J. Phys. Chem. 1996, 100, 3705-3712
Cation Distribution in Mixed-Alkali Silicate Glasses. NMR Studies by 23Na-{6Li} Spin Echo Double Resonance
3705 23Na-{7Li}
and
Becky Gee and Hellmut Eckert* Department of Chemistry, UniVersity of California, Santa Barbara, California 93106 ReceiVed: July 28, 1995; In Final Form: October 6, 1995X
The relative arrangement of sodium and lithium ions in mixed-alkali silicate glases of composition [(Li2O)1-y(Na2O)y]x[SiO2]1-x (y ) 0.25, 0.50, and 0.75; x ) 0.40 and 0.50) is studied by 23Na-{7Li} spin echo double-resonance (SEDOR) NMR spectroscopy, supplemented by additional 23Na-{6Li} experiments on isotopically labeled materials. The experimental results are compared with various cation distribution scenarios and found to be quantitatively most consistent with a model in which lithium and sodium ions occupy random positions on a cubic lattice mimicking a uniform (homogeneous) spatial cation distribution. The experimental data give no evidence for preferred interactions among unlike cations or cation-pairing models previously invoked to describe the structure of mixed-alkali glasses. To the contrary, if the overall cation distribution were to diverge from homogeneous, the data would be most consistent with preferred interactions among like cations.
Introduction The past decade has witnessed great progress in the development of highly conductive glassy solid electrolytes. One of the technologically interesting yet hitherto unexplained transport phenomena in these systems is the mixed-alkali effect.1-3 “Mixed-alkali” glasses, i.e. systems containing more than one type of alkaline cation, show appreciably reduced ionic conductivities compared to single-alkali glasses with comparable cation contents. In addition, the dependences of ionic conductivity and dielectric loss on composition are strikingly nonlinear and go through minima near equimolar proportions of the two types of alkali cations present. In the past, various physical models have been proposed to explain this behavior on the basis of the spatial distribution of the cations in the glass network. There has been widespread evidence from EXAFS and molecular dynamics simulations that the overal cation distribution in alkali silicate glasses is not spatially homogeneous and that cation rich “clusters” exist.4-6 For various types of glass systems, the mixed-alkali effect has been considered a consequence of preferred interactions (“pairing”) among unlike cations within such clusters, implying that such preferred interactions would pose impediments on cation transport in glasses.7-10 In apparent conflict with this concept, other mixed-alkali glasses appear to segregate into domains containing the two types of cations separately.11-13 More recently, EXAFS and molecular dynamics simulations have suggested that each type of cation is located in rather distinct local sites in mixed-alkali glasses.14-19 According to this hypothesis, the mixed-alkali effect then originates from the hindrance of alkali ions of one type to migrate to sites previously occupied by alkali ions of another type, if the two types of cations are intimately mixed.17 While random mixing of unlike cations has also been suggested in molecular dynamics simulations of rubidium sodium silicate glasses,18 direct experimental evidence for this hypothesis is still lacking. Clearly, additional work is required to characterize the state and distribution of alkali cations in mixed-alkali glasses. In principle, such information should be available from solid state NMR, which offers element-selective, inherently quantitative X
Abstract published in AdVance ACS Abstracts, February 1, 1996.
0022-3654/96/20100-3705$12.00/0
approaches to glass structure.20 However, while high-resolution, magic-angle-spinning (MAS) NMR has indeed proven a valuable tool for elucidating the structural organization of the network former component, very little has been learned to date by this method about the structural environment and the spatial distribution of the alkaline ions in glasses. First of all, strong second-order quadrupolar effects and distributions of quadrupolar coupling constants make it difficult to obtain accurate 23Na and 87Rb chemical shift distributions by MAS NMR. Secondly, due to the high degree of ionic bonding, the dynamic range observed for 7Li and 23Na NMR chemical shifts is extremely limited, and there is a lack of good theoretical models toward their interpretation. In this contribution, we present a new experimental approach to the structural origins of the mixed-alkali effect by focusing on internuclear magnetic dipole-dipole couplings rather than chemical shifts. As described previously, spin echo and spin echo double-resonance (SEDOR) techniques21-23 can be used to measure both homo- and heteronuclear dipole-dipole couplings in glasses and other disordered materials.24-26 On the other hand, dipole-dipole interactions are calculable in principle from internuclear distances and thus can provide quantitative criteria against which hypothetical structural models can be tested.27 In the present application, we address the lithium/sodium distribution in mixed lithium-sodium silicate glasses on the basis of 23Na-{7Li} and 23Na-{6Li} SEDOR data. Fundamental Concepts and Methodology 23Na-7Li (23Na-6Li)
