Unambiguous Description of the Oxygen Environment in

Article pubs.acs.org/JPCC

Unambiguous Description of the Oxygen Environment in Multicomponent Aluminosilicate Glasses from 17O Solid State NMR Computational Spectroscopy Alfonso Pedone,* Elisa Gambuzzi, and Maria Cristina Menziani Dipartimento di Chimica, Università di Modena e Reggio Emilia, Via G. Campi 183, 41125 Modena, Italy S Supporting Information *

ABSTRACT: Classical molecular dynamics simulations, density functional theory calculations, and spin-effective Hamiltonians have been used to simulate the 17O MAS and 3QMAS NMR spectra of Ca−Na silicate and aluminosilicate glasses and melts employed as simplified models for basaltic, andesitic, and rhyolitic magmas. The direct comparison of the theoretical NMR spectra of molecular dynamics derived structural models with the experimental counterparts available in the literature has allowed the investigation of the nature of nonframework cation mixing and the extent of intermixing among framework units in Na−Ca aluminosilicate glasses. In particular, in agreement with previous experimental evidence, the results show a nonrandom distribution of the network-modifying Ca and Na in soda-lime glasses with the prevalence of dissimilar Na−Ca pairs around nonbridging oxygens. The oxygen sites are not completely resolved in the MAS spectra of the aluminosilicate glasses. On the contrary, in the 17O 3QMAS spectra the multiple oxygen sites, in particular the Si−O−Si, Al−O−Al, Al−O−Si, and the nonbridging oxygen peaks, are distinguishable. The small amount of Al−O−Al sites found in the investigated glasses reveals that the Al avoidance rule is not respected in amorphous solids. The Si−O−Al sites are surrounded by Na ions, which play a preferential role as a charge-balancing cation, while Ca can act as a network-modifying cation. Finally, correlations between the structural characteristic and the values of the NMR parameters have been attempted with the aim of helping the interpretation of NMR spectra of glasses with similar compositions.

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INTRODUCTION It is well-known that geological processes, such as the generation, migration, and dynamics of magmas, are affected by the macroscopic properties of the constituent melts. For example, the viscosity of the magma is an important factor in determining whether a volcanic eruption will be explosive or nonexplosive. A low-viscosity magma, like basalt, will allow the escaping gases to migrate rapidly through the magma and escape to the surface. However, if the magma is viscous, like rhyolite, its high polymerization will impede the upward mobility of the gas bubbles. As gas continues to exsolve from the viscous melt, the bubbles will be prevented from rapid escape, thus increasing the overall pressure on the magma column until the gas ejects explosively from the volcano.1 Therefore, the macroscopic thermodynamic (e.g., crystalmelt partitioning coefficients, activity coefficients of silica) and transport properties (e.g., viscosity and diffusivity) of aluminosilicate glasses and melts, which are strongly dependent on the atomic and nanoscale structures of these systems, have major implications in geological science, stimulating numerous experimental and theoretical studies of glass structure.2−7 The structure of alkali or alkaline-earth aluminosilicate glasses has since long been understood in terms of a threedimensional connected structure of framework units, [SiO4]4− and [AlO4]5− tetrahedra, linked at the corners by bridging © 2012 American Chemical Society

oxygen (BO) atoms. Nonframework cations such as Ca and Na can act as either charge-balancing or network-modifying cations, depending on the ratio between the CaO and/or Na2O and the Al2O3 molar concentrations. The addition of modifier oxides to silica glass leads to the formation of nonbridging oxygens (NBOs) decreasing the extent of polymerization. Despite the importance of aluminosilicate glasses in geochemical science, their structure has not been well understood because geological glasses are multicomponent systems with a significant extent of topological and chemical disorder. Various important aspects of disorder include the nature of mixing of Ca/Na around NBO and the effect of Ca/ Na atoms on the degree of Al avoidance (mixing of Si and Al), the degree of polymerization, and the preferential bonding of the network-modifying cations to Si−NBO or Al−NBO bonds. An additional important type of disorder in Ca−Na aluminosilicate glasses is the possibility of preferential partitioning of nonframework cations between the NBO and BO (in particular, BO in the Si−O−Al unit), and the elucidation of the structural role played by Ca and Na as network-modifying or charge-balancing cations.3 Solid state Received: May 17, 2012 Revised: June 15, 2012 Published: June 15, 2012 14599

dx.doi.org/10.1021/jp304802y | J. Phys. Chem. C 2012, 116, 14599−14609

The Journal of Physical Chemistry C

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Table 1. Compositions (mol %) of the Glasses and Number of Atoms (N) for the Models Used mol % CS NS CSN NAS CAS CASN

