Crystallization of Na2OSiO2 gel and glass

Crystallization of Na2OSiO2 gel and glass

Journal of Non-Crystalline Solids 63 (1984) 365-374 North-Holland, Amsterdam 365 C R Y S T A L L I Z A T I O N OF N a 2 0 - S i O 2 GEL A N D G L A ...

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Journal of Non-Crystalline Solids 63 (1984) 365-374 North-Holland, Amsterdam

365

C R Y S T A L L I Z A T I O N OF N a 2 0 - S i O 2 GEL A N D G L A S S G.F. N E I L S O N and M.C. W E I N B E R G Jet Propulsion Laboratory, Applied Mechanics Division, California Institute of Technology, Pasadena, California 91109, USA

Received 14 October 1982 Revised manuscript received 11 January 1983

The crystallizationbehavior of a 19 wt% soda silica gel and gel-derivedglass was compared to that of the ordinary glass of the same composition. Both bulk and ground glass samples were utilized. X-ray diffraction measurements were made to identify the crystalline phases and gauge the extent of crystallization. It was found that the gel crystallized in a distinctive manner, while the gel glass behavior was not qualitatively different from that of the ordinary glass.

1. Introduction The behavior and properties of glasses prepared by chemical polymerization methods may differ from those of the corresponding glasses prepared by conventional techniques, In particular, it has been observed that the rate of phase separation of metal organic processed gel glasses may be accelerated [1-3]. Mukherjee et al. [1] have examined the crystallization of gel and ordinary glasses in the L a 2 0 3 - S i O 2 ( L S ) , La203-A1203-SiO2(LAS), and La203-ZrO2-SiO2(LZS ) systems. They observed that the degree of crystallization, for a given heat treatment, was greater in the gel glasses for all compositions. In addition, they noted that the crystallization morphology in the gel LS glass was more fine-grained. The crystalline phases which appeared in the two cases differed, too. In a separate study, Mukherjee et al. [2] investigated the effect of hydroxyl content on the crystallization behavior of LS glass. They heated ground gel and batch glasses at 1100°C, and observed via the X-ray diffraction patterns obtained that the gel glass crystallized to a greater degree. Additional heat treatment procedures coupled with T G A measurements led to the conclusion that the enhanced hydroxyl content of the gel glasses was responsible for this behavior. Recently, Mukherjee and Zarzycki [4] compared the crystallization tendencies of two LS amorphous gels prepared by different procedures. In one case the amorphous powder was produced by chemical polymerization techniques, while in the other a sol-gel method was used. They found that the same crystalline phases were formed upon heat treatment, but the powders crystal0022-3093/84/$03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

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lized at different rates. No comparison was made with the crystallization rates of the LS glasses under similar conditions. The purpose of the present work was to make a comprehensive study of the relative crystallization behavior of gel, gel glass, and ordinary glass in a composition in the Na20-SiO 2 system. In order to obtain a more meaningful and in-depth comparison of crystallization tendencies, we analyzed the crystallization of (1) powdered materials; gel precursor, ground gel glass, and ground batch glass, and (2) bulk glasses; gel glass and batch glass. In particular, we considered the phases produced, the time of appearance of the crystalline phases, and the crystallization rates (qualitatively) of the various crystalline forms. Since pulverization prior to heat treatment may drastically affect crystallization behavior, it is important to relate the transformations of the ground glass to those of the precursor gel. Crystallization of bulk samples was also studied for the purpose of comparison.

2. Experimental The soda-silica gel precursor was prepared from tetraethylsilicate and sodium nitrate by a standard procedure that has been described elsewhere [5]. X-ray diffraction analysis of the dried and ground gel disclosed that the material is amorphous with respect to SiO2, although it does contain an appreciable quantity of dispersed crystalline NaNO 3. The conventional precursor was prepared by thoroughly mixing high-purity Brazilian quartz and analytical-grade Na 2CO3. Both precursors were melted at 1565°C in Pt-Rh crucibles and then poured into steel molds. The conventional glass was melted for 72 h with continuous stirring, whereas the gel glass was melted for 3 h without stirring. Chemical analyses of these glasses were carried out by dissolving crushed and ground samples, and then determining the sodium ion concentration in a calibrated atomic absorption (AA) spectrometer. From multiple determinations an absolute error of +_0.1% is estimated for the measured percentage of Na20. The determinations yielded gel glass- 18.8% and conventional glass - 19.0% Na20, by weight. No aluminum ion (0.003 wt% A1) could be detected in either glass sample with the AA spectrometer. Both glasses were formulated to have a theoretical composition of 18.97 wt% Na20. In the crystallization experiments the gel and the glasses were all heated for various times at 720°C in a tube furnace having a temperature accuracy of +I°C. The X-ray diffraction measurements were carried out on a Philips NORELCO powder diffractometer equipped with a graphite crystal monochrometer, employing CuKa radiation. The peak intensities quoted are the measured peak heights over background. Angular (20) measurements are accurate to within + 0.05 °.

