J. Phys. Chem. 1995,99, 5 111-5 116
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The Structure of Sodium Tellurite Glasses: Sodium Cation Environments from Sodium-23 NMR S. L. Tagg, R. E. Youngman, and J. W. Zwanziger* Department of Chemistry, Indiana University, Bloomington, Indiana 47405 Received: October 6,1994; In Final Form: January 3, 1995@
In order to study the way in which the modifying sodium cations interact with the network in (Na2O),(Teoz)l-, glasses, we have probed the sodium sites using the dynamic angle spinning NMR experiment. By performing this experiment at two different magnetic field strengths, we extract the chemical shift and quadrupole coupling parameters, which we relate to the glass structure with the aid of an empirical model. Our results suggest that the sodium coordination changes from about six, at low modifier concentrations, to about five, at high concentrations. This decrease is not monotonic, however; it is relatively independent of concentration from 10 to about 18 mol %, at which point it begins to decrease. We interpret this change as due to the onset of formation of significant numbers of nonbridging oxygen.
1. Introduction Alkali tellurite glasses (M2O),(TeO2)1-, (M = Li, Na, K, or Rb) are of current interest from both technological and fundamental standpoints. The optical properties of these glasses include good transmittance of infrared light, and they are being investigated for use as all-optical switching devices. Fundamentally these materials are of interest because of their unusual glass-forming ability. TeO2 itself is only a conditional glassformer, requiring special fast-quenching procedures to vitrify; the resulting amorphous material is not stable with respect to crystallization.’ This behavior is in contrast to typical “good” inorganic glass formers that also have three-dimensional network structures, such as Si02 and BzO3. Both of the latter materials can be quenched from melts very slowly IUS) without crystallizing. However, when a modifier, such as Na20, is added to TeO2 in moderate concentration (10-30 mol %), the resulting material becomes a very good glass-former. This result holds for all the alkali oxides, but on the basis of stability against crystallization,2 Na2O seems to confer the most glass-forming character. The tendency to form glasses in this system is strongly composition-dependent in all the (MzO),(Te02)1-, materials, with the most stable glasses formed with modifier concentrations near 20 mol %. It is perhaps surprising that glass-forming ability peaks at this composition because for all the alkali metals MzTe409 forms a crystalline phase. Figure 1 shows the phase diagram of the (NazO),(Te02)1-, ~ y s t e mThe .~ glass-forming region spans the range from about 5 mol % modifier concentration up to about 33 mol %, the composition of the NazTe205 crystalline phase. There is also a eutectic at 16.7 mol % NazO, near to but still lower than the composition for optimum glass stability. The structure and glass-forming ability of (MzO),(Te02)1-, have been investigated recently by a variety of techniques, including c a l ~ r i m e t r y , ~vibrational .~*~ spectroscopies,2s6-8X-ray and neutron ~cattering,~ and tellurium NMR.l0 These studies have focused on the tellurium oxide network, and how it is modified upon addition of alkali oxides. Crystalline TeO2 consists of a three-dimensionalnetwork of comer-sharing TeO4 units (aform”) or a two-dimensional network of edge-sharing Te04 units (j3 form12). Addition of a modifier would be expected to cleave the TeO2 network into smaller fragments, @Abstractpublished in Advance ACS Abstracts, March 15, 1995.
