Nature of Chemical and Topological Disorder in Borogermanate Glasses

Nov 20, 2009 - Sung Keun Lee,* Hyun Na Kim, Bum Han Lee, Hyo-Im Kim, and Eun Jeong Kim. Laboratory of Physics and Chemistry of Earth Materials, ...
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J. Phys. Chem. B 2010, 114, 412–420

Nature of Chemical and Topological Disorder in Borogermanate Glasses: Insights from B-11 and O-17 Solid-State NMR and Quantum Chemical Calculations Sung Keun Lee,* Hyun Na Kim, Bum Han Lee, Hyo-Im Kim, and Eun Jeong Kim Laboratory of Physics and Chemistry of Earth Materials, School of Earth and EnVironmental Sciences, Seoul National UniVersity, Seoul, 151-742, Korea ReceiVed: September 28, 2009; ReVised Manuscript ReceiVed: NoVember 1, 2009

Knowledge of the extent of chemical and topological disorder in topological disordered oxide glasses and melts is essential for understanding the atomistic origins of their macroscopic properties. Here, we report the high-resolution B-11 and O-17 triple quantum magic angle spinning (3QMAS) NMR spectra for binary borogermanate glasses. The NMR results, together with quantum chemical calculations of cluster energy difference, allow us to estimate the extent of chemical disorder and topology variation with composition. The B-11 NMR result shows that the boroxol ring fraction decreases nonlinearly with increasing mole fraction of Ge and is smaller than that in binary borosilicate glasses, suggesting that the Ge/Si content influences the topological changes. Whereas oxygen clusters are not well resolved in O-17 NMR spectra, the Ge-O-Ge fraction apparently increases with increasing GeO2 content. The estimated degree of framework disorder (Q) in borogermanate glasses is approximately 0.4, according to quantum chemical calculations based on density functional theory. This is halfway between chemical order (Q ) 1) and a random distribution (Q ) 0). In contrast, Q is approximately -0.6 for borosilicate glasses, indicating a moderate tendency toward complete phase separation (Q ) -1). This result confirms that the degree of framework disorder shows a strong dependence on the type of framework cations (Si or Ge). The predicted configurational enthalpy of borogermanate glasses, explicitly considering both chemical and topological disorder, shows a negative deviation as predicted from the positive Q value. The results demonstrate that the macroscopic properties of topologically disordered noncrystalline solids can be established from the detailed quantification of topological and chemical disorder. Introduction The thermodynamic and transport properties of oxide glasses and melts are largely controlled by the chemical and topological distributions of the constituent framework units (e.g., [4]Si, [4]Al, [4] Ge, and [3]B) at varying temperatures and pressures, and thus the extent of chemical and topological disorder (e.g., refs 1-14 and references therein). For instance, as chemical order increases among [4]Si and [4]Al in aluminosilicate glasses and melts, the fraction of dissimilar pairs such as [4]Si-O-[4]Al is expected to increase. This leads to a decrease in the configurational entropy, a decrease in the activity coefficient of oxide, and an increase in the melt viscosity.5,15 In contrast, the fractions of [4] Al-O-[4]Al and [4]Si-O-[4]Si are expected to increase with increasing degree of disorder.16,17 These changes can account for the geophysical processes relevant to magma generation (e.g., melt composition), transport, and emplacement in the Earth’s crust and interior.9,18 Despite the importance and implications, a full understanding of these inherent aspects of disorder in noncrystalline oxides including germanates in general remains a difficult question for physical chemistry, condensed matter physics, glass sciences, and geochemistry because conventional scattering and spectroscopic techniques have limited usefulness in estimating the structure of noncrystalline oxides. It has recently been shown that, in diverse silicate glasses (e.g., aluminosilicate and borosilicate glasses), the framework disorder can be estimated using high resolution O-17 triple * To whom correspondence should be addressed. E-mail: sungklee@ snu.ac.kr. Home page: http://plaza.snu.ac.kr/∼sungklee. Phone: 822-8806729. Fax: 822-871-3269.

quantum magic angle spinning (3QMAS) NMR, in which the bridging oxygen (BO) clusters (e.g., [4]Si-O-[4]Si) are well resolved (e.g., refs 5 and 19-26). The cluster energy difference among BO clusters using quantum chemical calculation yielded improved understanding of the relative stabilities of these clusters and thus the chemical disorder.17 These studies allow us to propose two order parameters to quantify the intermixing of framework cations. The first is the degree of Al avoidance (Q), which describes the state of disorder from complete Al avoidance (Q ) 1) to a random distribution (Q ) 0). The second is the degree of phase separation (P), which estimates the intermixing between framework units from complete phase separation (P ) 1) to a random distribution (P ) 0).5,17,27 The degree of framework disorder shows a strong dependence on the type of framework cations. For instance, aluminosilicate glasses show a tendency toward chemical order.17 Borosilicate glasses show a tendency toward phase separation,17,28 which is consistent with the positive enthalpy of mixing in borosilicate glasses as determined by solution calorimetry.29 While germanium (Ge) is isochemical with silicon (Si), and germanates have often been used to provide insight into the structure of crystalline and amorphous silicates, the structure and properties of germanate glasses are quite different from those of silicates. The former show more diverse Ge coordination states (i.e., [4,5,6]Ge vs [4]Si) at l atm and exhibit larger compressibility30-33 as well as anomalous nonlinear changes in density with varying alkali content (e.g., the germanate anomaly) (e.g., refs 34-38; see also ref 39 for a review). The presence of a d-orbital in Ge and the longer Ge-O bond length (∼1.74

