a structural interpretation of b10 and b11 nmr spectra in sodium borate glasses

Journal of Non-Crystalline Solids 29 (1978) 187-206 © North-Holland Publishing Company

A STRUCTURAL INTERPRETATION OF B 10 AND B 11 NMR SPECTRA IN SODIUM BORATE GLASSES

G.E. JELLISON, Jr., * ** and P.J. BRAY

Department of Physics, Brown University, Providence, R.I. 02912, U.S.A.

Received 19 September 1977 Revised manuscript received 27 November 1977

It is shown that the B 10 spectra for sodium borate glasses are sensitive to the different structural groups in the glasses. Five boron sites are inferred from the data: two 4-coordinated sites and three 3-coordinated sites. The two 4-coordinated boron sites are identified as BO 4 units connected to all BO 3 units, and BO 4 units connected to one BO 4 unit and three BO 3 units. The three 3-coordinated boron sites are identified as BO 3 units connected to: (1) all BO 3 units; (2) a mixture of BO 3 and BO 4 units; and (3) all BO 4 units. These five sites can be interpreted in terms of Krogh-Moe's structural model of alkali borate glasses, wherein the fraction of each structural group can be determined for eight sodium borate glasses spanning the compositional range from 0 to 35 mol% Na20. The resulting fractions are consistent with Krogh-Moe's structural model.

1. Introduction

In earlier [1 -13] NMR studies of structure and bonding in borate glasses, the central transition (m = ½ ~ 1 ) of the B 11 isotope has been employed almost exclu-

sively. Because of the importance of dipolar broadening and the existence of dis-

tributions of the coupling constant Qce and the asymmetry parameter r/, only aver- age values of the coupling constant and asymmetry parameter were obtained from B 11 NMR. However, B 11 NMR has proved to be very useful for the determination

of N4, the fraction of 4-coordinated boron atoms. On the other hand, B 1° NMR affords three advantages over the use of the central transition of B 11 NMR: (1) dipolar broadening is much less important [14]; (2) the distribution of quadrupole coupling constants is directly obtainable from a part of the B 1° NMR experimental spectrum [14]; and (3) there exists another part of the B 1° NMR experimental spectrum that is sensitive to the distributions of the asymmetry parameter,

but insensitive to the distributions of the coupling constant [15]. These features of

* Based on the work performed by G.E. Jellison, Jr., in partial fulfillment of the requirements for the degree of Doctor of Philosophy at Brown University.

** Present address: US Naval Research Laboratory, Washington, DC.

187

188 G.E. Jellison, P.J. Bray / Structural interpretation o f B l O and B 11NMR spectra

the B 1° NMR spectrum can be employed in studying the structure of borate glasses. Sodium borate glasses are considered in this work.

It was first proposed by Krogh-Moe [16] that alkali borate glasses with less than 33-~ mol% alkali oxide contain mixtures of the four crystalline structural groups (boroxol, pentaborate, triborate and diborate, see fig. l a -d ) . This proposition was advanced on the basis of a comparison of the infrared (IR) spectra of the crystalline compounds and the glasses, which showed that the spectra of the glasses bear re- sembances to the spectra of the crystalline compounds. Recent Raman spectra studies by Konijnendijk [17] are consistent with the Krogh-Moe structural model. Rhee [18] has recorded the B 11 NMR spectra of the central transition for a series of sodium borate glasses and has measured the most probable values of the coupling constant and the asymmetry parameter from these spectra. His results agree quali- tatively with the results of Krogh-Moe [16], but he was unable to detect the indi- vidual structural groupings in the glass, since dipolar broadening, as well as the distributions of the quadrupole coupling constant and the asymmetry parameter, tend to smear out any identifiable features of the B 11 spectra. This paper presents the B 1° NMR spectra for a series of sodium borate glasses, and shows that a feature of the B l° spectrum can be employed to identify the different structural groups and to determine the abundance of each group in the glasses.

The theory of B 1° NMR powder patterns is presented in ref. [19] and will therefore be reviewed only briefly here. Fig. 2 shows a powder pattern for B 1° NMR. It

• b o r o n o o x y g e n

Fig. 1. The four crystalline structural groups found in sodium borate glasses [(a) boroxol, (b) pentaborate, (c) triborate and (d) diborate] and two structural groups found in sodium diborate crystal, but not found in the glass [(e) di-pentaborate, and (f) triborate with one non-bridging oxygen]. The tetraborate group is formed by connecting one oxygen atom of the BO4 unit in the triborate group to a BO 3 unit of the pentaborate group.

G.E. Jellison, P.J. Bray / Structural interpretation orB 10 and B 11 NMR spectra 189

I

o b c O e f

Fig. 2. B 1 o NMR powder pattern for two o f the six transitions at u 0 = 7 MHz. The shoulders b and f and the divergence c correspond to the 0 ,-, - 1 transition and the shoulders a and e and the divergence d correspond to the 1 ~ 0 transition.

is assumed that typical values of Qcc (= 5.5 MHz) and u o (= 7 MHz, v o being the spectrometer frequency) are employed. For higher values of/3 [/3 = vQ/Vo, vQ = 3 Q c c / 2 / ( 2 / - 1)], additional shoulders and divergences may appear [19]. The posi- tions of the shoulders and divergences of the powder patterns may be calculated exactly [20], since they correspond to critical points of the resonance surface v(O, ~), where 0 and ~ are the Euler angles of the principal axis system of the electric field gradient tensor with respect to the applied magnetic field. For the features identified in fig. 2, the expressions are:

a = - 2 +-~/3r/2 + s/32~72, (1)

b = - ( 1 + n) + ~ / 3 ( 3 - n) = + ~ / 3 = ( 3 - n)=(1 + n), (2)

c = - (1 - ~7) + 7 13(3 + r/) = + 2-~/32( 3 + r/)2( 1 - 7), (3)

S /32(3 d = +(1 - r/) + ~7a4 t3(3 + r?) 2 -- g-4 , + rT):(1 r/), (4)

e = +(1 + 7/) + 2-Z4/3(3 - r/): - 5 / 3 2 ( 3 _ rl)z(1 + r/), (5)

f = +2 + -~/3r/= - {/32r~ 2 . (6)

Eqs. ( 1 ) - (6 ) above are in units of uQ/4 with respect to v o. These equations have been calculated to third order employing perturbation theory.

