Q-Speciation and Network Structure Evolution in Invert Calcium

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Q-speciation and Network Structure Evolution in Invert Calcium Silicate Glasses Derrick C. Kaseman, Andreas Retsinas, Angelos G. Kalampounias, George N Papatheodorou, and Sabyasachi Sen J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.5b02469 • Publication Date (Web): 05 Jun 2015 Downloaded from http://pubs.acs.org on June 15, 2015

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The Journal of Physical Chemistry

Q-speciation and Network Structure Evolution in Invert Calcium Silicate Glasses

Derrick C. Kaseman1, A. Retsinas2, A. G. Kalampounias2,3 , G.N. Papatheodorou2, and S. Sen1

1

Department of Materials Science, University of California at Davis, Davis, California 95616, USA

2

Institute of Chemical Engineering and High Temperature Chemical Processes FORTH, P.O. Box 1414, GR-26504, Patras Greece 3

Department of Chemistry, University of Ioannina, GR-45110 Ioannina, Greece

1 ACS Paragon Plus Environment


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Abstract Binary silicate glasses in the system CaO-SiO2 are synthesized over an extended composition range (42 mol%≤ CaO ≤61 mol%), using container-less aerodynamic levitation techniques and CO2-laser heating. The compositional evolution of Q speciation in these glasses is quantified using

29

Si and

17

O magic angle spinning nuclear magnetic

resonance spectroscopy. The results indicate progressive depolymerization of the silicate network upon addition of CaO and significant deviation of the Q speciation from the binary model. The equilibrium constants for the various Q species disproportionation reactions for these glasses are found to be similar to (much smaller than) those characteristic of Li (Mg) -silicate glasses, consistent with the corresponding trends in the field strengths of these modifier cations. Increasing CaO concentration results in an increase in the packing density and structural rigidity of these glasses and consequently in their glass transition temperature Tg.

This apparent role reversal of conventional

network-modifying cations in invert alkaline-earth silicate glasses are compared and contrasted with that in their alkali silicate counterparts.


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Introduction Investigations into the structure-property relationships in silicate glasses are of key importance for compositional and processing-related optimization of commercial glasses and glass-ceramics as well as in earth science for understanding a broad range of magmatic processes.1-4 The binary alkali and alkaline-earth silicate glasses have served as model systems in understanding and developing structure-property relationships in complex, multi-component silicate glasses. The structures of these binary silicate glasses have therefore been studied extensively in the literature over the last several decades, using a wide variety of spectroscopic and diffraction techniques.1,2,5

One of these

techniques, 29Si nuclear magnetic resonance (NMR) spectroscopy, has been shown to be a unique and powerful tool for studying the connectivity of SiO4 tetrahedra in the structural network in these glasses as described by the Qn-speciation.5,6

The Qn

terminology corresponds to SiO4 tetrahedra where n ranges between 0 and 4 and denotes the number of bridging oxygen (BO) atoms i.e. Si-O-Si linkages, per tetrahedron. The Si-O-Si linkages progressively break to form non-bridging oxygen (NBO) upon addition of modifier alkali or alkaline-earth oxides to SiO2 such that Qn species are converted to Qn-1 species and the network connectivity decreases. In the case of strictly sequential Qn →Qn-1 conversion, the network may consist of at the most two types of Q-species i.e. a binary distribution, for a specific composition. The other extreme is a statistical distribution of Q species that may result from a random modification of the network. Previous studies in the literature indicate that neither of these extremes in Q species distribution is exactly followed by the binary alkali or alkaline-earth silicate glasses.5-10 However, the binary Q species distribution is more



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closely followed by silicate glasses with low field strength (charge:radius ratio) modifier cation (e.g. Na, K) while Q speciation in glasses with high field strength modifier cation such as Mg corresponds more closely to a statistical distribution .5-10 A measure of the deviation of Q-speciation from the binary model is the extent of the Q species disproportionation reactions of the type: 2Qn = Qn-1 + Qn+1 (1 ≤ n ≤ 3) in the network. This disproportionation reaction shifts to the right with increasing cooling rate of the glass but more remarkably with increasing field strength of the modifier catio.2,5,7,8 The equilibrium constant of the disproportionation reaction kn = [Qn-1][ Qn+1]/[ Qn]2 provides a quantitative measure of the disproportionation or the deviation from a binary distribution. A comparison of the literature-reported k1, k2 and k3 values between alkali silicate and Mg-silicate glasses clearly indicate that the latter glasses are characterized by some of the highest values of these equilibrium constants for binary silicate glasses, consistent with the high field strength of Mg2+.6-9

