16720
J. Phys. Chem. 1996, 100, 16720-16728
Network Modification in Potassium Borate Glasses: Structural Studies with NMR and Raman Spectroscopies Randall E. Youngman and Josef W. Zwanziger* Department of Chemistry, Indiana UniVersity, Bloomington, Indiana 47405 ReceiVed: May 17, 1996; In Final Form: July 23, 1996X
We have examined the structural changes in the boron-oxygen network that result from chemical modification of glassy boron oxide by potassium oxide. By means of boron-11 dynamic angle spinning (DAS) NMR and Raman spectroscopies, we have identified changes in the structure resulting from conversion of three-coordinate boron to four-coordinate species. We observe coordination changes in two different 3-fold coordinate boron sites: those in six-membered boroxol rings and those in nonring BO3 units. The DAS NMR data show that the fraction of boron in nonring three-coordinate sites decreases as modifier is added. Modification of the boroxol rings is also evident in the Raman data. Assignment of the NMR resonances is made with the help of comparison to spectra of related crystalline potassium borates. Using 11B DAS NMR and 17O magic angle spinning (MAS) NMR, we do not detect significant formation of nonbridging oxygen through 35% added modifier. The changes in the boroxol ring breathing mode in the Raman spectra are attributed to changes in the coordination of the boron that compose the boroxol ring, but coordination changes also occur in the nonring BO3 units. We propose a model that combines these NMR and Raman data, in which modification of both types of 3-fold coordinate sites is included. This model predicts a contribution to the formation of triborate units from nonring BO3 boron, as well as a slightly higher preference for modification of these sites over the boroxol ring boron.
1. Introduction The binary alkali borates, (A2O)x(B2O3)1-x (A ) Li, Na, K, Rb, Cs), are excellent glass formers, displaying a rich structural chemistry and substantial intermediate-range order (IRO).1 When modified with a salt, these materials can form superionic glassy electrolytes, such as the lithium chloroborates, {(LiCl)x(Li2 O)y(B2 O3)}.2-4 The structure of glassy alkali borates is a complex three-dimensional network of boron and oxygen, thought to be composed of larger structural units found in the analogous crystalline materials.1-5 These superstructural units are sketched in Figure 1. The notion of a disordered network comprised of well-defined structural units was first proposed by Ha¨gg in 1936,6 in response to the random network hypothesis of Zachariasen.7 Support for the Ha¨agg model was initiated in borate glasses by the pioneering work of Krogh-Moe.1 Through IR and physical property characterization of alkali borate glasses, he suggested that the structure could be rationalized by a random network of these superstructural units.1,8 Although the identity and concentration of such units are still in debate, numerous NMR and Raman studies of borate glasses have been interpreted in the vein of this model.5,9-24 The purpose of this paper is to present a structural model for potassium borate glasses formulated from the combined use of dynamic angle spinning (DAS) NMR and Raman spectroscopies. We implement a minimal version of the Ha¨gg and Krogh-Moe view, based on four structural units: boroxol and modified rings, loose BO3 and loose BO4-. The DAS NMR results give the populations of the three-coordinate sites and differentiate between boron atoms in rings and loose BO3 units, in addition to quantifying the BO4- fraction separately. The Raman spectra suggest direct changes in the rings. Our model describes the dependence of the four structural units on the modifier content * Correspondence to Professor J. W. Zwanziger, Department of Chemistry, Indiana University, Bloomington, IN 47405. Telephone: (812) 8553994. Telefax: (812) 855-8300. Internet:
[email protected]. X Abstract published in AdVance ACS Abstracts, September 1, 1996.
S0022-3654(96)01439-6 CCC: $12.00
Figure 1. Structural groups found in glassy and crystalline potassium borates: (a) boroxol ring; (b) nonring BO3; (c) nonring BO4-; (d) triborate; (e) diborate; (f) pentaborate; (g) di-triborate; (h) tetraborate; (i) ring-type metaborate; (j) chain-type metaborate. Filled circles and open circles represent boron and oxygen atoms, respectively. Dashed lines in the structures denote connections to the network, and charges are shown for the nonbridging oxygen (NBO) in the metaborate groups.
and to our knowledge is the first that attempts to quantify changes in both the ring and nonring structures in a borate glass. Boroxol rings, B3O3, are thought to exist already in pure boron oxide glass, though their concentration is still debated.25-29 B2O3 glass is generally presumed to consist of two different structural units: the six-membered boroxol ring and nonring BO3 units © 1996 American Chemical Society
Potassium Borate Glasses
J. Phys. Chem., Vol. 100, No. 41, 1996 16721
(parts a and b of Figure 1), linked together through bridging oxygen.1,5,25,26,29,30 The Raman spectrum shows a sharp feature at 808 cm-1, assigned to the boroxol ring breathing mode.31 This mode appears also in Raman spectra of liquid B2O3, and its intensity decreases with increasing temperature, presumably as the boroxol rings dissociate.32 Recently, this vibrational mode has been identified in inelastic neutron-scattering studies.33,34 The boroxol ring structure is a significant component of the glass: the neutron data suggest that 75% of the boron atoms are in boroxol rings, while NQR30 (nuclear quadrupole resonance) and wide-line boron and oxygen NMR25 put this figure slightly higher, at about 80%. Our high-resolution NMR data on boron29,35 and oxygen36 are consistent with 65% of the boron in boroxol rings. In any case there is a roughly even mixture of boroxol rings and nonring BO3 units in B2O3 glass (exactly 1:1 if 75% of the boron are in rings, since each ring contains three boron atoms). The addition of alkali oxide modifiers, A2O (with A ) Li, Na, K, Rb, Cs), to B2O3 results in significant changes in the boron coordination and hence the glass structure. The added modifier can act in two ways: by forming four-coordinate boron (BO4-) A2O
2(BO3) 98 2(BO4-) + 2A+
(1)
and by forming nonbridging oxygen (NBO) A2O
2(BO3) 98 2(BO3-) + 2A+
(2)