2. Experimental

Two sets of eight samples of sodium borate glass were prepared over the compositional range 0 - 3 5 mol% Na20 in intervals of 5 mol% Na20. One set was prepared by mixing the appropriate amounts of Fisher Reagent grade Na2CO3, H3BO3 enriched to 92% B 1° (obtained from the Oak Ridge National Laboratory) and about 0.3 mol% MnC12 (added to reduce the spin-lattice relaxation time of the glass samples). This mixture was heated to 1000°C for several hours and then poured

190 G.E. Jellison, P.J. Bray / Structural interpretation orB 10 and B 11 NMR spectra

into a carbon mold at room temperature, resulting in a solid casting. The other set was similarly made, except that the H3BO 3 was unenriched in B 1° and no MnC12 was added.

The B 1° and B 11 absorption derivatives were obtained using a Varian V4200 wide-line NMR spectrometer operating at 7 MHz for the B l° resonance, and at 16 MHz for the B 11 resonance. A Nicolet 1072 signal averager was used to accumu- late the signals over several days for the B 1° spectra, and over several hours for the B 11 spectra. The magnetic field was provided by a Varian V-3603 electromagnet and VFR-2501 power supply and was swept and regulated by a Mark I Fieldial. M1 spectra were taken at room temperature.

Calculations of the NMR lineshapes were made using a program by Taylor and Bray [21,22]. Results were plotted on a Calcomp mechanical plotter so that the computed spectra could be superimposed directly onto the experimental trace for convenience in analysis.

3. Results

3.1. B 1° spectra

Figure 3 depicts the B 1° NMR derivative spectra for several Na20-B203 glasses. The spectra of fig. 3 are distorted in two places: feature A to the left (or low- frequency side) of Uo, and feature B centered at u o. These distortions were caused by the magnetic field modulation and integration time constant required to see the rest of the spectrum.

Feature A arises from the 3-coordinated boron atoms and is shown in fig. 4, where the frequency scale is expanded and the magnetic field modulation and integration time constant have been decreased so that no distortion of the line-shape occurs. Note that this feature changes considerably as the sodium oxide content is increased. Feature B arises from the 4-coordinated boron atoms, which have a low Qcc, and is seen centered about v o in fig. 3. This feature is symmetric in the region between the highest and lowest points of the derivative spectrum. (A narrow trace of this feature, obtained with decreased magnetic field modulation and integration time constant, showed that it was symmetric between the highest and lowest points of the derivative.) The dot (o) of fig. 3 shows the lowest point of the derivative of feature B, assuming that the highest and lowest points of this feature are equidis- tant from the baseline (using the highest point as the standard).

3.2. Method o f analysis o f the B 10 spectra

The actual lineshape for a glass involving distributions of both v o and r7 is given by [141

1

K(u') : ? du o fd~ p(uQ, r/) R(v', vQ, r/), (7) 0 0

G.E. Jellison, P.J. Bray / Structural interpretation orB 10 and B l I NMR spectra 191

IV ~, oO

° ,~ o / ' ~// °/r

o '~'~ / o ,'/

/ "2o_0 ,

' %-.-4 25 ; ~° Oo

3 0 .,. / " ~ + ' ~ 3 0 kHz

z;

o~ >7,, 3 5/-'-" ~

Fig. 3. B l0 NMR derivative spectra for eight N a 2 0 - B 2 0 3 glasses. The computer-simulated spectra (the darker lines in each case) were computed using the five sites characterized in table 1, with the appropriate weighting factors given in table 4. Mol% Na20 is indicated to the right of each trace. The calibration given in the upper left-hand corner is for the glasses of composition 0, 5, 10, 15, 20, 25 and 30 mol% Na20, while the calibration given in the lower right-hand corner is for the 35 mol% Na20 glass. Features A and B are the features of maximum distortion due to magnetic field modulation and integration time constant for all glasses; the dot (o) represents the lowest position of feature B if these effects were not present.

Fig. 4. Experimental B l 0 derivative of the main feature (feature A of fig. 3) for 3-coordinated boron atoms for seven N a 2 0 - B 2 0 3 glasses (solid line). The simulated spectra (circles) were calculated using the five sites characterized in table 1, and the appropriate weighting factors given in table 4.

where p(uQ, 7) is the distribution function for vQ and rl, and R(u', uO, r~) is the dipolar-broadened shape function. It is assumed that the distribution function can be expressed as a sum of component parts, each component part representing one site

192 G.E. Jellison, P.J. Bray / Structural interpretation o f B 1 o and B 11 NMR spectra

in the glass (such as 3-coordinated boron atoms connected to all BO 3 units), i.e.

p(v~, 7) = ~piO'~, ~), (8)

where the sum extends over all possible sites inthe glass. For each distribution, Pi"

(vQ, rl), it is further assumed that the variables VQ and r/are uncorrelated; that is

Pi(V Q, 7) = Pi(V Q ) Pi (r/). (9)

This assumption is not entirely correct since r/ is a function of Vzz (the component o f the electric field gradient tensor that has the largest magnitude in the principal axis system) and therefore VQ. The exact correlation, however, is model- dependent and cannot be determined experimentally.

The calculated spectra were obtained by calculating several powder patterns, each calculated for a specific value of VQ and r/. These powder patterns were then appropriately weighted and summed, resulting in the final calculated spectrum (see ref. [21] and [22] for a description o f the procedure). There were five discernible sites in the Naz-B203 system: two sites with a low value of Qcc (corresponding to 4-coordinated boron atoms); and three sites with a higher value of Qcc, and a low value of r/ (corresponding to 3-coordinated boron atoms). (Each site is characterized by a most probable value and a gaussian width for the two parameters: VQ and r~.)

The solid wide line of fig. 3 superimposed upon the experimental spectra, and the circles of fig. 4 superimposed upon the experimental spectra, represent computer-simulated spectra obtained by using the five sites whose parameters are given in table 1. [The most probable value and the width of the gaussian distribution of Qee for sites 3, 4 and 5 (the 3-coordinated boron atoms) were determined in ref. [14] and are shown in table 2.] The weighting factors used for these computer simulations are given in table 3.

Table 1 Characterization of distributions of hamiltonian parameters for the five sites observed in Na20-B20 3 glasses for B 10 NMR.

