Nature of SiliconâBoron Mixing in Sodium Borosilicate Glasses: A

J. Phys. Chem. B 2003, 107, 10063-10076

Nature of Silicon-Boron Mixing in Sodium Borosilicate Glasses: A High-Resolution and 17O NMR Study

10063 11B

Lin-Shu Du* and Jonathan F. Stebbins Department of Geological and enVironmental Sciences, Stanford UniVersity, Stanford, California 94305-2115 ReceiVed: January 8, 2003; In Final Form: June 23, 2003

In several series of sodium borosilicate glasses, we have applied triple-quantum magic-angle spinning (3QMAS) 11 B and 17O NMR to obtain high-resolution information about short-range structure and the connections among various network structural units and their variations with composition. Oxygen-17 3QMAS spectra reveal changes in connectivities between silicate and BO3 ([3]B) and BO4 ([4]B) units, by quantifying populations of bridging oxygens such as Si-O-Si, Si-O-[3]B, Si-O-[4]B, [3]B-O-[3]B, and [4]B-O-[3]B and of nonbridging oxygens. Boron-11 MAS and 3QMAS at a magnetic field of 14.1 T allow proportions of several borate units to be determined, including [3]B in boroxol ring and nonring sites and [4]B with two, three, and four Si neighbors. By combining the 11B and 17O NMR results, detailed information on Si/B mixing in sodium borosilicates can be derived. Our results shows that [4]B is strongly associated with silicate units, nonring [3]B undergoes random mixing and ring [3]B tends to connect to borate groups. The behavior of Si/B mixing for each boron species can be quantitatively represented in terms of a parameter, θ, indicating the degree of random mixing, which is potentially useful for the thermodynamic modeling of such glass structures.

Introduction Borosilicate glasses are widely used in many applications, such as optical components, sealing materials, chemically resistant containers, and the sequestration of radioactive waste.1 It is well-known that liquid-liquid phase separation occurs in a range of compositions of sodium borosilicate glasses with proper heat treatment at temperatures well below the liquidus.2 Following acid leaching of the relatively soluble boron-rich phase, porous glasses can be made, which commonly serve as the base for separation membranes, enzyme, and catalyst supports.3,4 The degree of mixing among silicon and various boron structural species is thus a generally important issue in controlling and designing the physical properties of borosilicate glasses, such as chemical durability, strength at high temperature, and crystal nucleation rates. The extent of Si/B mixing is the shortest-range measure of the development of medium-range ordering that precedes actual phase separation. This parameter clearly must also be a major component of the overall configurational entropy of the glass and of corresponding liquids near the glass transition temperature, which in turn is of critical importance to models of viscosity5,6 and of the free energy needed to predict phase equilibria. Boron-11 NMR has long been one of the major tools to study the short-range structure of alkali borate and borosilicate glasses. Decades of work with 11B “wide-line” NMR accurately determined the fraction of tetrahedral (BO4 groups, denoted here as [4]B) and trigonal boron species (BO groups, [3]B) including 3 symmetric and asymmetric trigonal boron groups, which led to detailed structural models for sodium borosilicate glasses.7,8 Quadrupolar coupling constants (CQ) and asymmetry parameters (η) were also determined for these types of borate groups. CQ is the measure of the deviation from tetrahedral or higher * To whom correspondence should be addressed. E-mail: lsdu@pangea. stanford.edu.

symmetry of the local bonding environment and η measures the deviation from local cylindrical symmetry. High-resolution magic angle spinning (MAS) 11B NMR at high magnetic fields (preferably 11.7 T or above) also yields accurate relative concentrations of trigonal and tetrahedral boron species and can also provide quadrupolar parameters (CQ, η) as well as the isotropic chemical shifts (δiso) not obtainable from “wide-line” studies.9-13 The latter provide additional structural insights when correlated with variables such as coordination number, bond distance and angle, and first and second neighbor populations.9 The large value of CQ for trigonal boron (typically about 2.6 MHz) results in a significant second-order quadrupolar broadening and degrades the resolution of the 11B MAS spectra. Several techniques such as dynamic angle spinning (DAS)14 and triple quantum magic angle spinning (3QMAS)15,16 have been developed to eliminate this problem by providing two-dimensional (2-D) spectra with one dimension free of such broadening. Boron-11 DAS NMR has resolved and quantified [3]B in rings of three BO3 group (so-called “boroxol rings”) and nonring [3]B in B2O3 and alkali borate glasses.17-21 We have shown recently that even better resolution of such sites can be obtained with 11B triple-quantum 3QMAS, particularly at relative high magnetic fields such as 14.1 T.11,22,23 Oxygen-17 NMR can potentially provide a great deal of information about connectivities among various cations, network bond angles, and cation order/disorder, but it is complicated by often severe quadrupolar broadening and the need for 17O-enriched samples. However, the greatly improved resolution provided by 17O 3QMAS has allowed resolution of various types of bridging oxygen sites such as Si-O-Si, Si-O-B, and B-O-B as well as nonbridging oxygens.22,24-26 Relatively little work has been done to directly explore the degree of mixing in sodium borosilicate glasses. It was suggested by Bray and co-workers that borate groups start to mix with silicate groups at the molar ratio of Na2O to B2O3 (denoted as

10.1021/jp034048l CCC: $25.00 © 2003 American Chemical Society Published on Web 08/26/2003

10064 J. Phys. Chem. B, Vol. 107, No. 37, 2003 R) greater than 0.5.8 When R < 0.5, it was proposed that the addition of Na mainly influences the borate domain and generates sodium diborate groups (Na2O‚2B2O3). In contrast, Raman spectroscopic studies suggested that there is some mixing between silicate and sodium borate at R values lower than 0.5.27,28 From 29Si MAS NMR studies,29,30 it was also suggested that sodium cations start to be associated with silicate groups at R values lower than 0.5, depending on the Si/B ratio. Significant intensities of Si-O-B peaks in 17O 3QMAS spectra for samples with R < 0.5 have directly demonstrated a considerable degree of Si/B mixing.22,25 In the sodium-rich region of the ternary system, Raman and 11B, 29Si, 17O, and 23Na NMR studies suggested a more homogeneous glass structure with much better Si/B mixing, with a borosilicate network containing anionic [4]B and nonbridging oxygen (NBO) units to charge compensate the network modifier cations.28 More recently, linear dependencies of mean chemical shifts on compositional parameters were observed for B (including [3]B and [4]B), Si, and Na in sodium borosilicate glasses.31 The results again suggested considerable mixing of copolymerized [3]B and [4]B and [4]Si units and a more uniform distribution of Na cations in the whole composition range beyond the immiscibility region. In binary SiO2-B2O3 glasses, the degree of mixing of fourcoordinated silicon and three-coordinated boron has been quantified from 17O and 11B 3QMAS spectra combined with statistical thermodynamics and ab initio molecular orbital calculations.23,32 In this system, the NMR data show somewhat less than random mixing of Si and B, suggesting at least a tendency toward phase separation. A combination of 11B 3QMAS and 29Si{11B} double-resonance NMR techniques has also been applied to the binary system.33 The results were quantitatively interpreted in terms of a separation of the glasses into a virtually SiO2-free phase and a mixed borosilicate phase with Si/B ratio close to 1. In our recent NMR study of alkali borosilicate glasses,22 we showed that more detailed structural units can be found in both 17O and 11B 3QMAS spectra. This provides a greatly increased amount of information to explore interesting topics such us the effect of Na content, the effect of annealing at different temperatures, and the effect of different modifier cations on the glass structure. A preliminary approach to obtaining the mean number of Si coordinated to boron units by combination of 17O and 11B NMR data was proposed, and the results indicated that the order of the degree of Si/B mixing is [4]B > [3]B(nonring) > [3]B(ring). Here we report a more detailed 17O and 11B MAS and 3QMAS NMR investigation of sodium borosilicate glasses with a wider range of compositions and systematic changes in Na/B and Si/B ratios. We show the effect of composition on the speciation of oxygen and boron structural units as well as the changes in the degree of Si/B mixing in terms of the mean number of Si coordinated to each boron unit. Finally the nature of Si/B mixing of each boron unit is addressed and is quantified in terms of the degree of variation from random mixing. Experimental Section Sample Preparation. Samples were synthesized from dried Na2CO3, B2O3, and SiO2. Nominal compositions are represented in this paper by K and R values defined as the molar ratio of SiO2 to B2O3 and Na2O to B2O3, respectively. For K ) 2 and 4 compositions (denoted as NBS-K2 and NBS-K4, respectively), 17O-enriched SiO was used; for K ) 0.5 compositions (denoted 2 as NBS-K0.5), 17O-enriched B2O3 was used instead. To speed