SiO2

Al2O3

Na2O

CaO

NSi

NAl

NNa

NCa

NO

50 75 60 78 60 60

− − − 11 20 10

− 25 20 11 − 10

50 − 20 − 20 20

120 180 162 183 141 150

− − − 51 90 51

− 80 108 51 − 51

120 − 54 − 51 51

360 240 432 468 468 453

homemade packages, recently developed by Charpentier.17,19,31 This procedure has been recently employed to reproduce, for the first time, the MAS and triple quantum MAS (3QMAS) NMR solid state spectra of spin active nuclei for binary silicate17,32 and multicomponent aluminosilicate,33 phosphosilicate,18 and fluorine-containing glasses.34 The aim of the present work is to obtain an unambiguous view of the local structures around oxygen atoms in calcium silicate (CS), sodium silicate (NS), and calcium−sodium silicate (CSN) glasses with compositions of CaO·SiO2, Na2O·3SiO2, and CaO·Na2O·3SiO2, respectively, and calcium aluminosilicate (CAS), calcium−sodium aluminosilicate (CNAS), and sodium aluminosilicate (NAS) glasses with molar compositions of 20CaO·20Al2O3·60SiO2, 20CaO·10Na2O·10Al2O3·60SiO2, and 11Na2O·11Al2O3·78SiO2, respectively, which are probably among the most important and essential components of island-arc volcano eruptives.35,36 In the following sections, the theoretical solid state spectra of soda-lime silicate and aluminosilicate glasses will be compared with the experimental ones available in the literature with the aim of validating the molecular dynamics (MD) derived threedimensional structural models. Once validated, the threedimensional structural models will be employed to interpret the NMR spectra in terms of the nature of the nonframework disorder in soda-lime glasses and the extent of the framework disorder in aluminosilicate glasses.

NMR spectroscopy of 17O in aluminosilicate glasses is one of the most important tools for obtaining new important information on the structure from the “anionic” point of view; this constitutes a valuable complement to the more traditional investigation of cation coordination and connectivity.8−11 Dynamic angle-spinning (DAS), double rotation (DOR), or multiquantum magic-angle-spinning (MQMAS) NMR techniques have been used to resolve and distinguish peaks for bridging oxygens linking Si and Al as well as nonbridging oxygens.3,12−15 Although experiments of this kind allow a high resolution in crystalline materials, the chemical and topological disorder present in glasses and melts makes the interpretation difficult.16 In the past the interpretation of the spectra was based primarily on empirical correlations derived from the study of crystalline materials with known structures, but recent advances in theoretical calculations of NMR parameters have proved to be very helpful in interpreting the spectra of glasses.17−19 Earlier theoretical investigations were carried out on small molecular clusters using atomic orbital basis sets.20,21 Nevertheless, it was soon demonstrated that the accuracy of the cluster approach in reproducing NMR observables of threedimensional extended systems is limited by the size of the cluster and the treatment of the electrostatic interactions, especially in ionic solids.20,22 Moreover, in the special case of amorphous materials, this approach does not account for the correlations between structural factors that exist in solids and disorder in glasses. The introduction of effective methods specially devised to calculate NMR parameters in extended systems described within periodic boundary conditions, plane wave basis sets, and density functional theory23,24 have solved most of the aforementioned problems. In this framework, chemical shifts and electric field gradients can be obtained from first principles with the gauge including projector augmented-wave (GIPAW) and the projector augmented-wave (PAW) methods, respectively.23,24 These methods are able to deal with large systems (up to hundreds of atoms) and exhibit an outstanding accuracy, as demonstrated recently for various crystalline and amorphous solids.19,24−28 However, in the case of oxide glasses and melts, the calculation of NMR parameters is not always enough for a direct comparison with experimental observables, since the latter ones are usually derived from the empirical fitting of the NMR spectra, which are composed of several overlapping subspectra of the different structural units present in the glass.29,30 A possible way out for a direct comparison between theory and experiments, and thus for a detailed interpretation of solid state spectra aided by computer experiments, is to employ the computed NMR parameters to model the whole spectra by means of a spin-effective Hamiltonian encoded in

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COMPUTATIONAL DETAILS The computational protocol employed to simulate solid state NMR spectra consists essentially of three steps: (i) Classical molecular dynamics (MD) simulations are employed to generate the structural models of the glasses of interest. (ii) Periodic DFT calculations coupled with the gauge including projector augmented-wave (GIPAW) algorithm form the basis for the ab initio calculations of NMR parameters (chemical shielding and quadrupolar parameters). (iii) Spin-effective Hamiltonians encoded into the homemade package named fpNMR developed by Charpentier17,31 are employed to simulate the solid state spectra directly comparable with the experimental counterparts. Glass Generation. Three structural models for each glass composition reported in Table 1 were generated by means of classical molecular dynamics simulations. A shell model potential37,38 was used to include polarization effects by taking into account the large polarizability of the oxygen ions. In this model the total charge Z of the oxygen ions is split between a core (of charge Z + Y) and a massless shell (of charge −Y) which are coupled by a harmonic spring. Besides the damped harmonic interaction with the corresponding core, the oxygen 14600



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Figure 1. Computed 17O MAS and 3QMAS spectra of NS, CS, and CSN glasses. The spectra of the different O sites are highlighted in color. The experimental 17O MAS spectra taken from the literature are also reported for the NS2 and CS15 glasses. Modifier cations surrounding BOs are reported in square brackets, while those surrounding NBOs are in parentheses.

shells interact with each other and with Si, Al, Ca and Na cations through a short-range Buckingham term, whereas Coulombic forces act between all species which bear full formal charges. Three-body screened harmonic potentials are used to control the intra-tetrahedral O−Si−O and O−Al−O angles during dynamics. The complete potential model and the parameters used39 are reported in Table S.1 of the Supporting Information. The leap-frog algorithm encoded in the DL_POLY package40 has been used to integrate the equation of motions with a time step of 0.2 fs, i.e., small enough to control the high frequency motion of the core−shell spring during MD simulations.41 The initial configurations were generated by placing randomly the number of atoms reported in Table 1 in a cubic box, whose dimension allows the experimental density to be reproduced. The systems were heated and held at 3200 K for 100 ps in the NVT ensemble, ensuring a suitable melting of the samples. The liquids were then cooled to 300 K at a nominal cooling rate of −5 K/ps. The resulting glass structures were subjected to a final equilibration run of 200 ps.7,42,43