Site Q° c (MHz) OQc c (MHz) r~ 0 o H

1 0.8 0.2 0.5 0.5 2 1.5 1.0 0.0 0.5 3 a) a) 0.12 ± 0.02 0.05 ± 0.01 4 a) a) 0.26 -+ 0.02 0.05 ± 0.01 5 a) a) 0.08 + 0.02 0.05 + 0.01

a) The value of Qo and aQc c for sites 3, 4 and 5 vary from glass to glass and are given in table 2.

G.E. Jellison, P.J. Bray/Structural interpretation o f B l O and B 11 NMR spectra 193

Table 2 Experimental values of Q° c and OQc c for sites 3, 4 and 5 in sodium borate glasses (from ref. [ 14]). Values of ~o and a.q for these sites are given in table 1.

Mol% Na20 Q° c (MHz) aQc c (MHz)

0 5.51 0.21 5 5.48 0.22

10 5.48 0.21 15 5.45 0.21 2o 5.41 0.21 25 5.41 0.21 30 5.37 0.23 35 5.39 0.23

3.2.1. Determinat ion o f the parameters o f the sites shown in table 1

The de te rmina t ion o f the dis t r ibut ion parameters for sites 1 and 2, which bo th

y ie lded narrow lines (since Q~c was low for bo th cases), was under taken by fi t t ing

the narrow lines o f the 5 and 30 tool% Na20 glasses, respect ively, since site 1 pre-

domina tes in the 5 mol% N a 2 0 glass and site 2 predomina tes in the 30 tool% Na20

glass. Several dis tr ibut ions o f the hami l tonian parameters UQ and r~ were postula ted

and the resulting spectra were calculated using the m e t h o d presented above. Tile

calculated spectra, p lo t ted by a Calcomp mechanica l p lo t ter , were then compared

wi th the exper imenta l trace. Because there are no p rominen t features on the narrow

lines, several drastically di f ferent dis t r ibut ions fit the exper imenta l spec t rum well.

However , it was clear f rom the analysis o f the spectra that the most probable value

Table 3 The fractions of sites l, 2, 3, 4 and 5 determined by the computer-fitting procedure given in the text, for a series of Na20-B203 glasses. The notation 74, D 4, B 3, T 3 and D 3 is explained in table 4. The quantity 6 is the excess number of diborate borons from the predicted by the lever rule (a negative values of 6 indicates that there are fewer diborate borons than are predicted by the lever rule). All fractions are rounded to two significant figures.

Glass Site 1 Site 2 Site 3 Site 4 Site 5 6 (T 4) (D 4) (B 3) (T 3) (D 3)

5 0.05 - 0.79 0.16 10 0.10 0.01 0.58 0.30 0.01 15 0.15 0.03 0.38 0.44 0.03 20 0.17 0.08 0.16 0.51 0.08 25 0.14 0.19 0.04 0.44 0.19 30 a) 0.11 0.28 0.33 0.28 35 a) 0.08 0.34 - 0.24 0.34

0.01 0.03 0.08 0.02

-0.08 0.14

a) Borons bonded to a non-bridging oxygen have been ignored for these glasses.

194 G.E. Jellison, P.J. Bray / Structural interpretation orb 10 and B 11 NMR spectra

of the coupling constant for site 2 was considerably higher than for site 1. Theval- ues quoted in table 1 are in no sense unique, and should be viewed simply as values that fi t ; they do not necessarily have any physical significance.

The determination of the distribution parameters for sites 3, 4 and 5 was made from the large feature on the low-frequency side of u o (feature A of figs. 3 and 4). It was assumed that all the distributions pi(pQ) and Pi(~) [see eq. (9)] were gaussian. It was further assumed that pi(pQ) w a s the same for all three sites, but changed from glass to glass. (This distribution was determined in ref. [14] for the same series of Na20-B203 glasses. Note that the values change very little over the entire compositional range.) Since site 3 is predominant in the 0 molar% Na20 glass, site 4 in the 20 tool% Na20 glass, and site 5 in the 30 tool% Na20 glass, the distribution parameters for sites 3, 4 and 5 were determined from the 0, 20 and 30 tool% Na20 glasses, respectively. Several distributions of the asymmetry parameter were postulated and the resulting spectra were calculated using the method presented above. The calculated spectra, plotted by a Calcomp mechanical plotter, were then compared with the experimental trace. The 20 and 30 tool% Na20 glasses contained 3-coordinated sites other than the predominant one, but the presence of these other sites did not interfere with the determination of the distribution of r/, since their intensities were low. In this way, the distribution parameters can be determined with reasonable accuracy.

3.2.2. A ssignment o f the sites to structural groupings

Krogh-Moe's interpretation [16] of the IR spectra for alkali borate glasses states that below 20 tool% alkali oxide, the addition of one "molecule" of alkali oxide to boron oxide results in the formation of one triborate group (fig. lc) and one pentaborate group (fig. lb). These groups are connected, the BO4 unit of the triborate group being connected to one of the BO3 units of the pentaborate group, so it is convenient to refer to the triborate-pentaborate pair as a tetraborate group. Above 20 tool% alkali oxide (up to 33~ tool% alkali oxide), diborate units will increase at the expense of tetraborate units. Therefore, the 0 tool% Na20 glass will consist mainly of boroxol units, the 20 tool% Na20 glass will consist mainly of tetraborate units and the 30 mol% NazO glass will consist mainly of diborate units, according to Krogh-Moe's model.

The assignment of the five sites to various BO3 and BO 4 units must be made, keeping in mind that the NMR quadrupole interaction is proportional to 1/r 3, where r is the distance between the nucleus under investigation and the charge creating the electric field gradient. Therefore, only nearest neighbors or, at most, next- nearest neighbors need be considered.