Moreover, another kind of

disproportionation reaction of the type 2Q0 = 2Q1 + O2− has been reported for extremely silica-deficient orthosilicate and sub-orthosilicate (≤ 33 mol% SiO2) MgO-SiO2 and (Ca0.5Mg0.5)O-SiO2 glasses where only Q0 species is expected from a binary model. The “free” O2− ion is only bonded to the M2+ cations in the glass structure.7,8,11,12 In contrast to binary alkali silicates and Mg-silicates, Q-speciation studies on CaO-SiO2 glasses have remained largely limited to the metasilicate composition CaSiO3.10,13-15 Raman and

29

Si NMR spectroscopic studies on this glass identified the

presence of multiple Q(n)species and significant deviation from the binary model. These results are somewhat consistent with the field strength of Ca2+ ion that is intermediate, between those of alkali and Mg2+ cations. While

29

Si NMR studies have not been


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extended to other CaO-SiO2 glass compositions, Q speciation quantitation by Raman spectroscopy has suffered from unknown scattering cross sections and challenges with spectral peak assignments.14,15 However, a recent study in the literature has attempted to address these issues using statistical optimization techniques in the deconvolution of the Raman spectral line shapes and reported Q speciation in CaO-SiO2 glasses with 45 to 52 mol% SiO2.15 The results of this study have yielded a rather low k2 value (~0.07) for Casilicate glasses which is intermediate between those reported for CaSiO3 glass by Murdoch et al. (k2 = 0.032) and by Zhang et al. (k2 = 0.156), on the basis of spectroscopic results.10,13,15

29

Si NMR

The lower k2 values between 0.03 and 0.07 are indeed

comparable to those reported in the literature for Li-slicate glasses (0.08≥ k2 ≥0.04) and much lower than 0.22≥ k2 ≥0.17, reported for Mg-silicate glasses.7-9,15 Considering the Ca-O coordination number to be between 6 and 7, the field strength of Ca2+ in silicate glasses is expected to be between 1.9 and 2.0 while those for Li+ and Mg2+ are 1.7 and 2.8, respectively.8,16-18 Therefore, in spite of the limited data available in the literature in Q-speciation of Ca-silicates, the similarity in the k2 values between these glasses and Lisilicates and the significantly high k2 of Mg-silicate glasses are consistent with the trend in the field strengths of these modifier ions. In this study we report the results of a systematic study of the Q speciation in CaO-SiO2 glasses with CaO contents ranging between 42 and 61 mol%, using 29Si magicangle-spinning (MAS) NMR spectroscopy.

These glasses were prepared by melt

quenching using aerodynamic levitation and CO2 laser heating that allowed for a significant extension of the glass formation range on the low-silica side, beyond those reported (up to 57 mol% CaO) in previous studies. The structural results are correlated to



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the compositional variation of the glass transition temperature Tg and density. Finally, the “invert” alkaline-earth silicate glasses with Q2>Q1. This result is in agreement with the previously reported trend of decreasing sensitivity of the δiso of these Q-species in the same direction, on the Si-O-Si bond angle(Table 1).20 Similar observations were also made in previous

29

Si

MAS NMR spectroscopic studies of Li2O-SiO2 and MgO-SiO2 glasses.7,9 The Q speciation in CaO-SiO2 glasses as obtained from these simulations is compared in Fig. 2 with those expected from the binary and the statistical distribution models. The experimental values clearly fall between these two extremes. As noted earlier, the deviation of the Q-speciation from the binary model can be quantified using the equilibrium constant of the Q species disproportionation reaction kn since a binary distribution is characterized by k1=k2=k3=0.

The Q speciation in Table 1 and Fig. 2

yields k1 = 0.07 (±0.005) while 0.08 ≤ k2 ≤ 0.13 (±0.01).