Du and Stebbins

Figure 1. Compositions of sodium borosilicate glasses described in this study. The area inside the ellipse roughly indicates the region of immiscibility at 720 °C and is not intended to exactly reproduce the known phase diagram. K is the molar ratio SiO2/B2O3; R is Na2O/B2O3.

TABLE 1: Sample Names and Nominal Compositions mole fraction sample name

Na2O

B2O3

SiO2

NBS-K0.5R0.25 NBS-K0.5R0.5 NBS-K0.5R0.75 NBS-K2R0.25 NBS-K2R0.50 NBS-K2R0.75 NBS-K4R0.25 NBS-K4R0.50 NBS-K4R0.75

0.143 0.250 0.333 0.077 0.143 0.200 0.048 0.091 0.130

0.571 0.500 0.444 0.308 0.286 0.267 0.190 0.182 0.174

0.286 0.250 0.222 0.615 0.571 0.533 0.762 0.727 0.696

spin-lattice relaxation and allow more rapid NMR data collection, about 0.2 wt % Co3O4 was added to each 300-mg sample. Oxygen-17 enriched silica or boric acid was prepared by hydrolyzing silicon tetrachloride or boron trichloride with 47% 17O-enriched water in a diethyl ether solvent, followed by dehydration at high temperature in Ar. The starting materials were ground together, then heated in platinum crucibles in Ar first at 600 °C to allow decarbonation and then at 1000 to 1200 °C (depending on the liquidus temperature) for 30-45 min. Each sample was quenched by dipping the bottom of the crucible in cold water. All resulting glasses were optically homogeneous on examination at 400× with an optical microscope. Nominal compositions are shown in Figure 1 and Table 1. In some cases, the fraction of total boron in tetrahedral sites measured by NMR is slightly lower than expected from the extensive previous 11B “wide-line” NMR work on these compositions,7,8,34 probably indicating some loss of Na during melting of these small sample batches. However, given the nature of the conclusions drawn here, such deviations do not pose a serious problem. NMR Data Collection. NMR spectra were collected on a Varian Unity/INOVA 600 spectrometer (14.1 T) at 81.3 and 192.4 MHz for 17O and 11B, respectively. 17O and 11B chemical shifts are expressed in parts per million (ppm) relative to 17O-enriched H O at 0 ppm and 1.0 M boric acid at 19.6 ppm. 2 A Varian/Chemagnetics T3 probe with 3.2-mm ZrO2 rotors and spinning speeds of 20 kHz were used. The 11B MAS spectra were obtained by using a single hard pulse, with radio frequency (rf) powers of 160 kHz. To obtain more quantitative spectra, an rf tip angle of less than one-third of the solid 90° pulse duration was employed, resulting in 0.3 µs long pulses for single-pulse experiments. Relaxation delays of 5 s were used for 11B MAS experiments. Both 17O and 11B 3QMAS spectra were acquired by using a shifted-echo pulse sequence.35 For 17O 3QMAS experiments, the optimized lengths of the triple quantum excitation and reconversion pulses were about 3.0 and 1.0 µs, with an rf power of 125 kHz. A soft 180° pulse, selecting

Nature of Silicon-Boron Mixing

J. Phys. Chem. B, Vol. 107, No. 37, 2003 10065

Figure 3. Contour plot of the 11B 3QMAS spectrum for NBS-K4R0.5 glass. The spectra projected (summed) along both dimensions are also displayed adjacent to the axes. Peak assignments are labeled as discussed in the text.

Figure 2. Boron-11 MAS spectra for (a) NBS-K0.5, (b) NBS-K2, and (c) NBS-K4 glasses at R ) 0.25, 0.5, and 0.75. Here and in the following figures, the intensity of each spectrum is normalized to that of its highest peak.

the central transition only, immediately after an echo time of 1 ms, was set to 24 µs at an rf power of 9 kHz. 80-120 t1 increments with 96-192 FIDs per t1 point were collected with a delay of 8-10 s. For the 11B 3QMAS experiments, the optimized lengths of first and second pulses with an rf power of 160 kHz were about 3.6 and 1.1 µs. The length of the third pulse was about 34 µs with an rf power of 10 kHz after an echo time of 3 ms. 240 t1 increments with 48-96 FIDs per t1 point were collected with a delay of 8-10 s. All 3QMAS data were processed by using the “RMN” program (P. J. Grandinetti, Ohio State University), including a shear transformation. Central transition line shapes of the 11B MAS spectra were simulated with the program “Wsolid” (R. E. Wasylishen and K. E. Eichele, Dalhousie University, 1999) with an approximation of infinite spinning speed. Initial constraints on isotropic δiso, quadrupolar CQ, and η for each boron site were taken from the quadrupolar coupling parameter PQ ()CQ(1 + η2/3)1/2) and δiso obtained from the centers of gravity of the peaks in the two dimensions of the 11B 3QMAS spectra as previously described.16,36,37 Estimates of δiso and PQ for oxygen sites were derived in a similar manner from the 17O 3QMAS spectra with no attempt at fitting the unresolved MAS spectra. Results Boron-11 NMR. The 11B MAS spectra of the sodium borosilicate glasses with K ) 0.5, 2, and 4 as a function of Na content (R values) are shown in Figure 2. Signals from [3]B and [4]B groups (centered around 12 and 0 ppm, respectively) are very well resolved at this field (14.1 T) as recently noted,11,22 and therefore the relative intensities of the two types of sites can be easily determined by integration. Results agree reasonably well with previous studies.8

