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Mechanical properties evolution during sintering of optical sol-gel silica
132
Journal of Non-Crystalline Solids 121 (1990) 132-135 North-Holland
MECHANICAL PROPERTIES EVOLUTION DURING SINTERING O F O P T I C A L S O L - G E L SILICA W.L. V A S C O N C E L O S a n d L.L. H E N C H Advanced Materials Research Center, University of Florida, One Progress Boulevard #14, Alachua, FL 32615 USA
As the densification of sol-gel derived optical silica monoliths proceeds, the mechanical properties of the material change continuously, corresponding to changes in structure. As shown by flexural, uniaxial compression, diametral-compression and dynamic mechanical testing, the evolution of mechanical properties can be divided into two regions: the first region corresponds to lower sintering temperatures and is characterized by relatively little increase in strength; in the second region, at higher densification temperatures, there is a pronounced increase in strength as densification proceeds. Changes in mechanical properties with densification are best described in terms of topological parameter, y, the relative genus.
1. Introduction T h e e v a l u a t i o n o f m e c h a n i c a l p r o p e r t i e s is very i m p o r t a n t in the d e v e l o p m e n t of s o l - g e l d e r i v e d p r o d u c t s [1-3]. H o w e v e r , o n l y recently have relationships between mechanical properties and structural properties, including topological parameters, been e x p l o r e d [4-7]. T o p o l o g i c a l p a r a m e t e r s yield structural inform a t i o n n o t a v a i l a b l e f r o m the m o r e c o m m o n l y used metric p a r a m e t e r s such as v o l u m e fraction a n d surface a r e a p e r unit volume. F o r a given p o r e n e t w o r k , the c o n v e n i e n t t o p o l o g i c a l p a r a m e t e r s used to c h a r a c t e r i z e the structure are the n u m b e r of n o d e s b e t w e e n p o r e s N v, the n u m b e r of p o r e b r a n c h e s B v, the n u m b e r of s e p a r a t e p a r t s Pv a n d the genus G v [8-10]. T h e genus can be d e f i n e d as " t h e m a x i m u m n u m b e r of n o n s e l f - r e e n t r a n t closed curves which m a y b e c o n s t r u c t e d on the surface w i t h o u t d i v i d i n g it i n t o two s e p a r a t e p a r t s " [11]. Based on gas a d s o r p t i o n m e a s u r e m e n t s a n d g e o m e t r i c m o d e l i n g , t o p o l o g i c a l p a r a m e t e r s such as Bv, N v, G v a n d Pv of the p o r e structure c a n be e s t i m a t e d [4]. In o r d e r to facilitate c o m p a r i s o n s b e t w e e n different s t r u c t u r a l c o n d i t i o n s , the conc e p t of relative genus ), is i n t r o d u c e d as follows
[4]: Gv 3 ' - Go , where G ° is the genus of a d r i e d sample.
(1)
T h e s t r u c t u r a l e v o l u t i o n of s o l - g e l silica m o n o liths d u r i n g sintering c a n be d i v i d e d i n t o two d i s t i n c t regions: in the first region, c o r r e s p o n d i n g to low d e n s i f i c a t i o n t e m p e r a t u r e s , the s t r u c t u r a l p a r a m e t e r s c h a n g e relatively little with the increase in d e n s i f i c a t i o n t e m p e r a t u r e , while in the s e c o n d higher t e m p e r a t u r e region the s t r u c t u r a l t r a n s f o r m a t i o n s are very t e m p e r a t u r e d e p e n d e n t [1]. T h e objective of this w o r k is to a n a l y z e the m e c h a n i c a l p r o p e r t i e s of s o l - g e l silica m o n o l i t h s a n d to d e v e l o p r e l a t i o n s h i p s b e t w e e n those p r o p erties a n d the t o p o l o g i c a l p a r a m e t e r s .
2. Experimental procedure S o l - g e l silica m o n o l i t h s were p r e p a r e d b y acid catalysis (HNO3) of tetramethylorthosilicate (TMOS) and deionized-water (DI-water). The m o l a r r a t i o T M O S / D I - w a t e r was 1 / 1 6 . T h e samples were aged at 60 ° C for two d a y s a n d d r i e d at 1 8 0 ° C in T e f l o n ® containers. T h e s a m p l e s were d e n s i f i e d using c o n t r o l l e d h e a t i n g rates (average o f 20 ° C / h ) , a n d the m a x i m u m d e n s i f i c a t i o n temp e r a t u r e s were in the r a n g e of 5 0 0 - 1 1 0 0 ° C in a d r y - a i r ( D A ) a t m o s p h e r e , in a c h l o r i n e a t m o sphere at 1 1 5 0 ° C . F o r all s a m p l e s the h e a t i n g schedule was the s a m e a n d the h o l d i n g time at the m a x i m u m t e m p e r a t u r e was 1 h. These s a m p l e s are t e r m e d ' t y p e A s a m p l e s ' in this work. A set of silica gel s a m p l e s was p r e p a r e d in a similar
0022-3093/89/$03.50 © 1990 - Elsevier Science Publishers B.V. (North-Holland)
W.L Vasconcelos, L L
Hench / Sintering of optical sol-gel silica
manner, but the densification took place in a furnace with no flow of dry-air and open to the ambient atmosphere (OF). A third set of samples was prepared using H F as the catalyzer. This third set of samples is referred to as ' t y p e B samples'. Four-point bending tests [12] were performed in a MTS 810/442 testing machine at a cross-heat speed of 0.016 m m / m i n in ambient air. F r o m these tests the flexural modulus E b w a s calculated as follows [4]:
-
-
32Awt3 ,
(2)
where P is the load of fracture, L is the distance between the lower supporting points, A is the m a x i m u m displacement on the center of the specimen, w is the width and t is the thickness of a tested sample. Uniaxial compression [13] and Brazilian tests (or diametral-compression test) [14,15] were carried out in a MTS 810/458 testing machine at a cross-head speed of 0.02 m m / m i n in ambient air. F r o m the uniaxial compression tests, the compression modulus ( E c) was calculated as follows [4]: Ec-
Aoc &,
140"
120100 80 0
60 40
x
20
W
0
200
400
600
800
1000 1 2 0 0
TEMPERATURE(°C)
7PL 3 Eb
133
(3)
where A% is the variation of stress and Ac is the variation in the strain. F r o m the Brazilian testing, a value for tension strength o t was obtained using [151
Fig. 1. Variation of the flexural modulus as a function of densification t e m p e r a t u r e f o r t y p e A silica gels.