0022-365419512099-5111$09.0010
which can include nonbridging oxygen (NBO). On the basis of Raman spectra, Sekiya et aL6 proposed that these fragments include well-known tellurium oxide structural units such as Te2052- and Te032-, both of which contain NBO. Furthermore, they suggest that Te032- trigonal pyramids having NBO are initially formed in the modifier concentration range approaching 20 mol %. A similar interpretation of Mossbauer spectra of iron in (Na~O)XTeO2)9s-,*5Fe203has been suggested by Nishida et al? In contrast, Heo et aL2interpret their X-ray photoelectron spectra of the oxygen 1s peak as indicative of a change in charge distribution, but not of nonbridging oxygen formation. Sodium tellurite glasses also display anomalous thermal behavior near which may be a direct result of the 20 mol % compo~ition,~,~ structural rearrangements. For instance, there is a large difference between the glass transition and crystallization temperature at this composition, which is evidence that the glass is particularly resistant to devitrification.2 On the other hand, this stability may be merely due to a relatively constant glass transition temperature as a function of composition, coupled with a rapidly decreasing liquidus temperature (see Figure 1). There is little information, however, on how the modifier cations interact with the tellurium oxide network and what role they play in inducing the strong composition dependence of the glass-forming tendency. It has been conjectured that the cations may be strongly associated with the NBO,and the glassforming tendency in this system is then discussed in terms of a constrained network? In alkali silicates, however, EXAFS measurements show that the sodium cations are coordinated to typically five oxygens, which indicates that both nonbridging and bridging oxygens interact with the cations.I3 We have shown that, in crystalline Na2Te409, there are both bridging and nonbridging oxygens and that the sodium cations interact with both about eq~al1y.l~ We report here on NMR measurements of the sodium sites in (NazO),(Te02)1-, glasses, as a function of composition. We used a two-dimensional Nh4R experiment in two different magnetic fields to resolve the quadrupole and chemical shift interactions. We relate these parameters to the structure using an empirical model15 that we have validated on crystalline sodium te1l~rites.l~Finally, through the twodimensional NMR line shapes, we are able to estimate the distribution of these parameters and the disorder in the binding sites. 0 1995 American Chemical Society
5112 J. Phys. Chem., Vol. 99, No. 14, 1995
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700
s
600
W
b 500
400 Na,Te409
+
300 Glass
Transition Temperatures
0
10
20
30
40
50
Mol-% Na20 Figure 1. Phase diagram of (Na20),(Te02)1-,, after Gmelin.3 Data on crystal melting temperatures are from ref 29; glass transition temperatures are from ref 2.
2. Experimental Methods The sodium tellurite glasses were prepared as follows. Stoichiometric mixtures of TeOz (99.995%, Aldrich) and Na2C03 (99.995+%, Aldrich) were placed in silica tubes in 2-2.5 g amounts, heated at 750 'C for approximately 8 min, and then poured onto a stainless steel plate. The resulting glasses, between 10 and 33 mol % Na20, were clear and colorless. For NMR analysis, the glasses were ground into fine powders. Selected compositions, including samples near the limiting compositions of glass formation, were shown to be amorphous by X-ray powder diffraction. Sodium-23 nuclear magnetic resonance spectra of the various compositions were obtained using a home-built spectrometer at both 7.1 and 8.4 T magnetic field strengths (Larmor frequencies of 79.4 and 95.2 MHz, respectively). We used the dynamic-angle spinning (DAS) NMR experiment, which correlates isotropic and anisotropic information in two dimensions.16-21 One dimension yields resonances shifted by the combined effects of the isotropic chemical shift and the isotropic part of the second-order quadrupole interaction, while the second dimension provides the corresponding powder patterns due to anisotropic spin interactions. We obtained purely absorptive line shapes by using the shifted-echo hypercomplex DAS sequence described by Gran-
dinetti et aL20 (see also ref 21). Data were collected with spinning speeds between 5.5 and 6.0 kHz and rotor orientation angles of 37.38' and 79.19' (powder patterns were acquired with the rotor axis 79.19' with respect to the magnetic field). The experiments at 8.4 T typically consisted of 16 scans at each of 96 delay times while the 7.1 T experiments each had 128 scans at 24 delay times. The relaxation times in representative samples were determined by saturation-recovery experiments and found to be on the order of 1 s. Consequently, signal averaging was performed with a 5 s delay between scans. 3. Results Figure 2 shows a representative magic-angle spinning 23Na NMR spectrum of (Na20)l8(Te02)82 glass. Figure 3 illustrates a representative two-dimensional DAS spectrum of 23Nain the 20 mol % glass composition in an 8.4 T field. These spectra include projections onto the isotropic shift dimension and the anisotropic plus isotropic shift dimension. The shift of the peak in the isotropic dimension is the primary observable of interest in these experiments-it reflects the most probable value of the distribution of the sodium isotropic shifts. These most probable shifts, taken at the maximum of the peak in the isotropic projection, are shown in Figure 4 and Table 1 as a function of composition, in both fields, referenced to solid NaCl.