In reaction 1, all of the oxygen are bridging between boron atoms. In reaction 2, one of the oxygen atoms in each of the BO3- units is nonbridging. The existence of four-coordinate boron is clear from boron NMR, in which its nearly tetrahedral symmetry gives rise to a relatively narrow resonance, sharp enough to be quantified accurately despite overlap from the three-coordinate sites.37,38 The fraction of four-coordinate boron (N4) in modified borates has been studied extensively for a wide variety of modifiers, indicating that the process in reaction 1 is dominant below 30% added modifier.11,15,37 The rate of fourcoordinate boron formation decreases as the size of the alkali cation increases, which is attributed to increasing formation of NBO (reaction 2).19,22,39,40 Above approximately 40% added modifier, NBO formation is dominant and N4 decreases to zero.11,15 Quantification of the four-coordinate boron and NBO is the essential first step in understanding the structure of the modified glasses. After this quantification is accomplished, however, considerable latitude remains as to how these structural changes are incorporated into the network. Magnetic resonance has been used successfully to probe the short-length-scale changes in the network. Bray and co-workers inferred the existence of multiple three- and four-coordinate boron sites in their 10B NMR spectra, differing in near-neighbor bondingconfigurations.9,12 Using 11B NQR, they also observed changes in the three-coordinate boron sites in modified borate glasses.30,41,42 We have recently resolved three boron sites in rubidium borate glasses: the threecoordinate boron types present in pure B2O3 and the fourcoordinate boron formed by the addition of Rb2O.43 The DAS NMR data show that the increase in four-coordinate boron occurs mainly at the expense of the nonring BO3 sites. The peak intensity assigned initially to three-coordinate boron in boroxol rings remains essentially constant through 35% added Rb2O. Raman spectroscopy is capable of detecting larger structures in these glasses and can be used to monitor changes in the network.5,18,44 As the modifier content is raised, a feature
between 740 and 780 cm-1 gradually replaces the 808 cm-1 band. This has been attributed to conversion of the boroxol rings to other ring-type structures containing four-coordinate boron (Figure 1).5,16,18,31 Owing to the disorder of the glasses, assignment of the Raman features is made by comparison with the spectral features of crystalline alkali borates. Modified boroxol rings of the type in Figure 1 dominate the structure of many of the crystalline alkali borates. However, direct comparison of the crystalline and glassy spectra is not unambiguous, since crystalline samples that contain metaborate, diborate, and triborate rings all show features between 700 and 800 cm-1.16 Furthermore, the large Raman cross section of the boroxol ring may overemphasize the changes in the Raman data.33,45 Unfortunately, Raman spectroscopy is relatively insensitive to the nonring BO3 units (though they do give rise to a broad, weak feature between 300 and 800 cm-1 32,46), and therefore, interpretation of the spectra has been limited to consideration of the changes in the boroxol rings. In this view, the conversion of three-coordinate to four-coordinate boron occurs only in the boroxol rings, resulting in a variety of modified rings. In the present paper we combine NMR and Raman spectroscopies to investigate the structural changes in potassium borate glasses. We use DAS NMR of boron and magic angle spinning (MAS) NMR of oxygen to probe the short-range signatures of structural change and Raman spectroscopy to probe the intermediate-range structure. The magnetic resonance results for glassy potassium borates are complemented by Raman spectra of the glasses and DAS NMR of boron in crystalline potassium borates. The DAS NMR data show clearly the modification of nonring BO3 units, and the Raman spectra display the characteristic behavior of the vibrational modes between 700 and 810 cm-1, attributed to coordination changes in the boroxol rings. The boron DAS NMR data of the crystalline potassium borates show that the three-coordinate boron in modified rings has similar isotropic shifts to those in boroxol rings and therefore might contribute to the intensity of the boroxol ring resonance in the glass data. The 17O MAS NMR spectra show qualitative changes in the nonring oxygen sites, but poor resolution precludes the positive identification of NBO through 35% added K2O. In the following section we describe in detail our experimental methods and results based on 11B DAS NMR,17O MAS NMR, and Raman spectroscopies. This is followed by discussion of the binary glass structure, including a simple structural model that accounts for the DAS NMR and Raman data, and a short concluding section. 2. Experimental Methods 2.1. Sample Preparation. Glasses enriched to 90% in boron-10 were made by fusing together appropriate quantities of boric acid (Strem, 99.9995%), boric acid enriched to 97% in 10B (Aldrich) and potassium carbonate (Strem, 99.8+%) at 1000 °C. Depletion of the 11B isotope was necessary to alleviate spin diffusion in the DAS NMR experiments.29,43 The melts were held at this temperature for 1 h and quenched by removing the platinum crucible from the furnace and cooling in a dry nitrogen atmosphere. The clear, colorless glasses were broken into small pieces and stored under nitrogen to minimize absorption of water. After Raman data on the bulk samples were obtained, the glasses were powdered for NMR analysis. X-ray powder diffraction was used to verify the amorphous character of these samples. Final compositions were adjusted slightly to account for weight loss during the synthesis. Potassium borate glasses, enriched in oxygen-17, were prepared by fusing together appropriate amounts of 17O-enriched boron oxide and potassium carbonate. The synthesis of 17Oenriched B2O3 is described elsewhere.36 After thoroughly
16722 J. Phys. Chem., Vol. 100, No. 41, 1996 mixing these two materials, they were melted at 1000 °C for 15 min. The melts were quenched by cooling in a dry nitrogen environment. Crystalline potassium borates were obtained from stoichiometric quantities of boric acid and potassium carbonate. These compounds were also made with 90% enrichment of the boron10 isotope. The synthesis of K2O‚B2O3 and K2O‚2B2O3 is described elsewhere.43 K2O‚5B2O3 and K2O‚3.8B2O3 were prepared from aqueous reaction of the boric acid and potassium carbonate starting materials. After removal of the solvent, excess waters of hydration were removed by sintering slightly below the melting points of the crystalline phases, resulting in white powders. X-ray powder diffraction confirmed the identities of the crystalline potassium borates. 