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367

3. Identification of crystallization products All of the crystalline species which were observed in this study are discussed below. Denoting N for Na20 and S for SIO2, these phases (and their abbreviations in this paper) are low or a-cristobalite, a-Na2Si205 (NS2), Na6Si8019 (N3S8), and Na2Si409 (NS4). The NS4 phase was first reported by Mogensen and Christensen [6] and the N3S8 phase by Williamson and Glasser [7]. Powder X-ray diffraction data for the NS2 phase was also reported by these workers in another paper [8] where it was designated aillNa2Si2Os. Another crystal species detected in the present study, which we designate PNS3, may be similar, though not identical, to the Na2Si307 phase first reported by the above workers. Although all of these crystal species, with the possible exception of the PNS3 phase, have been previously described, the present study gives additional information regarding their formation and transformation behavior under several different conditions. The X-ray powder diffractometer patterns of the N3S8 and PNS3 phases are quite similar with many concurrent overlapping reflections, suggesting that their structures may be related. Also differences were found between previously reported angular locations and relative intensities of the reflections of the NS3 and N3S8 phases and those obtained in this study. This made the unambiguous identification of N3S8 and NS3 phases difficult. This problem was particularly acute when both crystal species formed concurrently, as was usually the case. Therefore, in order to allow positive identification and to determine relative amounts of the N3S8 and PNS3 phases from the diffractometer tracings, a detailed analysis of the assignment of all observed reflections was carried out. The results of this study are also included in this section. Accurate powder X-ray diffraction data on the various crystal modifications of silica are given in the ASTM card files. Interestingly, the only crystal species of silica which could be detected in any of our crystallized materials was a-cristobalite, even though the crystallization temperature was in the regime where a-tridymite would be expected to form. These results are in contrast to those found by other workers [6,8]. However, it should be noted that the time-temperature heat treatment conditions used in our study, as well as the glass composition were somewhat different from those employed in ref. 6 and 8. NS2: This crystal species was only detected in the crystallized gel precursor, along with a-cristobalite. Excellent agreement of the d-values and relative intensities for most of the observed reflections of this phase with those reported by Williamson and Glasser [8] for their OtllI NS2 phase was obtained. N3S8: The powder diffraction data as well as the single crystal derived space group and lattice parameter data for this phase was also reported by the above investigators [7]. It is pseudo-orthorhombic with a = 4.90 + 0.02, b = 23.4 + 0.1, c = 15.4 + 0.1 A, fl = 90.0 °. The measured d values and relative intensities (1/11) of the reflections assigned in the present study to the N3S8 phase are tabulated in table 1. Also

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G.F. Neilson, M.C. Weinberg / Crystallization of Na20 - SiO 2 gel and glass

Table 1 X-ray powder and single crystal d spacings for N3S8 d

1/11

dhk t

(hkl)

d

1/11

dhk t

(hkl)

11.8 7.70 6.45 5.853 5.492 5.005 4.685 4.481 4.29 4.146 3.891 3.851 3.782 3.646 3.449 3.378 3.098 3.043 2.970 2.82 2.716

10 20 5 5 20 40 20 20 10 15 20 10 30 100 60 15 10 50 40 5 10

11.7 7.70. 6.43 5.85 5.48 5.01 4.68 4.48 4.29 4.15 3.90 3.86 3.78 3.65 3.45 3.38 3.10 3.05 2.97 2.82 2.72

020 002 022 040 032 013 050 051 033 130 122 043 061 141 034 142 152 160 054 134 171

2.619 2.587 2.538 2.445

2 5 15 30

2.38

5

2.342 2.31

5 2

2.265

5

2.242

5

2.179

15

2.110 2.049 1.992 1.935 1.909

15 10 5 10 10

2.62 2.59 2.54 2.45 2.44 2.38 2.37 2.34 2.32 2.31 2.27 2.26 2.24 2.24 2.18 2.17 2.11 2.05 1.99 1.94 1.91

