR data from previous studies. It should be noted that fixing the H positions within the unit cell results in a lowering of the symmetry and produces 20 and 36 distinct O species for chondrodite and clinohumite, respectively (as opposed to the 5 and 9 species found in the original crystal structures). Interpretation of 17O MQMAS NMR Spectra of HydroxylHumites. We consider first the interpretation of the experimental isotropic 17O MQMAS NMR spectra10 of chondrodite and clinohumite, which are reproduced in part a of Figure 3. For chondrodite, we see four resonances with intensity ratio 1:1:1: 1, although the two central peaks are barely resolved. These correspond to the four distinct silicate oxygen species. The hydroxyl oxygen (O5) was not observed owing to its larger quadrupolar coupling constant and the relatively slow MAS rate employed. For clinohumite, the spectrum consists of five resonances with intensity ratio 2:2:2:1:1, in order of decreasing δ1 shift. It is thought these peaks correspond to the eight distinct nonbridging oxygens predicted, with three doubly intense peaks as a result of spectral overlap. As with chondrodite, the hydroxyl oxygen (O9) is not observed.

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Griffin et al.

Figure 3. (a) Experimental10 and (b, c) calculated 17O (9.4 T) isotropic MQMAS (mI ) +3/2 T -3/2) NMR spectra of hydroxyl-chondrodite (top) and hydroxyl-clinohumite (bottom). In (b), the spectrum results from summation of the 17O isotropic spectra calculated for each oxygen within the unit cell for each of the four proton arrangements shown in part b of Figure 2, whereas in (c), the mean value of the four sets of calculated isotropic shifts was used for each oxygen species in the unit cell.

TABLE 1: Experimental10 and Calculated 17O NMR Parameters (Isotropic Chemical Shift (δiso), Quadrupolar Coupling Constant (CQ), Asymmetry (ηQ), and MQMAS/STMAS Isotropic Shift at B0 ) 9.4 T (δ1)) for Hydroxyl-Chondrodite and Hydroxyl-Clinohumitea δiso (ppm)

ηQ

CQ/MHz

site

exptl

calcd

exptl

O1 O2 O3 O4 O5

63(1) 59(2) 60(2) 52(1)

63.2 57.6 59.4 50.9 14.3

2.5(1) 2.3(1) 2.3(1) 2.7(1)

O1 O2 O3 O4 O5 O6 O7 O8 O9

49(1) 64(1) 58(1) 61(1) 53(1) 64(1) 61(1) 58(1)

45.8 63.0 58.3 59.9 50.3 63.2 60.3 58.0 14.5

2.7(1) 2.5(1) 2.4(1) 2.4(1) 2.8(1) 2.5(1) 2.4(1) 2.4(1)

calcd

δ1 (ppm)

exptl

calcd

exptl

calcd

Chondrodite -2.7 -2.5 -2.4 -2.9 -7.6

0.3(1) 0.3(1) 0.2(1) 0.2(1)

0.28 0.16 0.10 0.06 0.18

40(1) 36(1) 37(1) 34(1)

39.5 35.6 36.5 33.6 46.9

Clinohumite -3.0 -2.7 -2.5 -2.5 -3.0 -2.6 -2.5 -2.4 -7.6

0.3(1) 0.3(1) 0.3(1) 0.2(1) 0.2(1) 0.3(1) 0.2(1) 0.3(1)

0.24 0.37 0.15 0.15 0.06 0.34 0.14 0.17 0.18

31(1) 40(1) 37(1) 38(1) 34(1) 40(1) 38(1) 37(1)

31.1 39.4 36.0 37.0 33.3 39.5 37.2 35.8 46.7

a Calculated parameters are the mean of those resulting from the four different arrangements of the hydroxyl groups shown in part b of Figure 2.

Using the four sets of calculated NMR parameters for each compound, isotropic 17O MQMAS NMR projections were simulated assuming either static or dynamic disorder of the hydroxyl protons. First, we consider the case of static disorder, such that the crystal structure is made up of equal proportions of unit cells with each of the four structures described in part b of Figure 2, and assume that the hydroxyl group arrangement within a particular unit cell does not change. In this case, isotropic 17O MQMAS NMR projections for chondrodite and clinohumite were calculated after the summation of the four sets of isotropic shifts and are shown in part b of Figure 3. Comparing these to the experimental 17O MQMAS NMR spectra, it is immediately apparent that the agreement between the two sets of data is very poor. In both cases, the models predict many more peaks than are observed in the experimental spectra, even discounting the O5 and O9 hydroxyl species. Experimentally, only one resonance is observed for each group of four nominally equivalent oxygen sites in each unit cell. However, in the calculated spectra, additional peaks are observed