2.2. NMR Spectroscopy. NMR spectra were obtained with a home-built spectrometer and commercial probe at field strengths of 8.4 and 4.7 T. MAS NMR data were taken with a Hahn-echo pulse sequence. Oxygen data were collected with short pulse lengths, 2-3 µs and repetition times of 3-30 s. The oxygen data were acquired by the signal averaging of 2000-6000 experiments. We used the hypercomplex shifted echo experiment described by Grandinetti et al. to acquire pure phase DAS NMR data of the amorphous potassium borates.47 All experiments were performed using the 37.38° and 79.19° DAS angle pair.48 To compensate for the different nutation behavior of the three- and four-coordinate boron sites, which arises from the large differences in e2Qq/h, we utilized short π/2 pulses, typically 2.4 µs at 79.19° and 4 µs at 37.38°. Under these pulse conditions, and at 8.4 T, we have observed that the different boron sites behave similarly. Loss of signal intensity to spinning sidebands was minimized by spinning the samples at 6-7 kHz. The spectra of the glasses were obtained with 64-128 acquisitions at each of 80 delay values with 15-60 s between scans to allow for full relaxation of all sites. DAS NMR of 11B in the potassium borate crystalline compounds were collected in a similar manner, with 16-32 acquisitions at each of 64-128 delay values and 600 s between scans to account for the significantly longer T1 relaxation. These DAS NMR data were acquired with a pure-phase shifted-echo experiment without the hypercomplex data treatment.47 The isotropic and anisotropic sweep widths were 20 and 30 kHz, respectively, for the glass data and 10 and 30 kHz, respectively, for the crystalline compounds. Boron-10 enrichment was necessary in all samples to quench homonuclear dipolar coupling of the boron-11.29 No smoothing of any kind was used in the processing of the DAS NMR data. 2.3. Raman Spectroscopy. Raman data were obtained using a commercial spectrometer (SpectraCode, West Lafayette, IN) consisting of a liquid nitrogen-cooled charge-coupled device (CCD) detector and integral holographic filtering. The excitation source was the 632.8 nm line of a 30 mW helium-neon laser, and the spectral resolution was 3 cm-1. Data were obtained using large pieces of glassy sample, sealed in a quartz sample cuvette. The scattering intensity was integrated over 600 s of detector exposure time. 3. Results Figure 2 shows the 2D DAS NMR spectrum of boron-11 in glassy (K2O)0.33(B2O3)0.67 obtained at 8.4 T. The high-resolution isotropic 11B NMR spectrum is given as a projection of the DAS NMR data onto the isotropic shift axis. Anisotropic slices are shown for the two resolved boron sites. Figure 3 shows a contour plot of the 11B DAS NMR data (8.4 T) for glassy (K2O)0.18(B2O3)0.82, with the isotropic projection and anisotropic slices of the data at the isotropic shift positions of the three
Youngman and Zwanziger
Figure 2. DAS NMR spectrum of 11B in (K2O)0.33(B2O3)0.67 glass at 8.4 T (115.6 MHz resonant frequency): (a) two-dimensional contour plot with a projection of the data onto the isotropic shift axis with contours at (30 ppm due to spinning sidebands; (b) slice of the data at -0.3 ppm, corresponding to the isotropic shift of the four-coordinate boron; (c) slice of the data at 4.7 ppm, showing the anisotropic line shape due to three-coordinate boron. Shifts are relative to Et2O‚BF3.
Figure 3. DAS NMR spectrum of 11B in (K2O)0.18(B2O3)0.82 glass at 8.4 T (115.6 MHz resonant frequency): (a) two-dimensional contour plot with the isotropic projection of the data, where contours at (30 ppm are spinning sidebands; (b) slice at -0.3 ppm, the isotropic shift of the four-coordinate boron; (c) slice at 1 ppm, the nonring BO3 isotropic shift; (d) slice at an isotropic shift of 4.7 ppm, the shift of the ring three-coordinate boron. Shifts are relative to Et2O‚BF3.
boron resonances. Isotropic DAS NMR data for the entire (K2O)x(B2O3)1-x glass series at 8.4 T are included in Figure 4. Oxygen-17 MAS NMR spectra of potassium borate glasses, at 8.4 T (48.8 MHz resonant frequency), are shown in Figure 5. Isotropic 11B NMR spectra of four polycrystalline potassium borates are shown in Figure 6. These data were constructed by projecting the two-dimensional DAS NMR data, obtained at 8.4 T, onto the isotropic shift axes. Representative Raman spectra are shown in Figure 7 for glass samples containing 0, 8, 18, 28, and 33 mol % potassium oxide. Raman features are marked with the vibrational shifts of the peaks. 4. Discussion 4.1. NMR of Potassium Borate Glasses. The contour plots of the DAS NMR data in Figures 2 and 3 show clearly the existence of multiple boron sites in potassium borate glasses. At 33 mol % K2O, Figure 2, two peaks are well resolved. The isotropic shifts of these two peaks are 4.7 and -0.3 ppm, assigned to three-coordinate boron in rings and four-coordinate boron species.43 These isotropic shifts include both the isotropic chemical shift and the isotropic second-order quadrupole shift.49,29 The anisotropic slices in Figure 2 aid in the assignment of these two features. The slice at 4.7 ppm has the characteristic shape of a three-coordinate boron powder pattern.
Potassium Borate Glasses
J. Phys. Chem., Vol. 100, No. 41, 1996 16723
Figure 6. 11B DAS NMR isotropic spectra of four crystalline potassium borates at 8.4 T (115.6 MHz resonant frequency): (a) potassium diborate, K2O‚2B2O3; (b) K2O‚3.8B2O3; (c) potassium pentaborate, K2O‚5B2O3; (d) potassium metaborate, K2O‚B2O3. Shifts are relative to Et2O‚BF3. Figure 4. Isotropic shift spectra of 11B in (K2O)x(B2O3)1-x glasses from the DAS NMR at 8.4 T (115.6 MHz resonant frequency): (a) x ) 0.00 (glassy B2O3; (b) x ) 0.08; (c) x ) 0.13; (d) x ) 0.18; (e) x )0.23; (f) x ) 0.28; (g) x ) 0.33; (h) x ) 0.38. The vertical lines are drawn at the isotropic shifts of the three sites, as defined in the text. Solid line represents at 4.7 ppm the ring three-coordinate boron shift. Long dashed line represents at 1 ppm boron in nonring BO3 units, and short dashed line represents at -0.3 ppm four-coordinate boron. The shifts are relative to Et2O‚BF3.
Figure 5. 17O MAS NMR spectra of glassy (K2O)x(B2O3)1-x at 8.4 T (48.8 MHz resonant frequency) obtained with spinning speeds of 7 kHz: (a) x ) 0.00 (glassy B2O3); (b) x ) 0.10; (c) x ) 0.20; (d) x ) 0.35. Spinning sidebands are marked with asterisks. The 17O shifts are relative to H2O.
Figure 7. Raman spectra of (K2O)x(B2O3)1-x glasses: (a) x ) 0.00 (glassy B2O3; (b) x ) 0.08; (c) x ) 0.18; (d) x ) 0.28; (e) x ) 0.33. Raman shifts are marked on the spectra. The two sharp features at 400 cm-1 are from the quartz sample holder.
The slice at -0.3 ppm is much more symmetric, owing to the tetrahedral symmetry of the 4-fold coordinate boron sites. The significantly smaller quadrupolar coupling of boron in a tetrahedral environment contributes to both the isotropic shift of the resonance and the shape of the 79.19° spinning powder pattern.
