JOURNAL OF
Journal of Non-Crystalline Solids 147&148 (1992) 213-221 North-Holland
NON-CRYffALLINE SOLIDS
Section 5. Growth reactions, densification and crystallization
Chemistry-crystallization relations in molecular mullite gels Jeffrey C. Huling and Gary L. Messing Department of Materials Science and Engineering, Pennsylvania State University, University Park, PA 16802, USA
Sol-gel chemistry profoundly affects the crystallization of molecular aluminosilicate gels. Segregation of transition alumina-yielding species during gel synthesis results in the epitaxial nucleation of spinel at 980°C. When synthesis conditions leading to alumina segregation are avoided, t-mullite crystallizes at 980°C. However, it is shown, for the first time, that these gels are phase-separated prior to crystallization by a hydrothermal reaction known as dealumination. When the molecular gels are synthesized and heated to avoid this mechanism of phase separation, the gels crystallize directly to o-mullite at 700°C. This crystallization temperature for o-mullite in aluminosilicate gels is ~ 500°C lower than those previously reported.
1. Introduction Mullite crystallization in aluminosilicate solgels occurs in several distinct temperature regimes, depending on the nature of the alumina and silica precursors and the process by which they are combined [1]. The transformations generally match those in kaolin minerals, with the lowest crystallization temperature at ~ 980°C. The ~ 980°C transformation has attracted considerable attention because it can result in pseudo-tetragonal mullite (i.e., t-mullite) ( ~ 2 A 1 2 0 3 " SiO2), a poorly-crystalline spinel ( ~ 6 A 1 2 0 2 " S i O 2 [2]), or a mixture of these two phases. Indeed, interest in the origin of the 980°C transformation temperature in kaolin minerals originally prompted the chemical synthesis of aluminosilicates. Regardless of phase composition after the 980°C transformation, heating to > 1200°C is necessary for crystallization of the stable, orthorhombic form of mullite (i.e., o-mullite, 3A1203 • 2SIO2). Chemical processing routes for mullite are commonly classified according to the assumed homogeneity of aluminosilicate mixing in the gel. Usually, 'single phase', 'polymeric', or 'molecularly mixed' gels are derived from aluminum and silicon salts or alkoxides, whose co-precipitation or co-hydrolysis ostensibly retains the intimate
nearest-neighbor homogeneity of the aluminum and silicon species mixed in solution [2-4]. These gels have been used to study phase development at ~ 980°C and have the most to offer for elucidating precursor chemistry-crystallization relationships. 'Colloidal' or 'diphasic' gels contain alumina and silica precursors that are present as discrete entities (10-100 nm) prior to heating [4,5]. Chemical reactions between the alumina and silica precursors are minimal during gelation, and at ~ 1250°C o-mullite crystallizes from a mixture of transition alumina and amorphous silica. Few definitive relations between sol-gel chemistry and mullite crystallization are known because uncertainty persists about the structural and chemical similarity of single phase gels prepared from different solution precursors. Progress is hampered by the large differences in the hydrolysis and condensation rates of dissolved aluminum and silicon species [6-8]. In effect, the early clay mineral precursors of low and variable purity, but having a common ultrastructure, were replaced in investigations by gels of high purity but having uncharacterizable and variable ultrastructures. The problem is further complicated by the inability to directly quantify the alumina-silica homogeneity of gels, so the mechanisms of crystallization in aluminosilicate gels cannot be firmly
0022-3093/92/$05.00 © 1992 - Elsevier Science Publishers B.V. All rights reserved
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J.C. Huling, G.L. Messing / Molecular mullite gels
established. To date, only the following generalities are known about chemistry-crystallization relations in molecular aluminosilicate gels: (1) 'homogeneous' alumina-silica mixing promotes crystallization of t-mullite at ~ 980°C; (2) alumina-silica homogeneity insufficient for ~ 980°C t-mullite crystallization leads to ~ 980°C formation of spinel. Hybrid gels permit more direct control over gel structure than possible in single phase gels by combining separately processed gels [9-11]. The effects of local changes in alumina-silica homogeneity on crystallization can then be determined, both by introducing known amounts of colloidal precursors into a solution-derived gel (or vice versa) and by in situ control of aluminosilicate reactions during heating. 1.1. Hybrid gels