163 115 083 200 036 145 221 0.10.0 093 231 075 116 174 0.10.2 136 223 1.10.0 0.11.2 057 0.12.1 215

given in table 1 are c o r r e s p o n d i n g d values c a l c u l a t e d b y indexing an o r t h o r h o m b i c unit cell having the N3S8 crystal lattice p a r a m e t e r s q u o t e d above. A s a t i s f a c t o r y m a t c h b e t w e e n m e a s u r e d a n d c a l c u l a t e d d values for all o b s e r v e d p o w d e r reflections c o u l d b e o b t a i n e d , which indicates that all of o u r p o w d e r results are c o m p a t i b l e with the single crystal d a t a for N3S8. W e n o t e that the o b s e r v e d reflection having d = 5.85 A might b e e r r o n e o u s l y a t t r i b u t e d to the s t r o n g reflection of "y-NS2 having d = 5.90 ,~ (ref. 8) a n d thus be incorrectly i n t e r p r e t e d as an i n d i c a t i o n of the presence of a small p r o p o r t i o n of this l a t t e r phase. Also, when the e x p e r i m e n t a l d a t a of table 1 are c o m p a r e d to the p o w d e r d a t a values r e p o r t e d b y W i l l i a m s o n a n d Glasser, several discrepancies are f o u n d in p e a k assignments, a n d in p e a k intensities a n d positions. F o r instance, the d values of 10.70 a n d 7.14 A that were r e p o r t e d for this p h a s e are i n c o n s i s t e n t with the single crystal lattice p a r a m e t e r d a t a a n d m a n y i n d i c a t e misassignment. PNS3: Several glass s a m p l e s which were h e a t - t r e a t e d at 720°C f o r m e d a p h a s e whose p o w d e r p a t t e r n a p p e a r s quite similar to one f o u n d b y W i l l i a m s o n a n d G l a s s e r for the lower t e m p e r a t u r e NS3 phase. However, a c o m p a r i s o n b e t w e e n c o l u m n s 1 - 2 a n d 3 - 4 of table 2 indicates t h a t some differences exist b e t w e e n the d-spacings a n d intensities of these two patterns, a n d hence we d e s i g n a t e the p h a s e which we o b s e r v e d as PNS3. It is difficult to ascertain if N S 3 a n d P N S 3 are different phases, or if they are identical a n d the d i s c r e p a n cies a l l u d e d to a b o v e are m e r e l y due to e x p e r i m e n t a l artifacts. I n the fifth

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369

Table 2 d spacing data for PNS3 and NS3 Powder data

Calculated

PNS3

NS3

d

1/11

10.07 6.015 5.071 4.87 4.681 masked 3.949 3.840 3.77 3.445 3.387

d

10 5 20 2 50 10 60 10 90 100

-

10 10 5 10 5 20 10

3.247

3.006 2.90 2.87 2.705 2.650 2.62

5 15 2 5 10 2 10 5 5

-

1.91 1.876 1.777

column

10 5

of

table

w w s m

3.87 3.79 3.46 3.41

s vw vs vs

3.31

m

2.86 2.66 2.63 2.56 2.47 2.42 2.35 2.23 2.14 2.01 1.971 -

vw

d

10.3 6.20 5.15 4.72 3.84 3.43 3.40

10.15 6.015 5.071 4.681 4.250 3.946 3.848 3.812 3.439 3.382

-

1.921

w

vw vw vw vw vw

2

the

However,

3.272 3.008 2.904 2.857 2.703 2.647 2.628

2.00 1.96 1.92 1.92 1.87 1.79 1.78

1.998 1.954 1.935

ms

d values

calculated

d a t a f o r N S 3 (8) ( o r t h o r h o m b i c

perfect accord with our powder

3.25 2.84 2.71 2.68 2.62 2.58 2.45 2.35 2.13

mw vw

c = 2 0 . 6 ,~) a r e l i s t e d . I t s h o u l d b e n o t e d predicted.