Dipole-Dipole Couplings. The most direct link between NMR spectroscopy and local structure is provided by magnetic dipole-dipole couplings, which in multispin systems are most effectively treated by a moments analysis. According to van Vleck theory,27 the direct contribution to the second moment, M2, for a nucleus dipolarly coupled to surrounding heteronuclei, can be calculated directly from internuclear distances:
M2 ) (4/15)(µ0/4π)2γI2γS2p2S(S + 1) ∑ rij-6
(1)
i>j
where γI is the gyromagnetic ratio of the observed nuclei, and © 1996 American Chemical Society
3706 J. Phys. Chem., Vol. 100, No. 9, 1996
Gee and Eckert
γS and S are the gyromagnetic ratio and spin quantum number of the nonresonant nuclei coupled to the observed nuclei. Dipole-dipole interactions among unlike nuclei in static samples are efficiently measured by the spin echo doubleresonance technique, originally developed by Slichter and coworkers.21-23 In the present experiment, we measure the decay of the 23Na spin echo signal, obtained by a 90°-t1-180°-t1 pulse sequence, while a 7Li (or 6Li) inversion pulse, applied at the time t1, i.e. simultaneously with the 23Na 180° pulse, prevents the refocusing of the heterodipolar 23Na-7(6)Li interactions. As a result, the 23Na spin echo intensity decays with the overall evolution time 2t1 under the combined influence of the homonuclear 23Na-23Na and the heteronuclear 23Na-7(6)Li dipoledipole couplings. For many-spin systems, the central limit theorem predicts a Gaussian dependence on the dipolar evolution time 2t1:
I(2t1)/I0 ) [exp -{(2t1)2M2Na-Na/2}][exp -{(2t1)2M2Na-Li/2}] (2) In a second experiment with the 7(6)Li pulse absent, the decay arising from the homonuclear 23Na-23Na interaction is measured separately as a decay function F(2t1) underlying the SEDOR decay. Thus, the combination of both results affords a selective measurement of the second moment M2dNa-Li describing the heterodipolar interaction:
I(2t1)/I0 ) {F(2t1)/F(0)}{exp -(2t1)2M2Na-Li/2}
(3)
This value can then be compared with the result obtained from a van Vleck simulation based on hypothetical Na/Li distribution models. In a glass, the M2Na-Li values have to be viewed as averages over a distribution function whose shape is generally not known. Furthermore, imperfect 180° pulses on the lithium channel may lead to incomplete spin inversion, particularly for some lithium nuclei that are shifted far offresonance by quadrupolar interactions. As a result, the experimentally measured SEDOR decay is somewhat slower than theoretically expected, and comparison with standard compounds, whose dipolar coupling can be calculated from known crystal structures, is advisable. In the present study, the SEDOR technique has been calibrated with LiNaSO4 as a standard compound. Incomplete 7Li inversion is accounted for by an efficiency factor f, which influences the experimental SEDOR decay according to
I(2t1)/I0 ) {F(2t1)/F(0)}{1 - f{1 -{exp -(2t1)2M2/2}}} (4) To explore whether the conclusions of this study are affected by such incomplete 7Li inversion effects, 23Na-{6Li} SEDOR decay studies were carried out on selected samples isotopically enriched with 6Li. Since the first-order quadrupole splitting of 7Li is on the order of 50 times as large as that of 6Li, such off-resonance effects would be clearly much more important in a 23Na-{7Li} SEDOR experiment than in a 23Na-{6Li} SEDOR experiment. 23Na-23Na Dipole-Dipole Couplings. In principle, complementary quantitative information about the dipolar interactions among like cations (23Na-23Na or 7Li-7Li) should be extractable from single-resonance 23Na and/or 7Li 90°-t1-180°-t1 spin echo experiments. As shown by Haase and Oldfield,28 this possibility holds for quadrupolar nuclei in the limit HQ(1) . Hrf . Hd > HQ(2), where the latter four terms of the spin Hamiltonian describe the perturbations due to first-order quadrupolar effects, radio frequency irradiation, dipolar interactions,
