Nuclear magnetic resonance investigations of sodium borosilicate glasses

Journal of Non-Crystalline Solids 52 (1982) 171- 179 North-Holland Publishing Company

171

NUCLEAR MAGNETIC RESONANCE INVESTIGATIONS OF SODIUM BOROSILICATE GLASSES X I A O Shaozhan Beijing Glass Research Institute, Hong-Qiao, Beijing 100062, China

GUO Quanzhong NMR Laboratory, Institute of Physics, Chinese Academy of Sciences, PO Box 603, Beijing, China

The lib Fourier transform spectra have been used to study the structure of Na20-B203-SiO2 glasses. Based on the measurements of the fraction N4 of boron atoms in the boron oxygen tetrahedra, a structural model has been proposed to explain the change of N4 with composition in the region of high alkali (Na20/B203 = R >/2) and high silica (SiO2/B203 = K >/8). It is claimed that in this region boron atoms may only exist in reedmergnerite [BSi3Oi0]- I units and pyroborate [B205] -4 units. In addition, a sharing rule for Na20 between the borate and silicate networks is postulated. In the corresponding composition region, when one molecule of Na20 is taken up by the borate network, two [BSi4Olo]- l units are destroyed to create one [B205]-4 unit.

1. Introduction In the 1970s, m a n y N M R studies were focused o n the N a 2 0 - B 2 0 3 - S i O 2 glass system [1-8] for analysing the fraction N 4 of b o r o n atoms in the b o r o n - o x y g e n tetrahedra as a f u n c t i o n of composition. I n particular, Y u n a n d Bray [7,8] have proposed a structural model where both their own data and those in refs. 1 - 4 are included in a set of general equations. Xiao [9] has presented a different model from the a b o v e - m e n t i o n e d authors to explain the structural change in the high alkali region of the ternary glass based on an analysis using their experimental data [7]. This study is a c o n t i n u a t i o n of the work in ref. 9.

2. Experimental Seven glass samples were prepared, their compositions, d e t e r m i n e d by chemical analysis, are listed in table 1. Reagent grade N a 2 C O 3, H3BO 3 a n d SiO 2 were mixed, a n d then melted with p l a t i n u m crucibles in an electric furnace at 1 3 0 0 - 1 4 2 0 ° C for 3 - 7 h. The melts were p o u r e d o n t o a metal plate which was originally at room temperature, a n d quickly covered with a metal block. While for glass No. 18, besides the technique described above, a n o t h e r m e t h o d was applied: a b o u t 30 g of melt were poured onto the plate, then 0 0 2 2 - 3 0 9 3 / 8 2 / 0 0 0 0 - 0 0 0 0 / $ 0 2 . 7 5 © 1982 N o r t h - H o l l a n d

172

Xiao Shaozhan, Guo Quanzhong / NMR investigations of sodium borosilicate glasses

Table 1 Chemically determined compositions, experimental values N4~E)and theoretical values ~~l~r) "4(C), ~~a~s) "4(C)

calculated from the two approaches, respectively Sample

K

R

First approach

Second approach

Nn~E)

N~f)c)

0.98N~E )

N~)c,

0.85 1.00 0.89 0.81 0.88 0.83 0.96 1.00

0.85 1.00 0.93 0.77 0.88 0.82 0.96 1.00

0.83 0.98 0.87 0.79 0.86 0.81 0.94

0.84 0.94 0.89 0.79 0.86 0.82 0.92

No.