PNS3

d

w vw vw

1.787 -

20

parameter

5.11 4.94 4.72 4.08

NS3

-

-

2.53 2.457 2.42 2.337 2.126 2.088 2.00l 1.962 1.936

I

pattern,

if we assume

from

the

2.536 2.458 2.340 2.125

1.911 1.879 1.781 1.774

single crystal

lattice

u n i t cell w i t h a = 6.50, b = 4.90, a n d that these d values are also not in with many

that the PNS3

observed phase

reflections not

is m o n o c l i n i c

with

a = 6.02, b = 4.68, c = 2 0 . 3 0 ,~ a n d fl -- 9 2 . 0 ° , t h e n t h e p o w d e r p a t t e r n r e s u l t s for PNS3 may be quite well accounted

for (compare

columns

1 and 6 of table

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G.F. Neilson, M.C. Weinberg / Crystallization of Na20-

SiO 2

gel and glass

Table 3 X-ray powder data for NS4 Neilson-Weinberg

Mogensen-Christensen

d

1/11

d

I

4.585 4.238 3.898 3.560 3.289 3.176 2.861 masked 2.607 2.473 2.397 2.373 2.013 1.948 1.751

100 10 20 90 5 40 15

4.60 3.90 3.57 3.185 2.66 2.609 2.469 -

m s m w w w m -

2 5 2 5 10 10 15

2). Unit cells of higher s y m m e t r y were found to be inadequate to account for the positions of the major observed reflections. Thus, in light of the fact that the characteristics of our powder pattern do not show a good correspondence with those found for the NS3 single crystal, and that they are compatible with the crystal unit cell proposed above, it is unlikely that PNS3 is identical with the latter phase. NS4: This is a metastable crystal species reported by Mogensen and Christensen [6]. T h e y determined its powder diffraction pattern by inference when it was present in relatively large amounts along with other crystal phases. Their X-ray p o w d e r results are reproduced in the last two columns of table 3. T h r o u g h two-stage heat treatments, this phase was well developed in our glasses without the concurrent development of significant NS3 and N3S8. The diffraction peaks we obtained for this phase (also shown in table 3) are in excellent agreement with those reported by Mogensen and Christensen, with the exception of a discrepancy in intensities found for the 3.90 ,~ peak.

4. Results and discussion The results of our crystallization studies are succinctly presented in table 4. A l o n g the top portion of this table indication is given of the length of time the samples were heated. The designation M refers to gel glass and B to batch glass. The column on the left specifies the various crystalline phases. The abbreviations (S), (G), and (P) refer to a surface slice of the bulk glass, the g r o u n d glass and the precursor gel, respectively. A semi-quantitative evaluation of the degree of crystallization is made employing a scale ranging from 0

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G.F. Neilson, M.C Weinberg / Crystallization of Na20-SiO 2 gel and glass

Table 4 Crystal species present in gel and glasses after heating at 720°C 5h ot-C (S) (G) (P) NS2 (S) (G) (P)

7h

M

B

M

2 3 5

2 3

. -

0 0 4

0 0

0 .

9h B 3 .

.

16h

M

B

M

B

M

B

3

3

4 5 .5

3 4

3 5 5

2 4

0

0 0

0 0

0 0 4

0 0

. -

0 .

0 .

.

-

66h

-

4

PNS3

(S)

1

a

-

(G)

4

4

.

(P) NS4 (S) (G)

0

0

-

1 0

0 0

.

(P)

N3S8 (S) (G) (P)

0

2 1 0

3

3

.

.

3 .

1 . -

3

4

4

0

5

4

-

0

0 0

4 .

3

3

.

-

0 0

4

.

-

2 .

1 .