As was described in our previous paper,22 more detailed boron structural units can be obtained with 11B 3QMAS. This technique produces two-dimensional (2-D) spectra generally displayed as contour plots. One dimension retains the secondorder quadrupolar broadening and is equivalent to a somewhat distorted version of the MAS spectrum; the other (isotropic) dimension is free of second-order quadrupolar broadening, often providing much higher resolution.15,16,35 Figure 3 shows a 11B 3QMAS spectrum for a typical sodium borosilicate glass (NBS-K4R0.5). There are at least three peaks partially resolved in the 2-D plot and in the isotropic dimension. Two peaks associated with [3]B having significant broadening in the MAS dimension, along with a less broadened peak associated with [4]B, are centered at about 42, 33, and -2 ppm, respectively, in the isotropic dimension. It is convenient to display the isotropic projections in order to observe the trend of evolution of peaks with changes in composition. Figure 4 shows the isotropic projections for all samples. Two roughly Gaussian components for [3]B and at least two for [4]B are observed in the spectra, distinguished primarily by chemical shift differences which become particularly noticeable at the high external magnetic field employed here. Based on recent high-resolution 11B NMR studies,9,17-20,22,23,38 the two components of the [3]B NMR peak can be attributed to boron in rings of three planar BO3 groups (“boroxol” rings) and to [3]B in nonring sites. The unresolved peaks at about 0 and -3 ppm in the isotropic dimension were assigned as [4]B(1B,3Si) and [4]B(0B,4Si), respectively. This was based on the detailed comparison between the chemical shifts of these peaks and the known boron species in crystalline materials as well as the relationship between the evolution of the peak shapes and the changes of boron species with Si/B ratio.22 The addition of Na results in increases in the peak intensity for [4]B as well as decreases in the peak intensity of [3]B(nonring). This is consist with our previous study,22 indicating that the addition of Na mainly converts [3]B(nonring) to [4]B species. The effect of Si/B ratio on boron speciation can be found by comparing the glasses with the same value of R. Figure 4d shows the isotropic projections of glasses at R ) 0.25 (denoted as NBSR0.25) with different K values, i.e., different SiO2/B2O3 ratios. The ratio of populations for [3]B(nonring) to [3]B(ring) clearly increases with K. The fact that nonring [3]B groups are favored

10066 J. Phys. Chem. B, Vol. 107, No. 37, 2003

Du and Stebbins TABLE 2: NMR Parameters Obtained from Fitting of 11B MAS Spectra of NBS-K0.5 Glasses

sample name NBS-K0.5R0.25

sites [3]

B(ring) [3] B(nonring) [4] B(2B,2Si) [4] B(1B,3Si) [4] B(0B,4Si) NBS-K0.5R0.5 [3]B(ring) [3] B(nonring) [4] B(2B,2Si) [4] B(1B,3Si) [4] B(0B,4Si) NBS-K0.5R0.75 [3]B(ring) [3] B(nonring) [4] B(2B,2Si) [4] B(1B,3Si) [4] B(0B,4Si)

CQ, rel δiso, intensity ppm MHz η ((0.1) ((0.05) ((0.1) ((0.002) 17.5 14.0 1.5 -0.2 -2.2 18.0 14.7 1.5 -0.3 -2.2 18.3 15.5 1.5 -0.3 -2.2

2.60 2.60 0.3 0.3 0.3 2.65 2.55 0.3 0.3 0.3 2.60 2.55 0.3 0.3 0.3

0.2 0.2 0 0 0 0.2 0.2 0 0 0 0.2 0.2 0 0 0

0.537 0.231 0.069 0.136 0.027 0.486 0.087 0.108 0.258 0.061 0.471 0.042 0.158 0.305 0.024

TABLE 3: NMR Parameters Obtained from Fitting of 11B MAS Spectra of NBS-K2 Glasses

sample name NBS-K2R0.25

sites [3]

B(ring) B(nonring) [4] B(2B,2Si) [4] B(1B,3Si) [4] B(0B,4Si) NBS-K2R0.5 [3]B(ring) [3] B(nonring) [4] B(2B,2Si) [4] B(1B,3Si) [4] B(0B,4Si) NBS-K2R0.75 [3]B(ring) [3] B(nonring) [4] B(2B,2Si) [4] B(1B,3Si) [4] B(0B,4Si) [3]

Figure 4. Isotropic projections of 11B 3QMAS spectra for (a) NBSK0.5, (b) NBS-K2, (c) NBS-K4, and (d) NBS-R0.25 glasses. The dotted lines are guides indicating the approximate positions of the peaks associated with [3]B(ring), [3]B(nonring), [4]B(2B,2Si), [4]B(1B,3Si), and [4] B(0B,4Si), labeled as 1, 2, 3, 4, and 5, respectively. Peak assignments are discussed in the text.

at higher Si/B values may result from the better degree of Si/B mixing for nonring boron than for ring species. The center of gravity of the [4]B peak shifts to higher frequency in the isotropic dimension with decreasing K. As we showed previously,22 the chemical shift of [4]B is mainly influenced by its first cation neighbor, i.e., the relative numbers of Si and B. It is thus necessary to introduce a third, unresolved peak located at an isotropic dimension frequency higher than that of [4]B(1B,3Si). This is assigned to [4]B(2B,2Si), which is likely to become significant at lower Si/B ratio. To obtain the populations of each B species, δiso and PQ were first estimated from the centers of gravity in the 2-D spectra as described in the Experimental Section, and slices through the peaks in the 2-D spectra along the MAS dimension were fit to estimate the η values. These results were then used as starting points for fits of the MAS spectra based on a five-species model (two [3]B and three [4]B site types). The systematic difference between the intensities for the [3]B and [4]B species caused by their very different CQ and η values was been taken into account when estimating their relative populations from the peak areas in center bands.39 Results are tabulated in Tables 2-4, and Figure 5 shows an example of a fully simulated spectrum. Note that in our previous study on NBS-K2 glasses22 the populations of B species were obtained based on a four-species simulation (without considering [4]B(2B,2Si)). The result of five-species simulation in this study shows that the fractions of [4]B(2B,2Si) are below 0.03, indicating there are only minor differences between the two studies. Oxygen-17 NMR. Figure 6 displays a 17O 3QMAS spectrum for a typical Na borosilicate glass (NBS-K2R0.75). As we showed previously for borate and borosilicate glasses,22-26,40 resolution in conventional MAS spectra (or MAS projections, Figure 6) is poor, but at least four peaks are partially resolved in the 2-D plot and in the isotropic projection. These peaks can

CQ, rel δiso, intensity ppm MHz η ((0.1) ((0.05) ((0.1) ((0.002) 17.3 13.2 1.5 -0.2 -2.2 17.3 13.9 1.5 -0.3 -2.2 17.65 14.9 1.5 -0.3 -2.0

2.65 2.62 0.3 0.3 0.3 2.65 2.62 0.3 0.3 0.3 2.65 2.62 0.3 0.3 0.3

0.2 0.2 0 0 0 0.2 0.2 0 0 0 0.2 0.2 0 0 0

0.385 0.428 0.011 0.144 0.032 0.400 0.196 0.027 0.249 0.128 0.306 0.128 0.052 0.325 0.189

TABLE 4: NMR Parameters Obtained from Fitting of 11B MAS Spectra of NBS-K4 Glasses

sample name NBS-K4R0.25

sites [3]

B(ring) B(nonring) [4] B(2B,2Si) [4] B(1B,3Si) [4] B(0B,4Si) NBS-K4R0.5 [3]B(ring) [3] B(nonring) [4] B(2B,2Si) [4] B(1B,3Si) [4] B(0B,4Si) NBS-K4R0.75 [3]B(ring) [3] B(nonring) [4] B(2B,2Si) [4] B(1B,3Si) [4] B(0B,4Si) [3]

CQ, rel δiso, intensity ppm MHz η ((0.1) ((0.05) ((0.1) ((0.002) 17.2 13.0 na -0.2 -2.2 17.2 13.4 1.5 -0.3 -2.2 17.2 13.6 1.5 -0.3 -2.2

2.65 2.62 na 0.3 0.3 2.60 2.65 0.3 0.3 0.3 2.60 2.62 0.3 0.3 0.3

0.2 0.2 na 0 0 0.2 0.2 0 0 0 0.2 0.2 0 0 0

0.251 0.557 na 0.117 0.075 0.286 0.302 0.039 0.190 0.183 0.240 0.197 0.030 0.232 0.301

be easily assigned to bridging oxygens, Si-O-Si, Si-O-B, and B-O-B, and nonbridging oxygen (“NBO”), based on our previous studies of glasses and crystalline model compounds.22-26,40 The isotropic projections of the 17O 3QMAS (Figure 7) have three main peaks that originate from the three types of bridging oxygens, and their positions and relative intensities vary considerably with composition. The peak shapes for Si-O-B and B-O-B suggest that each is comprised of two components



Figure 5. Experimental 11B MAS NMR spectrum (solid line) and fitting results (dotted line, sum; dashed lines, components) for NBSK0.5R0.25 glass. The peaks for [3]B(ring), [3]B(nonring), [4]B(2B,2Si), [4] B(1B,3Si), and [4]B(0B,4Si) are labeled as 1, 2, 3, 4, and 5, respectively. Fit parameters are given in Table 4.