The vastly different hamiltonian parameters listed in table 1 for the five sites can be explained by the difference in the electronic distribution of the 3- and 4-coordinated boron atoms. One effect of this difference, which has been exploited exten- sively [1-13] , is that the distribution of electrons about 4-coordinated boron atoms in borate glasses is close to being tetrahedrally symmetric, which produces a

G.E. Jellison, P.J. Bray / Structural interpretation o rB 1 o and B 11 NMR spectra 195

weak quadrupole interaction (as measured by the quadrupole coupling constant); on the other hand, the distribution of electrons about 3-coordinated boron atoms in borate glasses, for the case when all oxygen atoms connect two boron atoms, is close to being axially symmetric, which produces a stronger quadrupole interaction with a low value of the asymmetry parameter. Another effect of this difference arises front the fact that a 3-coordinated boron is in an sp 2 hybridized state, while a 4-coordinated boron is in an sp 3 hybridized state. Therefore, the B - O bond of a BO 3 unit can possibly have n-character, while the B - O bond of a BO 4 unit cannot have n-character. This will strongly affect the electron concentration on the neigh- boring oxygen atoms, which will affect the electric field gradient at the next nearest atom (a boron atom). It seems logical, then, to consider the type of unit ( B O 3 o r BO4) connected to the subject unit in the assignment of the five sites. Retrospectively, the reason five sites were chosen can now be seen. There are at least two possible B O 4 sites: B O 4 units connected to all B03 units and BO 4 units connected to a mixture of BO3 and B O 4 units. (The possibility of BO 4 units being bonded to all BO 4 units is neglected, since this possibility has never been observed in crystalline borates.) There are three possible BO3 sites: BO3 units connected to (1) all BO3 units; (2) a mixture of B O 3 and BO4 units; (3) all BO4 units.

This difference between the BO3 and BO4 units has also been used by Bril [23] to explain the different Raman frequencies of boroxol rings and rings with one (or more) B O 4 units. The boroxol rings contain n o B 0 4 units; therefore n-character is to be expected in the B - O bonds in the ring, which will strengthen the inter- anular B - O bonds. If the ring contains one or m o r e BO 4 units (such as pentaborate, triborate, tetraborate or diborate groups), then there can be no n-character to the B O bonds of the B O 4 unit, weakening these bonds. This results in the breathing mode vibration being of a higher frequency for the boroxol ring compared to the ring with one or m o r e BO 4 units. Therefore, the 806 cm I Raman line observed in borate glasses is assigned to boroxol breathing mode vibrations, and the 770 cm -I Raman line is assigned to the breathing mode of a ring with one or m o r e BO 4 units.

Sites 1 and 2 can be assigned to B O 4 units, since the value of Qc°c is low for these sites; but there is a fundamental difference between the two sites: the value of Q°cc for site 1 is considerably lower than Q°cc for site 2. This implies that site 1 is closer to tetrahedral symmetry than site 2. The origin of this can be seen from X-ray diffraction studies of crystalline sodium tetraborate [24] (containing all tetraborate groups) and lithium diborate [25,26] (containing all diborate groups). The BO 4

units in sodium tetraborate are connected to four B03 units, while the B 0 4 unit in lithium diborate is connected to three B03 units, and o n e BO 4 unit; therefore, the electric field gradient at the site of the boron nucleus of a BO 4 unit in a tetraborate group will be closer to tetrahedral symmetry than a BO 4 unit in a diborate group. Therefore site 1, which has a low value of Qcc and is predominant at low sodium content, can logically be assigned to B04 units connected to all B03 units; while site 2, which has a higher value of Qcc and is predominant at high sodium content, can logically be assigned to BO 4 units connected to a mixture of B03 and BO 4

units.

196 G.E. Jellison, P,J. Bray / Structural interpretation o f B 10 and B 11 NMR spectra

Sites 3, 4 and 5 are assigned to BOa units (owing to their higher value of Q°c), but again there is a fundamental difference between the three sites, as exhibited by the differences in the values of the asymmetry parameter (see table 1): the value of 77 for site 4 is considerably higher than the values of ~ for sites 3 and 5, indicating that site 4 is less axially symmetric than sites 3 and 5.

The X-ray work of Mozzi and Warren [27] (as well as the interpretation of the 806 cm -1 Raman line [16]) of B20 3 glass indicates that this glass consists mostly of boroxol rings (see fig. la). Raman studies by Konijnendijk [17] show that the same line is present in glasses of the sodium borate system (though shifted 1 or 2 cm -I in frequency) up to approximately 20 mol% sodium oxide, indicating the presence of boroxol groups in sodium borate glasses up to 20 mol% Na20. Site 3, then, can be assigned to BOa units connected to three other BO3 units, since this site is highly axially symmetric and exists predominantly at low sodium content. The non-zero asymmetry parameter for site 3 can be attributed primarily to the non-equivalence of the three connecting oxygens [ 15].

At higher sodium content, according to Krogh-Moe's model, most groups present are tetraborate groups [ 16,17]. X-ray diffraction studies of crystalline sodium tetraborate [24] indicate that all the BO3 units of this compound are attached to one (or two) BO 4 units and two (or one) BO3 units. Therefore, the asymmetry parameter for BO3 units in tetraborate groups would be considerably higher than for BO 3 units in boroxol groups. This is confirmed by NMR measurements of crystalline sodium tetraborate [18] where ~ = 0.27 is recorded for 3-coordinated boron atoms in tetraborate groups. The agreement between the values of ~7 of crystalline tetraborate and of site 4 is excellent. Therefore, site 4 is assigned to BO3 units, connected to one (or two) BO 4 units and two (or one) BO3 units, such as are found in tetraborate groups. (It is impossible to distinguish between the two cases, since the tetraborate group contains both.)

X-ray diffraction investigations of crystalline lithium diborate [24,25] indicate that all BO3 units in diborate groups are connected to three BO4 units. (Sodium diborate is not appropriate for comparison, since the crystal structure does not contain diborate groups, but rather di-pentaborate groups and triborate groups with one non-bridging oxygen [28] - see fig. le, f.) These BO3 units are therefore near axial symmetry. Site 5, then, is assigned to BO3 units connected to three BO 4 units, since it occurs at high sodium content, where the predominant group present in the Krogh-Moe model is the diborate group, and since it has a low asymmetry parameter. However, NMR measurements of crystalline lithium diborate yield a value [29] 77 = 0.17, which is clearly greater than the value of 77 for site 5. This is possibly due to one B - O bond length being about 0.04 A shorter than the other two B-O bond lengths [26] for BO3 units in lithium diborate, which would tend to increase the asymmetry parameter. If this is the case, then the crystalline diborate groups in lithium diborate are more distorted, owing to crystal packing requirements, than the glassy diborate units.