These values of k1 and k2

obtained in this study for the CaO-SiO2 glasses are quite similar to those reported in a


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previous study for the Li-silicate glasses (k1 = 0.06 and 0.04 ≤ k2 ≤ 0.08) and significantly smaller than the corresponding values (0.12 ≤ k1 ≤ 0.19 and 0.17 ≤ k2 ≤ 0.22) reported for the Mg-silicate glasses.7-9 As noted earlier, this trend in the equilibrium constants for the Q species disproportionation reactions in binary silicate glasses can be ascribed largely to the field strengths of the modifier cations. The concentration of NBO atoms per Si in these CaO-SiO2 glasses as calculated from the Q speciation measured by 29Si MAS NMR spectroscopy is compared in Fig. 3 with the corresponding value expected from the chemical composition under the assumption that addition of each mole of CaO results in the formation of 2 mol of NBO. The expected and measured NBO/Si values are in reasonably good agreement over the entire composition range studied here which discards the possibility of the formation any significant fraction of the free O2− ion via the reaction: 2Q0 = 2Q1 + O2−, at least up to 61 mol% CaO. This conclusion is also corroborated by the 17O MAS NMR spectrum of the glass with 57.5 mol% CaO (Fig. 4). This spectrum displays two well resolved peaks corresponding to NBO and BO environments centered at ~105 and 55 ppm, respectively (Fig. 4), and simulation of the line shape yields a NBO:BO ratio of ~ 78:22 (±3%) which compares well within the uncertainties associated with the ratio 80.7:19.3 expected from the nominal chemical composition of this glass. Similar observations were also made for a Ca-silicate glass of comparable composition (57.1 mol% CaO) in a previous study on the basis of the analysis of

17

O MAS NMR spectra collected at different magnetic

fields.21 Moreover, no additional signal near ~ 290 ppm characteristic of the free O2− ion in Ca-silicate system could be detected in the

17

O MAS NMR spectrum reported in the

present study (Fig. 4).11 This result puts an upper limit of ~2% for the concentration of



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the free O2− ion in Ca-silicate glass with 57.5 mol% CaO. As mentioned earlier, high field strength cations are expected to drive the Q0 disproportionation reaction to the right and indeed previous studies indicated the presence of free O2− ions in the Mg2SiO4 glass with 66.66 mol% MgO.7,8,12 Thus, the apparent absence of free O2− ions in the CaO-SiO2 glasses with up to 61 mol% CaO also imply that the formation of this species may not be expected in alkali silicate systems with comparable or lower concentration of alkali oxide.22 The progressive modification of the Si-O network upon addition of CaO is also reflected in the monotonic increase in the density of the CaO-SiO2 glasses from 2.793 g/cm3 to 2.994g/cm3 with increasing CaO concentration from 42 to 61 mol% (Fig. 5). Correspondingly the molar volume decreases from 20.91 cm3 to 19.25 cm3. This increase in packing density in invert glasses is consistent with the progressive replacement of the silicate network dominated by Q3 and Q2 species with tightly packed corner and edge sharing Ca-O coordination polyhedra in the glass structure.17 The Tg values for these CaO-SiO2 glasses is shown in Fig. 6a.

The results

obtained in this study are consistent with those reported in a previous study by Micoulaut et al. for CaO-SiO2 glasses over a limited composition range.23 Also included in Figs. 6a and 6b for comparison purposes are the Tg values from literature of invert binary MgOSiO2 and ternary (Ca0.5Mg0.5)O-SiO2 glasses and those of invert Li2O-SiO2 glasses. All invert alkaline-earth silicate glasses show a monotonic increase in Tg with increasing modifier content. For comparable SiO2 contents, the mixed alkaline-earth (Ca0.5Mg0.5)OSiO2 glasses have Tg values lower than either Mg or Ca end members. This behavior can be explained by the “mixed-alkali” effect where the isothermal viscosity in mixed-alkali


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glasses are invariably lower than the single-alkali end members for the same SiO2 concentration, which presumably owes its origin to the configurational entropy of mixing of dissimilar modifier glasses.24 According to the conventional wisdom the Tg in silicate glasses is controlled by the connectivity of the silicate network and both are expected to decrease monotonically upon progressive addition of modifier cations. This expectation is indeed consistent with the composition dependence of Tg in invert Li2O-SiO2 glasses (Fig. 6b). However, the invert MgO-SiO2 and CaO-SiO2 glasses display an apparently anomalous increase in Tg with increasing modifier content (Fig. 6a). Similar to density, this increase in Tg can also be explained using the same scenario of structural evolution in invert glasses. As in the crystalline counterparts, the glass structure near the metasilicate composition with ~50 mol% SiO2 must be dominated by chains of Q2 tetrahedra interspersed with those of MO6 (M = Mg, Ca) octahedra.