Figure 7. Isotropic projections of 17O 3QMAS spectra for (a) NBSK0.5, (b) NBS-K2, (c) NBS-K4, and (d) NBS-R0.5 glasses. The dotted lines are guides indicating the approximate positions of the peaks for Si-O-Si, Si-O-[4]B, Si-O-[3]B, [4]B-O-[3]B, and [3]B-O-[3]B, labeled as 1, 2, 3, 4, and 5, respectively.

Figure 6. Contour plot of 17O 3QMAS spectrum for NBS-K2R0.75 glass. The spectra projected (summed) along both dimensions are also displayed adjacent to the axes.

at fixed frequencies whose relative intensities change with composition. In our previous study of NBS-K2,22 careful analysis of these spectra by curve fitting with different models confirmed this interpretation. The peaks centered at about -40, -45, -55, and -60 ppm in the isotropic dimension were assigned to Si-O-[4]B, Si-O-[3]B, [4]B-O-[3]B, and [3]B-O-[3]B, respectively, based on the changes in the populations of these species with respect to the change in the [4]B/[3]B ratio with varying R and an assumption that the energetically less favorable [4]B-O-[4]B has an insignificant concentration ([4]B avoidance rule).22 Increases in the intensity ratios of Si-O-[4]B to Si-O-[3]B and of [4]B-O-[3]B to [3]B-O-[3]B with increasing R were seen for each series with different Si/B ratios, as expected from the effect of R on [4]B/[3]B. The prominent peak on the high-frequency side of the 17O isotropic projection spectra can be uniquely assigned to Si-O-Si and varies considerably in intensity with composition, as expected from the Si/B ratio (Figure 7d) and the effects of

R on the extent of network mixing.22 Its significant change in position with composition is discussed below. Simulation of the 17O MAS spectra for these glasses is difficult due to their breadths and lack of significant discontinuities or other characteristic features. However, the isotropic projections of the 3QMAS spectra can each be fit with at least five Gaussian peaks, yielding relative intensities and δiso and PQ values. Our previous study has shown that because quadrupolar parameters are similar (4.8-5.5 for PQ and 0.3-0.4 for η) for each type of bridging oxygen in ternary borosilicate glasses, corrections for the effects of excitation and reconversion efficiencies are minor and thus have not been applied.22 The fitted areas are thus good approximations (within about 10%) of the proportions of different sites (Table 5). Note that PQ for nonbridging oxygen (NBO) associated with Si is smaller at about 2 MHz, and its relative 3QMAS peak intensity may thus be somewhat greater than its true population, although our recent 17O 3QMAS study of barium borosilicate glasses at the same magnetic and rf fields yielded surprisingly good agreement between NBO fractions derived from 3QMAS and MAS data.26 However, the fraction of NBO in these compositions is less than 5%, so that modeling of the BO populations alone accounts for most of the oxygen in the structure. Discussion Effect of Sodium-to-Boron Ratio on Boron Speciation. The effects of molar ratio of sodium to boron (R) on boron speciation are shown in Figures 8-10. Note that the data points at R ) 0 were interpolated from data on binary borosilicate glasses.32 As has long been known from early “wide-line” 11B studies,7,8 the most obvious effect of the addition of Na is on the ratio of [4]B to [3]B. In this compositional region [3]B is converted nearly stoichiometrically (at least at temperatures near to the glass transition) to [4]B by the addition of Na, as described by standard structural models.8


Du and Stebbins

TABLE 5: Relative Proportions of Oxygen Species in NBS-K0.5, NBS-K2, and NBS-K4 Glasses, Obtained from Fitting the Isotropic Projections of the 17O 3QMAS Data rel proportion sample name

Si-O-Si

Si-O-[4]B

Si-O- [3]B


0.116(2) 0.140(5) 0.098(5) 0.456(2) 0.369(2) 0.332(2) 0.643(2) 0.593(2) 0.600(2)

0.190(5) 0.269(5) 0.319(5) 0.112(5) 0.263(5) 0.384(5) 0.063(5) 0.194(5) 0.244(5)

0.096(5) 0.060(5) 0.044(5) 0.226(5) 0.112(5) 0.082(5) 0.221(5) 0.131(5) 0.089(5)

Figure 8. Variations of the fractions of boron species with R in NBSK0.5 glasses, as given in Table 2.

Figure 9. Variations of the fractions of boron species with R in NBSK2 glasses, as given in Table 3.

It is obvious that in all three glass series with different K values, the nonring [3]B species decreases in relative intensity with increasing R, but the relative population of ring [3]B does not vary greatly, as we noted previously for the NBS-K2 glasses.22 This result implies that the addition of Na does not significantly affect the population of boroxol rings but does convert nonring [3]B to [4]B species. Similar behavior was observed in alkali borate binary glasses.19,20 In those studies it was suggested that rings could be particularly stable with respect to the addition of modifier oxides. It may also indicate that ring [3]B groups tend to segregate in the B-rich regions in the structure, even in compositions well outside of the known metastable immiscibility field.

[4]

B-O-[3]B 0.439(5) 0.355(5) 0.350(5) 0.121(5) 0.152(5) 0.094(5) 0.051(5) 0.053(5) 0.034(5)

[3]

B-O-[3]B 0.159(5) 0.176(5) 0.152(5) 0.085(5) 0.104(5) 0.086(5) 0.022(5) 0.029(5) 0.033(5)

NBO na na 0.037(5) na na 0.022(5) na na na

Figure 10. Variations of the fractions of boron species with R in NBSK4 glasses, as given in Table 4.

Effect of Silicon-to-Boron Ratio on Boron Speciation. Lee and Stebbins have recently shown that the fraction of nonring boron increases with increasing Si/B ratio in binary borosilicate glasses using 3QMAS NMR.23,32 A similar trend is found in the ternary system studied here. The fractions of [3]B(nonring) versus XSi are depicted in Figure 11a, where XSi is the molar ratio of Si to network total formers (Si + B). The slopes of the observed linear relationships are inversely correlated with R. Our previous study showed that the degree of mixing for nonring [3]B is larger than that for ring [3]B.22 The increases in nonring [3]B with X may thus be driven by the configurational entropy Si (and free energy reduction) stemming from better Si/B mixing. The greater slope at lower R value results from the different degrees of Si/B mixing for different B species. In our previous study,22 we found the degree of Si/B mixing is in the following order: [4]B > [3]B(nonring) > [3]B(ring). At lower R values where [4]B/[3]B is lower, a greater rate of increase in [3]B(nonring) with increasing Si/B is apparently necessary in order to compensate the loss of configurational entropy caused by the lower fraction of [4]B. The fraction of [3]B(nonring) out of total [3]B also varies linearly with XSi for each R series (Figure 11b), but with slopes that are nearly independent of R. This implies that the nature of the mixing with Si for [3]B(nonring) is not influenced by the addition of Na. Effect of Sodium-to-Boron Ratio on Oxygen Speciation. The effect of R on oxygen species populations are graphed for each K series in Figures 12-14. The data at R ) 0 in these figures were again interpolated from the results for binary borosilicate glasses of Lee and Stebbins.23 Compositional effects are complex and we note here only several of the more obvious and interesting results. First, the fraction of Si-O-[4]B tends



Figure 13. Variations in the fractions of oxygen species with R for NBS-K2 glasses, as given in Table 5.