17 18 19 20 21 22 23 L a)

8.12 8.98 9.47 9.67 9.27 9.83 8.71 9.04

3.68 2.06 3.10 5.36 3.69 4.73 2.54 1.87

a) Value taken from ref. 2.

cooled in air. This sample was labelled No. 18(S). N o n e of the glasses were annealed. They were transparent and showed no sign of crystallization by means of X-ray diffraction techniques. After crushing, every sample was sealed in an evacuated glass tube free of B20 3. These tubes, with diameters about 10 mm, were filled to the same height (20 mm). The N M R experiments in this work were performed on a multi-nuclear pulse Fourier transform N M R spectrometer of Type SXP 4-100 at r o o m temperature. The signals of free induction decay of 11B were accumulated 50 times with an interval of 10 s. The sampling time TO was about 11 ~s in all our experiments. In accordance with Fourier transform theory, the area under an absorption peak is proportional to the value of F I D without any delay-time. It can be proved that in all of the spectra in this work, the largest relative error AA/A introduced by the delay-time TO is equal to the product of (To/T2)2 and (SAw/Ao~), where A, T2, Aw and 8A~0 are the area under the absorption peak, spin-spin relaxation time (several hundred #s), mean width at half-maximum and the largest difference of the widths a m o n g all the absorption curves, respectively. In our experiments (To/T2)2< 0.003, 8Aw/Ao~= 0.28. Thus the relative error in the area introduced by the delay time of 11/zs would be much less than the signal-to-noise ratio (about 0.01) of liB N M R spectrum lines.

3. Results and discussion Fig. 1 shows the I1B Fourier transform N M R spectra from the two samples Nos. 18(S) and 20. As discussed in ref. 10, a comparison of the area under the central peak with a standard yields the numbers of b o r o n atoms in the tetrahedra. In this work, glass No. 18(S) was used as the standard. Its value N 4 was assumed to equal 1, because the value N 4 of glass L equals 1 (see table 1)

Xiao Shaozhan, Guo Quanzhong / NMR investigations of sodium borosilicate glasses 0

25

173

KNz

t.~: 2~. O~STMHI

cO

~0

Fig. 1. liB Fourier transform NMR spectra from glasses Nos. 18(S) and 20.

as determined in ref. 2, the difference in compositions and thermohistory between the two glasses is small. The experimental values N4(E) of all the glasses are listed in table 1. Fig. 2 shows plot of N4(e) versus R. Here, we should point out that Zhdanov [6] has made an N M R study in the region, and reached the conclusion that N4 -= 1 for R >/ 1.5, K >/8. Perhaps, there was a large difference in the thermohistory between his samples and ours, which caused the contradictory results. The framework established by Yun and Bray [7] is still basically followed, whereas their assumption that the numbers of N a 2 0 shared by the borate network are equal to the numbers of additional N a 2 0 multiplied by 1/(1 + K ) is modified. The expression is rewritten as 1/(1 + / 3 K ) (see section 3.3 for details); /3 is called the "contending factor". In this work, two different postulates for/3 were selected, then, two different approaches were followed.

N~(E)

0.8 l'°

I r o

(

i

t

i

I

Fig. 2. Experimentalvalues N4(E) versus R, the two straight lines correspond to the theoreticaleq. (5), where K = 8.5 and K = 9.5, respectively.

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Xiao Shaozhan, Guo Quanzhong / N M R investigations of sodium borosilicate glasses

3.1. The first approach It has been assumed [7] that when K = 8, R = 1, this ternary glass consists entirely of reedmergnerite units ([BSi4010]-I + Na ÷t) which contains one [BO2 ]- i tetrahedron and four [SiO2] tetrahedra. Now, we continue to assume that when N a 2 0 is being continuously introduced, it is only taken up by [SIO2] tetrahedra, in the mean time [BO2]-l tetrahedra are constantly "reserved" in [BSi4Ol0 ]- 1 units, thus N 4 = 1. Taking an average, after every two [BSi4Olo ]- 1 units just combine with one molecule of N a 2 0 (now it is rewritten as [BO2]-1[Si408.5Na]), the corresponding value R at this time is defined as Ru, the following reaction starts: for K >~ 8, R >1 Ru, 2([ B O z ] - ' [ S i 4 O s . s N a ] + Na +' ) + 1 U a 2 0 --~ ([ B 2 0 5 ] - 4 + 4 Na +'), (1) where only the change concerning the boron is dealt with. The possibility of the existence of pyroborate [B205] - 4 units was mentioned in ref. 7. A [B205] 4 unit consists of two asymmetric boron-oxygen triangles containing two nonbridging oxygen atoms. In the course of reaction (1), the rate of decrease of [BO2 ]- 1 tetrahedra equals 2 per molecule of Na20. Then, as proved in ref. 11, the change of N4 is proportional to R, and the slope S equals one-half of the decreasing rate of [BO2]-1 tetrahedra. From the definition of Ru, K = 8 and Ru = 2; for K > 8, it is assumed that SiO 2 tetrahedra inside or outside ([BSiaOl0]-t + Na ÷ l) units could combine with N a 2 0 with almost the same probability, then we have Ru-1 K