as the oxygen species are now all inequivalent and experience different local environments as a result of the various hydroxyl group arrangements. The differences result in changes to the NMR parameters that are large enough to produce significantly different isotropic shifts. We now consider the case of fast interchange of the hydroxyl protons between the H1 and H2 sites, with a rate constant that is large compared with the different 17O isotropic shifts that result from the interchange of the proton positions. In this case, each oxygen will exhibit only a single isotropic shift, which we assume to be the arithmetic mean of the shifts calculated for the four different hydroxyl group arrangements (assuming all are equally likely). Mean NMR parameters obtained for one of each type of crystallographically distinct oxygen species calculated in this manner are shown in Table 1. These show good agreement with values extracted from experimental 17O MQMAS NMR spectra recorded in previous work (also shown in Table 1). Isotropic MQMAS projections simulated using the mean values for each oxygen species in the unit cell (20 for

Hydrous Magnesium Silicates

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chondrodite and 36 for clinohumite) are shown in part c of Figure 3. In contrast to the spectra resulting from the summation of the calculated results, there is remarkably close agreement with the experimental data (again, neglecting the hydroxyl oxygens O5 and O9 in chondrodite and clinohumite, respectively) and the experimentally observed 17O isotropic shifts are reproduced well by the calculations. This indicates that the hydroxyl disorder is dynamic, resulting in the observation of average NMR parameters in the MQMAS experiment. For chondrodite, the simulated spectrum shows four separate peaks, which can be associated with the silicate oxygens O1-O4 (with the two central peaks appearing closely spaced). The calculations support the previous assignment of the resonances (as O4, O2, O3, and O1 in order of increasing δ1 shift). This assignment was achieved from the experimental spectrum by comparing the local structure and NMR parameters of the oxygen species in chondrodite to those in forsterite and by exploiting the empirical relationship that the 17O chemical shift, δiso, tends to increase as the Si-O bond length increases.10-13 For clinohumite, the shifts and relative intensities of the peaks in the simulated spectrum are also consistent with those observed experimentally. However, the previous tentative assignment10 of the experimental spectrum is not in agreement with the calculated isotropic shifts. Specifically, the calculated spectrum shows two resonances assigned to (O4, O7) and (O3, O8) at 37 and 36 ppm, respectively. In the previous experimental study, the peak at higher ppm was assigned to (O3, O4), whereas that at lower ppm was assigned to (O7, O8).10 It was suggested that O3 and O4 in clinohumite might be expected to exhibit a similar isotropic shift to the O3 site in forsterite due to their similar local environments. However, the isotropic 17O MQMAS (9.4 T) NMR spectrum calculated for forsterite (shown in the Supporting Information) reveals that there is a 1.4 ppm frequency difference between the O3 sites in clinohumite and those in forsterite. Instead, O7 in clinohumite is found to exhibit an isotropic shift similar to that of the O3 species in forsterite, leading to an overlap of the O4 and O7 resonances. Interpretation of 17O STMAS NMR Spectra of HydroxylHumites. Unlike the MQMAS spectra, the published experimental 17O STMAS spectra of chondrodite and clinohumite display considerable broadening of some or all of the resonances.25 This phenomenon has been attributed to motional broadening of the satellite transitions caused by a reorientation or other change in the EFG tensor, V, resulting in a sudden jump, ∆νJ, in the quadrupolar splitting. If the rate constant for the molecular-scale dynamics, k, is comparable to ∆νJ, very significant broadening of the satellite transitions can occur. To accurately model the effect of H1-H2 exchange on the 17 O STMAS (mI ) (1/2 T (3/2) NMR spectra, it is necessary to consider how changes in CQ, ηQ, and the EFG tensor orientation contribute to motional broadening of the satellite transitions. For a single crystallite orientation, the splitting between the (1/2 T (3/2 quadrupolar satellite transitions and the central transition is equal to 2νQ. A change in the magnitude and/or orientation of the quadrupolar tensor will lead to a new splitting 2νQ′. The quadrupolar splitting parameter, νQ, is given by

νQ ) νQPAS[D20,0(R, β, γ) +

ηQ

√6

2 (R, β, γ)+D20,2(R, β, γ))] (D0,-2

(3) where D2m′,m(R, β, γ) is a rank l ) 2 Wigner rotation matrix element describing the orientation of the principal axis system

(PAS) of the EFG tensor in the laboratory frame in terms of Euler angles R, β and γ, and νQPAS is the quadrupolar splitting parameter in the PAS:

νQPAS )

3CQ 4I(2I - 1)

(4)

with spin I ) 5/2 for 17O. As m′ ) 0 in eq 3, νQ is a function of just two angles, β and γ. To calculate the splitting parameter, νQ′, for a tensor that changes its orientation, eq 3 can be expanded in terms of two successive rotations using 2