J. Phys. Chem., Vol. 99, No. 14, 1995 5113
Structure of Sodium Tellurite Glasses
120
80
40
0 PPm
-40
TABLE 1: Most Probable Isotropic Shifts, Quadrupole Product, and Isotropic Chemical Shift for Sodium in (NazO)x(TeOz)l-xas a Fumtion of Compositionn shift at shift at 6(cfl, ppm 8.4 T, ppm 7.1 T, ppm mol % NazO ( 1 0 . 8 ppm) (10.8 ppm) ( f 3 ppm) PQ,MHz -11 1.4 f 0.3 10 -16.5 -18.8 -12 1.2 f 0.4 12 -15.6 -17.4 -11 1.2 f 0.4 15 -14.5 -16.1 -6 1.7 f 0.3 18 -14.1 -17.6 -5 1.9 f 0.3 -14.8 - 19.0 20 -3 1.9 f 0.2 -17.7 25 -13.3 -4 1.8 f 0.3 -12.5 -16.3 28 -14.9 +1 2.0 f 0.2 33 -10.0
-120
-80
Figure 2. Sodium-23 MAS spectrum of (NazO)ls(TeOz)gz, at 8.46 T (95.2 MHz). Shift reference is solid NaC1.
I
I
I
I
50 0 -50 Isotropic + Anisotropic Shift (ppm) Figure 3. Sodium-23 DAS spectrum of glassy NazTe409, at 8.46 T (95.2 MHz resonance frequency). At the left is the projection onto the isotropic shift axis. The maximum of the peak in this projection gives the most probable isotropic shift.
0
10
20 30 mol-% Na20
40
50
Figure 4. Most probable isotropic shifts as a function of composition in (Na20)x(Te02)1-,,taken from the maximum of the DAS Nh4R peak, in two fields: 0 , 8.46 T (95.2 MHz); 0, 7.1 T (79.6 MHz). The reference is solid NaCl. 4. Discussion 4.1. Spin Interaction Parameters. Magic-angle spinning (MAS), the standard experiment for achieving high-resolution spectra of solids, is only partially effective for quadrupolar nuclei because it does not remove all of the second-order quadrupole broadening. For crystalline material this may be acceptable,
Shift reference is solid NaCl as the resulting spectra are composed of overlapping powder patterns that can often be successfully modeled. For a glassy material, however, the additional inhomogeneous broadening due to the site disorder renders MAS spectra of quadrupolar nuclei difficult to interpret. A typical 23NaMAS spectrum of (Na20),(Te02)1-, glass (Figure 2) is relatively uninformative, owing to the small chemical shift range of sodium, substantial second-order quadrupole broadening, and the disorder of the glass. Previous studies with MAS on sodium in silicates have met with similar difficulties.22 The DAS experiment circumvents these problems, however, because it removes the anisotropy broadening due to both the chemical shift and secondorder quadrupole interactions. Thus the shift of the resonance in the high-resolution dimension is a direct measure of the isotropic components of these two interactions. DAS does not remove homonuclear dipole broadening, but the concentration of sodium in the glasses studied here is low enough so that this is not a problem. The width of the DAS resonance is a measure of the disorder of the site. In each glass we studied we observed a single, broad DAS resonance, as in Figure 3, suggesting that there is a distribution of chemically similar sodium sites in these glasses. The shift of the DAS resonances as a function of composition represents the most probable sodium environment and is shown in Figure 4 for two different magnetic field strengths. For quantitative interpretation, we treat the sodium sites as describable by a chemical shift interaction and a quadrupole coupling, which leads to a total isotropic shift, observed in the DAS spectra, that is the sum of two component^:^^-'^
Here diso is the isotropic shift in ppm, ):d! is the isotropic chemical shift in ppm, I is the nuclear spin ( I = 3/2 for sodium23), and YO is the Larmor frequency in MHz. The quadrupole product PQ contains the asymmetry parameter of the electric field gradient, 7,and the quadrupole coupling constant, e2Qq/ h, which measures the magnitude of the gradient, through
P , = (e2qe/h)J1+ q2/3
(2)
The two contributions to the isotropic shift can be resolved through their differing field dependences. Using our data in and two different fields (Figure 4) and eq 1, we determine )d':! PQ for the sodium tellurite glasses as shown in Table 1 and Figure 5. In Figure 5 a distinct change in both d!:) and PQ at the 18 mol % composition is evident. 4.2. Interpretation of the Parameters. Chemical shifts and quadrupole parameters are measured by many methods including
5114 J. Phys. Chem., Vol. 99, No. 14, 1995
Tagg et al.
(a>
2 o
h
I
E
.B
' 9
I
: 0 0 . 5 0 10 20 30 40 50 -20 I 0 10 20 30 40 50 mol-% Na20
mol-% Na20
Figure 6. Estimated coordination number of sodium in (Na~O)*(TeOz)l-x, based on measured isotropic chemical shifts and the empirical model of Koller ef aZ.I5 (see eqs 4 and 5 ) . I
J J
chemical shift given by
d):!