10.1021/jp9093113  2010 American Chemical Society Published on Web 11/20/2009

Structure of Borogermanate Glasses Å compared with the Si-O length of ∼1.6 Å) may result in unique topological variations and affect the extent of chemical disorder in germanate glasses. Borogermanate glasses are of fundamental importance because of their implications for more common aluminosilicates upon substituting Al3+ with B3+ and Si4+ with Ge4+. In particular, binary B2O3-GeO2 glass is an ideal model system for testing the framework disorder between B and Ge in germanate glasses and framework borogermanate zeolites, because it is one of only a few glass-forming oxide systems consisting of only the framework cations. The inherent extent of framework disorder (Q) can be obtained without perturbation from network-modifying or charge-balancing cations (e.g., Li+, Na+, Ca2+). Ternary and multicomponent borogermanate glasses also have potential applications in the glass-ceramic industry (e.g., refs 40 and 41 and references therein) and as catalytic framework materials with unique topological variations (threering cluster and T-O-T angle smaller than that of typical Si-O-Si) and have also been widely used for nonlinear optical materials (e.g., La-borogermanates, alkali-, and REE containing borogermanate glasses).42-50 The chemical disorder of borogermanate glasses is likely to be quite different from that of borosilicate glasses: compared with silicate networks, germanate networks tend to show a better mixing with borate networks upon synthesis of crystalline borogermanates.42,46,50 No detailed estimation of the extent of framework disorder in borogermanate glasses has yet been reported. Together with framework disorder, understanding the boron topology of boron-containing glasses is necessary to fully understand the thermodynamic and transport properties of these glasses and their corresponding melts (e.g., refs 51-53). In particular, the presence of boroxol rings (the three-member planar rings B3O63-) is responsible for the unique properties and metastability of diverse borate glasses.53 Previous experimental and theoretical studies have confirmed that pure B2O3 glass consists of approximately 70% boroxol rings and 30% nonring borons (e.g., refs 54-60 and references therein). B-11 3QMAS NMR is effective in resolving these boron species21,61 and is thus suitable for analyzing the topological variations of boron with varying composition. The boroxol ring fraction is reported to decrease linearly with increasing mole fraction of Si in binary borosilicates,16 and depends also on alkali content in alkali borate glasses51 and pressure.56 Although earlier studies using vibrational spectroscopy provide a qualitatiVe estimation of the boroxol ring content,62 the detailed boron coordination environments and the topological variation in borogermanate glass are not well understood. The potential results of chemical and topological disorder in borogermanate glasses will be helpful to find a quantitatiVe link between microscopic atomic structure and macroscopic properties. For borosilicate glasses, both chemical and topological disorder estimated from spectroscopy and theoretical calculations can explain the macroscopic thermodynamic properties.17 It would be desirable to extend this previous study to have atomic-nano meter scale constraints on the macroscopic properties of borogermanate glasses. This would also provide the atomistic origins of the differences in macroscopic properties of germanate and silicate glasses. Here, we report the first high-resolution solid-state NMR spectra (B-11 and O-17) for binary borogermanate glasses, together with quantum chemical calculations based on density functional theory. These provide an insight into the effect of composition on the evolution of boron topology, and a quantitative estimate of the extent of the framework disorder (B-Ge). We also discuss the effect of Ge/Si on the framework mixing

J. Phys. Chem. B, Vol. 114, No. 1, 2010 413 TABLE 1: Chemical Composition of the Binary Borogermanate Glasses ICP analysis (mol fraction) sample

GeO2

B2 O3

GB91 GB82a GB82 GB64a GB64 GB46b GB28

0.916 0.817 0.829 0.648 0.623 0.382 0.160

0.084 0.183 0.171 0.352 0.377 0.618 0.840

a Used for the O-17 NMR experiment. b Used for both the O-17 and B-11 NMR experiments.