Intermediate compositions, such as 18% K2O, show peak intensity from at least three types of boron sites (Figure 3). Slices at the isotropic positions of the resonances, as shown in Figure 3, confirm the presence of three boron types. The anisotropic slices at 4.7 and 1 ppm are characteristic of the three-coordinate powder patterns of boroxol and nonring BO3 units, as in pure
16724 J. Phys. Chem., Vol. 100, No. 41, 1996
Youngman and Zwanziger
B2 O3 glass.29 The slice at -0.3 ppm resembles that of the four-coordinate boron powder pattern, as identified in Figure 2. DAS NMR in different magnetic fields enables us to obtain both the isotropic chemical shift and the quadrupolar coupling product PQ for each site through the field dependence of the isotropic shift. Here,
PQ ) e2qQ/hx1 + η2/3 with e2qQ/h the quadrupole coupling constant and η the asymmetry parameter for the quadrupole coupling. The 3-fold coordinate boron in glassy (K2O)0.33‚(B2O3)0.67 has a chemical shift of 18.2 ( 0.4 ppm and PQ ) 2.69 ( 0.04 MHz. This compares to a chemical shift of 17.8 ( 0.2 ppm and PQ ) 2.66 ( 0.04 MHz for three-coordinate boron in boroxol rings.29 The similarities of these boron resonances requires careful assignment of the 4.7 ppm resonance in the isotropic DAS NMR data obtained at 8.4 T. We have previously determined the nonring BO3 boron to have a chemical shift of 13.3 ( 0.2 ppm and PQ ) 2.61 ( 0.04 MHz.29 The four-coordinate boron atoms, owing to the field dependence of the resonances in Figures 2 and 3, have an isotropic chemical shift of -0.3 ( 0.2 ppm and PQ ) 0.220 ( 0.04 MHz. These values are in good agreement with other measurements of the tetrahedral boron site in modified borate glasses.43,15,50 The behavior of the boron resonances, as a function of potassium oxide, can be followed in Figure 4. At zero and low modifier levels, two dominant features exist at 4.7 and 1 ppm. These belong to the boroxol ring and nonring BO3 sites. As the amount of potassium oxide increases, the peak at 1 ppm is gradually replaced by a resonance at slightly negative isotropic shift (-0.3 ppm), resulting from formation of four-coordinate boron. These two resonances, highlighted with dashed vertical lines, are due to nonring BO3 and four-coordinate boron sites. As can be seen in the isotropic projections, the nonring BO3 site intensity decreases as the K2O content is raised. Corresponding increases in the four-coordinate site intensity indicate conversion of the nonring BO3 sites to tetrahedral BO4- sites. Careful fitting of the isotropic DAS NMR data allows us to quantify changes in the three boron sites. The lower modified samples, 0 and 8 mol % K2O, give the exact isotropic shifts of both three-coordinate sites. The highly modified glasses, above 28 mol % K2O, give the isotropic shift of the four-coordinate peak. Gaussian fits to these data, shown in Figure 8, were performed by fixing the peak positions of the three sites to the measured isotropic shifts and varying the widths and amplitudes to obtain the best fit. The fitting parameters are listed in Table 2. The data and fits in Figure 8 show clearly the resolution of multiple boron sites in the compositional range of potassium borate glasses studied here. We show fits to three peaks in the isotropic spectrum of glassy (K2O)0.18(B2O3)0.82 and two peaks in B2O3 and (K2O)0.33(B2O3)0.67 glasses. The quality of the fits is shown by the residual difference between the fit and isotropic NMR data (in bold). All of the isotropic data in Figure 4 can be similarly fit to two or three peaks. As indicated by the tabulated fit parameters, the widths of the three boron resonances do not change appreciably upon modification, with only slight changes attributed to variance in the disorder of each site. We have previously checked the reliability of these intensity measurements by performing DAS NMR on crystalline compounds of known structure and comparing the measured site intensities to the crystal structure results.43 This verification, in addition to the methods in which the DAS NMR data were obtained, ensures that the site intensities resulting from the above fitting routine are accurate. These site intensities are plotted
Figure 8. Gaussian fits of the isotropic shift data: (a) two-peak fit to the DAS NMR data obtained for vitreous B2O3 at 8.4 T; (b) threepeak fit to the DAS NMR data for (K2O)0.18(B2O3)0.82 at 8.4 T; (c) two-peak fit to the DAS NMR data for (K2O)0.33(B2O3)0.67 at 8.4 T. Differences between the fits and the NMR data are in bold. Shifts are referenced to Et2O‚BF3. Fit parameters for all (K2O)x(B2O3)1-x glass data are summarized in Table 2.
TABLE 1: DAS NMR Isotropic Shifts of the Boron Sites at 8.4 T and Raman Features Attributed to Structural Units Present in Both Crystalline and Glassy Binary Alkali Boratesa structural unit
δiso at 8.4 T (ppm)
prominent Raman bands (cm-1)
boroxol nonring BO3 nonring BO4triborate diborate pentaborate metaborate di-triborate
4.7 1.0-2.3 -0.3 3.8 5.4 3.7 4.9 5.4
808, 126031,59 300-80032,46 500, 9005,18 540, 760, 93060,5 730, 790, 102060 500, 660, 770, 93060,5 470, 611, 768, 155031,61 500, 735, 79060
a Downfield shift of nonring BO (2.3 ppm) was obtained from 3 crystalline K2O‚2B2O3, where this boron has two four-coordinate boron neighbors.
as a function of K2O in Figure 9. Our estimates of N4 are compared to wide-line boron NMR results in Figure 10 and agree well with these values.15 The solid curve is the fraction of four-coordinate boron predicted from the relation N4 ) R, where R is the mole fraction of alkali oxide modifier. N4 remains slightly less than the quantity predicted by the composition stoichiometry, indicating the possible formation of NBO, as in reaction 2. Both processes can occur in these glasses, but our data indicate that the formation of four-coordinate boron is favored through at least 28 mol % K2O. Above this composition, the formation of NBO becomes a possible mechanism of network modification.
Potassium Borate Glasses
J. Phys. Chem., Vol. 100, No. 41, 1996 16725
TABLE 2: Linewidths and Relative Site Intensities Resulting from Gaussian Fits to the Isotropic DAS NMR Dataa ring BO3
BO4-
nonring BO3
mol % K2O
width (ppm)
rel pop (%)
width (ppm)
rel pop (%)
0 8 13 18 23 28 33 38
2.29 2.70 2.30 2.30 2.77 2.74 2.66 2.63
65 67 66 68 65 62 60 60
3.41 2.64 3.04 2.64 2.30 1.83
35 29 23 17 13 3
width (ppm)
rel pop (%)
2.97 2.97 3.14 2.77 3.14 3.04 2.84
4 11 15 22 35 40 40
a Fits were performed by fixing the centers of the peaks to the measured isotropic shifts of the three boron resonances and varying the widths and amplitudes to obtain the best statistical fit.