"
I
0
10
20 30 mol-% Na20
40
50
(a) Most probable chemical shift of sodium in (Na20),(Te02)1,, as a function of composition. The reference is solid NaC1. (b) Most probable quadrupole product PQ of sodium in (Na20),(TeO&,, as a function of composition. In both plots, 0 represents glass compositions and W represents crystalline phases (Na2Te409 and NaZTeO3). Figure 5.
NQR, NMR, and Mossbauer spectroscopies. These parameters contain information about the local electronic and magnetic environment of the nucleus, and it is of general interest to correlate parameters on the basis of structural models to values determined by experiment. Correlations between NMR parameters and the local bonding environment are well-known and have been observed for a variety of species in crystals and glasses. Such correlations are observed also for sodium and have been treated quantitatively recently by Xue and st ebb in^^^ and Koller e? a1.15 (see also ref 14). The chemical shift of an atom is in general related in a complex way to its bonding interactions with neighboring atoms,24making ab initio treatment difficult. For this reason, empirical approaches are often preferable. For sodium in solid oxides, Koller et al. found that the chemical shift correlates well with the parameter A, where
A=Ci
Wi ri3
(3)
Here, the sodium atom of interest is a distance ri from the ith oxygen, which has valency Wi. The valency is computed using the empirical values for bond valencies given by Brown and AltermattZ5and Brese and O'Keeffe.26 This approach refines the general concept of valency to reflect subtle differences between bonding geometries of the oxygens. While all the oxygens, both bridging and nonbridging, have Wi RZ 2, those with more close contacts have Wi > 2, while those with less have Wi < 2. This parameter thus gives a more precise description of the coordination environment of each oxygen, including both its interaction with the sodium cation and with its other neighbors. By studying primarily sodium silicates, Koller et al. arrived at a correlation between A and the sodium
= -133.6A
+ 107.6
(4)
Distances being equal, lower oxygen valency shifts the resonance downfield. However, eq 3 shows that the chemical shift parameter, A, is sensitive to small changes in r. Previously we found reasonable agreement between our experimental chemical shifts for sodium in crystalline Na2Te409 and NazTeO3, and the values derived from eqs 3 and 4,and the crystal structure^.'^ Therefore, application of the chemical shift correlation to the sodium tellurite glasses seems appropriate. Because of the strong distance dependence (eq 3), we assume that the chemical shift is dominated by the first coordination sphere of the sodium. Then we can rewrite eq 3 in terms of an average valence and bond distance, summed over the coordination sphere:
where n is the coordination number of the sodium. We estimated the quantity (W/$) by assuming a typical oxygen valency of two and oxygen-sodium distances of 2.35 8, (the sum of ionic radii). We verified that these approximations are good by comparing to the value derived from the crystal structure of Na2Te409. Finally, from our determined chemical shifts, combined with eqs 4 and 5 , we get an estimate of the sodium cation coordination number, as shown in Figure 6. We found that, at low concentrations of sodium oxide, the coordination is roughly six and decreases to a value near five at the higher concentrations. These coordinations are similar to those observed in crystalline Na~Te409and NazTeO3 and those determined by E M S measurements in sodium silicate g1as~es.l~ It may be argued that we could be overestimating the coordination, by treating the contact distances to all oxygen as roughly equivalent, when in fact distances to nonbridging oxygens may be thought to be significantly shorter than to bridging oxygens. In crystalline Na2Te409 this is not the case, however: l4 while contacts to nonbridging oxygens in this material are never the longest in the sodium coordination sphere, neither are they noticeably shorter than the others. Moreover, if the sodium coordination was dominated by, say, a single nonbridging oxygen, the A value would be very small, leading to shifts of the order of 80 ppm, far larger than is seen for sodium. This sort of structure has been conjectured for (Na20),(TeO2)1-, (ref 4),but on the basis of our results, we do not believe it is a common one. We suggest that the cause of this change in coordination number as a function of composition is the generation of a