Hybrid gels, composed of a minor fraction of a molecular gel dispersed in a colloidal gel, were originally reported for in situ homoepitaxial nucleation of mullite [9]. Upon heating, mullite crystallites form in situ at 980°C and serve as nucleation sites for the higher temperature crystallization of the colloidal gel. The sintered mullite grain sizes of the hybrid gels were reduced compared with the colloidal (unseeded) gel, as a result of the induced increase in nucleation number frequency. Additionally, the shorter diffusion distances to grain boundaries associated with the smaller grains allowed intragranular porosity, characteristic of colloidal gel-derived mullite, to be readily eliminated. An implicit assumption in the mechanism of hybrid gel crystallization is that the molecular and colloidal gel components crystallize independently except for the epitaxial nucleation of mullite. However, the extensive interfacial area between t h e gel components - not a consideration in the behavior of either gel separately - significantly influences the hybrid gel crystallization. At ~ 980°C, the molecular gel in the hybrid system does not crystallize to t-mullite seeds, but to a mixture of spinel and amorphous silica [10,11]. The preferred crystallization of spinel, rather than t-mullite, was traced to its epitaxial nucleation on
the isostructural ~/-A1203, a constituent resulting from the y-A1OOH in the colloidal gel. So while the molecular gel was originally intended to provide mullite seed crystals and epitaxially nucleate mullite crystallization in the colloidal gel matrix, the molecular gel's own crystallization to spinel was induced by the matrix. Promoting the intrinsic, direct formation of mullite in the molecular gel component of the hybrid therefore required isolating it to some extent from the colloidal gel matrix. This was accomplished by clustering the molecular gel units with excess amorphous silica to increase their size prior to incorporation into the hybrid. By reducing the interfacial area between the colloidal gel and molecular gel in this manner (type II hybrids), significantly less molecular gel was needed to reduce the grain size and to lower the crystallization peak temperature to those observed when the colloidal gel is seeded with solid mullite particles [10]. The significance of the ~ 980°C phase development change in the molecular gel component of the hybrid gels extends beyond seeding of the 1250°C o-mullite crystallization. Much has been written about t-mullite vs. spinel formation at ~ 980°C in kaolinite and aluminosilicate gels, but the important parameters have always been assumed to be the overall alumina-silica homogeneity or the extent of A I - O - S i bonding in the gel. However, the ability of as little as a few percent of boehmite-derived y-A120 3 in the molecular gel to alter phase development shows that spinel nucleation is the controlling factor [11]. Mullite crystallization is precluded by that of spinel when the nucleation density of the spinel is increased. The spinel is, in effect, seeded by y - A l 2 0 3 that locally crystallizes when aluminasilica segregation is present, even when most of the alumina and silica in the gel is mixed on a scale that would otherwise allow t-mullite growth at ~ 980°C. It is reasonable to propose that nanometerscale alumina-rich regions in any 'molecularly mixed' gel results in spinel formation. Because the enhancement of spinel nucleation associated with even a few percent segregated alumina is sufficient for spinel to dominate crystallization at
J.C. Huling, G.L. Messing / Molecular mullite gels
~ 980°C, direct t-mullite formation requires nearly complete molecular-scale uniformity. In light of such a stringent requirement, the inability of most sol-gel processes in the literature to yield substantial amounts of t-mullite at ~ 980°C is readily explained by the difficulty of achieving a n d / o r maintaining chemical homogeneity and the use of process conditions favoring alumina segregation. The favored formation of spinel in most syntheses can be interpreted in terms of those reactions and experimental conditions that lead to segregation of alumina and silica in alkoxide-derived gels [1,2,8]. The most commonly discussed factors involve the concentration, p H and rate of introduction of the water required for hydrolysis. Slowing the hydrolysis of the more reactive aluminum species, such as by adding acidic water in dilute water-in-alcohol solutions or, at the extreme, by allowing reaction with atmospheric humidity [8] over a period of several months, promotes simultaneous (rather than consecutive) incorporation of aluminum and silicon into the gel. This, in turn, impedes formation of the aluminarich spinel nuclei upon heating and allows t-mullite to crystallize at ~ 980°C. By contrast, there are numerous reports of synthesis processes in which the hydrolysis of aluminum is accelerated by adding undiluted neutral or even basic water. By promoting the formation of aluminum hydroxides (i.e., spinel nuclei precursors), it is inevitable that spinel first crystallizes when the precursor is heated to 980°C. As a consequence of the recognized effect of '-/-alumina' on spinel formation, it is now possible to predict the crystallization path at 980°C on the basis of the precursor chemistry. The complete prevention of alumina-silica segregation is especially problematic in dual alkoxide systems simply because water for hydrolysis must be added as a separate precursor. For example, even dropwise addition of water creates instantaneous, locally high water concentrations. Replacing the aluminum alkoxide with a hydrated aluminum salt such as aluminum nitrate nonahydrate ( A l ( N O 3 ) 3 . 9 H 2 0 ) homogeneously distributes water from the outset in a loosely bound form that restricts its reaction. Although additional water, basic conditions or insufficient time