and second-order quadrupolar effects, respectively. In other words, the decay of the spin echo arising from selectively excited coherence among the central (1/2 Zeeman levels is governed by homonuclear dipole-dipole interactions. Unfortunately, application of this concept to measuring homonuclear interactions among Li or Na nuclei in glasses encounters some difficulties. For 7Li, the above conditions are generally not met, removing the theoretical foundations of the experiment. For 23Na, extensive model compound studies have indeed shown that 23Na spin echo decay spectroscopy is useful for estimating the strengths of 23Na-23Na homodipolar couplings,29 assuming that there is fast spin exchange among those neighboring 23Na nuclei that are in the two central spin states. Applicability of the last condition is uncertain for glassy systems, however, because due to site distribution effects, the spin exchange process among neighboring 23Na spins may be partially suppressed, and thus the dipolar coupling constants may be substantially reduced. Due to this fundamental difficulty, the 23Na spin echo decays and the corresponding homodipolar second moments obtained in this study as part of the SEDOR experiment must be treated with some caution. Experimental Section Sample Preparation and Characterization. Visually transparent and homogeneous mixed-alkali silicate glasses with nominal compositions [(Li2O)1-y(Na2O)y]x[SiO2]1-x (y ) 0.25, 0.50, and 0.75; x ) 0.40 and 0.50) were prepared by melting stoichiometric amounts of Li2CO3 (Aldrich, 99+%), Na2CO3 (Aldrich, 99.95%), and silica (Alfa, 99.9%) in a Pt/Au alloy crucible at 1375 °C for 3 h, followed by rapid quenching in liquid nitrogen.30 For the preparation of 6Li-enriched materials, the same procedure was employed using Li2CO3 with a 95% enrichment in 6Li (Isotec, chemical purity not specified). X-ray powder diffraction (using a Scintag diffractometer) and 29Si magic-angle-spinning NMR revealed the absence of crystalline impurities. Between duplicate preparations (natural isotope distribution and 6Li-enriched materials), reproducible 29Si MAS NMR spectra were obtained for each composition. The site speciations extracted from these spectra, using familiar literature procedures,31 were found to be very consistent with analytical sample compositions. All the samples were dried in a desiccator prior to use. Chemical analysis results by flame photometry are summarized in Table 1; reproducibility between different aliquots analyzed was generally within (10% or less of the values reported. Differences between nominal and actual compositions are largely attributed to alkaline oxide volatilization at the high melting temperatures. Sodium-lithium sulfate samples with natural isotope distribution were prepared from Li2SO4‚H2O (Sigma, 99%) and Na2SO4 (Sigma, 99.5%) as described in the literature.32 A 6Li-enriched sample was prepared in the same manner, using lithium sulfate with 98.6% 6Li enrichment (Isotec, chemical purity not specified). The purity of the LiNaSO4 samples synthesized was ascertained by X-ray powder diffraction. In addition, the absence of incorporated or surface-adsorbed water was confirmed by thermogravimetric analysis. Solid State NMR Spectroscopy. All the NMR experiments were carried out on a General Electric GN-300 spectrometer equipped with a 7 mm double broad band tuned probe from Doty Scientific. The resonance frequencies were 79.495, 116.795, and 44.02 MHz for 23Na, 7Li, and 6Li, respectively. The 7Li or 6Li irradiation frequencies were generated by mixing the pulsed 1H decoupler output with a local oscillator and subsequent amplification (Doty DSI 400B radio frequency amplifier). Typical 90° pulse lengths were 5-6 µs (23Na) and
Cation Distribution in Mixed-Alkali Silicate Glasses
J. Phys. Chem., Vol. 100, No. 9, 1996 3707
TABLE 1: Nominal and Analytically Determined Compositions of the Mixed-Alkali Silicate Glasses Studied (Natural Isotope Distribution) and Results from the 23Na-{7Li} SEDOR Experimenta composition batch
analytical
23Na-{7Li}
SEDOR M2Na-Li (106 rad2/s2)
23Na
spin echo M2Na-Na (106 rad2/s2)
Li2O
Na2O
Li2O
Na2O
exp ((10%)
Ia
Ib
IIa
exp
Ia
Ib
IIa
10 20 30 12.5 25
30 20 10 37.5 25
10.6 23.1 31.6 8.2 27.1
28.2 18.1 8.3 33.0 22.0
4.3-5.8 7.4-10.0 10.7-14.5 2.3-3.1 11.3-15.3
4.8 10.9 14.1 3.4 17.9
5.8 13.9 20.4 4.4 21.8
10.7 23.4 32.0 8.3 27.4
3.3 2.1 1.9 3.1 2.6
6.2 4.1 2.1 6.6 6.7
5.5 3.2 0.6 5.0 5.1
13.7 8.8 4.0 16.0 10.7
a Values for M2Na-Li and M2Na-Na measured are compared with values calculated for scenarios Ia, Ib, and IIa (see text). Experimental errors for M2 are within 10%. For M2Na-Li the lower limit of the range given is the uncorrected value, while the upper limit is the value corrected for incomplete 7Li excitation, assuming f ) 0.85 as measured in LiNaSO4.