. -

5 0

5 0

0

1

3 3 1

2 3

4

2

0 0

0

2 3 2

2 3

(none) to 5 (very large a m o u n t ) . D a s h e s i n d i c a t e t h a t no i n f o r m a t i o n was obtained. T h e m o s t striking feature of these results p e r t a i n s to the crystallization of the p r e c u r s o r gel. Its p a t t e r n s o f crystallization, n a m e l y the crystalline phases f o r m e d a n d the rates of crystallization, differs significantly from all o t h e r types o f samples. F o r example, o n l y in the p r e c u r s o r gel was the e q u i l i b r i u m NS2 p h a s e observed. F u r t h e r m o r e , the n o n - e q u i l i b r i u m P N S 3 a n d N S 4 phases were never f o u n d as crystallization p r o d u c t s u p o n h e a t treating the gel. T h e rate of cry'stallization in the p r e c u r s o r is larger than in o t h e r samples. I n s p e c t i o n of the u p p e r l e f t h a n d c o r n e r of table 4 shows that a very large a m o u n t of a - c r i s t o b a l i t e is f o r m e d when the gel p r e c u r s o r is h e a t e d for 5 h. By contrast, o n l y small a n d m o d e r a t e a m o u n t s o f a - c r i s t o b a l i t e are f o r m e d in the b u l k s a m p l e s a n d g r o u n d glass, respectively, w h e n they are h e a t e d for this time period. It is clear f r o m these results that the u n i q u e crystallization b e h a v i o r of the p r e c u r s o r c a n n o t be solely a t t r i b u t e d to its p o w d e r e d f o r m a n d it indicates p o t e n t i a l m i c r o s c o p i c structural differences b e t w e e n the gel a n d b o t h the b a t c h a n d gel glasses. E v i d e n c e for such structural m o d i f i c a t i o n s has b e e n offered b y M u k h e r j e e [9] for a gel in the N a 2 0 - B 2 0 3 - S i O 2 system a n d b y Y o l d a s [10] in the case o f silica. F u r t h e r m o r e , it has been a r g u e d b y Y o l d a s [11] a n d b y W i l l i a m s o n a n d G l a s s e r [8] that the f o r m a t i o n of n o n - e q u i l i b r i u m crystalline structures in glasses is quite sensitive to glass structure. The reasons for the

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G.F. Neilson, M.C. Weinberg / Crystallization of Na20- SiO2 gel and glass

formation of those specific phases which are observed in the gel are not well understood since the precise influence of glass structure upon stable or non-equilibrium crystalline phase formation is unknown. However, the rapid rate of a-cristobalite crystallization and the formation of the equilibrium NS2 and the very stable non-equilibrium a-cristobalite in the gel appears to indicate that the free energy barriers to crystallization are somewhat lower here than in the glasses. In general, the gel and batch glass crystallization patterns are similar. However, it is apparent that crystallization rates and the amount of crystalline material formed tends to be somewhat larger in the gel glasses. One striking observation is the absence of PNS3 phase in the ground gel glass at longer times. The reason for the disappearance of this phase is not known. It is also of interest to compare the surface crystallization in the bulk samples to the crystallization process in the ground samples. Except for the provisos mentioned previously with regard to d-spacing specifications, our results for the bulk sample crystallization behavior are generally not inconsistent with those found by Mogensen and Christensen [6] for their composition N20. From an inspection of table 4, one observes that the NS4 phase does not form in ground samples. Mogensen and Christensen found that the NS4 phase, unlike the other soda-silica phases which form at the surface and grow interdendritically, forms at the interface of the advancing front and the glassy region late in the crystallization sequence. This observation could explain the absence of NS4 phase in the ground samples. The typical particle size of the ground sample was under 0.1 mm. Thus, for most particles which crystallized one would expect the crystallization front to have advanced throughout the dimension of the particle on a time scale shorter than the incubation time for formation of NS4 phase. Since the NS4 phase, apparently, must form at the interface of the crystallization front and the glassy phase, this crystalline phase does not form under these circumstances. On the other hand, the NS3 phase, which appears in both bulk and ground samples, was noted to form at the surface and grow interdendritically [6]. The core sections of M and B bulk glasses which were heated for long tirhes (16 h and 64 h) were also examined. In all cases only a-cristobalite and N3S8 phases were observed. This behavior is in contrast to that observed in ref. [6]. Mogensen and Christensen found that in N20 (the 20% soda composition) only small amounts of N3S8 were formed and NS4 phase grew at a rapid rate after formation. However, the latter authors observed that a mixture of N3S8 and cristobalite grew at a rapid rate when a 22% soda sample was heated at 750°C. Although the composition used in the present study is closer to N20 and all samples were heat-treated at 720°C, other factors may have been operative causing a crystallization history more reminiscent of N22. For example, water content, impurity concentration, and glass preparation procedures may all influence crystallization processes. In summary, with the exception of PNS3 ground glass behavior, gel glasses crystallized faster than ordinary glasses and produced a greater volume frac-