Until now, Krogh-Moe's interpretation of IR data has been employed only as

G.E. Jellison, P.J. Bray / Structural h~terpretation o f B 10 and B 11 NMR spectra 197

supporting evidence; it is not central to the interpretation of the B 1° data and the assignment of the five sites to B03 or B04 units connected to a specified number of other BO 3 and BO 4 units. At this point, Krogh-Moe's model is taken as the basis of the analysis; it is assumed that the four structural units o f fig. l a - d exist in the glass. It will be seen that the B l° NMR data agree extemely well with Krogh-Moe's model, but this does not exclude other possible structural models. The B 1° spectra are more sensitive to differences in local structure than B 11 NMR, and present a unique form of structural information compared to other structural tools; however, as with all experiments employed for the determination of structure of glasses, the B 1° spectra can be only looked on as a restraint to a proposed structural model [301.

Given Krogh-Moe's model, there might be a tendency to extend the assignment of the live sites to the various structural groups themselves (site 3 might be assigned to 3-coordinated borons in boroxol rings, site 4 to 3-coordinated tetraborate borons and site 5 to 3-coordinated diborate borons); however, this is to be undertaken with great care as to the assumptions involved, since alternative assignments are possible. For example, it is possible in the glass that a diborate BO 3 unit might be connected to two BO4 units (in the diborate unit itself) and to one BO 3 unit not associated with the diborate group. However, restrictions can be imposed, assuming that the sodium borate glass system contains only "loose" BO 3 units (BO3 units not associated with any structural group), loose BO 4 units, boroxol groups, tetraborate groups and diborate groups. (This is justified by the Raman studies of Konijnendijk [17].) These restrictions are listed in table 5. If the loose units are neglected (the Raman studies indicate that their percentages are small [17]), then the only ambiguity comes from sites 2 and 4. Site 1 could come only from tetraborate BO 4 units; site 3 could only come from boroxol BO 3 units; and site 5 could only come from diborate BO 3 units. However, site 2 could come from tetraborate BO 4 units, as well as diborate BO 4 units, if two tetraborate groups were connected by BO 4 units. This does not occur in crystalline sodium tetraborate [24], where aH BO 4 units are connected to four BO 3 units. The ~ modification o f sodium triborate contains pentaborate and diborate units [31 ]. Site 2 occurs in this compound, but only associated with the diborate units. Since this is the only occurrence of site 2 in compounds of

Table 4 Symbols used to denote the fractions of borons in each structural group.

Symbol Unit Coordination Site

T 4 tetraborate 4 1 D 4 diborate 4 2 B 3 boroxol 3 3 T 3 tetraborate 3 4 D 3 diborate 3 5

198 G.E. Jellison, P.J. Bray / Structural interpretation o r B 10 and B 11 NMR spectra

Table 5 Possible origins o f the five sites described in table 1

Site Loose Boroxol Tetraborate Diborate

BO 3 BO 4 BOa BO 3 BO 4 BO 3 BO4

1 X X 2 X X 3 X X 4 X X X X 5 X X

X

the sodium borate system, and since site 2 occurs only in diborate groups here, it is reasonable to rule out the possibility of site 2 coming from tetraborate BO 4 units. The real ambiguity, then, comes from site 4, where all possibilities actually occur in crystalline materials.

3.2.3. Assignment of weighting factors In order to make an assignment of the proper weighting factors, five assumptions

have been made: (1) Loose BO3 and BO4 units are neglected in this analysis. Konijnendijk [17]

indicated that there could be minor fractions of loose BO3 and BO4 units present in the glass. In addition, ref. [15] showed that between 10 and 25% of the borons in vitreous BzO 3 are outside the boroxol rings, though it was emphasized that this number is not accurate. In ref. [15], it was stated that these loose BO3 units all have bridging oxygens. Beyond that, however, nothing can be said about the expected hamiltonian parameters for the loose BO a units. Similarly, "loose" BO4 units will have a low value of o Qee" As the loose BO3 and BO4 units have no charac- teristic hamiltonian parameters, one is forced to neglect them.

(2) Other units that might possibly appear in minor amounts [such as di-pentaborate units or triborate units with one non-bridging oxygen (see fig. le, f)] are ignored.

(3) Pentaborate and triborate units (see fig. lb, c) are assumed to occur in pairs, and will be called tetraborate groups. The Raman studies of Konijnendijk [17] indicated that lone pentaborate units did not occur in the glass, supporting this assumption.

(4) Site 2 is postulated to consist entirely of BO 4 units in diborate groups. As discussed above, the X-ray diffraction studies of the crystalline materials support this assumption.

(5) Site 4 is postulated to consist entirely of BO3 units in tetraborate groups. Im- plicit in this assumption are the restrictions that boroxol groups are connected to other boroxol groups or to BO3 units of tetraborate groups, and that the BO3 units

G.E. Jellison, P.J. Bray / Structural interpretation of B 10 and B 11 NMR spectra 199

of the diborate groups are connected to B O 4 units of the tetraborate or other diborate groups.

Additionally, two facts should be noted: (1) the fraction of 4-coordinated diborate borons is equal to the fraction of 3-coordinated diborate borons; (2) the fraction of 4-coordinated tetraborate borons is equal to one-third the fraction of the 3-coordinated tetraborate borons. The rationale for this can be seen from fig. l b - d .

Table 3 shows the weighting fractions obtained by fitting the experimental spectra of figs. 3 and 4 for the five sites whose hamiltonian parameters are listed in table 1. Fig. 5 shows feature A for the 20 tool% Na20 glass superimposed upon three computer-simulated spectra calculated for three different weightings of the five

1.0-

09-

08-

0.7-

0.6-

05-

~ 0.5-

0.2-

01.

3 0 k Hz ~, I I V OI 0'.2 05 0.4 0.5 0.6

i

R

Fig. 5. Experimental B 1° derivative of the main feature for 3-coordinated boron atoms (feature A of fig. 3) in the 20 mol% Na20 glass (solid line). The simulated spectra (circles) were calculated using the five sites of table 1, and three sets of weighting fractions.

Simulation Site 1 Site 2 Site 3 Site 4 Site 5 6

a 0.19 0.06 0.12 0.57 0.06 0.06 b 0.17 0.08 0.16 0.51 0.08 0.08 c 0.15 0.10 0.20 0.45 0.10 0.10

The quantity 6 is discussed in the text.