Although upon increasing the modifier content the Q2

tetrahedral chains are progressively replaced by Q1 dimers and Q0 monomers, the glass structure effectively repolymerizes via formation of percolating domains of corner and edge -sharing MO6 octahedra with relatively strong M-O bonds that increases the rigidity of the structure.17,25 Similar structural evolution is also expected in the case of invert Li2O-SiO2 glasses as the Li4SiO4 crystal structure consists of corner and edge –shared LiO4, LiO5 and LiO6 polyhedra.26 However, the observation of substantial mobility of Li in such crystals and glasses suggests that Li-O bonds are significantly weaker compared to M-O bonds. Therefore, domains of corner and edge –shared Li-O polyhedra do not provide rigidity to the structure of invert Li2O-SiO2 glasses and Tg continuously decreases (Fig. 6b). Finally, a compositional trend in Tg similar to those in MgO-SiO2 and CaO-



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SiO2 glasses is also observed in (Ca0.5Mg0.5)O-SiO2 glasses but the Tg begins to linearly decrease beyond ~ 40 mol% SiO2 upon further addition of modifier oxides (Fig. 6a). This decrease in Tg was ascribed by Nasikas et al. to the formation and increasing concentration of the free O2− ion.11

Conclusions The compositional evolution of Q speciation in binary Ca-silicate glasses is shown to be commensurate with the field strength of Ca2+ ions in silicate glasses. The monotonic increase in density and Tg with CaO content in these glasses with 42 mol%≤ CaO ≤61 mol% is consistent with the progressive depolymerization of the silicate network and effective repolymerization of the structure with a network of tightly packed corner and edge -shared Ca-O coordination polyhedra.

While invert alkaline-earth

silicate glasses share this attribute of increase in Tg with increasing modifier content, their alkali silicate counterparts display an opposite trend that is conjectured to be related to the corresponding differences in the modifier-oxygen bond strengths.

ACKNOWLEDGMENTS

DK and SS were supported by the National Science Foundation grant DMR GOALI1104869. The financial support to G.N.P. from the Executive Board of FORTH is gratefully acknowledged.


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References 1. Mysen, B. O.; Richet, P. Silicate Glasses and Melts: Properties and Structure; Elsevier: Amsterdam, 2005. 2. Stebbins, J. F., McMillan, P.F., Dingwell, D.B., Eds. Structure, Dynamics, and Properties of Silicate Melts; Vol. 32; Mineralogical Society of America: Washington DC, 1995. 3. Shelby, J. E. Introduction to Glass Science and Technology, 2nd ed.; The Royal Society of Chemistry: Cambridge, U.K., 2009. 4. Rawson, H. Glasses and Their Applications; Royal Institute of Metals: London, 1991. 5. Greaves, G. N.; Sen, S. Inorganic Glasses, Glass-Forming Liquids and Amorphizing Solids. Advances in Physics 2007, 56, 1-166. 6. Eckert, H. Structural Characterization of Noncrystalline Solids and Glasses Using Solid State NMR. Progress in Nuclear Magnetic Resonance Spectroscopy 1992, 24, 159293. 7. Sen, S.; Maekawa, H.; Papatheodorou, G. N. Short-Range Structure of Invert Glasses Along the Pseudo-Binary Join MgSiO3-Mg2SiO4: Results from Si-29 and Mg-25 MAS NMR Spectroscopy. Journal of Physical Chemistry B 2009, 113, 15243-15248. 8. Davis, M. C.; Sanders, K. J.; Grandinetti, P. J.; Gaudio, S. J.; Sen, S. Structural Investigations of Magnesium Silicate Glasses by Si-29 2D Magic-Angle Flipping NMR. Journal of Non-Crystalline Solids 2011, 357, 2787-2795. 9. Larson, C.; Doerr, J.; Affatigato, M.; Feller, S.; Holland, D.; Smith, M. E. A Si-29 MAS NMR Study of Silicate Glasses with a High Lithium Content. Journal of PhysicsCondensed Matter 2006, 18, 11323-11331.