9-12 µs (7Li), for the 23Na-{7Li} SEDOR experiments, and 11-13 µs (23Na) and 6 µs (6Li), for the 23Na-{6Li} SEDOR experiments, respectively. As verified by separate nutation NMR experiments, these conditions corresponded to selective excitation of the central 1/2 f -1/2 transition of 23Na, whereas for the lithium nuclei the conditions were close to the nonselective excitation limit for all of the samples studied. Both the irradiation frequencies were carefully adjusted to minimize resonance offset effects. All the experiments were carried out at room temperature, with 1 min recycle delays, 7 µs dwell times, and 16 scans. I0, the SEDOR height at zero evolution time, was obtained from a Gaussian fit to the experimental data at short evolution times. Weak feedthrough signals arising from imperfect 180° pulses were removed by a 16-step phase cycle described previously.33 Results Model Compound. Parts a and b of Figure 1 summarize the 23Na-7Li and 23Na-6Li SEDOR data obtained on two samples of the model compound LiNaSO4, prepared with the natural isotope distribution and 98.6% 6Li enrichment, respectively. The experimental data relating to the 23Na spin echo decays in the absence of the 7Li (or 6Li) 180° pulses are fitted to empirical fourth-order polynomial (or, in case of the initial decays, Gaussian) curves, reflecting the homonuclear contribution of the SEDOR data. For both samples of LiNaSO4, the experimental 23Na-23Na second moments as determined from the spin echo decay at short evolution times (2t1 < 300 µs) are in satisfactory agreement with those calculated from the van Vleck equation. The experimental data relating to the spin echo decays in the presence of the 7Li (or 6Li) 180° pulses are compared with those calculated from eqs 1 and 3 (or 4), using the van Vleck equation with the known internuclear distances in LiNaSO4.34 For the 23Na-{7Li} SEDOR results, Figure 1a illustrates noticeable deviations between the experimental and calculated decay curves. Therefore, the apparent second moment measured via data analysis with (3) (12.2 × 106 rad2/s2) differs somewhat from the calculated value of 16.5 × 106 rad2/ s2. As discussed in the Fundamental Concepts and Methodology section, this situation probably arises from incomplete inversion of 7Li spins in the (3/2 Zeeman states. The 7Li nuclear quadrupole coupling constant of LiNaSO4 has been measured to be 180 kHz,35 and thus substantial off-resonance effects are expected due to the first-order quadrupolar splittings. Applying eq 4 to the experimental data, we determine an experimental inversion efficiency factor f ) 0.85. In contrast the 23Na{6Li} SEDOR decays are in excellent agreement with those predicted from the crystal structure, and the experimental M2 value of 1.4 × 106 rad2/s2 lies within experimental error of the calculated value of 1.3 × 106 rad2/s2. Since due to the much smaller nuclear electric quadrupole moment of 6Li, the resonance
Figure 1. (a) 23Na-7Li SEDOR NMR data on LiNaSO4. Shown are normalized 23Na spin echo intensities with a 90°-t1-180°-t1 pulse sequence as a function of dipolar evolution time 2t1 in the absence (open circles) and presence (filled circles) of the 7Li defocusing 180° pulse. Dashed curve: empirical polynomial fit to the 23Na spin echo decays. Solid curve: calculated SEDOR decay using eq 1 with crystallographic information and eq 3. Dotted curve: calculated SEDOR decay, using eq 1 with crystallographic information and eq 4 with f ) 0.85. (b) 23Na-6Li SEDOR NMR data on LiNaSO4, isotopically enriched to 98.6% 6Li. Shown are normalized 23Na spin echo intensities with a 90°-t1-180°-t1 pulse sequence as a function of dipolar evolution time 2t1 in the absence (open circles) and presence (filled circles) of the 6Li defocusing 180° pulse. Dashed curve: empirical polynomial fit to the 23Na spin echo decays. Solid curve: calculated SEDOR decay using eq 1 with crystallographic information and eq 3.
splitting is only on the order of 1 kHz, no artifacts due to incomplete spin inversion are expected here. However, in the 6Li-enriched material, the overall heteronuclear magnetic dipolar coupling measured is distinctly weaker, because of the much smaller gyromagnetic ratio of 6Li (compared to 7Li). For this reason, the study of 23Na-7Li interactions is generally prefer-
3708 J. Phys. Chem., Vol. 100, No. 9, 1996
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Figure 2. 23Na spin echo data (open circles) and 23Na-{7Li} SEDOR data (filled circles) of lithium-sodium silicate glasses: (A) 31.6% Li2O 8.3% Na2O; (B) 23.1% Li2O 18.1% Na2O; (C) 10.6% Li2O 28.2% Na2O; (D) 27.1% Li2O 22.0% Na2O; (E) 8.2% Li2O 33.0% Na2O.