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373

tion of crystals. However, the phases produced in both cases were identical and the differences in crystallization behavior were not dramatic. In contrast, the precursor gel crystallized in a unique manner, yielding large amounts of the most stable phases. We have stressed previously [3,5] that gel glasses, in some respects, behave differently from their counterparts produced by ordinary methods. We have demonstrated that the thermodynamics and kinetics of liquid immiscibility in the gel glass of this composition are quite different from those of the ordinary glass. This difference may be partially attributed to the enhanced OH content of the gel glass. Similarly, the enhanced rate of crystallization of the gel glasses observed here may be in part due to an elevated water content. On the other hand, the crystallization scheme of the gel precursor was qualitatively different from that of either gel or batch glass. It is unlikely that this divergence may be solely attributed to water content, but rather reflects structural differences between the gel and glass. Mukherjee has observed that the IR absorption band of the Si-O-Si stretching vibration is shifted from 1100 cm -a (where it occurs in vitreous silica) to anywhere from 1080 to 1000 cm -1 in the gel, depending upon preparation procedure [9]. These shifts are indicative of the occurrence of different structural units in the gel. For example, it is possible that a broad distribution of chain lengths occurs in the gel in contrast to the monolithic three dimensional network existent in the glass. If this were the case, then it is plausible to expect that structural rearrangements could occur more easily in the gel than in the glass. Thus, crystallization of the more thermodynamically favorable crystalline phases could take place in the former material with less impedance. Yoldas [10,11] has demonstrated that relatively minor changes in the gel polymerization procedure can lead to significant structural differences in the polymerized gel. Furthermore, he observed that such structural modifications persist in the gel glasses, even when the latter are produced by high temperature melting procedures. Yoldas finds that these structural variations in the gel glass in turn lead to deviations in glass properties and crystallization behavior when ordinary batch glass is taken as the norm. Yoldas' findings are in accord with out previous results [3,5] concerning phase separation behavior, save one significant feature. While Yoldas has obtained direct experimental evidence for structural variations in the gel prepared silica glass, structural differences between gel and ordinary soda-silica could not be detected in our studies. We have compared the IR spectra of the gel prepared and ordinary glass in the 4-25 /Lm region, and found no difference in the spectral patterns obtained. Of course, in the shorter wavelength region differences do exist which reflect the difference in hydroxyl incorporation in the glasses. This may account for the qualitative similarity in crystallization behavior in the present study between the conventional glass and the gel glass made with NaNO 3. In the studies by Yoldas [10,11] where differences in oxygen equilibrium and crystallization behavior were noted, the gel-derived starting materials were prepared from all metal-organic precursors.

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5. Summary We have studied the crystallization behavior of a 19 wt% soda silica gel, gel glass, and ordinary glass. The ordinary and gel glasses exhibit qualitatively similar crystallization behavior, but the volume fraction of crystallites found in the gel glass is generally somewhat greater than that found in the ordinary glass when b o t h are subjected to identical heat treatments. The soda-silica gel, however, exhibits a unique crystallization behavior, with the appearance of different phases in significantly different amounts. This behavior probably reflects the sharply different structural nature between the gel and the glasses of b o t h types. The ,authors gratefully acknowledge the financial support for this work provided by the National Aeronautics and Space Administration under Contract No. NAS7-100. Also, we are indebted to G a r y Smith and Kathleen Baird for sample preparations and X-ray diffraction measurements, respectively.

References [1] S.P. Mukherjee, J. Zarzycki and J.P. Traverse, J. Mat. Sci. 11 (1976) 341. [2] S.P. Mukherjee, J. Zarzycki, J.M. Badie and J.P. Traverse, J. Non-Crystalline Solids 20 (1976) 455. [3] M.C. Weinberg and G.F. Neilson, J. Mater, Sci. 13 (1978) 1206. [4] S.P.iMukherjee and J. Zarzycki, J. Amer. Ceram. Soc. 62 (1979) 1. [5] G.F. Neilson and M.C. Weinberg, Proc. Materials Research Society Symp. on Materials Processing in the Reduced Gravity Environment of Space, Vol. 9, ed., G.E. Rindone (North-Holland, New York, 1982) p. 333. [6] G. Mogensen and N.H. Christensen, Phys. Chem. Glasses 22 (1981) 17. [7] J. Williamson and F.P. Glasser, Science 148 (1965) 1589. [8] J. Williamson and F.P. Glasser, Phys. Chem. Glasses 7 (1966) 127. [9] S.P. Mukherjee, Proc. Int. Conf. Frontiers of Glass Science, eds., J.D. Mackenzie and J.R. Varner (UCLA, July 1980); J. Non-Crystalline Solids 42 (1980) 447. [10] B.E. Yoldas, J. Non-Crystalline Solids 51 (1982) 105. [11] B.E. Yoldas, J. Amer. Ceram. Soc. 65 (1982) 387.