Figure 10. Measurements of the fraction of four-coordinate boron in potassium borate glasses as a function of K2O: (O) our DAS NMR results; (3) values extracted from the wide-line NMR data of Zhong and Bray.15 The solid line is that predicted from the relation N4 ) R ) x/(1 - x). Deviation of the four-coordinate boron fraction from this curve indicates the extent of nonbridging oxygen formation.
Figure 9. Plot of peak intensities as a function of K2O modifier content obtained from fits to the isotropic projections of the DAS NMR data: (0) 4.7 ppm resonance; (4) nonring BO3 site; (O) four-coordinate boron. The 4.7 ppm resonance may contain contributions from the threecoordinate boron in boroxol, metaborate, and modified rings.
To probe the formation of NBO, and to examine the effects of chemical modification on the oxygen sites in general, MAS NMR spectra of 17O in a series of potassium borate glasses were obtained (Figure 5). The MAS NMR spectra of oxygen are complicated by the large quadrupolar coupling of 17O and also by the presence of several overlapping resonances.25,36 However, the data reflect several qualitative changes in the glassy network with an increase of K2O modifier. As can be seen in the spectra of B2O3 and 10 mol % K2O glasses (parts a and b of Figure 5), much of the upfield intensity has been lost, owing to modification of the glassy network. In vitreous B2O3, this part of the 17O MAS spectrum was assigned predominantly to oxygen bridges between nonring BO3 units.36 The modifier apparently affects the concentration of this oxygen site. Even at the highest modifier levels (Figure 5d), we do not observe any new spectral features assignable to NBO. We cannot rule out the formation of NBO, but the concentration must be small. From the NMR parameters of NBO in related silicates,51,52 we would expect to see a relatively sharp feature on the downfield side of these resonances (between 50 and 100 ppm) if the concentration of nonbridging oxygen was above approximately 10%. 4.2. NMR of Crystalline Borates. To explore further the structural similarities in the glasses and crystals, we have obtained high-resolution DAS NMR data of 11B in a series of
polycrystalline potassium borates. The isotropic spectra in Figure 6 resolve multiple boron sites in several different crystalline compositions. The spectra for potassium diborate, K2O‚2B2O3, and potassium metaborate, K3B3O6, have been assigned.43 K3B3O6 is composed of metaborate rings, giving rise to the 4.9 ppm resonance in Figure 6d. The boron atoms in these rings resemble those in boroxol rings, except a single oxygen neighbor is now nonbridging (Figure 1h). Apparently, this has little effect on the isotropic shift of these boron atoms (cf. boroxol ring boron isotropic shift of 4.7 ppm). Potassium diborate53 shows three resolved resonances (Figure 6a). We assigned these to boron in diborate and di-triborate rings (peak at 5.4 ppm), boron in nonring BO3 units (peak at 2.3 ppm), and four-coordinate boron (peak at -0.4 ppm).43 The structure of the potassium borate glasses might resemble this crystalline compound, as proposed by other Raman studies.16,18,5 The diborate and di-triborate rings in K2O‚2B2O3 are unique, modified boroxol rings, since the three-coordinate boron atoms in these rings have two nearest neighbor four-coordinate boron atoms. The influence of second-neighbors on the 11B NMR spectra is not well understood. Therefore, we have also measured the 11B DAS NMR spectra of two other crystalline potassium borates, which contain slightly different ring structures. The isotropic spectra of 5K2O‚19B2O3 and potassium pentaborate, K2O‚5B2O3, are shown in parts b and c of Figure 6. 5K2O‚19B2O3 contains seven three-coordinate and three fourcoordinate boron sites.54 DAS NMR resolves two resonances, the three- and four-coordinate boron, and peak intensities are consistent with those for the crystal structure. The DAS NMR isotropic shift of the three-coordinate boron sites is 3.8 ppm, which is slightly different from the boroxol ring and nonring BO3 sites in the glasses but distinct from the diborate and ditriborate sites in K2B4O7. The three-coordinate boron atoms are part of pentaborate, triborate, and nonring BO3 units (Figure 1). K2O‚5B2O3 also contains 3- and 4-fold coordinate boron sites in a ratio of 4:1.55 The isotropic 11B NMR spectrum of K2O‚5B2O3 (Figure 6d) shows two resolved peaks. The peak at 3.7 ppm is due to three-coordinate boron in pentaborate groups, close to the shift of similar boron in 5K2O‚19B2O3. The peak at -0.2 ppm is due to the four-coordinate boron in this sample. The 3.7 and 3.8 ppm resonances in these crystalline potassium borates, assigned to three-coordinate boron in triborate and pentaborate groups, are similar to the 4.7 ppm resonance
16726 J. Phys. Chem., Vol. 100, No. 41, 1996
Youngman and Zwanziger
in the glass DAS NMR data. Therefore, these structural units may contribute to the structure of the potassium borate glasses, as proposed by the Raman studies.5 These modified rings may also contribute to the relatively constant 4.7 ppm peak intensity. 4.3. Simple Structural Model. As mentioned in the Introduction, the types of structures, and their interconnections, occurring in modified borates have been a matter of debate for some time. The prevailing view, based primarily on Raman spectra, is that the conversion of boron from 3-fold to 4-fold coordination occurs at boron atoms that are in boroxol rings. We have examined this behavior in the potassium borate glasses with Raman spectroscopy of the same samples used in the NMR studies. The spectra in Figure 7 show the replacement of the boroxol ring mode at 808 cm-1 with a Raman band at 770 cm-1 as the amount of modifier is increased. The 770 cm-1 band has been assigned to rings containing four-coordinate boron, such as pentaborate, triborate, and diborate rings.31 We observe in Figure 7 spectra of potassium borate glasses identical to those obtained in independent studies.18,19,16 Wide-line NMR spectra have been interpreted with modification of boroxol rings as well.9,12 The result of modification is the direct formation of modified ring structures (see Figure 1). The interconnection of these structures has been modeled by Kerner and colleagues in a way that is consistent with bulk properties such as the compositional dependence of the glass transition temperature.56,57 The nonring BO3 units, and their modification, are ignored in these treatments. This is justified explicitly by their low initial abundance and implicitly by the fact that Raman spectroscopy and wide-line NMR do not give well-resolved spectral features for these units. Hence, it is difficult to quantify their compositional dependence. In contrast to the above models, we suggested in an earlier publication that modification of the BO3 groups is preferred over modification of the boroxol rings in rubidium borate glasses.43 We argued for this view based on the observation that the spectral feature in the DAS spectrum initially assigned to boroxol ring boron was roughly constant as modifier was added, while the nonring BO3 site smoothly decreased in intensity as the 4-fold site increased. We conjectured that sample preparation differences and/or NBO formation accounted for the differences with the earlier models. From a chemical point of view, both of the above interpretations, namely modification only at ring or at nonring sites, are extreme. The slight chemical shift difference between the two boron species suggests that their local electronic configurations are nearly the same. Hence, one expects their reactivity to be about the same. Then differences from a uniform reactivity model should arise only from more global stabilization effects of the rings in the melt; for example, such effects could of course be large. Since we now have a substantial data set that includes highresolution NMR and Raman spectra on the same samples, as well as reference spectra of crystalline compounds made with the same alkali oxide modifier, we are in a position to propose a new, more unified model of structural changes due to modification. In particular, our NMR data provides quantitative information on the relative amounts of BO3 groups within and outside rings as a function of modifier. First, the resonance at 1 ppm gives directly the population of nonring BO3 groups. Table 1 shows that the various BO3 sites in rings do not overlap this site. Thus, by the fit of the data for this resonance plotted in Figure 9, the fraction of boron in nonring BO3 groups (which we label L3) is