215
for cohydrolysis will still result in heterogeneity sufficient for spinel nucleation, t-mullite formation at ~ 980°C has been achieved more readily from the aluminum nitrate n o n a h y d r a t e - T E O S system [2-4,9] than from any combination of aluminum and silicon alkoxides. The above discussion focussed on how the crystallization path can be directed by changes in nucleation frequencies (of spinel at ~ 980°C and o-mullite at ~ 1250°C). Interestingly, there has been virtually no effort to consider the origin of the consistency of the 980°C crystallization temperature or to question why o-mullite does not crystallize directly from the aluminosilicate gel. Indeed, these observations suggest that crystallization at 980°C is not simply a matter of nucleation and growth limitations but is controlled by other factors. Recent observations in our laboratory indicate that when alumina-silica homogeneity is maximized during gel processing, then the 980°C tmullite crystallization is limited by phase separation in the gel. Recognizing this, experiments involving gel drying, aging and heat treatment have been carried out to understand the mechanism and origin of phase separation. When phase separation is suppressed, the gel precursor transforms directly to o-mullite at 700°C. Below we discuss our preliminary experiments and interpretations concerning the direct transformation of aluminosilicate gels to o-mullite.
2. Experimental procedure Mullite crystallization at temperatures up to 980°C was investigated in two aluminosilicate gels whose processing methods differ only by an aging treatment. These gels were both derived from the same aluminum nitrate n o n a h y d r a t e TEOS molecular sol used in our earlier hybrid gel study [9]. The 'fresh' gel was prepared by rapid, dropwise drying of the molecular sol in a beaker heated to ~ 120°C. Foam-like gel pieces were then easily crushed to powder with a high purity alumina mortar and pestle. The 'aged' gel was prepared from the fresh gel by spreading the fresh gel powder in a several
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J.C Huling, G.L. Messing /Molecular mullite gels
millimeter thick layer in a partially covered 90 m m diameter container. The container was placed above deionized water in a covered beaker heated to ~ 80°C. After 6 - 8 h, water begins to infiltrate the fresh gel layer, presumably by capillary condensation. After 10-12 h, the gel layer is translucent and rubbery or leathery in texture. Water continues to be adsorbed by the gel until a clear, low viscosity sol is obtained after 36-48 h with a total weight gain of ~ 150%. The 'aged' gel was obtained by spreading the clear sol on glass plates and drying at 80°C to obtain gel flakes up to several millimeters in diameter and several micrometers in thickness. Heating of the gels was divided into calcination and crystallization steps. The gel was placed as a small mound, ~ 0.125 g, in a platinum foil pan and heated at 20°C/min to the calcination t e m p e r a t u r e and held for 1.5-15 rain. The pan and gel were then rapidly inserted into the tube furnace held at the crystallization temperature. T e m p e r a t u r e s during both steps were monitored using c h r o m e l - a l u m e l thermocouples located ~ 2 cm from the gel. T E M samples were prepared by ion milling aged gel flakes mounted on copper grids.
3. Results
3.1. Phase separation and t-muIlite crystallization The differential thermal analysis of the fresh gel shows that crystallization occurs during a single, sharp and extremely intense exotherm at ~ 980°C. X R D of the fresh gel heated to just above the 980°C exotherm reveals nearly complete crystallization to t-mullite. The formation of this metastable, alumina-rich mullite agrees with the results of all previous studies in which t-mullite has crystallized at ~ 980°C from gels, clay minerals and rapidly quenched glasses [12-15]. The microstructure of the fresh gel is shown in T E M micrographs in fig. 1. After heating at 20°C/rain to 900°C and holding for 2 h, the fresh gel remains amorphous but displays an interconnected two-phase morphology characteristic of a phase separated material. The microstructure shown in fig. l(a) is identical to those observed by Jantzen et al. [16] and attributed to phase separation in rapidly-quenched aluminosilicate glasses. Comparison with the microstructures of other amorphous aluminosilicate gels, however, is not possible because their microstructural develop-
Fig. 1. TEM micrographs of fresh molecular gel heated to (a) 900°C for 2 h and (b) 1000°C for 2 h.