2 Dm’,m (R, β, γ) )

2 2 (R1, β1, γ1)Dn,m (R2, β2, γ2) ∑ Dm’,n

(5)

n)-2

where the Euler angles (R2, β2, γ2) relate the PAS of the EFG tensor in its first orientation to the PAS of the tensor in its second orientation and (R1, β1, γ1) relate this to the laboratory frame. The frequency jump, ∆νJ, is therefore

∆νJ ) 2νQ′ -2νQ

(6)

where νQ is a function of νQPAS, ηQ, β1, and γ1, whereas νQ′ is a function of the Euler angles relating the two tensors, R2, β2, and γ2, in addition to the new quadrupolar parameters νQPAS’ and ηQ′, and also β1 and γ1. In a powdered solid, there will be a distribution of ∆νJ values due to the dependence on the angles β1 and γ1 and so we will consider the root-mean-square (RMS) frequency jump

∆νrms )

√∫

2π

γ1)0

∫βπ)0 (∆νJ)2sin β1dβ1dγ1 ⁄ ∫γ2π)0 ∫βπ)0 sin β1dβ1dγ1(7) 1

1

1

as an appropriate mean of the powder distribution. ∆νrms is thus a function of the quadrupolar parameters before and after the frequency jump (CQ, ηQ and CQ′, ηQ′, respectively), and the relative orientation of the two EFG tensors is described by the Euler angles R2, β2, and γ2.34 For each silicate oxygen species in chondrodite and clinohumite, the rms frequency jumps, ∆νrms, due to H1-H2 rearrangement were obtained by evaluating eq 7 numerically by powder averaging over 360 β1 angles and 720 γ1 angles. All quadrupolar parameters were obtained from the CASTEP calculations described in the previous section, and Euler angles describing the relative quadrupolar tensor orientation were calculated from eigenvectors obtained directly from the CASTEP output. RMS frequency jumps were calculated for each of the six possible rearrangements of the hydroxyl protons shown in Figure 2, that is, rearrangements (1 T 2), (1 T 3), (1 T 4), (2 T 3), (2 T 4), and (3 T 4). The average value of these frequency jumps was then used as a representative value, thereby making the assumption that all possible rearrangements were equally likely. For each crystallographically distinct oxygen, the average value for the four species in the unit cell was then calculated. The results are shown in part a of Figure 4 for each of the oxygen species in chondrodite (red squares) and clinohumite (blue diamonds). Comparison of the calculated rms frequency jumps with the crystal structures reveals that O sites closest to the hydroxyl groups (namely O1 and O2 in chondrodite and O6 and O8 in clinohumite) appear to be influenced most, as predicted in ref 25, with the largest frequency jumps in the range of 16-20 kHz. Other sites in these same silicate tetrahedra, namely O3 and O4 in chondrodite and O5 and O7 in clinohumite, exhibit slightly lower values between 8 and 14 kHz. The smallest rms frequency jumps, between 2 and 6 kHz, were calculated for sites O1, O2, O3, and O4 in clinohumite,

470 J. Phys. Chem. C, Vol. 113, No. 1, 2009

Griffin et al. a single frequency jump, ∆νJ. Subsequent work on this spinecho model has, through comparison with exact numerical simulations, demonstrated the validity of this intentionally simplistic approach in both fast- and slow-MAS regimes, particularly if the value of the rms frequency jump ∆νrms is used for ∆νJ.35 Using the calculated rms frequency jumps in part a of Figure 4, this method was used to predict satellite-transition motional broadening (shown as log10(∆ν1/2ST)) as a function of k for each oxygen site in the two minerals, shown in parts b and c of Figure 4. As in previous work,35 an underlying homogeneous contribution to the line width (of 50 Hz) was also included. Variable-temperature 17O MAS NMR experiments on chondrodite showed line narrowing at higher temperatures, suggesting that at ambient temperatures the rate constant for H1-H2 interchange is to the right of the apex of the plotted functions in Figure 4.25 In view of this, isotropic STMAS NMR projections were simulated for both solids for log10(k/s-1) ) 5.0, 5.5, 6.0, 6.5, and 7.0 by applying a fwhh of iso ∆ν1⁄2 )

Figure 4. (a) rms jump in (mI ) (1/2 T (3/2) satellite-transition frequency for each type of silicate oxygen species in hydroxylchondrodite (red) and hydroxyl-clinohumite (blue), assuming all four hydroxyl arrangements are equally likely. (b, c) Log-log plots of the motionally broadened (mI ) (1/2 T (3/2) satellite-transition line width ∆ν1/2ST (including an underlying line width of 50 Hz) as a function of rate constant, k, for the average rms frequency jumps in (b) hydroxylchondrodite and (c) hydroxyl-clinohumite.