The main issue with this technique is that the short time and length scales of current computer simulations require cooling rates which are several orders of magnitude greater than the rates achieved experimentally.44,45 The significant effect of quench rate and temperature on framework ordering in aluminosilicate melts has been deeply discussed in the literature.46,47 Although simulated glass structures have glass transition temperatures significantly higher than the actual one, the information obtained on glass structures and geological melts are of primary importance. This is because the structure observed on a glass represents that of the liquid at its transition temperature. Since the computational glass transition temperatures are higher than the experimental ones, it is possible to predict properties (for example, viscosity or solid−liquid phase equilibria) of melts with relatively cheap costs instead of using expensive high temperature NMR experiments. NMR Parameter Calculation. Geometry optimization of the classical MD-derived structural models and subsequent NMR calculations were carried out with the CASTEP48 density functional theory (DFT) code using the GIPAW23 algorithm, which allows the reconstruction of the all-electron wave 14601



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Table 2. Computed NMR Parameters and Population of the NBO Speciation in the CSN Glass Obtained from MD Simulations and Random Distribution of Na and Ca Cations around Oxygena

a

NBO species

δiso [ppm]

CQ [MHz]

ηQ

MD site pop.

random site pop.

Si−NBO(Na) Si−NBO(1Na) Si−NBO(2Na) Si−NBO(3Na) Si−NBO(4Na) Si−NBO(Ca) Si−NBO(1Ca) Si−NBO(2Ca) Si−NBO(3Ca) Si−NBO(Ca,Na) Si−NBO(1Ca,1Na) Si−NBO(1Ca,2Na) Si−NBO(1Ca,3Na) Si−NBO(1Ca,4Na) Si−NBO(2Ca,1Na) Si−NBO(2Ca,2Na) Si−NBO(3Ca,1Na)

47.4(8.5) − 54.1(7.0) 47.7(7.4) 43.7(9.9) 107.6(16.0) 89.7 105.4(18.5) 113.9(8.7) 83.8(16.7) 85.0(14.3) 75.6(10.3) 70.1(15.3) 83.3(8.6) 100.5(12.3) 83.4(8.9) 114.2(18.0)

2.57(0.27) − 2.78(0.13) 2.57(0.23) 2.67(0.31) 2.73(0.28) 2.62 2.75(0.31) 2.69(0.27) 2.74(0.31) 2.70(0.24) 2.71(0.29) 2.66(0.31) 2.37(0.72) 2.85(0.33) 2.65(0.29) 2.91(0.02)

0.38(0.18) − 0.25(0.15) 0.43(0.17) 0.31(0.20) 0.39(0.21) 0.35 0.43(0.24) 0.35(0.19) 0.32(0.17) 0.33(0.20) 0.31(0.14) 0.44(0.19) 0.36(0.07) 0.28(0.16) 0.33(0.18) 0.26(0.20)

7.2 − 0.9 4.2 2.1 4.6 0.2 2.8 1.6 37.9 5.1 15.7 4.6 0.2 11.1 1.0 0.2

15.5 0.1 4.0 9.8 1.6 2.4 0.1 1.0 1.3 30.7 3.8 13.4 3.2 0.0 7.2 2.3 0.8

Standard deviations are given in parentheses.

function in the presence of a magnetic field. The generalized gradient approximation (GGA) PBE49 functional was employed, and the core−valence interactions were described by ultrasoft pseudopotentials (PP) generated on the fly.50 For 17O, the 2s and 2p orbitals were considered as valence states with a core radius of 1.3 au; for 29Si and 27Al, core radii of 1.8 au and 2.0 au, respectively, were used with 3s and 3p valence orbitals; for 23Na, a core radius of 1.3 au was used with 2s, 2p, and 3s valence orbitals; for 43Ca, a core radius of 1.6 au was used with 3s, 3p, and 4s valence states. For the PAW and GIPAW calculations, we used two projectors in each s and p angular momentum channel for O, and in the s, p, and d channels for Si, Al, and Ca. To reproduce well the Ca chemical shielding, the Ca PP was modified by shifting the 3d orbitals of 3.2 eV as previously proposed by Profeta et al.25 This is necessary because it has been demonstrated that, in the PBE approximation, the energy of Ca 3d orbital is too low and the hybridization with the 2p orbitals of oxygen and fluorine is overestimated.34 As a consequence, the 17O chemical shifts computed with PBE are affected by very large errors (up to 124 ppm) for O sites close to Ca atoms. Before computing the NMR parameters, constant pressure geometry optimizations of the classical generated models were performed at the Γ point.51 Wave functions were expanded in plane waves with the kinetic energy cutoff of 700.0 eV; this has been demonstrated to be long enough to reach energy and NMR chemical shift converged values.17,52 In this work, the δiso of 17O was evaluated using the shielding reference (σref) of 260.5 ppm obtained with α-cristobalite while the quadrupolar coupling constant was evaluated by employing the experimentally determined quadrupolar moment, eQ, of 25.58 mB.53 The aforementioned approach is a common procedure in ab initio calculations of glasses which enables only short-range relaxations at the ab initio level, whereas the medium-range structure is “frozen” to the initial configuration obtained by classical MD. However, several papers have demonstrated that the present approach is adequate to study the local structure, such as the coordination environment of ions in bioactive glasses,54,55 as

well as important vibrational features 56−58 and NMR parameters.18,32,34 The simulation of the solid state MAS and 3QMAS NMR spectra from the CASTEP outputs has been carried out by means of the software fpNMR.17,31