J.C. Huling, G.L. Messing / Molecular mullite gels ment during heating has not been characterized by TEM. After heating at 20°C/min to 1000°C and holding for 2 h, the fresh gel is predominantly crystalline, consisting of t-mullite that has consumed the alumina-rich amorphous phase (fig. l(b)). The silica-rich phase remains amorphous and is enveloped by the metastable t-mullite. The mullite grains have impinged throughout the gel, although only two isolated grains can be seen in dark contrast in fig. l(b). An identical 'rosette' grain morphology was observed by MacDowell and Beall [17] in rapidly quenched glasses reheated for mullite crystallization, thus supporting the proposal that the microstructure observed at 900°C is in fact a result of phase separation rather than, say, microporosity. It is well established that ~ 980°C t-mullite crystallization is directly related to phase separation in rapidly-quenched aluminosilicate glasses [17,18]. Indeed, phase separation occurs in even the most r a p i d l y - q u e n c h e d aluminosilicate glasses, indicating an exceptionally high driving force for unmixing a n d / o r significant atomic mobility below the consolute temperature of the miscibility gap. By contrast, the fundamental relationship between phase separation and ~ 980°C
217
mullite crystallization has not been addressed with respect to aluminosilicate gels. Although quenched aluminosilicate glasses are always phase separated at room temperature, it should be possible to use the sol-gel transition to chemically build a multicomponent network at low temperatures that remains homogeneous prior to heating. 3.2. Direct crystall&ation of o-mullite The differential thermal analysis of the aged gel is shown in fig. 2 for a heating rate of 10°C/min. There is a prominent exotherm at 980°C, although its intensity is diminished from that observed for the crystallization of the fresh gel. More importantly, a broad and weak exotherm also appears at 847°C. X-ray diffraction of samples heated to just below and just above the 847°C exotherm demonstrates that it corresponds to crystallization of ~ 10 wt% o-mullite as indicated by the distinct (120)-(210) X R D reflections in the X-ray diffraction patterns. Because orthorhombic mullite typically forms only above ~ 1200°C, the true reduction in o-mullite crystallization temperature is > 350°C. A common practice for accentuating weak exotherms due to nucleation and growth con-
0.05
DTA - AGED GEL 10°C/min 0,04-
0,03-
0.02-
J
847°C 0.0i-
0.00-
750
e~o
8~o
~do Temperature
9~o
iobo
(°C}
Fig. 2. Differentialthermal analysis of aged molecular gel(10°C/min).
i050
J.C. Huling, G.L. Messing / Molecular mullite gels
218
0,04-
DTA - AGED GEL
'~
20°C/min 834°C
0.03-
o
c
o.o2o
o.o~
0.00
7go
860
B~o Temperature
96o
(°C)
Fig. 3. Differentialthermal analysis of aged molecular gel showing lower exothermic peak temperature with increasing heating rate.
trolled transformations is to increase the heating rate at which the D T A is performed. By increasing the heating rate, the transformation peak height increases in magnitude and shifts to higher temperature. Increasing the heating rate of the aged gel, however, shifts the initial exotherm to lower temperatures (fig. 3). Further, while the intensity of the initial exotherm is increased at the higher heating rates, the intensity of the ~ 980°C exotherm is decreased. Thus, the change in heating rate not only changes the depiction of the crystallization reaction by DTA, but, more significantly, it also changes the fundamental nature of the reaction. The reduction in the mullite formation temperature from the ~ 980°C exotherm with increasing heating rate suggests that heating the aged gel isothermally may maximize crystallization kinetics. When the aged gel is rapidly transferred to and from the furnace, the degree of o-mullite crystallization increases steadily from 10 wt% at 700°C to ~ 95 wt% at 780°C (fig. 4). The results in fig. 4 are for 5 min holds following rapid heating. Kinetic experiments demonstrate that o-mullite crystallization stops in less than 1 min, however, and no further crystaUiza-
tion occurs until the ~ 980°C exotherm is reached. The aged gel therefore crystallizes much more readily at the outset than it does after only a very short time at temperature. This behavior indicates a time-dependent change in the nature of the alumina and silica in the aged gel which is consistent with a competition between crystallizaSUB-980°C M U L L I T E C R Y S T A L L I Z A T I O N : Isothermal heat treatment - 5 minutes 1.0 0.8-
0.60.4. [] 0.2-
0.0 680
[] •
!
i
!