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10. Zhang, P.; Grandinetti, P. J.; Stebbins, J. F. Anionic Species Determination in CaSiO3 Glass Using Two-Dimensional Si-29 NMR. Journal of Physical Chemistry B 1997, 101, 4004-4008. 11. Nasikas, N. K.; Edwards, T. G.; Sen, S.; Papatheodorou, G. N. Structural Characteristics of Novel Ca-Mg Orthosilicate and Suborthosilicate Glasses: Results from Si-29 and O-17 NMR Spectroscopy. Journal of Physical Chemistry B 2012, 116, 26962702. 12. Sen, S.; Tangeman, J. Evidence for Anomalously Large Degree of Polymerization in Mg2SiO4 Glass and Melt. American Mineralogist 2008, 93, 946-949. 13. Murdoch, J. B.; Stebbins, J. F.; Carmichael, I. S. E. High-Resolution Si-29 NMRStudy of Silicate and Aluminosilicate Glasses - the Effect of Network-Modifying Cations. American Mineralogist 1985, 70, 332-343. 14. Tsunawaki, Y.; Iwamoto, N.; Hattori, T.; Mitsuishi, A. Analysis of CaO-SiO2 and CaO-SiO2-CaF2 Glasses by Raman-Spectroscopy. Journal of Non-Crystalline Solids 1981, 44, 369-378. 15. Herzog, F.; Zakaznova-Herzog, V. P. Quantitative Raman Spectroscopy: Challenges, Shortfalls, and Solutions-Application to Calcium Silicate Glasses. American Mineralogist 2011, 96, 914-927. 16. Taniguchi, T.; Okuno, M.; Matsumoto, T. X-Ray Diffraction and EXAFS Studies of Silicate Glasses Containing Mg, Ca and Ba Atoms. Journal of Non-Crystalline Solids 1997, 211, 56-63. 17. Skinner, L. B.; Benmore, C. J.; Weber, J. K. R.; Tumber, S.; Lazareva, L.; Neuefeind, J.; Santodonato, L.; Du, J.; Parise, J. B. Structure of Molten CaSiO3: Neutron Diffraction


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Isotope Substitution with Aerodynamic Levitation and Molecular Dynamics Study. Journal of Physical Chemistry B 2012, 116, 13439-13447. 18. Eckersley, M. C.; Gaskell, P. H.; Barnes, A. C.; Chieux, P. Structural Ordering in a Calcium Silicate Glass. Nature 1988, 335, 525-527. 19. Retsinas, A.; Kalampounias, A. G.; Papatheodorou, G. N. Reaching the Ionic Limit in the (1-X) Ca-0.5-Mg-0.5 O-XSiO2 Pseudo Binary Glass System with 0.5 < X < 0.27: Glass Formation and Structure. Journal of Non-Crystalline Solids 2014, 383, 38-43. 20. Angeli, F.; Villain, O.; Schuller, S.; Ispas, S.; Charpentier, T. Insight into Sodium Silicate Glass Structural Organization by Multinuclear NMR Combined with FirstPrinciples Calculations. Geochimica et Cosmochimica Acta 2011, 75, 2453-2469. 21. Lee, S. K., & Stebbins, J.F. Disorder and the Extent of Polymerization in Calcium Silicate and Aluminosilicate Glasses: O-17 NMR Results and Quantum Chemical Molecular Orbital Calculations. Geochimica et Cosmochimica Acta 2006, 70, 4275-4286. 22. Stebbins, J. F.; Sen, S. Oxide Ion Speciation in Potassium Silicate Glasses: New Limits from O-17 NMR. Journal of Non-Crystalline Solids 2013, 368, 17-22. 23. Micoulaut, M.; Malki, M.; Simon, P.; Canizares, A. On the Rigid to Floppy Transitions in Calcium Silicate Glasses from Raman Scattering and Cluster Constraint Analysis. Philosophical Magazine 2005, 85, 3357-3378. 24. Richet, P. Viscosity and Configurational Entropy of Silicate Melts. Geochimica et Cosmochimica Acta 1984, 48, 471-483. 25. Kohara, S.; Suzuya, K.; Takeuchi, K.; Loong, C. K.; Grimsditch, M.; Weber, J. K. R.; Tangeman, J. A.; Key, T. S. Glass Formation at the Limit of Insufficient Network Formers. Science 2004, 303, 1649-1652.