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RESULTS AND DISCUSSION Cation Distribution around Oxygen Atoms in Na−Ca Silicate Glasses. Figure 1 reports the simulated 17O MAS and 3QMAS spectra at 14.1 T of the CS, NS, and CSN glasses, together with the available experimental counterparts for the glasses CS and NS, taken from the literature.2,15 The excellent agreement between the theoretical 17O MAS NMR and experimental spectra validates the structural models obtained by MD simulations, allowing the inference of relationships between structural data and NMR response. The theoretical 17O MAS and 3QMAS spectra for the different oxygen speciation present in the MD simulations derived three-dimensional models of the glasses studied show that the oxygen atoms at the Si−O−Na sites are more shielded (peak about 25 ppm, Figure 1a) than the ones at the Si−O−Ca site (peak maximum about 100 ppm, Figure 1c). Thus, the signals of the Si−O−Na and Si−O−Si sites are overlapped, while the signals of the Si−O−Ca and Si−O−Si ones lie in different zones of the MAS spectra. All these peaks are well resolved in the theoretical 3QMAS spectra; thus their detection is straightforward. Both the MAS and 3QMAS spectra show that the spread of the chemical shift distribution of NBO in the NS glass is smaller than that of the NBO in the CS glass, indicating that Ca is found around oxygen in a more disordered arrangement with respect to the Na atoms. Moreover, a wide distribution of chemical shifts of NBOs belonging to the Si−O−Na and Si− O−Ca sites is observed in the CSN glass, since the peak positions of the mixed Si−O−(Na,Ca) sites move toward higher chemical shifts as the Ca content around oxygen increases. Albeit not all the oxygen sites are distinguishable in the MAS spectra of the NS and CS glasses, they are better resolved in the 3QMAS spectra. Conversely, as for the CSN glass, the simulated 17O 3QMAS spectrum reported in Figure 14602



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Table 3. Computed NMR Parameters and Population of the BO Speciation in CSN Glass Obtained from MD Simulations and Random Distribution of Na and Ca Cations around Oxygena

a

BO species

δiso [ppm]

CQ [MHz]

ηQ

MD site pop.

random site pop.

Si−BO−Si(Na) Si−BO−Si(1Na) Si−BO−Si(2Na) Si−BO−Si(3Na) Si−BO−Si(Ca) Si−BO−Si(1Ca) Si−BO−Si(2Ca) Si−BO−Si(Ca,Na) Si−BO−Si(1Ca,1Na) Si−BO−Si(1Ca,2Na) Si−BO−Si(1Ca,3Na) Si−BO−Si(2Ca,1Na) Si−BO−Si

63.7(7.7) 62.6(7.5) 64.6(7.3) 69.0(10.3) 72.8(10.1) 72.8(10.1) − 72.2(8.4) 72.4(9.5) 72.5(4.4) 65.8 74.8 59.8(10.7)

5.05(0.45) 5.09(0.45) 5.03(0.43) 4.74(0.60) 5.02(0.49) 5.02(0.49) − 4.65(0.42) 4.70(0.45) 4.39(0.29) 4.93 4.36 5.27(0.49)

0.37(0.18) 0.37(0.18) 0.37(0.18) 0.38(0.22) 0.46(0.22) 0.46(0.22) − 0.50(0.19) 0.50(0.19) 0.51(0.30) 0.41 0.49 0.27(0.15)

35.7 20.4 14.1 1.2 5.6 5.6 − 4.4 3.2 0.7 0.2 0.2 4.6

25.9 17.4 7.8 0.6 10.6 8.6 1.9 9.1 7.6 0.9 0.1 0.5 4.6


4.4 and 5.2%, respectively; therefore, BOs prefer to be surrounded by sodium ions rather than by calcium. The results reported in Table 3 also highlight that, as a consequence of the interaction between the network-modifying cations and the bridging oxygen network, the isotropic chemical shift of BOs increases with the number of Na or Ca ions within the first coordination sphere of the oxygens. The most common environments around NBO and BO, that is, the Si−NBO(1Ca,2Na) 15.7%, Si−NBO(2Ca,1Na) 11.1%, Si−BO−Si[1Na] 20.4%, and Si−BO−Si[2Na] 14.1% sites, are shown in Figure S.1 of the Supporting Information. Cation Distribution around Oxygen Atoms in Na−Ca Aluminosilicate Glasses. Figure 2 reports the theoretical 17O MAS NMR spectra of the three aluminosilicate glasses studied,