Fig. 6. Fractions of B 3 (A), T 3 (o), D 3 and D 4 (=) and T 4 (+) plotted as a function of R (= x/(1 - x), x = molar fraction Na20). The straight line segments are plotted for the case where the lever rule is obeyed (see text).

200 G.E. Jell&on, P.J. Bray / Structural interpretation orB 10 and B 11 NMR spectra

sites. As can be seen, this feature is very sensitive to changes in the weighting fractions.

The determination o f the fractions of the five sites by the lever rule (denoted by B 3, T 3, D 3, T~o and D 4) - assuming only boroxol, tetraborate and diborate groups are present - is shown by the solid line of fig. 6 plotted versusR = x/(1 - x ) ( x = molar fraction alkali oxide). At 0 mol% Na20, 100% of the borons will be in boroxol groups (according to the lever rule). As the mol% Na20 is increased, the percentage of tetraborate borons will increase until, at x = 0.20, T 3 = 0.75, T~o = 0.25, and Bo 3 = 0. Above x = 0.20, as x increases, the percentage of diborate groups will increase at the expense of the tetraborate groups until, at x = ½, D 4 = Do 3 = 0.5, To 3 = T~o = Bo 3 = 0. Above x = ½, the diborate groups will be destroyed and 3-coordinated borons with non-bridging oxygens will be created [4]. However, the rate at which the diborate groups will be destroyed is unknown. It has been determined emperically by Greenblatt and Bray [4] that the destruction rate of 4-coordinated borons is 0.5 (each Na20 "molecule" added beyond the x = ½ composition destroys half o f a BO 4 unit.) If it is now assumed that only diborate groups and BO3 units with one (or two) non-bridging oxygens and two (or one) bridging oxygens exist above the x = -~ composition, the fraction Do 3 = D 4 will be as shown in fig. 6. This assumption is somewhat tenuous, but since the largest mol% Na20 glass used in this study is the 35 tool% Na20 glass, which is not far above x = ½, the effects of this assumption are negligible.

In determining the weighting factors of table 3 for the glasses with x = 0.25 and below, only a quantity 6 is varied, where 6 represents the fraction of diborate borons in excess of the fraction of diborate borons expected by the lever rule, that is,

D 3 = D 4 = D o 3 +6. (10)

Now, since N4 must [2] have the value

N 4 =X/(1 - -x) , (11)

it is necessary that the total numbers o f 3-coordinated and 4-coordinated borons be unaffected by the departure of the number of diborate units from the value predicted by the lever rule. Therefore,

T 4 + D 4

and

B 3 + T 3

But since

T 4 = T3/3,

and

D 4 = D 3 '

= T 4 + D 4, (12)

+ D 3 = B 3 + T 3 + D 3. (13)

D 4 =Do 3, (15)

T~o = T~/3, (14)

G.E. Jellison, P.J. Bray /Structural interpretation orB 10 and B 1 I NMR spectra 201

then eqs. (10), (120 and (13) can be solved forB3, T3,D 3, 7 "4 andD 4, yielding

B3 =Bo3 +26, T3 = To3-36, D3 =Do3 +6 , 74 = T 4 o - 6 '

D 4 = D 4 + 8. (16)

That is, if a diborate boron is "created", then two boroxol borons must be "created", and three tetraborate (3-coordinated) borons must be "destroyed". Fig. 5 shows the experimental spectrum of the x = 0.2 glass superimposed upon three computer-sinmlated traces for different values of 6. Clearly, fig. 5b represents the best fit. It should be emphasized that only the single parameter 6 is varied in ob- taining the fit in fig. 5 ; the variations of the five-site weighting fractions given in the caption of fig. 5 follow from eqs. (16) when/5 is varied. Fig. 6 presents as a function o fR = x/(1 - x ) the values of B 3, D 3, D 4, T 3 and 74 given by eqs. (16) and the value of 6 determined for each glass.

For the 30 and 35 tool% Na20 glasses, it was necessary to relax the condition that N4 = x/(1 - x ) ; otherwise it was not possible to fit the central line (due to the 4-coordinated borons) and the broad line (due to the 3-coordinated borons) simul- taneously. However, from the Raman studies of Konijnendijk [17], it is possible to say that B 3 = 0 for these glasses. Since the total number of boron atoms is fixed for a particular composition, it must be true that

r 3 + 7 ,4 +D 3 + D 4 = To a + T~o +Do 3 +Do 4 = 1.00. (17)

Using the relations of eqs. (14) and (15) and setting D 3 = Do 3 + 6, eq. (17) yields

g 3 = 0 , T 3 = T 3 o 36/2, Da =D~ +6, T4 + T~o - 6/2,

D 4 = D ~ +6, (18)

(Note that 6 will be negative for these glasses. Also, the number of oxygens will not be conserved by this transformation, since the condition on N4 is relaxed; this is because non-bridging oxygens have been ignored.) Clearly, the "disassociation" of one diborate group will "create" half of a tetraborate group. (The diborate group has two 3-coordinated boron atoms and two 4-coordinated borons for a total of four; the tetraborate group has six 3-coordinated borons and two 4-coordinated borons for a total of eight.)

3.3. B 11 N4 measurements

The experimental derivative of the B 11 NMR lineshape was obtained for the pur- pose of determining N 4. This lineshape was then integrated, using the integration option on the Nicolet 1072 signal averager, yielding the B 11 NMR absorption pattern (see fig. 7). The central peak near u o is due to 4-coordinated borons; the broad line is due to 3-coordinated borons. The ratio of the area of the central peak (area A of fig. 7b) to the total area is just the fraction of 4-coordinated borons (N4) in

202 G.E. Jellison, P..L Bray / Structural #zterpretation orB l 0 and B 11 NMR spectra

N4

0.5:

0,4-

.-~ 0.3-

0.2-

0.1-

.....................'"" .......................... ... + [ , o

(~.1 0'.2 0'.3 0[4 0'.5 ) R l:ig. 7. B 11 NMR derivative of the absorption wave (a) and the B 11 absorption curve itself (b) taken at v 0 = 16 MHz for the 20 tool% Na20 glass. The absorption curve (b) has been displaced to the left to get both spectra in the figure. From the absorption curve (b), N 4 can be determined as N 4 = area A/(area A + area B). In this case, N 4 = 0.25.