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26. Tranqui, D.; Shannon, R. D.; Chen, H. Y.; Iijima, S.; Baur, W. H. Crystal Structure of Ordered Li4SiO4. Acta Crystallographica, Section B 1979, 35, 2479-2487. 27. Wilding, M. C.; Benmore, C. J.; Tangeman, J. A.; Sampath, S. Coordination Changes in Magnesium Silicate Glasses. Europhysics Letters 2004, 67, 212-218. 28. Hushur, A.; Kojima, S.; Kodama, M.; Whittington, B.; Olesiak, M.; Affatigato, M.; Feller, S. A. Elastic Anomaly of Glass Transitions in Lithium Silicate. Japanese Journal of Applied Physics Part 1 2005, 44, 6683-6687. 29. Tatsumisago, M.; Minami, T.; Tanaka, M. Glass Formation by Rapid Quenching in Lithium Silicates Containing Large Amounts of Li2O. Yogyo-Kyokai-Shi 1985, 93, 581584.


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Table 1. Fit parameters (isotropic shift δiso and full width at half-maximum ∆) for the 29Si MAS NMR spectra and relative fractions (%) of different Q species in CaO-SiO2 glasses

mol% CaO

(ppm)

Q0 ∆ (ppm)

42 46 50 52 55 58 61

−70.0 −70.0

8.8 8.7

δiso

Q1

Q2

δiso %

15.1 20.1

(ppm) −74.7 −74.7 −74.7 −74.7 −74.7 −74.4 −74.6

Q3

δiso ∆ (ppm) 9.0 9.3 9.3 9.3 9.3 9.6 9.3

% 5.0 6.1 16.6 29.6 48.2 65.3 65.8

(ppm) −82.0 −82.0 −81.6 −81.2 −81.2 −81.5 −81.5

Q4

δiso ∆ (ppm) 10.5 11.2 11.0 11.0 10.2 11.0 11.0

% 36.5 52.5 64.4 60.4 46.0 19.6 14.1

(ppm) −90.7 −90.7 −91.0 −91.0 −91.0

∆ (ppm) 13.0 12.0 12.0 13.0 13.0

%∗ 50.2 34.2 19.0 10.0 5.8

δ (ppm) −103.0 −103.0

∆ (ppm) 15 15

*The error associated with the percent fraction values is ±5%


%∗ 8.3 7.2


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Figure Captions Figure 1. Experimental (solid black line) and simulated (dotted line) 29Si MAS NMR spectra of CaO-SiO2 glasses with corresponding modifier concentrations given alongside. Individual Gaussian simulation components corresponding to Q4 (purple), Q3 (pink), Q2 (green), Q1 (orange) and Q0 (teal) species are also shown.

Figure 2. Compositional variation of the relative fractions of various Qn species (symbols) as obtained from simulation of the 29Si MAS NMR spectra. The black, red, green, blue, and aqua colored symbols correspond to Q4, Q3, Q2, Q1 and Q0 species, respectively. Solid and dot-dashed lines of corresponding colors represent the compositional fractions of Qn species as predicted by the binary and statistical models, respectively.

Figure 3. Comparison of the experimental (symbols) and calculated (solid line) number of non-bridging oxygen atoms per Si in CaO-SiO2 glasses. Solid line through the data points is a guide to the eye.

Figure 4. Experimental (solid black line) and simulated (red dotted line) 17O MAS NMR spectrum of the Ca-silicate glass with 57.5 mol% CaO. Asterisks denote locations of spinning sidebands. Individual simulation components corresponding to NBO (purple) and BO (green) species are also shown.


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Figure 5. Compositional variation of density in CaO-SiO2 glasses. Error bars are within the size of the symbols.

Figure 6. (a) Compositional variation of Tg of CaO-SiO2 glasses (red circles) determined in this study is compared with those of MgO-SiO2 (black squares) and (Ca0.5Mg0.5)OSiO2 (blue triangles) glasses reported in literature.11,27 Dashed lines through the data points are guide to the eye. (b) Compositional variation of Tg of Li2O-SiO2 glasses as reported in the literature. Data points from two separate studies are denoted by green stars28 and blue diamonds29.



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Figure 1 22 ACS Paragon Plus Environment

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Figure 3


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Figure 4



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Figure 5


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Figure 6



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TOC- jp-2015-024692 Kaseman et al.


Q-Speciation and Network Structure Evolution in Invert Calcium

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