L3 ) 0.35 - 0.75R
(3)
Figure 11. Plot comparing predictions of the structural model to site intensities measured with DAS NMR at 8.4 T, where the DAS NMR isotropic peak intensities are plotted against the mole fraction of modifier, R: (0) relative intensity of the 4.7 ppm resonance with the predicted fraction of three-coordinate boron in rings (Rg3, solid line); (4) relative intensity of the 1 ppm resonance due to nonring BO3 units, along with the model fit of this site (L3, long dashes); (O) relative intensity of the -0.3 ppm resonance assigned to four-coordinate boron with the model prediction (Rg4 + L4, short dashes).
Likewise, we take the fraction of boron in 4-fold coordinate sites, both loose and bound in rings, as
L4 + Rg4 ) R
(4)
where L4 is the fraction of boron in loose BO4- sites and Rg4 is the fraction of boron in 4-fold-coordinate sites that are in rings. These boron atoms all have isotropic shifts of about -0.3 ppm (Table 1). Notice that eq 4 presupposes that no NBO atoms are formed; that is, that each modifying cation gives rise to a four-coordinate boron in some way. This simplifying assumption is fairly accurate, as can be seen from Figure 10, where the fraction of four-coordinate boron is seen to be almost equal to R, the ratio of modifier to boron in the glass. Finally, the remaining boron atoms are both 3-fold coordinate and members of rings, since the other possible sites have been accounted for above. Call this fraction Rg3. By normalization,
Rg3 ) 1 - L4 - Rg4 - L3 ) 0.65 - 0.25R
(5)
Equations 3-5 can be compared directly to the DAS NMR data. The only additional assumption necessary is that all threecoordinate ring sites contribute to the isotropic resonance at 4.7 ppm. This is reasonable in light of the small differences in isotropic shift seen between different modified rings in crystalline potassium borates and boroxol rings (less than 1 ppm). Furthermore, by not making this assumption, we would be assuming implicitly that no boroxol rings are modified or that the modified rings are invisible in the NMR data, both of which seem to us untenable. With this assumption the model can be compared to the NMR data, as shown in Figure 11. The qualitative agreement is good, the main deviation being that the three-coordinate ring resonance is predicted to fall off with R slightly faster than it does, while the four-coordinate resonance grows in slightly more slowly. The discrepancy may be due to small amounts of NBO forming that we could not detect directly. The above model determines the partitioning between ring and nonring units but does not specify what types of modified rings are present (these structures are not individually resolved in the DAS NMR data). Thus, there are a variety of possible realizations of the model. To refine the model further, we will assume that the modified rings consist of tetraborate and diborate
Potassium Borate Glasses
J. Phys. Chem., Vol. 100, No. 41, 1996 16727
units. These structures have been used to model a large body of data in this field, both NMR and Raman. Because our Raman spectra are essentially identical with earlier results on these compositions, we can be confident that this structural assignment is reasonable here. Now our results on the partitioning between the ring and nonring structures can be combined with the assumption of tetraborate and diborate units to develop the complete model. We call the fraction of boroxol rings at any composition, x, of tetraborate groups, y, of diborate groups, z, of loose BO3 groups, V, and of loose BO4- groups, w. The fractions are normalized to unity. The total amount of boron, in terms of these fractions, is 3x + 8y + 4z + V + w (that is, three boron atoms per boroxol ring, eight per tetraborate, etc.). Equations 3 and 4 constrain these fractions as follows:
L3 )
V ) 0.35 - 0.75R 3x + 8y + 4z + V + w
L4 + Rg4 )
w + 2y + 2z )R 3x + 8y + 4z + V + w
(6) (7)
(eq 5 does not provide an additional independent constraint). Next, the Raman data are used to estimate the dependence of the fraction of boroxol rings on R. Some reports have considered the boroxol rings to vanish as early as R ) 0.25;16 if only modification at rings occurred, and no NBO formed, the rings would presumably be gone by modifications as low as R ) 0.33. Our DAS NMR data suggest that, in contrast, the nonring sites are modified as well. Thus, the boroxol rings may be modified more slowly with R. We will assume their R dependence is given by
x(R) ) x(0) -
x(0) R 0.5
(8)
which is to say that no pure boroxol rings remain by R ) 0.5. This is in reasonable agreement with our Raman spectra (Figure 7), where the 808 cm-1 band disappears between R ) 0.4 and R ) 0.5, and with earlier NMR studies.9,12 The linear dependence on R is also in qualitative agreement with the Raman spectra. The quantity x(0) can be estimated from the DAS NMR data at R ) 0.0, which gives directly the fractions of boron in boroxol ring and nonring BO3 groups; we find x(0) ) 0.38. As our final independent constraint, we adopt Jellison and Bray’s estimate of the diborate concentration in the glass.9 This constraint is chosen because our data end at the diborate composition, R ) 0.5. Jellison and Bray estimated the ratio of boron in diborate groups to boron in rings (boroxol, tetraborate, and diborate). Their results are roughly linear and are expressed in our notation as
{
0 4z ) 1.7R - 0.17 3x + 8y + 4z
for R < 0.1 for R g 0.1
(9)
Equations 6-9 in conjunction with the normalization can be solved for V - z as functions of R to give a model that is consistent with both the DAS NMR and Raman data. The predicted fractions of the building blocks are shown in Figure 12. This model is like earlier models in that it predicts modification of the boroxol rings and formation of tetraborate and diborate units. The relative amounts of these units are approximately the same as was inferred in earlier 10B NMR experiments.9 The model also predicts the modification of nonring BO3 groups and formation of loose BO4- groups. Both of these events seem chemically reasonable but are not treated in earlier models. Interestingly, the model predicts that modified rings form faster (with R) than the boroxol rings disappear, and
Figure 12. Fraction of structural groups in the (K2O)x(B2O3)1-x glasses predicted from the model developed in the text: (0) boroxol rings; (4) diborate; (O) metaborate; (3) loose BO3; (]) loose BO4-.