able, in spite of the small systematic error caused by imperfect excitation of the 7Li spins. Glasses. Figure 2 summarizes the 23Na spin echo and 23Na-{7Li} SEDOR data on the mixed alkali silicate glasses. For several compositions, data from two separate measurements revealed excellent reproducibility. As Figure 3 illustrates for a representative sample, SEDOR results measured at -110 °C were found to be in excellent agreement with those obtained at room temperature, indicating that at room temperature the results are unaffected by ionic motion. While over the whole range of evolution times studied the experimental decays are nonGaussian, indicating distributions of 23Na-23Na and 23Na-7Li dipolar coupling strengths, the data are still reasonably well approximated by Gaussians in the limit of short evolution times. Average second moments M2Na-Li and M2Na-Na obtained from
analysis of these initial decays over the range 0 e 2t1 e 0.35 ms are summarized in Tables 1 and 2 for samples with the natural isotopic abundance distribution and the 6Li-enriched glasses, respectively. In the case of the 23Na-{7Li} SEDOR data, a range of two values of M2Na-Li is reported: the lower limit represents uncorrected results, whereas the upper limit accounts for incomplete 7Li spin inversion, assuming that the efficiency factor f in the glasses is the same as that in LiNaSO4 (f ) 0.85). This assumption is supported by the similar 7Li nutation behaviors of glasses and the model compound and also by the fact that the conclusions from the 23Na-{6Li} SEDOR results are similar to those from the 23Na-{7Li} SEDOR results (see below). Figure 4 indicates that M2Na-Na tends to decrease, while M2Na-Li strongly increases with increasing concentration of Li2O. This compositional dependence clearly reflects the
Cation Distribution in Mixed-Alkali Silicate Glasses
J. Phys. Chem., Vol. 100, No. 9, 1996 3709
TABLE 2: Nominal and Analytically Determined Compositions of the Mixed-Alkali Silicate Glasses Studied (95% 6Li enrichment) and Results from the 23Na-{6Li} SEDOR Experimenta composition batch
analytical
Li2O
Na2O
10 20 30
30 20 10
Li2O
23Na-{6Li}
SEDOR M2Na-Li (106 rad2/s2)
23Na
spin echo M2Na-Na (106 rad2/s2)
Na2O
exp ((10%)
Ia
Ib
IIa
exp
Ia
Ib
IIa
28.4 not det. 27.7 11.4
0.70 0.85 ( 0.15 1.28
0.33 0.75 1.14
0.35 0.93 1.38
1.31 2.98 4.12
1.4 0.8 1.4
6.4 4.6 2.9
5.5 3.5 0.8
13.8 9.7 5.5
8.8
a Values for M Na-Li and M Na-Na measured are compared with values calculated for scenarios Ia, Ib, and IIa (see text). Experimental errors for 2 2 M2 are within 10% unless noted otherwise.
Figure 3. 23Na spin echo and 23Na-7Li SEDOR NMR data of lithiumsodium silicate glass containing 31.6% Li2O and 8.3% Na2O at room temperature (open symbols) and -110 °C (filled symbols).
Figure 4. Dependence of M2Li-Na and M2Na-Na (in units of 106 rad2/s2) on mol% Li2O in [(Li2O)y(Na2O)1-y]x(SiO2)1-x glasses (x ) 0.4, 0.5) as determined from the 23Na-{7Li} SEDOR experiments. Solid and dashed lines are linear least squares fits to the data.