and the topological evolution of oxide glasses. Finally, we present an analytical expression for the configurational enthalpy of the binary compounds (applicable to any A-B pair) that considers both topological and chemical disorder in the glasses. We use this to predict the configurational enthalpy of borogermanate glasses. Experiments and Theoretical Calculations Sample Preparation. Borogermanate glasses with varying GeO2/B2O3 ratios [e.g., nominal GeO2:B2O3 ratio of 9:1 (GB91), 8:2 (GB82), 6:4 (GB64), 4:6 (GB46), and 2:8 (GB28)] were synthesized from mixtures of 40% O-17 enriched GeO2 (prepared by hydrolyzing germanium ethoxide with 40% 17Oenriched H2O) and B2O3 glass (synthesized from boric acid powder by heating above 773 K). Approximately 0.2 wt % Co oxide was added to enhance the spin-lattice relaxation and thus reduce the total collection time. The mixtures were fused at 1100-1500 °C in an Ar environment for 1 h and then quenched into glasses by manually lowering a Pt crucible into water. The chemical compositions of the glasses were analyzed using inductively coupled plasma/atomic emission (ICP/AE); the results are summarized in Table 1. NMR Spectroscopy. The B-11 NMR spectra for the borogermanate glasses were obtained using a Bruker Avance II 500 MHz spectrometer at 11.7 T with a Larmor frequency of 160.491 MHz and a 2.5 mm Bruker triple-resonance probe. The B-11 3QMAS NMR spectra were collected using shifted-echo pulse sequences [3.6 us - delay - 1.8 us - echo delay (approximately 0.5-0.8 ms) - 15 us] with a phase table with 96 cycles, which is suitable for the selection of the whole echo for spin-3/2 nuclides including B-11.63,64 The spinning speed was 20 kHz with a recycle delay of 1 s. The spectra were referenced to a 0.2 M H3BO3 solution and then corrected to the standard reference of BF3(CH3CH2)2O whose resonance is located at -19.6 ppm relative to the H3BO3 solution. The O-17 NMR spectra for the glasses were collected using a Bruker Avance 400 MHz spectrometer at 9.4 T with a Larmor frequency of 54.23 MHz and a 4 mm triple-resonance probe. The O-17 3QMAS NMR spectra for the glasses were collected using fastamplitude modulation based shifted-echo pulse sequences [5.5 us - delay - 2 us - echo delay (approximately 0.5 ms) - 20 us].64-67 The recycle delay is 1 s, and a magic angle spinning speed of 14 kHz was used. The O-17 NMR spectra were referenced to external tap water. Quantum Chemical Calculations. Quantum chemical calculations using Gaussian 03 were performed to estimate the extent of framework disorder.68,69 The model borogermanate oxygen clusters are [4]Ge-O-[3]B [(OH)3Ge-O-B(OH)2], [4] Ge-O-[4]Ge [(OH)3Ge-O-Ge(OH)3], and [3]B-O-[3]B

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Figure 1. 11B 3QMAS NMR spectra for binary borogermanate (B2O3-GeO2) glasses with varying B2O3/GeO2 ratios.

[(OH)2B-O-B(OH)2]. These clusters were optimized with the B3LYP hybrid density functional theory and the 6-311+G(2d,p) basis set. The hydrogen-oxygen bond length and H-O-[4]Ge and H-O-[3]B angles are the same for each coordination polyhedron ([4]Ge and [3]B) in the clusters. Single-point energy calculations were performed using the B3LYP/6-311+G(2d,p) basis set. Results and Discussion B-11 3QMAS NMR Results. Figure 1 presents the B-11 3QMAS NMR spectra for binary borogermanate (B2O3-GeO2) glasses with varying B2O3/GeO2 ratios and pure B2O3 glass. The partially resolved features correspond to three coordinated borons ([3]B) in boroxol rings (rings of a three-trigonal borate group, at approximately 47 ppm in the isotropic dimension, δ3QMAS) and borons in nonrings (δ3QMAS of approximately 41 ppm).17 No detectable [4]B was found in the spectra (approximately 0 ppm in the MAS dimension, δMAS).61 The fraction of boroxol rings in borogermanate glasses apparently decreases with increasing GeO2 content. The B-11 MAS NMR spectra for borogermanate glasses do not provide a clear resolution of nonring and ring boron sites (not shown here). Figure 2 (top) shows the total isotropic projections of the B-11 3QMAS NMR spectra, demonstrating that the boroxol ring content decreases with increasing GeO2 content. Figure 2 (bottom) presents the results of fitting two Gaussian functions to the total isotropic projection of the B-11 3QMAS NMR spectra. We applied several fitting constraints to avoid reducing the uniqueness of the results. The initial ranges of peak positions and widths for boroxol rings and nonrings were roughly estimated from the 2D B-11 3QMAS NMR spectra (Figure 1). The positions and widths of the nonring and ring

Figure 2. (top) Total isotropic projection of 11B 3QMAS NMR spectra for binary borogermanate glasses (B2O3-GeO2) with varying B2O3/ GeO2 ratios. (bottom) Result of fitting Gaussian functions (thin lines) to the isotropic projection of 11B 3QMAS NMR spectra for binary borogermanate glasses (B2O3-GeO2) with varying B2O3/GeO2 ratios. Thick lines refer to the experimental spectra.

peaks were allowed to vary because it was not possible to fit the entire set of spectra using a fixed peak position and width for each boron cluster; this suggests composition dependencies. However, we were able to simultaneously fit two spectra with similar compositions by using a fixed peak width and position for each boron cluster (i.e., B2O3 glass-GB28, GB28-GB46, GB46-GB64, GB64-GB82, and GB82-GB91). Thus, with the exceptions of the end members (B2O3 and GB91 glass), each spectrum was fitted twice using different peak widths and positions. The fitting results in Figure 2 (bottom) are based on