likewise, the loose BO3 groups disappear faster than the loose BO4- groups are formed. This suggests that as loose BO3 groups are modified, there is a tendency for the newly formed BO4- groups to be incorporated into modified ring structures immediately, using other nonring BO3 groups to complete the ring. Since the chemistry occurs in the melt, not the glass, this type of mechanism is quite plausible and argues for a stabilization effect due to ring formation. Furthermore, since loose BO4groups form with R at a higher rate than boroxol rings are destroyed, it appears that the nonring BO3 units have a higher chemical reactivity than do the boroxol ring boron atoms. The conclusion is that rings are especially stable in the liquid phase of these materials, both physically and chemically. A complication to the above model is the possible formation of NBO in the potassium borate glasses. From our 17O MAS NMR studies (Figure 5), we have not observed any measurable fraction of NBO. The upper limit to the concentration of NBO from these spectra is approximately 10%. Unfortunately, 11B DAS NMR in the glasses does not resolve metaborate and boroxol ring boron, the isotropic shifts of which are 4.9 and 4.7 ppm, respectively. If NBO atoms contribute appreciably to the structure of these glasses, an important parameter to measure is the quadrupole asymmetry, η, which is sensitive to the symmetry of the boron coordination. Three-coordinate boron sites with all-bridging oxygen have η ) 0.2 ( 0.1, while a single NBO in the boron coordination would increase η to over 0.5.15 Changes in η should be apparent in the powder patterns of the boron resonances. Unfortunately, at 79.19°, the anisotropic line shapes from these disordered materials are relatively insensitive to changes in η. We have performed DAS NMR experiments with detection at 54.74°, the magic angle, to see changes in η.58 This experiment has quite low signalto-noise, since it involves not just one but many rotor hops and concomitant storage periods during each scan of the twodimensional experiment. Even at 38 mol % K2O, we do not observe substantial changes in the asymmetry parameter of the boron in the 4.7 ppm resonance. The lack of positive NBO signal in the 17O MAS NMR spectra and only minor changes in the quadrupolar asymmetry of the boron resonances confirm the low abundance of NBO measured previously with Mo¨ssbauer spectroscopy.39,40 The present model appears to work well for the compositions of potassium borate glasses examined in this paper, up to about 33 mol % modifier. At higher modifier levels, where N4 deviates substantially from the R ) x/(1 - x)
16728 J. Phys. Chem., Vol. 100, No. 41, 1996 curve, NBO will play an important role and this model will not suffice to explain the glassy microstructure. Further work on highly modified alkali borates is in progress. 5. Conclusions The structural chemistry of potassium borate glasses has been examined with a variety of experimental probes, including 11B DAS NMR, 17O MAS NMR, and Raman spectroscopies. The NMR data show significant decrease of the loose BO3 site resonance with added modifier and a much slower decrease in the resonance assigned in B2O3 to boroxol rings. The Raman spectra confirm the disappearance of the boroxol ring mode at 808 cm-1, which implies changes in the boroxol rings sites. A model has been formulated to explain the structural changes in these glasses due to the increase in K2O modifier concentration. In the general case, this model predicts the formation of both modified rings containing four-coordinate boron and loose (nonring) BO4- units in response to modification. By assuming that the modified rings include tetraborate and diborate units, the latter increasing at the rate inferred in earlier work,9 we could formulate a complete model of the structure of the modified glass, which includes for the first time definite predictions of the loose 3- and 4-fold coordinate boron fractions. The loose 3- and 4-fold coordinate units are a significant component of the glass structure, which could not previously be studied directly. We also believe that this model should apply at least generally to other alkali borate glasses, including the rubidium borate compositions studied earlier by us43 (thus reconciling the apparent discrepancies between the DAS NMR data and the Raman data). The rate of growth with R of the various sites indicates that the chemical reactivity of the loose BO3 sites is somewhat higher than that of the boroxol ring boron and additionally that when loose 4-fold sites are created, they are preferentially incorporated into rings using existing nonring BO3 sites. Acknowledgment. The authors thank Dr. Scott Haubrich for assistance in the synthesis of oxygen-17-enriched boric acid, Professor Edward Grant and Dr. Kenneth Haber at Purdue University for assistance with the Raman measurements, and Dr. Ulrike Werner-Zwanziger for many helpful discussions. This research was supported by the National Science Foundation under Grant Nos. DMR-9115787 and DMR-9508625. References and Notes (1) Krogh-Moe, J. Phys. Chem. Glasses 1965, 6, 46. (2) Trunnell, M.; Torgeson, D. R.; Martin, S. W.; Borsa, F. J. NonCryst. Solids 1992, 139, 257. (3) Levasseur, A.; Menetrier, M. Mater. Chem. Phys. 1989, 23, 1. (4) Tatsumisago, M.; Angell, C. A.; Martin, S. W. J. Chem. Phys. 1992, 97, 6968. (5) Meera, B.; Ramakrishna, J. J. Non-Cryst. Solids 1993, 159, 1. (6) Ha¨gg, G. J. Chem. Phys. 1935, 3, 42. (7) Zachariasen, W. J. Am. Chem. Soc. 1932, 54, 3841. (8) Krogh-Moe, J. Phys. Chem. Glasses 1962, 3, 1. (9) Jellison, G., Jr.; Bray, P. J. Non-Cryst. Solids 1978, 29, 187. (10) Bray, P.; Feller, S.; Jellison, G., Jr.; Yun, Y. J. Non-Cryst. Solids 1980, 38-39, 93. (11) Yun, Y.; Bray, P. J. Non-Cryst. Solids 1981, 44, 227. (12) Feller, S.; Dell, W.; Bray, P. J. Non-Cryst. Solids 1982, 51, 21. (13) Bray, P.; Geissberger, A.; Bucholtz, F.; Harris, I. J. Non-Cryst. Solids 1982, 52, 45. (14) Bray, P. J. Non-Cryst. Solids 1985, 75, 29. (15) Zhong, J.; Bray, P. J. Non-Cryst. Solids 1989, 111, 67. (16) Konijnendijk, W.; Stevels, J. J. Non-Cryst. Solids 1975, 18, 307.