Fig. 8. N 4 versus R[ = x/(1 - x ) ] from B 1 ! NMR (o) and B 10 NMR (+). The straight line is determined by summing T~O +D 4 from fig. 6. The dotted line is from 13eekenkamp [37].

the glass [13,32]. The resulting values o f N 4 are shown in fig. 8 by the circles (o)- The B 1° values in fig. 8 are the sum of T a a n d D 4 from table 3.

4. Discussion

The assignment o f weighting fractions has been made on the somewhat unjust i- fied assumpt ion that all site 4 borons arise from BO3 units in tetraborate groups.

However, the comparison of results presented here and Raman work presented by

Bril [23] lends this assumpt ion a degree of validity. The ratio of the n u m b e r of boroxol rings to the n u m b e r of rings conta in ing one or more BO 4 units is given by

B3/3 _ I B 3 (19)

3 X T3/6 + D 3 3 T3/2 + D 3

if the postulate that all site 4 borons arise from BO 3 units in tetraborate groups is assumed. These fractions are plot ted with circles in fig. 9. A similar fraction can be obta ined from Raman data. Bril [23] measured the fraction of the intensit ies o f the 8.06 cm-1 line to the 770 cm -I line. (The 806 cm - l line arises from a breathing mode vibrat ion of the boroxol ring [16], while the 770 cm -1 line arises from a breathing mode of rings conta in ing one or more BO4 units [17,23]) . The data of Bril, mult ipl ied by a normalizing factor 0.4, are plot ted in Fig. 9 with crosses (the normalizing factor is necessary to correct for differences in l inewidths, scattering cross-sections, etc.). The normalizing factor was assumed to be constant over the

G.E. Jellison, P.J. Bray/Structural interpretation o rB 10 and B 11 NMR spectra 203

5-

2

I-

" 2 0

Molar % Na20

Fig. 9. Ratio of the number of boroxol groups to the number of other rings with one or mor~ BO 4 units. The ckeles represent points calculated from the data presented in this paper using eq. (19), while the crosses represent the data of Bril [23], multiplied by a normalizing factor of 0.4, and the X's represent the data of Bartoluzza et al. [34 ].

range 5 - 2 0 tool% Na20. [Bril assumed that this normalizing factor was 1 ; he did not take into account the fact that the peak width of the 770 cm -1 line is 2.5 3 times that of the 806 cm -1 line at 15 tool% Na20 (this would yield a normalizing factor of 0 .4 -0 .33 , other effects being equal). His assumption was based on the observation that the ratio of these two peak heights for Cs20 • 9 B203 is 2 : 1 (which corresponds to the ratio of boroxol rings to triborate rings [33] in crystalline Cs20 - 9 B203). However, he ignored any differences in the peak widths which could affect the ratio drastically. Ideally, a computer fit should be attempted to get the ratio of the intensities.] Another comparison can be made with the Raman data of Bartoluzza et al. [34]. The ×'s in fig. 9 represent the ratio of the height times the width of the 806 cm -1 line divided by the height times the width of the 770 cm-1 line. The agreement is excellent. Although other conclusions could be drawn from this result, it is consistent with the assumption that all the site 4 borons arise from BO 3 tetraborate units.

The assignment o f site 4 entirely to BO3 units in tetraborate groups [see postulate (5) above] contains a possible explanation to the observed subliquidus immiscibility in sodium borate glasses [35]. Shaw and Uhlmann observed that, between 7 and 24 tool% Na20, small ( 7 0 - 1 0 0 A dia.) two-phase structures were observed, if the samples were heat-treated for approximately 30 min. The samples used in this study were quenched in a carbon mold at room temperature, so the cooling rate was greater than that required to see two-phase structures 70 )~ in dimnter, but smaller two-phase structures could very well have been formed. If, in fact, very few boroxol borons are connected to BO 4 units in the region 0 - 2 0 mol% Na20, then

204 G.E. Jellison, P.J. Bray / Structural interpretation orB 10 and B 11 NMR spectra

the tetraborate groups would tend to be connected to each other. This would result in phase separation - one type of region being rich in tetraborate units and the other type of region being poor in tetraborate groups.

Below the subliquidus immiscibility region (0 -7 mol% Na20), no phase separation is observed. In this region the tetraborate groups are most likely not connected to one another, and are preferably connected to boroxol groups. The tetraborate group has six oxygens with which it can bond to other groups (see fig. lb, c; remember that the triborate group is connected to the pentaborate group by the BO4 unit): one is associated with a BO 4 unit, while five are associated with BO3 units. This would result in 14.3% of the site 4 borons arising from boroxol borons connected to BO 4 units; at 5 tool% Na20, this amounts to 2.2% of the total borons in the sample. This is within the experimental error of the present work.

Therefore, in the region 0 - 2 0 mol% NazO, assumption (5) can be reasonably justified. However, for larger sodium concentrations, these justifications are no longer valid. The numbers of tetraborate BO 3 units (as well as tetraborate BO 4

units) could be somewhat smaller, and the numbers of diborate BO3 and BO 4 units could be somewhat larger.

An examination of fig. 6 shows that the fractions B 3, D 3 and l )4 are above, while the fractions T a and 74 are below, the values predicted by the lever rule, in the compositional region 0 - 2 5 mol% Na20. This would also be true if assumption (5) were violated, since any violation of assumption (5) would tend to decrease T 3.

It can be concluded from the data of fig. 6 and the supporting arguments given above that, in the compositional region 0 -25 mol% Na20 some of the tetraborate units predicted by the lever rule have been "disassociated" into diborate groups and additional boroxol groups. A convenient parameter for measuring the amount of "disassociation" is the parameter 6 used in this work, where 6 represents the number of 3- or 4-coordinated diborate borons "created" (i.e. in excess of that predicted by the lever rule). Such "disassociation" was predicted by Krogh-Moe [36] in his interpretation of melting-point depression data for melts of the Na20-B203 system. He found that the best fit of the experimental data in the region near x = 0.2 occurred when tetraborate, boroxol and diborate units were present, and when some of the tetraborates, which would be present according to the lever rule, were "disassociated" into boroxol units and diborate units. Furthermore, Raman studies by Konijnendijk [17] and Bril [23] indicate the existence of boroxol groups at 20 mol% Na20 , and IR measurements by Krogh-Moe [16] indicate tile existence of diborate groups at the same composition. Therefore, for the compositional region x = 0 to x = 0.2, the conclusion can be drawn that the glass is composed of the three principal structural groups (boroxol, tetraborate and diborate), but that the fractions of these groups in the glasses for which x = 0.10, 0.15 and 0.20 do not correspond to the values predicted by the lever rule.