Structure of Borogermanate Glasses

Figure 3. (top) Variation of the boron cluster population with GeO2 content in binary borogermanate (B2O3-GeO2) glasses. Closed circles and squares refer to boroxol ring and nonring clusters. The open circles denote boron clusters in binary borosilicate glasses.17 The thin curves show the trend lines connecting the experimental data. (bottom) Variation in peak position of ring and nonring clusters in the isotropic dimension (δ3QMAS) in borogermanate glasses. The black and red circles denote those δ3QMAS values estimated from the simultaneous fitting of three and two spectra, respectively (see text).

averages of the peak widths, positions, and intensities for the two adjacent compositions. The isotropic spectra for three spectra were then fitted simultaneously, using the same component positions and widths for both boroxol rings and nonrings (i.e., B2O3 glass-GB28-GB46, GB28-GB46-GB64, GB46-GB64GB82, and GB64-GB82-GB91). With these constraints, each spectrum except B2O3 and GB91 is fitted two or three times, possibly with different peak positions and widths. The two sets of fits show similar changes in peak positions, widths, and intensities with compositions. This approach thus gives relatively robust fractions of ring/nonring clusters and their uncertainties. Effect of Composition on the Fraction of Boroxol Rings in Binary Borogermanate Glasses. Because the B-11 quadrupolar coupling constant (Cq) is similar for each boron cluster (approximately 2.7-2.9 MHz),17 the 3QMAS NMR signal intensity (which depends on Cq)70-72 for ring and nonring clusters can be directly used to provide their quantitative fractions without further calibration of the intensity. The fitted result for pure B2O3 glass is also roughly consistent with estimated fractions from previous studies (i.e., approximately 30% nonrings and 70% boroxol rings).51,54,57,73 Figure 3 (top) shows the variation in boron cluster population with GeO2

J. Phys. Chem. B, Vol. 114, No. 1, 2010 415 content in binary borogermanate (B2O3-GeO2) glasses. Here, the fractions obtained from the two different fits [i.e., simultaneous fitting of two spectra (red curve with closed circles) and three spectra (black curve with closed circles)] show similar results. For comparison, the boron cluster population in binary borosilicate glasses is also shown.17 Although both glasses show a trend of decreasing fraction of boroxol rings with GeO2 content (mole fraction of Ge), for a given B2O3 content, the ring population in borosilicate glasses is apparently larger than that in borogermanate glasses. This suggests that changes from rings to nonrings are affected by the types of framework cations (Ge vs Si) partly due to the difference in the degree of framework intermixing between B-Ge and B-Si. Greater intermixing between framework cations can lead to the formation of nonrings, while enhanced mixing between B and Ge in borogermanate glasses is likely to reduce the formation of boroxol rings compared with borosilicate glasses, as shown in Figure 3. The fitted results show that δ3QMAS for nonrings decreases with decreasing GeO2 content, whereas the change in δ3QMAS for boroxol rings is negligible. This implies that the boroxol rings are not in close proximity to the Ge clusters (Figure 3, bottom). O-17 3QMAS NMR Results for Binary Borogermanate Glasses. Figure 4 shows the O-17 3QMAS NMR spectra for binary borogermanate glasses with varying B2O3/GeO2 ratios. While the oxygen peaks are not well resolved, the predicted peak position (δ3QMAS) of [3]B-O-[3]B in the O-17 3QMAS NMR spectra for pure B2O3 (at 9.4 T) is approximately -70 ppm74,75 and δ3QMAS for [4]Ge-O-[4]Ge in pure GeO2 is approximately -60 ppm.35,36 This relatively small difference in δ3QMAS for each oxygen site and the possibility of a [4] Ge-O-[3]B peak between the [4]Ge-O-[4]Ge and [3] B-O-[3]B peaks pose a challenge for obtaining detailed information on oxygen in borogermanate glasses. The δ3QMAS of the oxygen features, however, decreases with increasing Ge/B ratio, and the peak position in the MAS dimension (δMAS) also decreases with increasing Ge, suggesting that oxygen configuration changes with GeO2 composition. We also note that, while projection in the MAS dimension (or the O-17 MAS NMR spectra) could be helpful, additional constraints on quadrupolar asymmetry parameters for the cluster are necessary to obtain better insights into the structure. Currently, it is difficult to find nonunique values for the quadrupolar asymmetry parameters because of overlap in the MAS dimension. Figure 5 (top) presents the total isotropic projection of the O-17 3QMAS NMR spectra for binary borogermanate glasses: δ3QMAS of the oxygen peak gradually decreases with decreasing GeO2 content. Despite a relatively small difference in the peak positions for pure GeO2 and B2O3 in the isotropic dimension and thus a considerable peak overlap in the isotropic projection, the spectra indeed indicate the effect of GeO2 on changes in the oxygen cluster populations. To derive a qualitatiVe trend for the variation in oxygen clusters as the composition changes, we assume that the isotropic projection of the O-17 3QMAS NMR spectra can be decomposed into three Gaussian peaks representing three oxygen sites (e.g., [4]Ge-O-[4]Ge, [3]B-O-[3]B, and [4]Ge-O-[3]B) and that the δ3QMAS of each oxygen site in the isotropic dimension does not vary with Ge/B. The positions and widths of the [4]Ge-O-[4]Ge and [3]B-O-[3]B peaks are relatively well constrained by the spectrum for pure GeO2 and B2O3 glasses.35,36,74 The position and width of the [4]Ge-O-[3]B peak are assumed to be the average values of the [4]Ge-O-[4]Ge and [3]B-O-[3]B peaks. With these constraints, the isotropic spectra for binary borogermanate glasses were fitted simulta-