2-1 8

'

thus Ru = ( K / 8 ) + 1.

(2)

It is postulated that in the region of this work, the change of B with K is approximately linear, that is, for 10 >1K >1 8, R ~ Ru, /3 = 1.23 + 0.067 ( K - 8).

(3)

Consequently, we have for K >~ 8, Ru >1 R >~ 1 N4~c) = 1,

(4)

for K>~ 8, R >~Ru N4~(f) -

c)-

1

1

1 +ilK

( R - Ru).

(5)

The theoretical values N~°c) calculated from eqs. (4) and (5) are listed in table 1. Fig. 3 shows theoretical values N4~) versus experimental values Na~E). A conclusion can be drawn that the theory is in good agreement with the experiment within experimental error.

Xiao Shaozhan, Guo Quanzhong / NMR investigations of sodium borosilicate glasses

175

i,l ( f

.-(c) I.O

o.9

o,~

0.8

o

0.8 0.9 I.o I

•4(e)

Fig. 3. Theoretical values N~0c) calculated from the first approach versus experimental values N4~e~. A straight line indicates N ~ c ) = N,~e ).

3.2. The second approach If the value N4 of sample No. 18(S) used as the standard is slightly less than 1, for example, it equals 0.98, then, the experimental values N4~E) of all of the other samples would be multiplied by 0.98. Correspondingly, it can be assumed that only when R = 1, K >/8, could all of the boron atoms exist in [BSiaO10 ]- i units, then N 4 = 1. Once R > 1, reaction (1) occurs. Neglecting the small change of/3 with K and taking fl = 2, we have for K >/8, R >/ 1 N4 s) -- l

(c)-

1

1 + 2K

(R - 1).

(6)

The theoretical values ~(~) "4(C) calculated from eq. (6) are also listed in table 1, which should be compared with the values 0.98N4~E). It can be seen that the second approach is as effective as the first, within experimental error. The two approaches discussed above include certain subjectivity, but the experimental evidence found in this work is worth emphasizing.

3.3. Application of the "contending factor" fl to the other range of the ternary glass It seems to us that, from the extensive and systematical experimental data published by Yun and Bray [7], interesting information could be extracted about the change of the "contending factor" fl with K. Yun and co-workers [7,8] have proposed the following reaction model which starts at R m,x and ends at Ro: for Rmax ~< R ~
1.5Na+'),

(7)

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Xiao Shaozhan, Guo Quanzhong / NMR investigations of sodium borosilicate glasses

Here, [8407] -2, [B306] -3 and [ B O 2 ] - I denote a diborate unit, ring-type metaborate unit and loose boron oxygen tetrahedron, respectively. A [B407]-2 unit consists of two tetrahedra and two symmetric triangles, while a ring-type metaborate unit consists of three asymmetric triangles having one non-bridging oxygen atom. They assumed that the numbers of N a 2 0 introduced are proportionally shared according to the molar concentrations of B203 and SiO 2. Then, from reaction (7) it is possible to write $4(c) = - 0 . 2 5 / ( 1 + K ) ,

(8)

S3A(C) = 1.25/(1 + K ) .