1f shows that the Si−O−(Na,Ca) signals completely overlap with the Si−O−Ca and Si−O−Na ones; therefore, a direct fitting of the experimental spectrum without the help of constraints derived from NMR calculations is more difficult.18 The computed mean NMR parameters (δiso, CQ, ηQ) and the population of the NBO and BO sites present in the CSN MDgenerated glass model are reported in Tables 2 and 3, respectively. The MD oxygen site populations are compared to those calculated for a random distribution of Na and Ca around oxygen atoms. As already highlighted, the isotropic chemical shift of NBO atoms decreases with the number of Na cations around the oxygens, whereas it increases with the amount of Ca cations. Table 2 also shows that, on average, the structural models investigated contain a majority of NBO coordinated to Ca and Na in a mixed state. The total amount of Si−NBO(Na,Ca) sites is 37.9%, while the NBOs coordinated to only Na or Ca species amount to 7.2 and 4.6%, respectively, of the total oxygen atoms present. The amount of Si−NBO(Ca,Na) sites is higher than that predicted by employing a random distribution of cations around NBO (30.7%), whereas the amount of Si−NBO(Na) sites is lower than that predicted by a random distribution (15.5%), and the amount of Si−NBO(Ca) sites is higher than that predicted by a random distribution (2.4%). Therefore, these results clearly indicate that there is extensive mixing of Ca and Na around NBO in soda-lime silicate glasses. The strong tendency for the formation of dissimilar cation pairs observed for the CSN glass is probably due to the very similar ionic radii of Ca and Na. In fact, previous studies on Ba−Mg59 and K−Li60 silicate glasses have shown that larger differences in ionic radii increase the site mismatch energy, thus contributing to the marked ordering around NBO. However, the achievement of a homogeneous distribution of charges in the glass can also play an important role in the formation of dissimilar pairs. The nonrandom distribution of Ca and Na ions in silicate glasses affects the dynamics of Na+ and the related transport properties.42,61 Conversely, a detailed characterization of the environment of the BO sites, whose different populations are reported in Table 3, shows that the population of BOs surrounded by sodium (Si−BO−Si[Na]) within a cutoff of 3.2 Å is 35.7% in the present MD three-dimensional structural models, whereas those of the Si−BO−Si[Ca,Na] and Si−BO−Si[Ca] sites are

Figure 2. Theoretical 17O MAS NMR spectra at 14.1 T for NAS, CAS, and CNAS glasses. The spectra of the different O sites are highlighted in color. The experimental 17O MAS spectra taken from the literature are also reported for the NAS5 and CAS14 glasses. 14603



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Figure 3. Theoretical 17O 3QMAS NMR spectra at 14.1 T for CAS, CNAS, and NAS glasses. The spectra of the different O sites are highlighted in color.

the whole 17O MAS and 3QMAS spectra, have been reported in previous studies, and it will be not detailed here.21,33 However, it is worth recalling that the NMR parameters of the OAl2Si and OAlSi2 sites fall in the same range covered by those of the Si− O−Si and Si−O−Al sites, and since these triclusters are present in the glass in very small quantities, it is very unlikely that 17O MAS and 3QMAS NMR spectroscopies could detect them. Conversely, the NMR parameters of the OAl3 triclusters fall close to the edge of the main Si−O−Al peak, and their position is found to be in nice agreement with experimental evidence.14 Figure 2c shows that the large peak between 110 and 60 ppm in the 17O MAS spectra of the CNAS glass stems from different types of NBOs (Si−NBO−Ca and Si−NBO−(Ca,Na)). Regarding the BO sites, Figure 2 also shows that there is a significant overlap among the Si−O−Si, Si−O−Al, and Al−O− Al peaks in the 17O MAS spectra, a fact that makes it difficult to quantify the fractions of oxygen sites and explore the effect of composition on the topological disorder in the Si−O−Al sites from experiments alone. The 17O 3QMAS spectra, reported in Figure 3, show better resolved multiple oxygen sites. In particular, the 17O 3QMAS spectra of the NAS and CNAS glasses show that the contributions provided by the Si−O−Si, Si−O−Al and Al− O−Al sites are well separated, while the Si−O−Al spectrum is overlapped with those of Si−O−Si and Al−O−Al for the CAS glass. The ordering of framework Si and Al cations in aluminosilicate glasses can be deduced by comparing the number of T−O−T bridges (T = Al/Si) obtained by MD simulations and the site populations provided by a random distribution of Al and Si around BOs (see Table 4), recalling

together with the contributions of the different oxygen speciation found in the MD-derived structural models. The overall shape of the spectra well reproduces the experimental ones available in the literature for the NAS5 and CAS14 glasses and reported for validation purposes. Both the CAS and NAS glasses have a tectosilicate composition, in which the [CaO]/[Al2O3] and [Na2O]/ [Al2O3] ratios are equal to 1. Therefore, in accordance with the compensated continuous random network model of aluminosilicate glasses these systems should reach maximum polymerization, and no NBO and three bridging oxygen (TBO) species should be detected. However, MD simulations show an incomplete polymerization of both glasses and the presence of NBOs in the system. At the same time, to preserve the total number of Al−O and Si−O bonds, the presence of NBO is compensated by TBO species, in agreement with previous high resolution 3QMAS NMR14 and viscosity measurements62 carried out on similar compositions. A detailed analysis of the relative amount of such tricluster sites shows that CAS and NAS glasses contain 4.9 and 1.7% TBO, respectively. Thus, higher field strength cations promote the formation of NBO and TBO because of the competition for low-coordinate environments with respect to lower field strength cations. In fact, Ca prefers to be coordinated by NBO than by BO in its first coordination shell.63 Interestingly, in agreement with experimental evidence,64,65 all the NBOs are associated with Si atoms rather than Al ones. This is observed also for the CNAS glass, whose composition allows NBO to be present in the structure. However, in this case no TBOs have been found in the MD-derived structural models. The characterization of the TBOs in terms of NMR parameters, and their contributions to 14604



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that when the ratio is equal to 1 the network framework cations are randomly distributed.