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Figure 4. 17O 3QMAS NMR spectra for binary borogermanate (B2O3-GeO2) glasses with varying B2O3/GeO2 ratios. Contour lines are drawn from 13 to 93% of the relative intensity with a 5% increment and added lines at 4, 7, and 10%.

neously, using the same component positions and widths for both. The results are given in Figure 5 (bottom), showing that the [4]Ge-O-[4]Ge fraction increases with GeO2 content while the fraction of [4]Ge-O-[3]B is apparently constant. We again note that, because of the peak overlap and the above assumptions, the fits show only the qualitative trend. Quantum Chemical Calculations. Figure 6 shows the optimized model borogermanate clusters with equilibrium bond length and angle for the clusters. The [3]B-O and [4]Ge-O bond lengths are 1.357-1.361 and 1.754-1.769 Å, respectively, which is consistent with known bond lengths for crystalline and noncrystalline germanates and borates (e.g., refs 39 and 57 and references therein). The bond angle for each BO cluster is also shown in Figure 6. The calculated oxygen cluster energy difference [2W, 2[[4]Ge-O-[3]B (-2556.671 hartree)] [[4]Ge-O-[4]Ge (-4684.632 hartree) + [3]B-O-[3]B (-428.710 hartree)]] is -4.2 kJ/mol, suggesting a tendency toward chemical order (favoring the formation of [4]Ge-O-[3]B). The previous estimation of the 2W value for binary borosilicate glasses using

Lee et al.

Figure 5. (top) Total isotropic projection of 17O 3QMAS NMR spectra for binary borogermanate glasses (B2O3-GeO2) with varying B2O3/ GeO2 ratios. (bottom) Result of fitting Gaussian functions (thin lines) to the isotropic projection of 17O 3QMAS NMR spectra for binary borogermanate glasses (B2O3-GeO2) with varying B2O3/GeO2 ratios. Thick lines refer to the experimental spectra.

O-17 NMR is approximately 5.4 kJ/mol, which shows a remarkable similarity to the theoretical results at the B3LYP/ 6-311+G(2d,p)//HF/3-21G level (5.8 kJ/mol) and the B3LYP/ 6-311+G(2d,p)//B3LYP/6-311+G(2d,p) level (9.0 kJ/mol).17 These positive 2W values in borosilicate glasses suggest a tendency toward clustering (or phase separation) of B-rich and Si-rich units. The 2W difference between borosilicate and borogermanate glasses calculated at the B3LYP level of theory with an extended basis set is somewhat larger than the uncertainty of the current quantum chemical calculations. The results indicate the effect of Ge/B on the framework disorder and show that Ge and B tend to be more intermixed than Si and B in binary borosilicate glasses. As we utilized relatively smaller oxygen clusters (e.g., Ge-O-Ge) for cluster energy

Structure of Borogermanate Glasses

Figure 6. Optimized geometry of bridging oxygen clusters in binary borogermanate glasses. [4]Ge-O-[3]B [(OH)3Ge-O-B(OH)2], [4] Ge-O-[4]Ge [(OH)3Ge-O-Ge(OH)3], and [3]B-O-[3]B [(OH)2B-O-B(OH)2].

calculations, the calculation of the cluster energy difference (2W) value using larger clusters (beyond the second nearest neighbors around oxygen) may be necessary to further explore the effect of cluster size on the 2W value. The effect of cluster size was often observed on the calculation of O-17 NMR parameters (e.g., electric field gradient and NMR chemical shift) for oxides (e.g., refs 76 and 77). While this can be performed by considering clusters with varying ring size (e.g., 4-, 5-, and 6-member rings), the ring-size statistics for the borogermanate is not currently available, making potential results with arbitrarily chosen borogermante ring clusters rather speculative. The Extent of Framework Disorder in Binary Borogermanate Glasses and Its Effect on the Configurational Thermodynamic Properties. Chemical disorder and the topological variation estimated from NMR and quantum chemical calculations allow us to measure the extent of disorder in the glasses. To quantify the degree of disorder, we previously used two order parameters: the degree of chemical order [Q, varying from 1 (chemical order) to 0 (random distribution)] and the degree of phase separation [P, varying from 1 (clustering or phase separation) to 0 (random distribution)].8,17 Here, the previous definition of P is slightly modified in a way such that a single parameter for the degree of framework disorder (Q) [ranging from 1 (chemical order) to -1 (phase separation)] can be used:

Q ) 1 - exp[2W/kTf], if 2W e 0 ) -P ) exp[-(2W/kTf)] - 1, if 2W g 0 (1) where 2W is the cluster energy difference between oxygen clusters, k is the Boltzmann constant, and Tf is the compositiondependent fictive temperature, i.e., the temperature below which the structure of supercooled liquids is frozen.78 On the basis of the 2W value for borogermanate glasses estimated directly from quantum chemical calculations, the degree of framework disorder (Q) in binary borogermanate glasses is estimated to be approximately 0.4 at a constant Tf value of 680 K, which is halfway between chemical disorder (Q ) 1) and a random distribution (Q ) 0). The 2W value for binary borosilicate glasses using O-17 NMR is approximately 5.4 kJ/mol, which leads to ∼ -0.62 as the estimated extent of framework disorder (Q). As the quantum chemical simulations at the B3LYP level of theory with an extended basis set (e.g.,

J. Phys. Chem. B, Vol. 114, No. 1, 2010 417 6-311+G(2d,p)) yield results similar to the O-17 NMR data for binary borosilicate glasses (where the oxygen sites are well resolved)17 and there is no perturbation from network modifying cations, the framework disorder found using quantum chemical calculations for binary borogermanate clusters is likely to describe the nature of Ge-B mixing (see below for further discussion). The results suggest that mixing of the framework cations is more prevalent in binary borogermanate glasses than in borosilicates. We also note that the extent of mixing among network polyhedra (e.g., [4]Si, [4]Al, [4]Ge, and [3]B) in covalent oxide glasses can be obtained by probing the oxygen environment, as discussed in detail in our previous study.5 The population of the oxygen cluster A-O-B (where A and B are the framework cations, e.g., [4]Ge-O-[3]B) can be obtained from the following relationship based on quasi-chemical approximations taking into consideration the coordination numbers of framework cations and the degree of framework disorder (Q):

XA-O-B ) 4XA′ XB′ β ) √1 - 4XA′ XB′ Q,

( β +1 1 )

(2)

if 2W e 0

β ) √1 - 4XA′ XB′ (Q/(Q + 1)),

if 2W g 0

where XA′ ) zAXA/(zAXA + zBXB) and XB′ ) zBXB/(zAXA + zBXB) refer to the normalized mole fractions of A and B, while zA and zB are their coordination numbers. XA and XB are the mole fractions of A and B [i.e., XA ) A/(A + B)]. Note that this relationship is applicable to any crystalline or noncrystalline binary system. In binary borosilicate glasses, where the oxygen sites are well resolved in O-17 NMR, the estimated 2W value from the [4]Si-O-[3]B fraction with Si/B ratio (approximately 35% at XB ) 0.575) is relatively robust.17 The predicted [4] Ge-O-[3]B fraction (at XB ) 0.575, GB46) from the estimated Q value of 0.4 is approximately 59%. A quantitative estimate of the oxygen site fraction ([4]Ge-O-[3]B) in binary borogermanate glasses is, however, difficult to obtain from O-17 NMR due to the peak overlap and the large uncertainty in the BO fractions (Figures 4 and 5). The Cq of oxygen cluster is likely to vary from ∼5 MHz (for [3]B-O-[3]B) to ∼7 MHz (for [4] Ge-O-[4]Ge),35,74 and the fraction of [4]Ge-O-[4]Ge is greatly underestimated (i.e., approximately 60%).35 The Cq of [4] Ge-O-[3]B is also not known, which makes it more difficult to quantify the O-17 NMR spectra. Here, we thus used the framework disorder achieved by quantum chemical calculations to better describe the degree of intermixing between B and Ge in borogermanate glasses. Equation 2 can however be used to quantify the extent of disorder in diverse binary oxide glasses if the oxygen peaks are well-resolved. The chemical order difference between borosilicate (negative Q) and borogermanate glasses (positive Q) affects their macroscopic properties such as configurational enthalpy and activity coefficient of oxides. The measured extent of disorder suggests that the configurational enthalpy (Hconfig) for binary borogermanate glasses is expected to show a negative deviation, although the experimental data is not yet available. We showed that the experimental Hconfig obtained from calorimetry for binary borosilicate glasses shows a positive deviation, consistent with the prediction from Q (ref 17) and the slight discrepancy between the experimental Hconfig and the estimate from NMR considering only the chemical aspects of disorder was due to an increase in the boroxol ring content when the boron content was high.17 Hconfig in topological disordered solids is thus affected not only by the chemical mixing contribution but also by

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changes in the topology (ring and nonring fractions) as the composition changes. By considering both chemical mixing and the changes in topology, Hconfig can be expressed using a quasichemical approximation as follows:

Hconfig ) XA′ XB′

[

]