Figure 11. Plots of (a) fraction of [3]B(nonring) versus XSi and (b) fraction of nonring in [3]B versus XSi for binary (R ) 0) and ternary borosilicate glasses (R ) 0.25, 0.5, and 0.75). The data in (a) and (b) are fitted by linear regression and the results are shown in solid lines. The binary data R ) 0 here and in Figures 12, 13, and 14 were interpolated from a previous study by Lee and Stebbins.23

Figure 14. Variations in the fractions of oxygen species with R for NBS-K4 glasses, as given in Table 5. [3]B(nonring)

Figure 12. Variations in the fractions of oxygen species with R for NBS-K0.5 glasses, as given in Table 5.

to increase with R, presumably simply because the [4]B/[3]B ratio also increases with R. One might thus expect the fraction of both Si-O-[3]B and [3]B-O-[3]B to decrease with increasing R. This is indeed seen for Si-O-[3]B at each K value, but the fraction of [3]B-O-[3]B stays about the same if the binary data are excluded. From the 11B NMR results described above, the decrease in [3]B with increasing R mainly involves nonring species, while the fraction of ring species among total [3]B stays about the same. The 17O NMR results therefore confirm our previous suggestion that most of [3]B-O-[3]B may be associated with boroxol rings and does not mix extensively with Si, thus remaining approximately constant with variation in R. On the other hand, the majority of Si-O-[3]B may involve

because of this species’ greater tendency to mix with Si. Therefore, the decreasing [3]B(nonring) with increasing R leads to the decrease in the fraction of Si-O-[3]B. The lack of consistent trend for [4]B-O-[3]B may result from the complexities of the opposite effects of R on [4]B and [3]B contents. Extent of Overall Si/B Mixing. The fraction of Si-O-B is a good measure of the total extent of mixing of Si and B in the network (Figure 15). For the K ) 2 and K ) 4 series, local minima in the Si-O-B curves are located at R ) 0.25, which is in the center of the metastable liquid immiscibility field (Figure 1). Glasses in this region have either sub-optical scale, incipient phase separation or significant compositional heterogeneity in a single phase: the compositional tie lines indicate a tendency to separate to B-rich plus Si-rich regions.2 The compositions of the K ) 0.5 glasses are located outside of the immiscibility region, and no minimum is obvious in the Si-O-B variation with R. Effect of Silicon-to-Boron Ratio on Oxygen Speciation. The fraction of Si-O-B with varying XSi (Figure 16) is higher at higher R values, indicating greater overall Si/B mixing. This is expected from the higher [4]B/[3]B at higher R, as [4]B tends to mix well with [4]Si. The maximum fractions of Si-O-B for


Figure 15. Variations in the fractions of Si-O-B bridging oxygens with R for NBS-K0.5, NBS-K2, and NBS-K4 glasses. The gray area indicates a range of R values located in the center of the immiscibility region (shown in Figure 1).

Figure 16. Variations in the fraction of oxygen species in bridging oxygens with XSi for NBS-R0.25, NBS-K0.5, and NBS-R0.75 glasses.

each R value are located at XSi ≈ 0.4, because the mean coordination number for B is smaller than that for Si. In the binary borosilicate system (R ) 0),23 the fractions of Si-O-B are similar to those seen here for R ) 0.5, again indicating that the R ) 0.25 glasses, although optically clear, have considerable nanoscale heterogeneity since their compositions are located near the center of the immiscibility region. Degree of Mixing among Si and Different [3]B Units. The high resolution provided by 17O 3QMAS data, combined with the high resolution of 11B 3QMAS and high-field MAS spectra, allows further exploration of the network mixing.22 Just as the total fraction of Si-O-B measures the overall Si/B mixing, the fractions of Si-O-[3]B and Si-O-[4]B reveal more details about how this mixing takes place. The relationship between the fraction of Si-O-[3]B and the fractions of ring and nonring [3]B can be expressed as

(R + 2K2 + 3)I

Si-O-[3]B

) mJ[3]B(ring)+ nJ[3]B(nonring) (1)

where ISi-O-[3]B, J[3]B(ring), and J[3]B(nonring) represent the fractions of oxygens in Si-O-[3]B linkages and of borons in ring [3]B groups and nonring [3]B, respectively; m and n denote the mean

Du and Stebbins

Figure 17. Variation of the fraction of Si-O-[3]B multiplied by (R + 2K + 3/2) with the fraction of nonring [3]B groups, with lines fitted by linear regression for NBS-K0.5, NBS-K2, and NBS-K4 glasses.

TABLE 6: List of Values of Slopes and Intersects Obtained from Linear Regression Results in Figure 17, the Mean J[3]B(ring) and m and n K

intersect

slope

J[3]B(ring)

m ((0.05)

n ((0.05)

0.5 2 4

0.086 0.097 0.125

0.52 1.68 2.02

0.498 0.364 0.262

0.17 0.27 0.48

0.52 1.68 2.02

number of Si connected to each of the latter two species.22 The factor ((R+2K+3/2) normalizes the total number of borons and the total number oxygens. Plots of the fraction of the NMRderived fractions of Si-O-[3]B multiplied by ((R+2K+3/2) for the NBS-K0.5, NBS-K2, and NBS-K4 glasses each show a good correlation with the observed fraction of nonring [3]B (Figure 17). This observation, combined with relatively small variations with R in the fractions of ring [3]B and of [3]B-O-[3]B, suggests the approximations that the fraction of Si-O-[3]B involving boroxol rings can be treated as a constant and that the mean number of Si neighbors to each type of [3]B (ring and nonring) is approximately constant for each K value. The linear relations shown in Figure 17 are thus consistent with a modified version of eq 1:

(R + 2K2 + 3)I

Si-O-[3]B

) b + nJ[3]B(nonring)

(2)

where b is approximately constant and can be described as

b ) mJ[3]B(ring)

(3)

With the known average values of J[3]B(ring) obtained from the data (0.50, 0.36, and 0.26 for NBS-K0.5, NBS-K2, and NBS-K4 glasses, respectively), the intersects and slopes resulting from linear regressions of the data yield values for m and n. The results are summarized in Table 6, where n ) 0.52, 1.68, and 2.02 and m ) 0.17, 0.27, and 0.48 for K ) 0.5, 2 and 4, respectively. Only one-third of the oxygens bonded to [3]B in boroxyl rings are available to connect to Si. The observation that m is significantly less than one-third of n, at least for the higher two values of K, thus indicates that nonring [3]B mixes more with Si than does ring [3]B, suggesting once more that the latter aggregate into B-rich regions. The significance of these types of results can begin to be quantified by comparison to a model of random mixing. One mole of RNa2O‚B2O3‚KSiO2 composition contains K mol of Si and 2 mol of B. The mean number of Si connected to each boron species can be calculated if the mean number of moles 17O

Nature of Silicon-Boron Mixing (per formula unit, pfu) are known for of [4]B, [3]B(ring), [3]B(nonring), and [4]Si. Experimental values of mean J[4] and B J[3]B are 0.38 and 0.62, respectively. By plotting the mean fraction of nonring [3]B (denoted as 〈J[3]B(nonring)〉) versus XSi, a linear relationship can be found and expressed as

〈J[3]B(nonring) 〉 ) 0.016 + 0.495XSi = 0.5XSi

(

P(l) ) nCl


2.14θ + (4 - 1.14θ)XSi - θXSi2

(

(

nCl

)( )(

l 2.14 + XSi 2K 2.14 + XSi + 2K 2.14 + XSi + 2K l

4XSi

)

n-l

)

)

2.14 - 1.14XSi - XSi2

2.14 + 2.86XSi - XSi2 2.14 + 2.86XSi - XSi2

n-l

(5)

where the binomial coefficient is defined as nCl

)

n! l!(n - l)!