Table 6. BO Site Populations Obtained from MD Simulations and Computed NMR Parameters of CNAS Glassa

Table 4. BO Site Populations of the CAS, CNAS, and NAS Glasses Derived from MD Simulations and a Random Distribution of Al and Si Connected to the Central Oxygena CAS

CNAS

BO species Si−BO−Si [all] Si−BO−Si(Na) Si−BO−Si(1Na) Si−BO−Si(2Na) Si−BO−Si(Ca) Si−BO−Si(1Ca) Si−BO−Si(2Ca) Si−BO−Si(Ca,Na) Si−BO− Si(1Ca,1Na) Si−BO−Si(nc) Si−O−Al [all] Si−BO−Al(Na) Si−BO−Al(1Na) Si−BO−Al(2Na) Si−BO−Al(Ca) Si−BO−Al(1Ca) Si−BO−Al(2Ca) Si−BO−Al(Ca,Na) Si−BO− Al(1Ca,1Na) Si−BO−Al Al−O−Al [all] Al−BO−Al(Na) Al−BO−Al(1Na) Al−BO−Al(2Na) Al−BO−Al(Ca) Al−BO−Al(1Ca) Al−BO−Al(2Ca) Al−BO−Al(Ca,Na) Al−BO− Al(1Ca,1Na)

NAS

site

MD

random

MD

random

MD

random

Si−O−Si Si−O−Al Al−O−Al

0.28 0.54 0.06

0.36 0.48 0.16

0.36 0.38 0.04

0.44 0.29 0.05

0.57 0.38 0.01

0.61 0.34 0.05

a

In the latter calculation, it has been assumed that Al and Si cations are four-coordinated and that the total amount of BO is that given by the glass compositions.

In glasses where the number of Si−O−Al sites is lower and the number of Si−O−Si sites is higher than that obtained for a random distribution, the tendency toward clustering among framework units is more pronounced and phase separation can occur. However, this is not the case for the glasses studied here because the amount of Si−O−Al sites is always higher than the random one, thus denoting an extensive mixing of these framework units which has important implications for the macroscopic properties of magmas. The results of this study also show that the ratio between Al−O−Al sites derived by means of the MD simulations and a random distribution is higher for CAS (0.38) than NAS (0.20) glasses, denoting that higher field cations (Ca vs Na) tend to promote disorder. In the 17O 3QMAS spectra of the CNAS glass reported in Figure 3, the contributions of the BO[Na], BO[Ca,Na], and BO[Ca] sites are highlighted. These are located in slightly different regions of the whole spectrum because of the increase of the isotropic chemical shift with the number of Ca atoms in the first coordination sphere. The NMR parameters of the NBO and BO sites found in the CNAS glass and the relative populations of the different sites are reported in Tables 5 and 6, respectively. The corresponding data values for CAS and NAS glasses are reported in the Supporting Information.

a

site pop.

δiso [ppm]

CQ [MHz]

ηQ

Si−NBO [all] Si−NBO(Na) Si−NBO(2Na) Si−NBO(3Na) Si−NBO(Ca) Si−NBO(1Ca) Si−NBO(2Ca) Si−NBO(3Ca) Si−NBO(Ca,Na) Si−NBO(1Ca,1Na) Si−NBO(1Ca,2Na) Si−NBO(2Ca,1Na)

22.2 0.4 0.2 0.2 8.1 0.4 5.7 2.0 13.7 5.7 2.9 5.1

97.5(18.7) 65.7(15.1) 76.3 55.0 110.8(16.7) 100.6(12.0) 111.3(17.9) 111.9(14.3) 90.6(14.7) 86.6(12.0) 81.6(10.7) 100.3(14.5)

2.74(0.30) 2.25(0.22) 2.09 2.41 2.77(0.28) 2.68(0.18) 2.78(0.26) 2.75(0.38) 2.75(0.31) 2.78(0.28) 2.71(0.38) 2.73(0.30)

0.35(0.19) 0.41(0.19) 0.28 0.55 0.34(0.16) 0.46(0.23) 0.35(0.17) 0.30(0.14) 0.36(0.20) 0.32(0.18) 0.33(0.14) 0.41(0.24)

a

δiso [ppm]

CQ [MHz]

ηQ

36.3 16.0 13.6 2.4 8.4 8.2 0.2 1.5 1.5

65.1(12.3) 63.2(10.8) 63.3(10.3) 62.8(14.0) 74.9(11.9) 74.6(12.0) 84.4 75.6(4.6) 75.6(4.6)

5.00(0.56) 5.01(0.53) 5.02(0.57) 5.01(0.26) 4.66(0.43) 4.68(0.42) 3.94 4.36(0.61) 4.36(0.61)

0.43(0.23) 0.42(0.21) 0.44(0.21) 0.33(0.18) 0.60(0.22) 0.59(0.22) 0.62 0.65(0.18) 0.65(0.18)