Structure of Sodium Tellurite Glasses significant fraction of NBO at the higher modifier concentrations. This conjecture is based on a comparison with the sodium sites in crystalline Na~Te409(ref 14). There are two sodium environments in this material: one sodium ion is 5-coordinate, surrounded by two bridging and three nonbridging oxygens, and the other is coordinated to six oxygens, two of which are nonbridging. Here the sodium cation with the lower coordination has more nonbridging oxygen neighbors. We conjecture that this type of correlation between the sodium coordination and the number of nonbridging oxygens exists for the sodium ions in the corresponding glasses, Le., sodium coordination in the crystal and glasses is directly related to the number of nonbridging oxygen neighbors. This leads to the tentative conclusion, based on the decrease in the estimated sodium coordination in the glasses as mentioned above, that the number of nonbridging oxygens increases with respect to increased sodium oxide concentration. Xue and StebbinsZ3have also noted a positive correlation between sodium chemical shift and the number of NBOs per tetrahedral cation. In that correlation, however, the sodium coordination number is constant, and the change in chemical shift is ascribed to second-neighbor sodium interactions. Such a mechanism cannot be ruled out in the present case, especially in light of the significant distribution of chemical shifts for sodium at each composition (see below). This distribution means that the average coordination number may be changing somewhat less than Figure 6 indicates. We assume, however, that the local electronic environment of sodium will be dominated by the nonbridging oxygen and that second-neighbor interactions will be a minor effect. The trend in chemical shift of sodium in NazTe409 and NazTeO3 supports this assumption. The sodium sites in crystalline NazTe409 have shifts of -3 zk 5 ppm and 5 & 10 ppm, corresponding to the six- and five-coordinate sites, respectively, and 5.8 f 0.5 ppm and 17.0 f 0.5 ppm in NazTeOs. These shifts are determined primarily by the proximity of the NBO-shorter distances lead to larger values of A (see eq 3 ) and upfield shifts. In Na2Te409, with two or three nonbridging oxygens in the coordination sphere, the distances are a little shorter, as compared to NazTeO3, with six equally distributed nonbridging oxygen^.^^ The sodium shifts of the (NazO),(Te02)1-, glasses increase from roughly - 11 to 1 ppm (see Table 1 and Figure 5 ) as a function of composition. Reasoning in analogy with the structures of NazTe409 and NazTeO3, then, leads us to conclude a trend in glassy (Na20),(TeOZ)1-, as x increases is toward coordination spheres around the sodium with fewer oxygen atoms, but a higher proportion of NBO. As the number of NBOs in the coordination sphere increases, the distances to them from the sodium must also increase slightly, leading to smaller A parameters and downfield chemical shifts. Whereas from the chemical shift we can infer the coordination of the sodium sites, the quadrupole coupling gives information about the symmetry of the sites. Low-symmetry sites (less than tetrahedral) give large quadrupole couplings, while highsymmetry sites give small couplings. In crystalline Na2Te409 the two sodium sites have quadrupole couplings of 3.6 and 4.4 MHz; in NazTeO3, which has more nearly octahedral sodium coordination^,^^ the couplings are about 1.4 and 1.8 MHz (ref 14). By using eq 1 and data collected in two fields, we determined the most probable value of the quadrupole product PQ (eq 2 ) for each composition studied (see Table 1). We have no independent measure of the asymmetry parameter 7; for DAS NMR, this is usually extracted by fitting anisotropic powder pattems,17-19 but in the present case, the disorder makes that difficult. Nonetheless the line shapes suggest that 7 is generally
J. Phys. Chem., Vol. 99,No. 14, 1995 5115 small (near zero), and thus, we take as a reasonable approximation e2Qq/h E PQ. Figure 5 shows that the most probable value of PQ,and therefore of ezQq/h,is constant at low sodium oxide concentration, increases abruptly at the 18 mol % composition, and remains relatively unchanged above 18 mol %. We attribute the increase at 18 mol % to a substantial decrease in the local symmetry of the oxygen atoms surroundin”gthe sodium ions. However, while the sodium site symmetry decreases at this composition, the local coordination shell is evidently not as strained as in crystalline Na~Te409-the coupling in the glass increases only to about 2 MHz, substantially below the values for the sodium sites in the crystal. Both the increase at 18 mol %, and the fact that the interaction and hence site symmetries are very different from those in NaZTe409, suggest that the structure of the glass undergoes a significant change in this composition region, while still differing substantially, even at short length scales, from that of crystalline NazTe409. 