Ztot2W + EtopoXtopo(XB′ ) β+1

(3)

where Ztot ) zAXA + zBXB, Xtopo(XB′ ) refers to the compositiondependent mole fraction of a specific topology (e.g., a boroxol ring), and β is as previously defined. Etopo is the energy due to the change in topology as the composition changes, and in the present case, it measures the additional enthalpy due to the formation of boroxol rings. For binary borosilicate glasses, Xtopo(XB′ ) can be approximated to 0.7XB′ , and for borogermanate glasses, Xtopo(XB′ ) is smaller and can be directly estimated from Figure 3. All of the other variables have been defined above. The first term in the above equation considers chemical mixing,17 and the second term describes explicitly the effect of changes in the topology as the composition changes. If the coordination numbers of the framework units are identical, the second term can also explain the nonsymmetric excess free energy of mixing in the oxide glasses (beyond that of the regular solution model). Figure 7 shows Hconfig for borosilicate and borogermanate glasses. Here, we assume that Tf for binary borogermanate glasses varies linearly from the value for pure B2O3 (536 K) to that for GeO2 (851 K).79 The Tf values for binary borosilicate glasses are derived from previous studies.79 The contribution of chemical mixing between B and Si to the total Hconfig can partially explain the macroscopic configurational enthalpy in borosilicate glasses (approximately 3.2 kJ/mol at XB ) 0.66, red curve with BS label).17 Hconfig can be better reproduced by considering the Etopo of approximately 14 kJ/mol of unit boron (blue curve with a BS label, 28 kJ/mol of B2O3);17 this reproduces the experimental Hconfig obtained from solution calorimetry.29 While future experiments reveal differences in formation enthalpy for boroxol rings in borosilicates and borogermanates, we note that the estimated formation enthalpy of boroxol rings in borogermanate glasses from qualitative vibrational spectroscopy (∼28 kJ/mol) is also similar to the estimated formation enthalpy of boroxol rings in binary alkali borate glasses (∼24 kJ/mol)62 and the above Etopo value for binary borosilicate glasses.17 We thus used identical Etopo values for borogermanate glasses. Note again that Hconfig using quantum chemical calculations (quantum 1 and 2) is consistent with the results from NMR for binary borosilicate glasses. The predicted chemical contribution to Hconfig in binary borogermanate glasses using the 2W value from the quantum chemical calculations (-4.2 kJ/mol) shows negative values with a Q value of approximately 0.4 (at Tf ) 680 K). The topological contribution to Hconfig in binary borogermanate glasses is slightly smaller than that in binary borosilicate glasses, as expected from the smaller boroxol ring content, Xtopo(X′B), in borogermanate glasses (Figure 3). The resulting Hconfig (chemical and topological contribution) is expected to be negative except in the boron-rich region toward the B2O3 end member. This shows that a moderate prevalence of chemical mixing between B and Ge occurs in binary borogermanate glasses. These results yield the atomistic origins of the formation of stable Ge-O-B bonds without phase separation, as demonstrated in recently synthesized borogermanate framework materials (e.g, ref 42). In this study, we investigate quantification of the degree of the chemical and topological aspects of disorder in borogermanate glasses by using multinuclear high-resolution NMR and quantum chemical calculations combined with quasi-chemical

Figure 7. Configurational enthalpy (Hconfig) for binary borosilicate (red curves, labeled BS) and binary borogermanate glasses (black curves, labeled BG) with varying XB. Blue curves show the contribution from topological changes with XB with a constant Etopology of 14 kJ/mol per unit boron for borosilicate17 and borogermanate glasses (Figure 3). Curves labeled quantum 1 and 2 show the results obtained with 2W calculated at the B3LYP/6-311+G(2d,p)//HF/3-21G level (1) and at the B3LYP/6-311+G(2d,p)//B3LYP/6-311+G(2d,p) level (2) (ref 17). Closed red circles represent the experimental values obtained by calorimetry. The red curves labeled NMR-(BS) are calculated using eq 3 with the 2W value from O-17 NMR. The thick red curve labeled Q ) -0.65 + Htopology(BS) is the Hconfig value considering the formation of boroxol rings in borosilicate glasses.17 The thin black line (Q ) 0.5) refers to the calculated Hconfig (at Q ) 0.5, with a fixed Tf of 680 K, note that the Q value varies with Tf). The thick black curve (Q ) 0.4, Tf ) 680 K, 2W ) -4.2 kJ/mol) is the expected Hconfig considering only the chemical mixing of B and Ge. The thick black curve with label [Q ) 0.4 + Htopology(BG)] is the Hconfig due to both the chemical mixing of B and Ge and the topological variation as the composition changes.

approximation: we are able to yield new insights into the structure and disorder in archetypal binary oxide glasses. The result of the current study presents the first experimental and theoretical evidence for the detailed topology and chemical disorder in binary borogermanate glasses. We are also able to show how these experimental and theoretical findings provide insight into the effect of composition (Ge/Si) on the chemical and topological aspects of disorder in archetypal binary oxide glasses. The simpler and thus more general order parameter introduced in the current study (eq 1) can allow us to quantify the extent of chemical disorder. We present an analytical expression for the configurational enthalpy where both topological and chemical aspects of disorder are explicitly considered (eq 3). We then account for the macroscopic thermodynamic properties of simple model germanate glasses by using detailed experimental information on the degree of chemical and topological disorder.