10.4 38.0 17.1 13.8 3.3 10.8 10.4 0.4 3.3 3.3

58.6(9.6) 50.0(11.3) 44.9(7.3) 45.2(7.4) 43.8(7.2) 58.8(9.0) 58.3(8.8) 69.8(5.7) 60.5(9.2) 60.48(9.21)

5.35(0.41) 3.64(0.47) 3.69(0.41) 3.69(0.44) 3.70(0.31) 3.45(0.45) 3.45(0.45) 3.44(0.33) 3.37(0.44) 3.37(0.44)

0.27(0.16) 0.48(0.24) 0.43(0.21) 0.44(0.21) 0.38(0.20) 0.62(0.22) 0.63(0.21) 0.41(0.37) 0.61(0.21) 0.61(0.21)

6.8 3.5 1.8 0.9 0.9 1.3 1.1 0.2 0.4 0.4

43.9(11.5) 45.4(21.4) 30.7(11.8) 35.3(14.8) 26.1(7.2) 65.8(17.7) 65.8(19.8) 66.3 43.1(7.6) 43.1(7.6)

3.95(0.46) 2.06(0.38) 2.13(0.57) 2.18(0.31) 2.09(0.82) 2.04(0.36) 2.11(0.34) 1.67 1.84(0.40) 1.84(0.40)

0.31(0.20) 0.59(0.21) 0.53(0.26) 0.43(0.25) 0.62(0.25) 0.63(0.15) 0.64(0.16) 0.56 0.71(0.06) 0.71(0.06)


The analysis of the data listed in Tables 5 and 6 also reveals that for both NBO and BO species the isotropic chemical shift decreases with the number of Na cations and increases with the number of Ca ones. The quadrupolar coupling constant CQ is about 2.8 MHz for NBOs, 5 MHz for Si−BO−Si sites, 3.6 MHz for Si−BO−Al sites, and 2.1 MHz for Al−BO−Al sites. In the case of BOs, the CQ value of BO sites surrounded by only Na cations is higher than the one of BOs surrounded by only Ca cations, which in turn is higher than that of BOs coordinated in a mixed Na−Ca state. Therefore, these different types of O sites occupy well-defined regions of the (CQ,δ) space and are distinguishable in the 3QMAS spectra as demonstrated in Figure 3. Moreover, since the 3QMAS efficiency decreases at lower magnetic fields where the larger CQ sites (i.e., 5 MHz) are largely suppressed, experiments at low magnetic fields can selectively emphasize the NBO and Al−BO−Al sites with CQ values of about 2 MHz. A detailed analysis of the CNAS structural models reveals that, similarly to soda-lime silicate glasses, there is a considerable extent of mixing between Ca and Na around NBOs (13.7% Si−NBO(Ca,Na)). However, in general, the NBOs are not coordinated by Na ions, which instead prefer to compensate the negative charge excess of the Si−O−Al sites (17.1%) or surround Si−BO−Si sites (16%). The geometric

Table 5. NBO Site Populations Obtained from MD Simulations and Computed NMR Parameters of CNAS Glassa NBO species

site pop.

Standard deviations are given in parentheses. 14605



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Figure 4. Isotropic chemical shift of BO and NBO as a function of average Si−BO, Si−NBO, and M−NBO (M = Na/Ca) for NS, CS, and CSN glasses.

constant CQ and asymmetry parameter ηQ upon the Si−O−Si angle. Commonly used relationships are

configurations of the most populated oxygen sites are depicted in Figure S.2 of the Supporting Information. Correlations between 17O NMR Parameters and Local Geometry. Another interesting feature of NMR computational spectroscopy is the possibility of correlating the computed parameters with the local environment, that is, bond length, angles, and coordination numbers. The finding of accurate and simple quantitative structure−NMR parameter relationships would be immensely useful from both the experimental and computational points of view. In the former case, new insights into the atomic structure of multicomponent glasses could be gained from the extraction of the NMR parameter distributions,66 while, in the latter case, the NMR spectra of different glass structural models containing thousands of atoms could be straightforwardly calculated by skipping time-consuming ab initio calculations. For these reasons, several structural−NMR parameter correlations have been proposed and attempted in the past. The dependence of 17O NMR parameters upon the Si−O−Si bond angle and Si−O bond distance has been extensively studied with ab initio calculations on clusters67−69 and periodic6,31,32,70 silicate models. From these papers, a linear correlation between the Si−BO average bond length and the 17O δiso of BO and a linear correlation between the M−NBO (where M stands for modifier) average bond length and the isotropic chemical shift of NBOs were obtained, while no correlation was found between the isotropic chemical shift of NBO and the Si−NBO bond lengths.6,32 Moreover, several relationships have been proposed in order to describe the dependence of the BO quadrupolar coupling

α ⎛1 cos θ ⎞⎟ C Q (θ ) = A ⎜ + + ΔCQ ⎝2 cos θ − 1 ⎠

(1)