(6)

The mean number of Si associated with boron species, denoted as 〈l〉, can be expressed as

〈l〉 )

(

4nXSi

2.14 + 2.86XSi - XSi2

)

(7)

To simulate the data that deviate from a random mixing model due to preferential mixing with Si or B, a coefficient θ is introduced that varies from 0 to 1. When θ ) 1, the B species undergo fully random mixing without preference in associating with either Si or B, while θ ) 0 implies that the B species are strongly associated with B or Si. This simple probabilistic approach is an approximation only, in lieu of a more complete energetic description of the system based on more rigorous statistical mechanics, and cannot be extrapolated beyond the data set used to constrain it. For boron species that preferentially associate with B, the probability of finding [n]B((n-l)B,lSi) can be expressed as

(

P(l) ) nCl

)

4θXSi

l

2.14 + (4θ - 1.14)XSi - XSi2

(

2.14 - 1.14XSi - XSi2

2.14 + (4θ - 1.14)XSi - XSi2

)

n-l

(8)

The mean number of Si coordinated to boron species is

〈l〉 )

(

4nθXSi

2.14 + (4θ - 1.14)XSi - XSi2

)

(9)

For boron species that preferentially associate with Si, the probability of finding [n]B((n-l)B,lSi) is

)

2.14θ - 1.14θXSi - θXSi2

n-l

2.14θ + (4 - 1.14θ)XSi - θXSi2

(10)

The mean number of Si coordinated to boron species is

[4]B, [3]B(ring), [3]B(nonring),

P(l) ) nCl

(

(4)

The mean mole pfu values (averaged over data for R > 0) of and [4]Si are therefore 0.76, XSi, (1.24 - XSi), and K. Assuming there are no nonbridging oxygens, the moles pfu for oxygens associated with [4]B, [3]B(ring), [3]B(nonring), and [4]Si, which are available for randomly mixing with other boron or silicon species, are 1.52, 1.5XSi, (0.62 0.5XSi), and 2K, respectively. The total number of moles pfu of bridging oxygens associated with boron, which are available for random mixing, is therefore (2.14 + XSi) and the probability of finding oxygens associated with Si is 2K/(2.14 + XSi + 2K). Finally, the probability of finding [n]B((n-l)B,lSi) can be expressed as

)

l

4XSi

〈l〉 )

(

4nXSi

2.14θ + (4 - 1.14θ)XSi - θXSi2

)

(11)

The NMR-derived mean number of Si coordinated to the two types of [3]B groups (averaged over data from samples with varying R) are compared with model predictions in Figure 18. Calculations with θ values of 0.30 and 0.71 best match the observations for [3]B(ring) and [3]B(nonring), respectively, indicating considerably more deviation from random mixing (ordering) for the former. A tendency of [3]B(ring) to associate with boron is again obvious. Furthermore, it is likely that [3]B(ring) species have the tendency to aggregate together, since both [4]B and nonring [3]B mix well with Si. Effect of Sodium-to-Boron Ratio on the Degree of Si/B Mixing for [3]B and [4]B Units. We suggested above that the degree of mixing for [3]B(nonring) does not depend on R, based on the similar slopes at different R values observed in Figure 11b. In addition, the good linearity of each data series in Figure 17 also indicates that the mean number of Si neighbors to each type of [3]B (ring and nonring) is approximately constant. These results suggest that the addition of Na does not greatly affect the degree of mixing for [3]B species. The mean number of Si coordinated to [4]B for each glass composition can be expressed 4 l‚J[4]B((4-l)B,lSi) /J[4]B, where l is the number of Si coordias Σl)0 nated to [4]B, J[4]B((4-l)B,lSi) represents the fraction of borons in [4]B((4-l)B,lSi) groups and J[4] denotes the fraction of borons B in [4]B species. Figure 19 shows that these values also do not vary significantly with R. Thus, while the addition of Na changes the relative populations of each B species considerably, the degree of Si/B mixing for each species at a constant Si/B ratio remains approximately constant. Degree of Mixing among Si and [4]B Units. Since the mean number of Si neighbors per B is approximately constant for each glass with the same Si/B ratio, the mean number of Si neighbors coordinated to [4]B species, averaged over compositions with varying R, can be obtained for each series of glasses with different K values (Figure 20). The experimental points fall well above the curve calculated for random mixing with eq 7, indicating that [4]B groups have a strong preference to connect to Si instead B species. This tendency may result from some geometric preference for mixing of units with the same coordination ([4]B and [4]Si) as well as the energetic constraint of “[4]B avoidance”, where [4]B units tend to avoid connecting with each other because of the high charge on the resulting oxygen bridge. The experimental data were fitted by using eq 11, yielding a value of θ ≈ 0.23 (Figure 20). The relatively poor fit in comparison to Figure 18 may again support a preference in mixing of B among the different boron species, e.g., [4]B is preferentially associated with [3]B instead of [4]B. In the case of strict “[4]B avoidance”, the total number of moles pfu for bridging oxygen associated with boron which is available for random mixing with [4]B is (0.62 + XSi). The probability of finding [4]B((n-l)B,lSi) becomes


Du and Stebbins

Figure 18. Variations of the mean number of Si coordinated to ring and nonring [3]B with XSi. Dashed and dotted lines calculated via eq 7 represent the random Si/B mixing conditions for [3]B(ring) and [3] B(nonring), respectively. Experimental data were fitted via eq 9 (θ ) 0.30 and 0.71 for [3]B(ring) and [3]B(nonring), respectively) and the results are shown as solid lines.

Figure 19. Variations of mean number of Si coordinated to [4]B with R for NBS-K0.5, NBS-K2, and NBS-K4 glasses.

(

P(l) ) 4Cl

)

l

4XSi

0.62 + 4.38XSi - XSi2

(

)

0.62 + 0.38XSi - XSi2

0.62 + 4.38XSi - XSi2

4-l

(12)

The mean number of Si coordinated to [4]B can be expressed as

〈l〉 )

(

16XSi

0.62 + 4.38XSi - XSi2

)

(13)

Values calculated with eq 13 fit quite well in the higher Si region (Figure 20). Note that eqs 12 and 13 are only suitable when the amount of bridging oxygens associated with [4]B is smaller than the sum of all other bridging oxygens. All the glass compositions studied here obey this condition. In systems with low concentrations of Si and high [4]B/[3]B, or with higher field strength modifier cations (e.g., Ca2+ instead of Na+), strict “[4]B avoidance” may not be possible or may be energetically less predominant, as in the case of “aluminum avoidance”.41 Verifying Dell and Bray Model. The model of Dell and Bray8 successfully approximated the effect of composition on

Figure 20. Variations of the mean number of Si coordinated to [4]B with XSi. The dotted line calculated via eq 7 represents the random Si/B mixing conditions. The dashed line was calculated via eq 13 based on “[4]B avoidance”. Experimental data were fitted via eq 11 with θ ) 0.23 and the results are shown as a solid line.