significance of unlike-cation interactions in these glasses and rules out a microphase segregation model in which the cations are spatially separated. Discussion Qualitatively, the compositional dependence of the SEDOR data summarized in Figures 2 and 4 reveals clearly that the cations are mixed at the atomic level. For further quantitative information it is necessary to consider simulations of distinct relative Li-Na distribution scenarios. Such distribution scenarios in turn require assumptions on the overall spatial distribution of the cations (in relation to silicon) in these glasses. Simulation of the Spatial Cation Distribution. Information concerning the spatial cation distribution should be available in principle from spin echo decay spectroscopy of single-alkali glasses. Indeed, experimentally measured 23Na-23Na dipole-
dipole couplings measured for binary sodium silicate glasses appear to be substantially weaker than expected on the basis of the cluster models discussed in refs 4-6 and are quantitatively consistent with a cation distribution that is close to uniform.29 As discussed in ref 29, this conclusion is subject to an important caveat, namely, that spin exchange among neighboring sodium nuclei is not suppressed in the glassy state. Nevertheless, in view of the above agreement it appears not unreasonable to simulate the 23Na-{7Li} SEDOR results on the basis of a uniform cation distribution model (scenario I). To this end, the number of alkaline ions per cm3 is calculated for each glass composition, using linearly interpolated density data reported in the literature,36 and these ions are subsequently arranged on the cation sites of a cubic NaCl lattice. Due to the uniform spatial arrangement, the lattice constant decreases with increasing alkali content. For example, in samples containing 40 mol % alkali oxide, the simulation produces closest cation-cation spacings around 4 Å. An alternate set of simulations was carried out assuming a random cation distribution scenario (scenario II), based on the anti-fluorite structure of crystalline Na2O.37 To this end, only a fraction of the cation sites in this structure were occupied statistically, according to the overall alkaline content of the glass. Since the molar density of Na2O is very similar to that of sodium and lithium sodium mixed-alkali silicate glasses, a randomly occupied anti-fluorite structure is believed to be a realistic model for this kind of ordering principle in these materials. Evidently this model produces a range of closest cation-cation distances, the shortest one of which (2.8 Å) corresponds to the value in the anti-fluorite structure of Na2O. Simulation of the Li-Na Arrangement. To model the relative Li-Na arrangement for the uniform oVerall cation distribution scenario I, the two different types of alkaline ions are distributed according to two different principles: (a) a statistical arrangement and (b) an arrangement corresponding to maximized interactions among unlike cations. Thus, in scenario Ia the Na and Li nuclei are distributed randomly on the cation sites of the uniform NaCl lattice according to their analyzed compositions, while for scenario Ib hypothetical superstructures are simulated as follows: If the Na/Li ratio is near 3:1 or 1:3, the minority cation is placed on only one of the four general cation positions in the NaCl lattice, thereby generating a uniform distribution of the minority cation. This has the effect of minimizing the interactions among like cations, thereby maximizing the interactions among the unlike ones. For Na/Li ratios near 1:1, the cations are separated into successive layers. This procedure again minimizes the interaction among like cations, as it ensures that of the 12 nearest cations surrounding a central cation four (within the same layer) are of the same kind and eight (within the layers above and below) are of the other kind. Subsequently, the simulations are corrected to account for deviations from these precise ratios as indicated by the chemical analysis data. Using the van Vleck equation, average heterodipolar secondmoment values are then computed for each scenario (see Tables
3710 J. Phys. Chem., Vol. 100, No. 9, 1996
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Figure 5. 23Na-{7Li} SEDOR NMR data on Li-Na silicate glasses with the compositions indicated. Shown are normalized 23Na spin echo intensities obtained with a 90°-t1-180°-t1 pulse sequence as a function of dipolar evolution time 2t1 in the absence (open circles) and presence (filled circles) of the 7Li defocusing 180° pulse. In all of these plots, the upper dotted curve shows a polynomial fit to the 23Na spin echo decay data. The other curves correspond to simulations according to scenarios Ia, Ib, and IIa, respectively, calculated according to eq 4 with f ) 0.85.
1 and 2). 23Na-{7Li} SEDOR decays were simulated with eqs 1 and 4, using f ) 0.85, while 23Na-{6Li} SEDOR decays were simulated with eqs 1 and 3. Scenarios Ia and Ib produce particularly distinct SEDOR curves at compositions where the observed nuclei (23Na) are in the minority, i.e. at high Li/Na ratios. In contrast, at low Li/Na ratios, the differences between these two scenarios are too small to permit confident experimental differentiation, due to the experimental error of the measurement. Modeling on the basis of the random oVerall cation distribution scenario II was done assuming statistical mixing of lithium and sodium on the randomly occupied anti-fluorite lattice. As
expected, scenario II produces calculated SEDOR curves that are much steeper than those simulated with scenario I, as well as significantly enlarged M2Na-Na values. Comparison with Experiment. Figure 5a-e contrasts calculated 23Na-{7Li} SEDOR curves with experimental data, while Figure 6a,b shows the same comparisons for 23Na{6Li} studies carried out on selected samples. Figure 7 compares the experimental M2Na-Li values measured in the 23Na-{7Li} SEDOR experiments against those expected for each of the scenarios considered. Note the generally strong disagreement with scenario IIa, which will be discussed further below. Clearly, for most of the samples the simulations assuming
Cation Distribution in Mixed-Alkali Silicate Glasses
Figure 6. 23Na-{6Li} SEDOR NMR data on Li-Na silicate glasses with the compositions indicated. Shown are normalized 23Na spin echo intensities obtained with a 90°-t1-180°-t1 pulse sequence as a function of dipolar evolution time 2t1 in the absence (open circles) and presence (filled circles) of the 6Li defocusing 180° pulse. In all of these plots, the upper dotted curve shows a polynomial fit to the 23Na spin echo decay data. The other curves correspond to simulations according to scenarios Ia, Ib, and IIa, respectively, calculated according to eq 3.