4.3. Distributionsof the Parameters. The two-dimensional line shape exhibited in Figure 3 is unusual and deserves comment. We found that all the glass samples had spectra with roughly this line shape. The DAS NMR of crystalline materialsl6-I8 have line shapes consisting of narrow contours parallel to the anisotropic shift axis. The same is true for relatively ordered sites in glasses,21*28but as the disorder increases, the line shapes deviate from this limit. The deviation is due to distributions of quadrupole parameters, as has been shown in detail by Faman et al. for the case of silicate g1a~ses.l~ In the present case, the sodium DAS NMR line shape also arises from a distribution of the spin interaction parameters, as can be seen as follows. First take the chemical shift as fixed. Then, for small quadrupole coupling e2Qq/h, the isotropic shift will be near the chemical shift value and the associated powder pattern will be relatively narrow. For large e2Qq/h,the isotropic shift will appear upfield, since the second-order quadrupole effect always gives a negative shift (eq 1). Also, the powder pattem will be much broader. The two-dimensional line shape for this distribution will be roughly triangular, with one point at the downfield isotropic shift with small e2Qq/h,broadening out to form the opposite side of the triangle at upfield isotropic shift and large e2Qq/h. An example is shown in Figure 7a. This plot shows a simulation using spectral parameters identical to those of of Figure 3, including the most probable chemical shift, but with a Gaussian distribution of quadrupole couplings centered on the experimental most probable value and with width B = 0.75 MHz. This simulation produces a twodimensional line shape and projections in qualitative agreement with the experimental spectrum. When a distribution of chemical shifts is also taken into consideration, the line shape is smoothed and broadened. This is shown in Figure 7b, which is identical to Figure 7a but also includes a Gaussian distribution of chemical shifts, centered on the experimental most probable value with width B = 5 ppm. The agreement with experiment is improved. In fact, a distribution of asymmetry pattern 7 should also be considered, but the anisotropic line shapes for our glass spectra all indicate that 7 is small in these materials, and so we have held it fixed at 11 = 0.1 in the simulations. These results show that the sodium cations occupy a substantial range of sites, as might be expected. The distribution in quadrupole couplings implies that “typical” values range from about 1 MHz to about 2.5 MHz, at the 20 mol % composition, that is, from rather ordered sites to moderately disordered sites (though still locally symmetrical compared to crystalline NazTe409). The distribution of chemical shifts suggests that the coordination is somewhat variable from site to site. For a
5116 J. Phys. Chem., Vol. 99,No. 14, 1995
Tagg et al.
A n
-50
&
4.
c
.a
o a
0
.a
50
R b 2
U
50 0 -50 Isotropic + Anisotropic Shift (ppm)
composition, probably as the result of formation of a substantial fraction of nonbridging oxygen. The local symmetry of the sodium sites, as inferred from the values of the quadrupole coupling, decreases at this composition but does not resemble the local structure seen in crystalline Na2Te409. We are currently using NMR experiments to probe the structure around the tellurium sites, to try to correlate the network structure with that around the modifier cations.
Acknowledgment. We thank Professor P. Boolchand and Mr. Min Zhang for stimulating discussions and providing us with some samples in the early stages of this work. We are grateful to Professor M. D. Hollingsworth for access to his 7.1 T magnet. S.L.T. thanks the Department of Education for financial support. This research was supported by the National Science Foundation under Grant. No. DMR-9115787. References and Notes
!
;-5O
h
faa
50 0 -50 Isotropic +Anisotropic Shift (ppm) Figure 7. Simulations of DAS NMR spectra of sodium-23 (a) with 11 = 0.1, ' @ : = -5.3 ppm, and a Gaussian distribution of e2Qq/h centered on 1.86 MHz, with a width of 0.75 MHz, and (b) as in a, but additionally with a Gaussian distribution of Si,"n"centered on -5.3 ppm with a width of 5 ppm.
Gaussian distribution of chemical shift with width 5 ppm, we can estimate that the coordination number ranges from a most probable value of 5.5 (again, for the 20 mol % glass) to a low of 5.2 and a high of 5.8. Our simulated distribution includes no correlation between the chemical shift and the quadrupole coupling; within the empirical model this is reasonable, but it is easy to imagine that such correlations would in fact exist. They may well account for the details of the two-dimensional line shape that are not reflected in Figure 7. 5. Conclusions
On the basis of our determinations of the chemical shift and quadrupole interaction for sodium in (Na20),(Te02)1-, glasses, we believe that there is a significant change in the local glass structure at about the 18 mol % modifier concentration level. The trend we observe in the chemical shift indicates that the coordination number of the sodium begins to decrease at this
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