In the region x = 0.30 and 0.35, some of the diborate groups predicted by the lever rule have been "changed" into tetraborate groups, though the numbers presented in fig. 6 could be in error. The interpretation of melting-point depression

G.E. Jellison, P.J. Bray /S t ruc tura l in t e rpre ta t ion o f B l ° and B 11 N MR spectra 205

data by Krogh-Moe [36] of melts of the N a 2 0 - B 2 0 3 system in the region of x = 1 indicates that these two groups (tetraborate and diborate) are present. In addi- 3 tion, IR [16] and Raman [17] studies indicate that these two groups are the only major components of the glass in this region. In particular, the components of crystalline sodium diborate (the di-pentaborate and the triborate with one non-bridging oxygen, see fig. le, f) have been ruled out, since the NMR spectra indicated that no BO 3 units with one or two non-bridging oxygens were present. Therefore, the tetraborate and diborate groups are the only major components of the glasses for which x = 0.30 and 0.35; however, as mentioned above, the fractions T 3, T 4, D 3 and D 4 do not correspond to values predicted by the lever rule. In particular, the lever rule would predict T 3 = T 4 = 0 for the x = -~ glass. By interpolation, T 3 = 0.27, and 7 ̀4 = 0.09 at x -- -~, which are clearly not zero values. The main consequence of the "changing" of diborate groups into tetraborate groups for the glasses with x = .30 and 0.35 is that N 4 will fall below the x / ( 1 - x ) curve. Fig. 8 shows two indepen- dent measurements o f N 4 : (1) using B 11 NMR [shown by the circles (©) of fig. 8, described above); and (2) using B 1° NMR (N4 = 7 "4 + D 4, shown by the crosses (+) of fig. 8]. The solid line of fig. 8 is obtained by summing T~o + D~ (obtained from the lever rule) of fig. 6. The agreement of both methods is excellent; both methods indicate that the value of N 4 lies below the x / ( 1 - x ) curve for the glasses with x = 0.30 and 0.35. Also :ncluded in fig. 8 is the theoretical curve forN4 (shown by the dotted line) from Beekenkamp [37]. As can be seen, the experimental data points lie substantially above this theoretical curve.

The conclusions above on fractions T 3, T 4, D 3 and D 4 for the glasses with x = 0.30 and 0.35 are highly dependent on assumption (5). Any deviation from this assumption would tend to decrease T 3 and 7 -4 and increase D 3 and D 4, resulting in a larger value of N4. Therefore, any deviation from this assumption could not be too large without creating a disagreement with the B lj NMR N 4 measurements.

5. Summary

Here, B I° NMR has been used to study glasses of the sodium borate system. The analysis of these spectra that five sites are present in the glasses: two 4-coordinated and three 3-coordinated boron sites. The 4-coordinated sites can be further distinguished as BO 4 units with (1) all BO 3 units attached, and (2) a mixture of BO 3 and BO 4 units attached. The 3-coordinated sites can be distinguished as BO 3 units with (1) all BO 3 units attached, (2) a mixture of BO 3 and BO 4 units attached and (3) all BO 4 units attached. Krogh-Moe's model can then be invoked, and the fractions of the three major structural groups (boroxol, tetraborate and diborate) can be obtained. The fractions thus obtained indicate that the lever rule is violated prin- cipally at the 20 and 35 mol% Na20 compositions, which agrees with the interpretation of melting-point depression data of Krogh-Moe [36]. The B 11 NMRN4 measurements agree within experimental error with B l° N4 determinations.

206 G.E. Jellison, P.J. Bray / Structural interpretation o rB 10 and B 11 NMR spectra

Acknowledgement

This research was supported by the National Science Foundation Materials Science Program DMR 72-03023-A06.

References

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section 13,p. 1. [10] K.S. Kim and P.J. Bray, J. Non-metals 2 (1974) 95. [11 ] K.S. Kim and P.J. Bray and S. Merrin, J. Chem. Phys. 64 (1976) 4459. [12] K.S. Kim and P.J. Bray, Phys. Chem. Glasses 15 (1974) 47. [13] W. M/iller-Warmuth, W. Poch and G. Sielaff, Glastech. Ber. 43 (1970) 5. [14] G.E. Jellison, Jr. and P.J. Bray, Solid State Commun. 19 (1976) 517. [15] G.E. Jellison, Jr., L.W. Panek and P.J. Bray, J. Chem. Phys. 66 (1977) 802. [16] J. Krogh-Moe, Phys. Chem. Glasses 6 (1965) 46. [17] W.L. Konijnendijk, Thesis, Philips Res. Rep Suppl. No. 1 (1975); W.L. Konijnendijk and

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P.C. Taylor and P.J. Bray, Bull. Am. Ceram. Soc. 51 (1972) 234. [22] P.C. Taylor and P.J. Bray, J. Mag. Res. 2 (1970) 305. [23] T.W. Bril, Thesis, Technological University Eindhoven (1975). [24] A. Hyman, A. Perloff, F. Mauer and S. Block, Acta Cryst. 22 (1967) 815. [25] J. Krogh-Moe, Acta Cryst. 15 (1962) 190. [26] J. Krogh-Moe, Acta Cryst. B24 (1968) 179. [27] R.L. Mozzi and B.E. Warren, J. Appl. Cryst. 3 (1970) 251. [28] J. Krogh-Moe, Acta Cryst. B30 (1974) 578. [29] J.F. Baugher, H.M. Kriz, P.C. Taylor and P.J. Bray, J. Mag. Res. 3 (1970) 415. [30] D.L. Griscom, Proc. Alfred Conf. on Boron in Glass and Glass Ceramics (Alfred, N.Y.,

1977) p. 1. [31 ] J. Krogh-Moe, Acta Cryst. B30 (1974) 747. [32] M.E. Milberg, J.G. O'Keefe, R.A. Verhelst and H.O. Hooper, Phys. Chem. Glasses 13

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a structural interpretation of b10 and b11 nmr spectra in sodium borate glasses

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