Structure of Borogermanate Glasses Whereas a quantitative estimate of the extent of disorder in fundamental covalent oxides (aluminosilicates, borosilicates, and borogermanates) has begun to be revealed, further experiments are needed for diverse oxide glasses with varying types of cations (e.g., Ge, Ti, and P) and coordination numbers to yield a systematic and generalized interpretation of the intrinsic disorder in binary as well as multicomponent oxide glasses and melts at varying temperature and pressure. Together with the current results, it should be mentioned that recent progress and advances in through-bond and through-space correlations among framework cations and anions in solid-state NMR yields additional details of the extent of disorder (connectivity and proximity) in oxide glasses (e.g., refs 80-83 and references therein). The results with a single disorder parameter (Q) and eqs 1 and 3 can also be helpful to quantify the extent of disorder in diverse crystalline and amorphous oxides, including glasses, framework zeolites, and nanoparticles, leading to an enhanced understanding of both the nature of intermixing in the topologically disordered solids and their structure-property relationships. Acknowledgment. This study was supported by a grant from the National Research Foundation, Korea (2007-000-20120), to S.K.L. We thank P. Grandinetti for providing us with the RMN software for 2D NMR data processing and two anonymous reviewers for careful and constructive suggestions. References and Notes (1) Lee, S. K. J. Phys. Chem. B 2004, 108, 5889. (2) Allwardt, J. R.; Stebbins, J. F.; Schmidt, B. C.; Frost, D. J.; Withers, A. C.; Hirschmann, M. M. Am. Mineral. 2005, 90, 1218. (3) Hess, P. C. Thermodynamic mixing properties and structure of silicate melts. In Structure, Dynamics, and Properties of Silicate Melts; Stebbins, J. F., McMillan, P. F., Dingwell, D. B., Eds.; Mineralogical Society of America: Washington, DC, 1995; p 145. (4) Kelsey, K. E.; Stebbins, J. F.; Singer, D. M.; Brown, G. E.; Mosenfelder, J. L.; Asimow, P. D. Geochim. Cosmochim. Acta 2009, 73, 3914. (5) Lee, S. K. Geochim. Cosmochim. Acta 2005, 69, 3695. (6) Lee, S. K.; Cody, G. D.; Fei, Y. W.; Mysen, B. O. J. Phys. Chem. B 2008, 112, 11756. (7) Lee, S. K.; Lin, J. F.; Cai, Y. Q.; Hiraoka, N.; Eng, P. J.; Okuchi, T.; Mao, H. K.; Meng, Y.; Hu, M. Y.; Chow, P.; Shu, J. F.; Li, B. S.; Fukui, H.; Lee, B. H.; Kim, H. N.; Yoo, C. S. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 7925. (8) Lee, S. K.; Stebbins, J. F. Am. Mineral. 1999, 84, 937. (9) Mysen, B. O.; Richet, P. Silicate Glasses and Melts: Properties and Structure (DeVelopments in Geochemistry); Elsevier: Amsterdam, The Netherlands, 2005. (10) Navrotsky, A. Energetics of silicate melts. In Structure, Dynamics, and Properties of Silicate Melts; Stebbins, J. F., McMillan, P. F., Dingwell, D. B., Eds.; Mineralogical Society of America: Washington, DC, 1995; p 121. (11) Stebbins, J. F.; Dubinsky, E. V.; Kanehashi, K.; Kelsey, K. E. Geochim. Cosmochim. Acta 2008, 72, 910. (12) Angeli, F.; Delaye, J. M.; Charpentier, T.; Petit, J. C.; Ghaleb, D.; Faucon, P. Chem. Phys. Lett. 2000, 320, 681. (13) Xue, X.; Stebbins, J. F.; Kanzaki, M. Am. Mineral. 1994, 79, 31. (14) Yarger, J. L.; Smith, K. H.; Nieman, R. A.; Diefenbacher, J.; Wolf, G. H.; Poe, B. T.; McMillan, P. F. Science 1995, 270, 1964. (15) Richet, P. Geochim. Cosmochim. Acta 1984, 48, 471. (16) Lee, S. K.; Musgrave, C. B.; Zhao, P.; Stebbins, J. F. J. Phys. Chem. B 2001, 105, 12583. (17) Lee, S. K.; Stebbins, J. F. Geochim. Cosmochim. Acta 2002, 66, 303. (18) Stebbins, J. F. Dynamics and structure of silicate and oxide melts: nuclear magnetic resonance studies. In Structure, Dynamics, and Properties of Silicate Melts; Stebbins, J. F., McMillan, P. F., Dingwell, D. B., Eds.; Mineralogical Society of America: Washington, DC, 1995; Vol. 32, p 191. (19) Allwardt, J. R.; Schmidt, B. C.; Stebbins, J. F. Chem. Geol. 2004, 213, 137. (20) Dirken, P. J.; Kohn, S. C.; Smith, M. E.; Vaneck, E. R. H. Chem. Phys. Lett. 1997, 266, 568. (21) Du, L. S.; Stebbins, J. F. J. Non-Cryst. Solids 2005, 351, 3508. (22) Stebbins, J. F. Chem. Geol. 2008, 256, 80. (23) Stebbins, J. F.; Oglesby, J. V.; Xu, Z. Am. Mineral. 1997, 82, 1116.

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