(9)

Xiao [9] has suggested that in order to obtain better agreement with the experimental data [7] in the high alkali region, the changes of N4(c~ with R before and after the end point R 0 should be different rather than kept constant as described in ref. 8; moreover, the fraction N3sr of the loose symmetric triangles [BO~5] ° with three bridging oxygen atoms, which do not exist in [B407] -2 units and was neglected in reaction (7), should be considered. We define N3sr = N3S(E) -- N3s(c). N3S(E) and N3s(c ) can be calculated from N3S(E/C) = 1 - (N4(E/C)+ N3A(E/C)). While N4(E/c) and N3A(E/C) can be found from the relevant empirical or theoretical equations in ref. 7. Now, the experimental data points [7] corresponding to the region Rma~ ~< R ~< R 0 are singled out, and recalculated as empirical equations. The empirical values of slopes S4~E), S3A~E) and S3SL(E)calculated in this work are listed in tables 2 and 3, respectively. In order to approach these values of S(E), reaction (7) is correspondingly modified as follows: ([B407]-2 + 2Na+') + N a 2 0 = - ~

([B3061-3 + 3Na+') + 0.8[BO,.5] °

+0.4([B2051-4 + 4Na +') + 1 . 5 ( [ B O 2 1 - ' +

Na+').

(10)

Table 2 E m p i r i c a l values S4~E) and theoretical values $4(¢) calculated from eqs. (8) a n d (12), respectively. I I 2 (Note: H a v i n g i n t r o d u c e d / 3 we can prove that R 0 = 1 + i / 3 K - t6/~K . But, the c h a n g e for R 0 does n o t affect the results of calculation of the empirical e q u a t i o n s m e n t i o n e d above, because the g r o u p i n g of the c o r r e s p o n d i n g e x p e r i m e n t a l d a t a points is still not affected, t h o u g h the values of R 0 have been changed more or less.)

K

0.5 1 2 3 Average

S4(E)

-0.22 -0.14 - 0.10 - 0.055

S4~c)

0.25 1+ K

0.25 S'~c) = - 1 + / 3 K

S4(c)

84(C)

~S4(E (¢~)

84(C)

-0.17 -0.13 - 0.083 - 0.062

77.3 92.9 83 113 91.6

-0.21 -0.15 - 0.088 - 0.061

S4(c) S4(E~ (~) 95.5 107.1 88 110.9 100.4

S3AtE)

0.78 0.41 0.30 0.23

K

0.5 1 2 3 Average

0.83 0.63 0.42 0.31

S3A(C)

1.25 S3A(C)= 1 + K

106 154 140 135 133.8

S3A(C) S3A(E) (~) 0.71 0.51 0.30 0.21

S3A(C)

S3A(C)

0.85 1 + flK

91 124.4 100 91.3 I 01.7

S3AfC) -S3A(E) (~) 0.40 0.23 0.13 0.075

S3SL(E)

0.33 0.24 0.14 0.097

S3suc)

S3SL(C)

1 + flK

0.4

82.5 104.3 107.7 129.3 106

S3SL(C) -S3SL(E) (~)

Table 3 Empirical values S3A(E), S3SL(E)and theoretical values SaA(C) and S3sL(c) calculated from eqs. (9) and (13), (14), respectively. (Note: For the data groups K = 3, when S3A(E) is calculated the theoretical initial point (R = Rmax = 0.69, N3A = 0) is used, because there are only two data points nos. 33, 34.)

C,Q

5

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Xiao Shaozhan, Guo Quanzhong / NMR investigations of sodium borosilicate glasses

When considering the sharing of N a 2 0 , we suggest that it is more suitable to substitute the activity for the concentration. Let a s i o 2 = "Ysio2 .Csio2 and aB:o3 = 7B20~" CB2O3, where a, 3' and C are the activity, the coefficient of activity and the molar concentration, respectively. Then, from

aB2oJ( aB~o~ + asio:) we have 1/(1 + ilK), where /3 = ySiO2/YB2Oo, K = CsioJCB2o. In general, both y and 13 are related to (K, R). In ref. 7, the experimental data have approximately been treated as some straight lines, each corresponding to a constant value K. This implies that

OS4/OR = O/OR(-0.25/1 + ilK) = O, then OIl/OR = 0. Hence, the conclusion drawn is that /3 is only a function against K. What is postulated in this work is an empirical function of a parabola of higher order, which is illustrated in fig. 4 and written as follows: for 3>~K>~0 /3 = 0 . 9 7 5 K - 0.321K z + 0.0213K 3 + 0.0053K 4.