Figure 7. Plot of the experimental M2Na-Li values (in units of 106 rad2/ s2) versus the predicted values according to the distribution scenarios discussed in the text. The solid line shows the identity. Solid and open circles denote the prediction on the basis of scenarios Ia, Ib, and IIa, respectively.
statistically mixed Li and Na on homogeneously distributed cation sites (scenario Ia) agree most closely with the experimental data. This conclusion remains the same if the errors in
J. Phys. Chem., Vol. 100, No. 9, 1996 3711 sample composition (maximally 10% of the value reported, as estimated by duplicate analysis) and M2 determinations are taken into account. While for certain compositions (including those studied by 23Na-{6Li} SEDOR) the difference between scenarios Ia and Ib may be within experimental error, our results do not provide positive evidence for preferred interactions among unlike cations or even pair formation in lithium-sodium silicate glasses. This is true in particular, because any deviation of the overall spatial alkali distribution from uniform will result in steeper simulated decay curves that would be even further removed from the experimental data. As discussed above, complementary information should be available in principle from the compositional analysis of M2Na-Na, available from the 23Na spin echo experiment. However, Table 1 reveals that, except for the 31.6 mol % Li2O/ 8.3 mol % Na2O sample, the experimental M2Na-Na values measured are significantly smaller than the ones simulated for any of the scenarios considered and do not depend on Na content as strongly as expected. This behavior is attributed to partial suppression of spin exchange among neighboring 23Na nuclei due to differences in resonance frequencies caused by site distribution effects in the glassy state. Since this effect renders the structural analysis of the 23Na spin echo decays quantitatively unreliable, no further analysis is attempted here. Model Dependence. It is necessary here to discuss the dependence of our structural conclusions from the SEDOR data on the initial choice of the overall spatial cation distribution model. Since the homogeneous spatial distribution model minimizes cation-cation interactions, each of the scenarios, a or b, simulated on the basis of a nonuniform spatial cation distribution model would produce stronger dipolar couplings than observed experimentally and give rise to larger deviations between experimental and simulated SEDOR decays. In this sense, the SEDOR data may be viewed as experimental support for the assertion that the cation distribution in alkali silicate glasses is closer to homogeneous than widely believed. Alternatively, nonuniform spatial cation distributions with cation rich regions (as discussed in refs 4-6 and modeled in our study as scenario IIa) can only be made consistent with our SEDOR data if one were to assume substantial preference for proximity among like cations. While the small M2Na-Na values extracted from the experimental 23Na spin echo decays seem to argue against this scenario, the interpretation of these data is not sufficiently rigorous to rule out this possibility at the present time. Nevertheless, if the statistically occupied sodium oxide structure were assumed to be a realistic approximation of the overall spatial cation distribution in alkali silicate glasses, the preference for like-cation interactions over unlike-cation interactions could be quantified on the basis of these SEDOR data. The same is true if the overall spatial cation distribution became independently available from other experimental techniques. Finally, the present analysis assumes that only one cationordering regime occurs throughout the glass, i.e. that there are no large local variations in Li/Na ratios. In future studies it will be necessary to explore the latter possibility by spatially resolved X-ray fluorescence and electron microscopy experiments. The present contribution suggests that further such refinements in the structural description of mixed-alkali glasses can be put to a quantitative test against 23Na-{7Li} and 23Na{6Li} SEDOR spectroscopic data. Conclusions Spin echo double resonance is a powerful technique that allows a quantitative discussion of possible atomic distribution models in mixed-alkali silicate glasses. The results presented
3712 J. Phys. Chem., Vol. 100, No. 9, 1996 here for glasses in the system Li2O-Na2O-SiO2 give no evidence for preferred unlike-cation interactions, let alone unlike-cation pairs. For the majority of compositions studied, the experimental data are consistent with a spatially homogeneous cation distribution with statistical Li/Na mixing. On the other hand, if the spatial cation distribution is indeed nonuniform, as proposed by many recent molecular dynamics simulations, then the SEDOR data would indicate a distinct preference for interactions among like cations. Whichever model applies, the results cast doubt on the models previously invoked to describe the structure of mixed-alkali silicate glasses. Rather, they support the general concept that the transport anomalies seen in these systems are not due to specific cation-cation interactions but are a dynamic phenomenon related to the mismatch of sites available in the glass structure for the two types of cations present. Acknowledgment. Financial support by NSF Grant DMR 92-21197 is gratefully acknowledged. Thanks are also due to Peter Andersen for experimental assistance and to Dr. David Lathrop for help with the simulations. B.G. thanks the UCSB Graduate Division for a Graduate Opportunity Fellowship and a Presidential Dissertation Year Fellowship. Finally we thank two anonymous reviewers for constructive comments on the manuscript. References and Notes (1) Isard, J. O. J. Noncryst. Solids 1969, 1, 235. (2) Day, D. E. J. Noncryst. Solids 1976, 21, 343. (3) Ingram, M. D. Phys. Chem. Glasses 1987, 28, 215. (4) Greaves, G. N. J. Noncryst. Solids 1985, 71, 203. (5) Huang, C.; Cormack, A. N. J. Chem. Phys. 1990, 93, 8180. (6) Huang, C.; Cormack, A. N. J. Chem. Phys. 1991, 95, 3634. (7) Ingram, M. D. J. Am. Ceram. Co. 1980, 63, 248. (8) Hendrickson, J. R.; Bray, P. J. Phys. Chem. Glasses 1972, 13, 43, 107. (9) Moynihan, C. T.; Saad, N. S.; Tran, D. C.; Lesikar, A. V. J. Am. Ceram. Soc. 1980, 63, 458. (10) Sato, R. K.; Kirkpatrick, R. J.; Brow, R. K. J. Noncryst. Solids 1992, 143, 257.