the fractions of symmetric [3]B, asymmetric [3]B (associated with one or two NBO), and [4]B. Our 11B and 17O 3QMAS studies provide considerable detail of the boron and oxygen speciation, which can help both in testing this model and in suggesting needed modifications. According to the Dell and Bray model, in the R ) 0-0.5 region, the addition of Na causes the formation of diborate groups, Na2O‚2B2O3, which are composed of two [4]B and two [3]B interconnecting with each other. The sodium diborate and silicate regions of the glass are presumed not to mix. Based on this model, [4]B(3B,1Si), [4]B(4B,0Si) should be predominate among the [4]B species. This is inconsistent with our 11B NMR results, where [4]B(0B,4Si), [4]B(1B,3Si) are the main species and [4]B groups tend to mix well with [4]Si. Oxygen-17 NMR also shows large fractions of Si-O-B, again indicating that Si/B mixing is higher than the model prediction. In the R ) 0.5 to 0.5 + K/16 region, the Dell and Bray model suggested that [4]B species start to mix with [4]Si, forming reedmergerite groups (Na2O‚B2O3‚8SiO2, based on the structure of a mineral with NaBSi3O8 stoichiometry) in which [4]B is surrounded by four [4]Si species. This would result in a high population of [4]B(0B,4Si) groups. From our 11B results, it is apparent that [4]B(0B,4Si) and [4]B(1B, 3Si) are both dominant in K ) 2 and 4 glasses. However, [4]B(0B,4Si) is minor at lower Si/B, for K ) 0.5. Thus, there is no strong preference for the formation of [4]B(0B,4Si) only. Bunker and coworkers suggested the presence of danburite units containing [4]B(1B,3Si) (Na O‚B O ‚2SiO , by analogy to the mineral 2 2 3 2 danburite CaB2Si2O8, which has [4]B pairs), based on Raman and 29Si MAS NMR studies.28 The significant amount of [4]B(1B, 3Si) in 11B 3QMAS NMR spectra supports the presence of such linkages, but again there is no strong preference to form these uniquely. Furthermore, several aspects of our data set indicate that the boron linked to [4]B should be [3]B not [4]B. As was discussed in the previous section, [4]B tends to associate with [4]Si, therefore, higher numbers of Si coordinated to [4]B is expected, whose populations depend on the Si/B ratio. Effect of Composition on Oxygen Chemical Shifts. We have shown above that high-resolution 11B and 17O NMR spectra reveal considerable detail of the qualitative nature of interconnections among different network structural units and that, taken together, these data can be used to begin to develop quantitative models of the extent of mixing for different species. Detailed



Figure 21. Variations with mole fraction of Na of δiso (filled symbols; left scale) and of PQ (open symbols; right scale) for Si-O-Si oxygen species in NBS-K0.5, NBS-K2, and NBS-K4 glasses.

TABLE 7: List of Values of δIso and PQ for Si-O-Si Bridging Oxygen Obtained from the 17O 3QMAS Spectra of NBS-K0.5, NBS-K2, and NBS-K4 Glasses sample name

iso, MAS

δiso, ppm

PQ, MHz


-30.89, 18.39 -34.61, 28.00 -36.00, 31.60 -29.80, 15.69 -31.66, 20.49 -32.78, 25.79 -29.96, 15.99 -30.89, 18.39 -31.82, 20.79

42.3(2) 50.1(3) 53.0(3) 40.0(2) 43.9(2) 47.2(2) 40.3(2) 42.3(2) 44.2(2)

5.13(5) 4.94(7) 4.86(7) 5.18(5) 5.08(5) 4.86(5) 5.18(5) 5.13(5) 5.08(5)

analysis of the spectra also yields information on the effect of composition on the NMR parameters that describe the components of the spectra. These results can be independently used to complement and at least partially test conclusions about the network mixing based on species abundances. Beyond simply identifying which network cations are bonded to bridging oxygens (e.g., Si, Al, B), the systematic effects of structure on isotropic chemical shifts (δiso) for bridging oxygens are not well-known. However, correlations of CQ with bond angle for bridges between pairs of tetrahedral cations are well established by both experiment and theory.42-51 Relative changes in PQ (more directly observable in 3QMAS NMR) are similar to changes in CQ given similar η values for Si-O-Si in ternary borosilicate glasses. Both δiso and PQ for Si-O-Si oxygens depend strongly (but in opposite senses) on R and K (Table 7) and thus are inversely correlated with each other. This suggests that δiso, like PQ, is correlated with the bond angle. As R increases, PQ decreases, indicating a narrower mean Si-O-Si angle. This is expected if there are more Na ions interacting with Si-O-Si oxygens as R increases. It is worthy to note that in addition to a smaller Si-O-Si angle leading to a smaller PQ, the presence of alkali cations can also lower PQ for a given angle.48,51 The smaller bond angle along with more interaction with Na ions apparently also leads to less chemical shielding of the bridging oxygens. The rates of change in δiso and PQ with R are greater at smaller values of K, probably simply because of the higher Na content of the glasses at lower Si/B ratios. A plot of δiso and PQ versus mole fraction of Na among all atoms can help resolve the possible effects of R and K (Figure 21). Here it is clear that both NMR parameters are linearly correlated to the Na content, strongly implying that Na ions are well-mixed with Si-O-Si

oxygens. The discussion above showed that [4]B species are strongly associated with [4]Si species. If such species are wellmixed with Si-O-Si (for example, in the same ring structures in the network), the need for charge compensation of the Si-O-[4]B oxygens will bring Na ions near Si-O-Si oxygens, possibly producing the effects observed. Chemical shifts for other bridging oxygens show very little effect of R, probably because their angles are roughly constant, as might be the case if Na ions were preferentially associated with such charged oxygens or, for the uncharged [3]B-O-[3]B groups, oxygens are simply not highly mixed with Na ions. Effect of Composition on Boron Chemical Shift. Boron11 chemical shifts for [3]B(ring), [3]B(nonring), and [4]B are approximately 17, 14, and 0 ppm, respectively. Obviously the largest effect on δiso is the coordination of the boron (3 versus 4). It has been suggested that the smaller difference between ring and nonring [3]B is due to the contraction of the B-O bond length in [3]B(nonring) as compared with [3]B(ring), resulting in greater π-electron donation to the boron atom.17 The second-nearest neighbor (first cation neighbor, here Si or B) also affects 11B δiso. With increasing Si/B ratio, the center of gravity of the [4]B peak shifts to lower frequency in both 11B MAS spectra (Figure 2) and isotropic projections (Figure 4d), which we have modeled with changing proportions of [4]B(2B,2Si), [4]B(1B,3Si), and [4]B(0B,4Si) with δ iso values of approximately 2, 0, and -3 ppm, respectively, indicating a shift to higher frequency of 2-3 ppm when replacing a B by a Si. The boron cation coordinated to [4]B is most likely trigonal boron because of the difficulty of compensating the high charge of [4]B-O-[4]B oxygens with monovalent Na cations (“[4]B-O-[4]B avoidance”). Replacement of a sp2 hybrid [3]B by a sp3 hybrid [4]Si in the second-nearest coordination sphere of [4]B may increase the chemical shielding of [4]B, thus decreasing the chemical shift. The difference in Si/B mixing between ring and nonring [3]B will lead to a higher number of Si connected to the latter and may also contribute to its lower δiso. However, this effect is apparently smaller for [3]B than for [4]B: chemical shifts for ring and nonring [3]B in B2O3 glass (about 18 and 13 ppm, respectively17,52) are similar to those in borosilicates. δiso for nonring [3]B increases with R (Figure 22a). Because the mean numbers of Si neighbors to boron units do not vary significantly with R (see above), this variation is probably mostly related to changes in the number of adjacent Na cations. The rate of change in δiso is smaller at larger K values because of their smaller relative changes in Na mole fraction (Figure 1). δiso for nonring [3]B decreases with increasing XSi (Figure 22b), which seems to be consistent with the effect noted above of more Si neighbors to [4]B groups. However, decreasing XSi at a same R value is also correlated with higher total Na fraction, which again may also increase δiso. The mean numbers of Si neighbors to nonring [3]B at XSi ) 0.2 and 0.67 are 0.5 and 2.0, respectively, and difference in the mean δiso at these values is 1.1. Even if the relative fraction of Si and B neighbors was the only factor to influence δiso of this species, replacing a B by a Si seems to cause a shift of only 0.7 ppm, much smaller that observed for [4]B (∼2-3 ppm). On the other hand, δiso for nonring [3]B shows a strong linear correlation with the mole fraction of Na, regardless of the value of K (Figure 23). As discussed above, [4]B species, along with their charge-balancing Na cations, are strongly associated with [4]Si. [3]B(nonring) species are also well-mixed with [4]Si, which may bring Na ions near to [3]B(nonring) groups, possibly