!
700
720
740
760
,
i
780
800
Temperature (°C) Fig. 4. O-mullite crystallization in aged molecular gels as a function of isothermal heat treatment temperature (time = 5 rain).
J.C. Huling, G.L. Messing / Molecular mullite gels
tion of stoichiometric o-mullite at ~ 700°C and phase separation which leads to crystallization of alumina-rich pseudo-tetragonal mullite at 980°C. Rapid heating alone is insufficient to prevent phase separation, as isothermal heat treatment of the flesh gel results in only a trace of o-mullite at 780°C. Instead, there must be some aspect of the gel's aging process that slows phase separation relative to crystallization.
4. Discussion
The kinetics of phase separation and crystallization in silicate glasses are greatly accelerated by increases in water or hydroxyl content [19-22]. (Note that phase separation and crystallization are avoided in gel-derived vs. melt-derived glasses by lowering the temperature of heat treatment, not by lowering the concentration of chemisorbed water.) It is, however, the interaction of this water with the gels during calcination or rapid heating, rather than the amount present that is the important variable. The chemisorbed water may be released by condensation reactions that help to establish A I - O - S i bonds, or it may attack and hydrolyze existing A I - O - S i bonds as it diffuses from the gel: OH Si
/1\
OH +
A1
> ~Si--O--AI
+ H20,
/ \ (1) OH
J
Si--O--AI
+ H20
I
> / lSi \
OH
I
+ / AI\
(2) The local partial pressure of water vapor determines the relative extent of the above reactions. Low partial pressures of water vapor favor condensation (reaction 1). This is expected in the aged gels, whose high surface area of ~ 100 m2/g a n d / o r large, open pores allow water vapor to diffuse readily. Maintenance a n d / o r formation of A1-O-Si bonds promotes o-mullite formation below ~ 980°C. By contrast, high partial pres-
219
sures of water vapor at the gel surface during heating favor hydrolysis (reaction 2). In zeolites, phase separation of aluminum species by water corresponds to the well known phenomenon called dealumination [23,24]. In the fresh gels, low surface areas of ~ 3 m2/g a n d / o r closed or narrow pores obstruct the release of water from the gel and promote hydroxyl attack of the A1O-Si bonds. The net result of hydrolyis is phase separation and the formation of only pseudo-tetragonal, alumina-rich mullite at ~ 980°C. In typical glass-ceramic systems, phase separation is induced by additives and heat treatments to increase nucleation densities. Interface created by phase separation contains high energy sites preferentially 'consumed' by nucleation, or one of the unmixed phases has a composition more closely matching that of a crystalline phase than the original homogeneous material. In gels or glasses of 3A1203.2SIO 2 composition, however, phase separation would not promote crystallization of stoichiometric o-mullite. The localized compositional changes involved in phase separation ultimately preclude formation of stoichiometric mullite in favor of a metastable alumina-rich form. Under most conditions, however, phase separation proceeds more rapidly than crystallization to reduce the high excess free energy of the homogeneous amorphous system. Nucleation and growth of stoichiometric o-mullite must be controlled by suppressing phase separation, leading to a phase separation-crystallization relationship that is effectively reversed from that in a typical glass-ceramic system. Gels must be calcined to remove volatiles prior to crystallization. Since molecular mobility and rearrangement are inherent aspects of this heat treatment, it is an opportunity for phase separation if diffusion is not limited to volatile species. When the aged gel is calcined for 15 min at 520°C, there is nearly full crystallization of o-mullite at 780°C. For a calcination temperature of 600°C, however, there is no low-temperature omullite crystallization and t-mullite crystallizes at ~ 980°C. The lower o-mullite yields that follow higher calcination temperatures or longer calcination times reflect increasing phase separation prior to the crystallization heat treatment.