β ⎛1 cos θ ⎞⎟ ηQ (θ ) = B⎜ − + ΔηQ ⎝2 cos θ − 1 ⎠

(2)

where θ = . Other analytical forms such as cos θ and θ polynomials were also investigated but did not yield any significant improvement for predicting the NMR parameters. All these correlations have been obtained in vitreous silica and binary silicate glasses. In Figure 4, the 17O isotropic chemical shift of BOs and NBOs has been plotted as a function of the average Si−BO, Si−NBO, and M−NBO (M = Na and/or Ca) bond lengths for the NS, CS, and CSN glasses investigated in this work. Moreover, the 17O CQ, ηQ, and δiso of BOs plotted as a function of the Si−O−Si bond angles are presented in Figure 5. Both figures show poorer correlations with respect to those reported for vitreous silica and binary soda silicate glasses, where a correlation coefficient R of about 0.7−0.8 and standard deviations of about 0.15−0.20 MHz for CQ and 0.1 for ηQ were found.19,31 In this work, the quadrupolar parameters (CQ, ηQ) have been fitted by using eqs 1 and 2, also providing R values in the range 0.7−0.8, but the dispersion of the data is higher, with the standard deviations of about 0.2−0.3 MHz for CQ and 0.14 for ηQ. The isotropic chemical shift was found to be predicted poorly using the short-range information provided 14606



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Figure 5. NMR parameters of BOs as a function of Si−O−Si angle for NS, CS, and CSN glasses.

This might be considered a validation of the structural models obtained by MD simulations and demonstrates the reliability of the approach used, allowing the extension of the study to the analysis of the theoretically derived MAS and 3QMAS NMR spectra in terms of the nature of the nonframework disorder in soda-lime glasses and the extent of framework disorder in aluminosilicate glasses. The results clearly indicate that there is extensive mixing of Ca and Na around NBOs in soda-lime silicate glasses. In fact, the amount of Si−NBO(Na,Ca) sites, 37.8% of the total oxygen atoms present, is higher than that predicted by employing a random distribution of cations around NBO, whereas the amount of NBO coordinated to only one of the Na or Ca species (7.2 and 4.6%, respectively) is lower. This peculiar cation distribution leads to an increase in the viscosity of silicate melts over that predicted from a random distribution, as found in literature.4 The MD-derived three-dimensional structures of aluminosilicate glasses in tecto-aluminosilicate compositions, such as in the CAS and NAS glasses, present an excess of NBOs which are compensated by O triclusters. The latter are not present in the CNAS glass studied in this work. A detailed analysis of the relative amount of such tricluster sites show that CAS and NAS glasses contain 4.9 and 1.7% TBO, respectively. Thus, higher field strength cations promote the formation of NBO and TBO because of the competition for low-coordinate environments with respect to lower field strength cations. Instead, all the NBOs present in the three glasses are associated with Si atoms rather than Al ones. Moreover, an extensive mixing of framework units is observed in the CNAS glass, since the amount of Si−O−Al

by the Si−O−Si angle and Si−O distance; therefore, it seems to be sensitive to variation of structure beyond the first coordination sphere.22 Similarly, no simple correlations could be found for the isotropic chemical shift and T−O (T = Al/Si) bond lengths of aluminosilicate glasses. In Figure 6, the calculated quadrupolar couplings CQ and asymmetry parameter ηQ are depicted as a function of the T− O−T angle for each O atom. In both cases, it is difficult to extract a clear dependence of quadrupolar parameters on the T−O−T angle even if a rough trend can be detected. The CQ values tend to increase as a function of the angles and to be larger for the Si−O−Si sites than for the Si−O−Al ones. The dotted lines represent the best fit obtained by employing eqs 1 and 2. However, no correlations have been found for aluminosilicate glasses. It is worth noting that in a previous study very good correlations between the Si−O−Si angle and 17 O NMR parameters were obtained.67 However, according to our results, these correlations appear to be an artifact due to the use of small clusters which are not able to represent the chemical and topological disorder present in multicomponent glasses.

■

CONCLUSIONS Classical molecular dynamics simulations have been used to generate structural models of soda-lime silicate and aluminosilicate glasses of geological relevance. The theoretical 17O MAS spectra computed by employing DFT/GIPAW calculations and spin-effective Hamiltonians are found to be in excellent agreement with the experimental data available in the literature for the NS, CS, NAS, and CAS glasses. 14607



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Figure 6. NMR quadrupolar parameters of BO as a function of T−O−T angle for NAS, CAS, and CNAS glasses.

obtained from MD simulations. This material is available free of charge via the Internet at http://pubs.acs.org.

sites is higher than that predicted by a random distribution; also, a considerable extent of mixing between Ca and Na around NBOs is found in this glass, similar to soda-lime silicate glasses. Finally, simple and accurate relationships between NMR parameters and the local information such as Si−O distances and Si−O−T angles could not be found. Therefore, the generation of structural models of glasses and melts by means of MD simulations and the subsequent DFT/GIPAW calculations of the 17O NMR parameters remains mandatory for an unambiguous interpretation of very complex multicomponent systems such as those studied in this work.

■

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors thank the Italian Ministry of University and Research for funding (Project No. COFIN2008; Project No. 2008J9RNB3, “Integrazione Temporale per l’Evoluzione Molecolare”).

ASSOCIATED CONTENT

S Supporting Information *

■

Figures showing the most common oxygen environments in CSN glass and bridging oxygen environments in CNAS glass. Formulas for the calculation of random distributions of Na and Ca around oxygen atoms and of Al and Si around bridging oxygen atoms. Table listing shell model interatomic potentials; computed NMR parameters and populations of BO speciation, with respect to O, in CAS and NAS glasses obtained from MD simulations; and computed NMR parameters and population of NBO speciation, with respect to O, in CAS and NAS glasses

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Unambiguous Description of the Oxygen Environment in

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