Figure 22. Variations with (a) R and (b) XSi of δiso for species in NBS-K0.5, NBS-K2, and NBS-K4 glasses.

Du and Stebbins

[3]B(nonring)

Figure 23. Variations of δiso for [3]B(nonring) species with mole fraction of Na in NBS-K0.5, NBS-K2, and NBS-K4 glasses.

producing the effects observed through the interaction of Na with adjacent oxygens. Unlike for [3]B(nonring), δiso for [3]B(ring) does not show simple linear correlations with composition (Figure 24). However, the observed effects can again be rationalized in terms of the extent of cation mixing developed from the observed network species populations. Na cations are probably most strongly associated with [4]B groups for charge balancing. In additions, [4]B species have a high tendency of mixing with [4]Si. On the other hand, [3]B(ring) species tend to associate with boron species. Therefore at high Si contents, it is unlikely for [3]B(ring) to associate with [4]B since both species have low concentrations and no tendency to associate with each other. Few Na cations are near [3]B(ring) species in high K glasses, which results in δiso being invariant with R (e.g., the flat curve for K ) 4 glasses in Figure 24a). At high B contents such as K ) 0.5, the high proportion of boron species increases the

Figure 24. Variations with (a) R and (b) XSi of δiso for [3]B(ring) species in NBS-K0.5, NBS-K2, and NBS-K4 glasses.

probability of proximity of [3]B(ring) groups to [4]B, thus the increasing the effect of Na (and R) on δiso([3]B(ring)). For the K ) 2 glasses, the situation is in between. Here the value of δiso([3]B(ring)) is not affected at low R, but increases at higher R since more [4]B is generated in the latter, enhancing the mean proximity of Na ions to [3]B(ring) groups. Figure 24b shows that δiso([3]B(ring)) decreases with higher XSi, in agreement with the trend shown in δiso([3]B(nonring)). The smaller variation found for the R ) 0.25 series indicates that the change in δiso([3]B(ring)) with XSi may again be mainly influenced by the Na concentration, as the increase of Na concentration with decreasing XSi is smaller at lower R values (Figure 1). The difference in slopes for [3]B(ring) at low R versus high R is significant (Figure 24b), in contrast to that for [3]B(nonring) (Figure 22b). This is again due to the difference in mixing behavior for the two species. [3]B(ring) species tend to aggregate in ring-rich regions and therefore at low R there is not much effect by Na cations. In contrast, [3]B(nonring) species mix nearly randomly, and thus even at low R, the Na content has a noticeable effect. The relationship between δiso([3]B(ring)) and the mole fraction of Na becomes more linear at higher Na concentration and/or lower K value (Figure 25); i.e., in glasses with more Na and/or more [3]B(ring), the interaction between Na ions and [3]B(ring) becomes more significant. The glass compositions with nonlinear behavior in Figure 25 fall within the immiscibility region, supporting the conclusion that there is significant nanoscale heterogeneity in these glasses. The degree of change in δiso for [3]B(nonring) (Figure 23) is more than twice as large as that for [3]B(ring), again indicating better mixing between [3]B(nonring) and Na cations. Unlike the case of tetrahedral boron species, the changes in chemical shift of trigonal boron species is mainly influenced by the mole fraction of Na and the influence by the population of Si and B on the second-nearest neighbors of [3]B species is


J. Phys. Chem. B, Vol. 107, No. 37, 2003 10075 unit with varying Si/B ratio. The values of the parameter θ, representing the degree of random mixing, for [3]B(ring), [3]B(nonring), and [4]B are 0.30, 0.71, and 0.23, respectively. The result shows that [3]B(ring) tends to aggregate with other like units, [3]B(nonring) is approximately random mixed in the network, and [4]B is strongly associated with [4]Si. These results along with the known populations of boron units and [4]Si provide important new input into future detailed energetic and structure-based thermodynamic models of these glasses and corresponding liquids. Acknowledgment. This work was supported by the U.S. National Science Foundation, grants DMR-0100986 and DMR9802072. References and Notes

Figure 25. Variations of δiso for [3]B(ring) species with mole fraction of Na in NBS-K0.5, NBS-K2, and NBS-K4 glasses.

relatively small. We have suggested that the replacement of a sp2 hybrid [3]B by a sp3 hybrid [4]Si connected through oxygen to [4]B increases the chemical shielding, thus decreasing the chemical shift. The smaller influence on the chemical shift of [3]B may be due to the more rigid [3]B species in comparison to [4]B. On the other hand, the second-nearest neighbors for [3]B species could be [3]B, [4]B, and [4]Si. Replacement of a [4]B by a [4]Si may not significantly affect the chemical shielding. Finally, we note that sodium concentration does not significantly affect δiso for [4]B. This might be the case because Na cations are preferentially associated with [4]B for charge balancing. If “[4]B avoidance” is a good approximation in this system, then the addition of Na concentration may not have a large effect on the local concentration of [4]B species. Conclusions The improvement in NMR spectral resolution provided by higher magnetic fields and the triple-quantum magic-angle spinning technique greatly enhances the level of structural detail that can be obtained for sodium borosilicate glasses. The populations of [3]B(ring), [3]B(nonring), [4]B(2B,2Si), [4]B(1B,3Si), and [4]B(0B,4Si) can be obtained via 11B MAS and 3QMAS NMR. The results show that the population and bonding environment of [3]B in boroxol rings remains relatively constant as the value of R varies up to 0.75 at different Si/B ratios, while the nonring [3]B decreases systematically as [3]B is converted to [4]B. At fixed R values, the fraction of [3]B(nonring) among total [3]B increases linearly with XSi, possibly driven by the increased configurational entropy of better Si/B mixing of this species. Oxygen populations in Si-O-Si, Si-O-[4]B, Si-O-[3]B, [4]B-O-[3]B, and [3]B-O-[3]B linkages can be obtained from 17O 3QMAS NMR, which provides abundant information about the extent and type of mixing among network cations of varying coordination. The relatively lower fractions of Si-O-B in glasses whose compositions are located in the center of the immiscibility region suggest considerable nanoscale heterogeneity. The mean number of Si coordinated to each boron unit can be obtained by comparing the fractions of boron species and bridging oxygens. The degree of Si/B mixing of each boron unit does not vary significantly with R at a given Si/B ratio, and thus the change in the overall extent of Si/B mixing (fraction of Si-O-B) with the addition of Na is mainly caused by changes in the relative populations of boron units. The mixing behavior of each boron unit can be obtained by considering the change in the mean number of Si coordinated to each boron

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