Gee and Eckert (11) Bray, P. J.; Emerson, J. F.; Lee, D.; Feller, S. A.; Bain, D. L.; Feil, D. A. J. Noncryst. Solids 1991, 129, 240. (12) Emerson, J. F.; Bray, P. J. J. Noncryst. Solids 1994, 169, 87. (13) Bruce, A. J.; Duffy, J. A.; Ingram, M. D. Phys. Chem. Glasses 1981, 22, 104. (14) Bunde, A.; Ingram, M. D.; Maass, P. J. Noncryst. Solids 1994, 172-174, 1222. (15) Bunde, A.; Ingram, M. D.; Maass, P.; Ngai, K. L. J. Noncryst. Solids 1991, 131-133, 1109. (16) Balasubramanian, S.; Rao, K. J. J. Phys. Chem. 1993, 97, 8835. (17) Balasubramanian, S.; Rao, K. J. J. Noncryst. Solids 1995, 181, 157. (18) Vessal, B.; Greaves, G. N.; Marten, P. T.; Chadwick, A. V.; Mole, R.; Houde-Walter, S. Nature 1992, 356, 504. (19) Uchino, T.; Sakka, T.; Ogata, Y.; Iwasaki, M. J. Noncryst. Solids 1992, 146, 26. (20) Eckert, H. Prog. NMR Spectrosc. 1992, 24, 159. (21) Makowka, C. D.; Slichter, C. P.; Sinfelt, J. H. Phys. ReV. Lett. 1982, 49, 379. (22) Wang, P. K.; Slichter, C. P.; Sinfelt, J. H. Phys. ReV. Lett. 1984, 53, 82. (23) Shore, S. E.; Ansermet, J. P.; Slichter, C. P.; Sinfelt, J. H. Phys. ReV. Lett. 1987, 58, 953. (24) Boyce, B.; Ready, S. E. Phys. ReV. B 1988, 38, 11008. (25) Lathrop, D.; Eckert, H. J. Am. Chem. Soc. 1990, 112, 9017. (26) Franke, D.; Maxwell, R.; Lathrop, D.; Banks, K.; Eckert, H. Phys. ReV. B 1992, 46, 8109. (27) Van Vleck, J. H. Phys. ReV. 1948, 33, 1168. (28) Haase, J.; Oldfield, E. J. Magn. Reson. Ser. A 1993, 101, 30. (29) Gee, B.; Eckert, H. Solid State NMR 1995, 5, 113. (30) Maekawa, H.; Maekawa, T.; Kawamura, K.; Yokokawa, T. J. Noncryst. Solids 1991, 127, 53. (31) Stebbins, J. F. Nature 1987, 330, 465; J. Noncryst. Solids 1988, 106, 359. (32) Teeter, D.; Frech, R. J. Chem. Phys. 1982, 76, 799. (33) Kunwar, A. C.; Turner, G. L.; Oldfield, E. J. Magn. Reson. 1986, 69, 124. (34) Morosin, B.; Smith, D. L. Acta Crystallogr. 1987, 22, 906. (35) Junke, K. D.; Mali, M.; Roos, J.; Brinkmann, D.; Lunden, A.; Graneli, B.; Solid State Ionics 1988, 28-30, 1287. (36) Bansal, N. P.; Doremus, R. H. Handbook of Glass Properties; Academic Press: New York, 1986; p 54. This reference lists the densities of pure lithium and sodium silicate glasses. Mixed-alkali glass densities were interpolated linearly from the respective alkaline contents. (37) National Bureau of Standards Monograph 10, 1972.
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