(11)

Consequently, we have 0.25 1 + ilK'

$4(c) =

(12)

0.85 1 + ilK'

S3A~C)

(13)

0.4 SOSL(C)

1 + ilK"

(14)

The theoretical values of S(c) calculated from eqs. (8), (12) and eqs. (9), (13), (14) are listed in tables 2 and 3, respectively. Fig. 5 shows the values S4 versus K. It can be seen that having introduced the "contending factor" /3, the -$~ o -So(E) ---

1.0

0.~

0

0.2c

o. 1~

[,~ o.4,t 0.68 o.9~, t,o,J

I

O 0.5

I

i

I

1

2

3

xo \

4-', I

R

0

I

I

I

1

2

3

K

Fig. 4. Function 13 versus K, the values 13 at corresponding values K are listed in the insertion. Fig. 5. Plot of $4 against K.

Xiao Shaozhan, Guo Quanzhong / NMR investigations of sodium borosilieate glasses"

179

behaviour of the corresponding curve $41c) calculated theoretically provides a well-balanced fit a m o n g the experimental data points. However further verification for the behaviour of the f u n c t i o n / 3 ( K ) is still required. Bray [12] has proposed another model, which is in good agreement with our experiment and still claims/3 = 1. It appears that an investigation for the combination of N a ~O with the silicate network would offer complementary information about /3 versus K.

4. Summary. The ~B Fourier transform N M R spectra have been used to study the structure of N a 2 0 - B 2 0 3 - S i O 2 glasses. In the region of high alkali ( R >/2) and high silica (K>~ 8), when K = constant and R increases, N 4 decreases with approximate linearity. A possible model has been proposed, where the following assumptions are included. (1) The numbers of N a 2 0 shared by the borate network are equal to the numbers of additional N a 2 0 multiplied by 1/(1 + / 3 K ) , /3 is called the " c o n t e n d i n g factor". (2) In the corresponding composition region, when every molecule of N a 2 0 is taken up by the borate network, two [BSi4010 ]- i units are destroyed to create one pyroborate [B205] - 4 unit. Based on the analysis of experimental data in literature, a conclusion could be drawn that the "contending factor" 13 might be useful for estimating the variation of sharing of the modifier N a 2 0 between the borate and silicate networks. The authors express their appreciation to Mr Jian Z h o n g a o for the chemical analysis of the glass compositions, to M a d a m G u a n Huizhi for performance of X-ray diffraction checks, and to Professor P.J. Bray for making an enlightening c o m m e n t on this paper [12].

References [1] S.P. Zhdanov, I. Kerger and E.V. Koromal'di, Dokl. Akad. Nauk SSSR 204 (1972) 622. [2] M.E. Milberg et al., Phys. Chem. Glasses 13 (1972) 79. [3] J. Scheerer et al., Glastech. Ber. 46 (1973) 109. [4] M.P. Brung and E.R. McCartney, Phys. Chem. Glasses 16 (1975) 48. [5] S.P. Zhdanov, Proc. 10th Int. Congr. Glass, Kyoto, Japan (Ceram. Soc. Japan, 1974) p. 13. [6] S.P. Zhdanov and G. Shmigel', Fizika i Khim. Stekla 1 (1975) 452. [7] Y.H. Yun and P.J. Bray, J. Non-Crystalline Solids 27 (1978) 363. [8] Y.H. Yun, S.A. Feller and P.J. Bray, J. Non-Crystalline Solids 33 (1979) 273. [9] S.Z. Xiao, J. Non-Crystalline Solids 45 (1981) 29. [10] P.J. Bray and J.G. O'Keefe, Phys. Chem. Glasses 4 (1963) 37. [11] S. Greenblatt and P.J. Bray, Phys. Chem. Glasses 8 (1967) 190. [12] Private communication in July, 1981.