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J.C. Hufing, G.L. Messing / Molecular mullite gels
p h a s e s e p a r a t i o n arising f r o m w a t e r v a p o r ind u c e d hydrolysis of A I - O - S i bonds. Thus, gel systems t h a t w e r e originally c l a i m e d to b e single p h a s e [4], a r e in r e a l i t y diphasic. By s u p p r e s s i n g this m e c h a n i s m of d e - h o m o g e n i z a t i o n , it was d e m o n s t r a t e d t h a t a t r u e m o l e c u l a r gel can directly crystallize to o - m u l l i t e at t e m p e r a t u r e s as low as 700°C, which is 500°C l o w e r t h a n o b s e r v e d for ' m o l e c u l a r ' gels t h a t first crystallize to e i t h e r spinel o r t-mullite.
Fig. 5. TEM micrograph of aged gel calcined at 550°C for 1.5 rain and 780°C for 5 min.
T h e a u t h o r s gratefully a c k n o w l e d g e f u n d i n g from the Industrial Co-op Program of the Center for A d v a n c e d M a t e r i a l s a n d t h e Division o f M a terials Research of the National Science Foundation.
References In a d d i t i o n to c h a n g e s in t h e a g e d gel's lowt e m p e r a t u r e o - m u l l i t e yield with calcination, subs t a n t i a l c o n t r o l is p o s s i b l e over t h e m u l l i t e mic r o s t r u c t u r e . T h e m i c r o s t r u c t u r e of the a g e d gel a f t e r c a l c i n a t i o n for 1.5 m i n at 550°C a n d r a p i d h e a t i n g to 780°C is shown in fig. 5. A l t h o u g h t h e s a m p l e is n o t d e n s e , its ~ 15 n m g r a i n size is t h e finest g r a i n size yet shown for fully crystalline o-mullite. This results f r o m b o t h an e x t r e m e l y high n u c l e a t i o n d e n s i t y a n d t h e a b s e n c e o f coarse n i n g as a result o f t h e e x t r e m e l y low crystallization t e m p e r a t u r e .
5. Summary C r y s t a l l i z a t i o n of spinel in m o l e c u l a r aluminosilicate gels occurs as a r e s u l t o f initial s o l - g e l c h e m i s t r y c o n d i t i o n s in which p r e f e r e n t i a l hydrolysis or c o n d e n s a t i o n of a l u m i n u m p r e c u r s o r s l e a d s to f o r m a t i o n of 7 - A 1 O O H , a n d h e n c e -y-A120 3 d u r i n g heating. This ~ - A 1 2 0 3 serves as an e p i t a c tic s u b s t r a t e for spinel crystallization. M o l e c u l a r a l u m i n o s i l i c a t e gels p r e p a r e d to avoid c h e m i c a l s e g r e g a t i o n crystallize to t - m u l l i t e at 980°C r a t h e r t h a n o-mullite. T h e crystallization o f a l u m i n a - r i c h t - m u l l i t e r a t h e r t h a n s t o i c h i o m e t r i c o - m u l l i t e in h o m o g e n e o u s m o l e c u l a r gels is a t t r i b u t e d to
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J.C. Huling, G.L. Messing / Molecular mullite gels [14] I.M. Low and R. McPherson, J. Mater. Sci. 24 (1989) 926. [15] D.X. Li and W.J. Thomson, J. Mater. Res. 6 (1991) 819. [16] C.M. Jantzen, D. Schwahn, J. Schelten and H. Herman, Phys. Chem. Glasses 22 (1981) 122. [17] J.F. MacDowell and G.H. Beall, J. Am. Ceram. Soc. 52 (1969) 17. [18] S.H. Risbud, in: Mullite and Mullite Matrix Composites, Ceramic Transactions, Vol. 6, eds. S. Somiya, R.F. Davis and J.A. Pask. (American Ceramic Society, Westerville, OH, 1990) p. 61.
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[19] M.S. Maklad and N.J. Kreidel, in: Proc. 9th Int. Congr. on Glass, Vol. 1 (Institut du Verre, 1971) p. 75. [20] C.J.R. Gonzalez-Oliver, P.S. Johnson and P.F. James, J. Mater. Sci. 14 (1979) 1159. [21] K.T. Faber and G.E. Rindone, Phys. Chem. Glasses 21 (1980) 171. [22] G.F. Neilson, M.C. Weinberg and G.L. Smith, J. NonCryst. Solids 82 (1986) 137. [23] G.T. Kerr, J. Phys. Chem. 71 (1967) 4155. [24] G.T. Kerr, J. Catal. 15 (1969) 200.