Youngman and Zwanziger (17) Loro¨sch, J.; Couzi, M.; Pelous, J.; Vacher, R.; Levasseur, A. J. Non-Cryst. Solids 1984, 69, 1. (18) Kamitsos, E.; Karakassides, M.; Chryssikos, G. Phys. Chem. Glasses 1989, 30, 229. (19) Chryssikos, G.; Kamitsos, E.; Karakassides, M. Phys. Chem. Glasses 1990, 31, 109. (20) Kamitsos, E.; Chryssikos, G.; Karakassides, M. J. Non-Cryst. Solids 1990, 123, 283. (21) Voron’ko, Y.; Gorbachev, A.; Kudryavtsev, A.; Sobol’, A. Neorg. Mater. 1992, 28, 1707. (22) Dwivedi, B.; Rahman, M.; Kumar, Y.; Khanna, B. J. Phys. Chem. Solids 1993, 54, 621. (23) Massot, M.; Souto, S.; Balkanski, M. J. Non-Cryst. Solids 1995, 182, 49. (24) Dwivedi, B.; Khanna, B. J. Phys. Chem. Solids 1995, 56, 39. (25) Jellison, G. E., Jr.; Panek, L. W.; Bray, P. J.; Rouse, G. B., Jr. J. Chem. Phys. 1977, 66, 802. (26) Johnson, P.; Wright, A.; Sinclair, R. J. Non-Cryst. Solids 1982, 50, 281. (27) Williams, S.; Elliott, S. Proc. R. Soc. London, Ser. A 1982, 380, 427. (28) Verhoef, A.; den Hartog, H. J. Non-Cryst. Solids 1994, 180, 102. (29) Youngman, R. E.; Zwanziger, J. W. J. Non-Cryst. Solids 1994, 168, 293. (30) Gravina, S. J.; Bray, P. J. J. Magn. Reson. 1990, 89, 515. (31) Bril, T. Philips Res. Rep. Suppl. 1976, 2, 1. (32) Walrafen, G.; Samanta, S.; Krishnan, P. J. Chem. Phys. 1980, 72, 113. (33) Hannon, A.; Wright, A.; Blackman, J.; Sinclair, R. J. Non-Cryst. Solids 1995, 182, 78. (34) Hannon, A.; Grimley, D.; Hulme, R.; Wright, A.; Sinclair, R. J. Non-Cryst. Solids 1994, 177, 299. (35) Youngman, R.; Werner-Zwanziger, U.; Zwanziger, J. Z. Naturforsch., in press. (36) Youngman, R.; Haubrich, S.; Zwanziger, J.; Janicke, M.; Chmelka, B. Science 1995, 269, 1416. (37) Silver, A.; Bray, P. J. Chem. Phys. 1958, 29, 984. (38) Bray, P. J. Non-Cryst. Solids 1987, 95-96, 45. (39) Nishida, T.; Shiotsuki, T.; Takashima, Y. J. Non-Cryst. Solids 1980, 41, 161. (40) Nishida, T.; Takashima, Y. J. Non-Cryst. Solids 1980, 37, 37. (41) Bray, P.; Emerson, J.; Lee, D.; Feller, S.; Bain, D.; Feil, D. J. NonCryst. Solids 1991, 129, 240. (42) Bray, P.; Lee, D.; Mao, D.; Petersen, G.; Feller, S.; Bain, D.; Feil, D.; Pandikuthira, P.; Nijhawan, S. Z. Naturforsch. 1992, 47A, 30. (43) Youngman, R.; Zwanziger, J. J. Am. Chem. Soc. 1995, 117, 1397. (44) Rahman, M.; Dwivedi, B.; Kumar, Y.; Khanna, B. Indian J. Phys. 1992, 66B, 365. (45) Hannon, A.; Sinclair, R.; Blackman, J.; Wright, A.; Galeener, F. J. Non-Cryst. Solids 1988, 106, 116. (46) Sharma, S.; Simons, B.; Mammone, J. J. Non-Cryst. Solids 1980, 42, 607. (47) Grandinetti, P.; Baltisberger, J.; Llor, A.; Lee, Y.; Werner, U.; Eastman, M.; Pines, A. J. Magn. Reson. A 1993, 103, 72. (48) Mueller, K.; Sun, B.; Chingas, G.; Zwanziger, J.; Terao, T.; Pines, A. J. Magn. Reson. 1990, 86, 470. (49) Baltisberger, J. H.; Gann, S. L.; Wooten, E. W.; Chang, T. H.; Mueller, K. T.; Pines, A. J. Am. Chem. Soc. 1992, 114, 7489. (50) van Wu¨llen, L.; Mu¨ller-Warmuth, W. Solid State Nucl. Magn. Reson. 1993, 2, 279. (51) Chmelka, B. F.; Mueller, K. T.; Pines, A.; Stebbins, J.; Wu, Y.; Zwanziger, J. W. Nature 1989, 339, 42. (52) Mueller, K. T.; Baltisberger, J. H.; Wooten, E. W.; Pines, A. J. Phys. Chem. 1992, 96, 7001. (53) Krogh-Moe, J. Acta Crystallogr. 1972, B28, 3089. (54) Krogh-Moe, J. Acta Crystallogr. 1974, B30, 1827. (55) Krogh-Moe, J. Acta Crystallogr. 1972, B28, 168. (56) Kerner, R. J. Non-Cryst. Solids 1991, 135, 155. (57) Barrio, R.; Duruisseau, J.; Kerner, R. Philos. Mag. B 1995, 72, 535. (58) Grandinetti, P.; Baltisberger, J.; Farnan, I.; Stebbins, J.; Werner, U.; Pines, A. J. Phys. Chem. 1995, 99, 12341. (59) Windisch, C, Jr.; Risen, W., Jr. J. Non-Cryst. Solids 1982, 48, 307. (60) Konijnendijk, W. L. Philips Res. Rep. Suppl. 1975, 1, 1. (61) Chryssikos, G.; Kapoutsis, J.; Patsis, A.; Kamitsos, E. Spectrochim. Acta 1991, 47A, 1117.
JP961439+