which lie in silicate groups within a forsterite-like layer furthest from the hydroxyl groups. This analysis of calculated frequency jumps can be extended further to obtain an estimate for the rate constant, k, of the H1-H2 exchange process. In the previous NMR study of chondrodite and clinohumite,25 it was shown that motional broadening in MAS NMR spectra can be modeled by an approach that approximates MAS as a train of spin echoes and powder-averaged dynamics by a two-site exchange process with

24 ST 7 ∆ν + ∆νCT 31 1⁄2 31 1⁄2

(8)

where ∆ν1/2ST is the motionally broadened satellite-transition homogeneous line width plotted in parts b and c of Figure 4 (including the underlying broadening of 50 Hz) and ∆ν1/2CT is the central-transition homogeneous line width, which we also assume to be 50 Hz.24 The simulated isotropic projections are shown in Figure 5, with the experimental projections also reproduced for comparison. For both chondrodite and clinohumite, close agreement between the experimental and simulated projections is obtained for log10(k/s-1) ≈ 5.5, corresponding to a rate constant of k ≈ 3.2 × 105 s-1 at 294 K. This reproduces well the approximate ratios of peak intensities and line widths observed in the experimental clinohumite spectrum in part b of Figure 5. In particular, the broadening of the (O3, O8) peak causes an unresolved shoulder on the resonance assigned to (O4, O7), as observed experimentally. Furthermore, the considerable broadening of the O5 peak relative to the O1 peak explains its apparent absence in the experimental clinohumite spectrum. Conclusions For chondrodite and clinohumite, simulated isotropic 17O MQMAS NMR projections based on calculated parameters show that site occupancy disorder of the hydroxyl protons is not static in nature at room temperature. Instead, using a model that assumes fast interchange between the proton sites H1 and H2 on the time scale of the isotropic shift differences, isotropic NMR spectra simulated using mean 17O parameters calculated

Figure 5. Experimental25 and simulated 17O (9.4 T) isotropic STMAS (mI ) (1/2 T (3/2) NMR spectra of (a) hydroxyl-chondrodite and (b) hydroxyl-clinohumite. Line widths in the simulated STMAS isotropic projections were calculated using satellite-transition line widths, ∆ν1/2ST, extracted from parts b and c of Figure 4 at different values of log10(k/s-1) and ∆ν1/2CT ) 50 Hz.

Hydrous Magnesium Silicates for unit cells with different hydroxyl proton arrangements show close agreement with previous experimental isotropic 17O MQMAS NMR data. The calculated NMR parameters were further analyzed to give an insight into peak broadenings observed in a 17O STMAS NMR study of the same materials. Under the assumption that this broadening is due to H1-H2 exchange, powder-averaged differences in the quadrupolar splitting between oxygen sites in unit cells with different hydroxyl arrangements were determined using NMR parameters obtained directly from the CASTEP calculations. A previously described simple analytical model for estimating line broadening due to motional effects in MAS spectra was then used to obtain estimates of the line widths for different rate constants. Isotropic 17 O STMAS NMR projections were simulated using these estimated values; simulated spectra using line widths calculated for rate constants of ∼3.2 × 105 s-1 were in good agreement with experimental spectra previously obtained. This work demonstrates the complex effects that dynamics can produce in solid-state NMR spectra and highlights the role calculations can play in gaining insight into spectral interpretation, particularly for quadrupolar nuclei, where the quadrupolar broadening can hinder detailed analysis of simple MAS spectra. Despite the inherent requirement for the calculation approach to be applied to periodic, ordered systems, we have shown how the consideration of NMR parameters calculated for simplified model systems can be used to elucidate the nature of the disorder and motional processes present. While variable-temperature static 2H NMR experiments have perhaps been the method of choice in the past for studying 1H dynamics in simple systems, spectral analysis can become complicated if a number of distinct species are present, as a result of the overlap of the quadrupolarbroadened lineshapes. We have shown here that isotropic 17O NMR spectra (and indeed those of other half-integer quadrupolar nuclei) also appear to be a useful probe of dynamics, even for species that at first sight appear remote from any significant structural changes. In addition to the extraction of more quantitative information, this work provides a warning that the interpretation and analysis of apparently simple NMR spectra should be undertaken with care in systems where motion and disorder are possible complications. We believe, therefore, that the combination of high-resolution NMR (using a combination of experiments) with state-of-the-art first-principles calculations offers exciting possibilities for the future investigation and understanding of complex and disordered systems. Acknowledgment. We are grateful to EPSRC for the award of Grant No. EP/E041825 and to the research councils for an RCUK Academic Fellowship to S.E.A. We would also like to thank Miss Caroline Pringle for her assistance with some of the calculations. This work has also made use of the resources provided by the EaStCHEM Research Computing Facility (http://www.eastchem.ac.uk/rcf). This facility is partially supported by the eDIKT initiative (http://www.edikt.org).

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