clamps the sample, k is the spring constant of the flexure pivots of the clamp arms, L v is the clamping distance, H is the sample width, D is the sample length and B is the sample thickness.
3. Results and discussion As the densification temperature increases the flexural modulus increases, as shown in fig. 1. For lower densification temperatures the increase in modulus is relatively small, but for higher temperatures the modulus increases more sharply. The variation of compression modulus with densification temperature is depicted in fig 2, for samples densified in a dry-air (DA) atmosphere and in a furnace with no flow of dry-air (OF). As seen in
2P ot- vDH'
(4)
where here P is the applied load, D is the diameter of the specimen and H is the length of the specimen. Dynamic mechanical tests were performed in a dynamic mechanical analyzer type DMA-982 (Dupont Instruments). The resonant frequency f0 of the mechanical system formed by the D M A and the sample is related to the Young's modulus E of the sample as follows [16]:
(4"~2f2Jo-k) ('~D 3 E= 2H( D / 2 + L v ) t - B ' ] '
a'~" .
o~ •
where Jo is the moment of inertia of the arm that
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400 600 800 TEMPERATURE(°C)
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.
.
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Fig. 2. Variation of compression modulus as a function of densification temperature for type A samples densified in dry-air (DA) and ambient (OF) atmospheres.
134
W.L Vasconcelos, L.L. Hench / Sintering of optical sol-gel silica 100
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.
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Fig. 3. Variation of tensile strength (Brazilian test) as a function of densification temperature for type A and B samples. FQ represents fused quartz samples.
fig. 2, the use of dry-air or ambient atmosphere seems to have little influence on the compression modulus of sol-gel silica in the temperature range explored. The tensile strength obtained from the Brazilian tests for type A silica gels densified in the range of 180-1150 o C is shown in fig. 3. The tensile strength increases relatively very little as the densification temperature increases from 1 8 0 ° C to about 900 o C, and increases sharply at 1150 o C. Figure 3 also shows that the tensile strength of type B silica gel samples (average pore radius of 82 .~) is smaller than for type A samples (average pore radius of 12 A). Tensile strength values of fused quartz samples are comparable to the values of type A sol-gel samples sintered at 1150 o C.
-
i
,
i
•
.
0.4
0.6 0.8 R E L A T I V E GENUS
•
.
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,
1.2
Fig. 5. Variation of the flexural modulus as a function of relative genus 7.
The variation of tensile modulus (DMA) measured in the temperature range 25-400 o C for type A samples densified in the range 1 8 0 - 1 0 0 0 ° C is shown in fig. 4. As the testing temperature increases, the tensile modulus decreases for all samples. At a given testing temperature the tensile modulus increases continuously with increasing densification temperature, and that increase is more pronounced for temperatures > 700 o C. The experimental results depicted in figs. 1 - 4 show that the strength of sol-gel silica increases as densification proceeds. Also, we suggest the presence of two distinct regions of mechanical properties behavior. In the first region, which corresponds to low densification temperatures, there is a relatively minor increase in strength with increasing sintering temperature. The strength increases considerably in the second region, at high
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'
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"
'
"
1000 1200
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Fig. 4. Variation of the tensile modulus (DMA) as a function of densification temperature for type A samples. The key indicates the testing temperatures.
0 o
0 0.0
0.2
0.4
0.6
0.8
1.0
1.2
RELATIVE GENUS
Fig. 6. Variation of the compression modulus as a function of relative genus %
W.L. Vasconcelos, LL. Hench / Sintering of optical sol-gel silica
densification temperatures. Previous studies [1-4] show that the structural evolution of sol-silica can also be divided into two regions, similar to the variation of mechanical properties. As the connectivity (as indicated by the relative genus, ~,) of the pore network decreases, the flexural modulus increases, as shown in fig. 5. Similarly, as the relative genus (T) decreases, the compression modulus increases, as depicted in fig. 6. Figures 5 and 6 indicate a relationship between the genus of the pore network and mechanical properties. It is possible that such a relationship is associated with decreasing levels of stress concentration as the number of pore branches associated with the pore nodes (pore coordination number) decreases.
4. Conclusions
With densification, the strength of optical solgel silica monoliths increases continuously, as shown by flexural, uniaxial compression, diametral-compression and dynamic mechanical testing. The evolution of mechanical properties can be divided into two regions: the first region corresponds to low sintering temperatures and is characterized by a relatively small increase in strength; in the second re#on, at high densification temperatures, there is a pronounced increase in strength as densification proceeds. We suggest that the relationship between mechanical properties and relative genus T shows that sol-gel silica strength depends on the local stress concentration associated with pore connectivity. The authors acknowledge the support of the US-AFOSR (contract no; F49620-88-C-0073). One of the authors (W.L.V.) is indebted to the support of U F M G (Federal University of Minas Gerais) and CAPES (Brazilian Agency of Post-Graduation).
135
References [1] J. Zarzycki, in: Ultrastructure Processing of Ceramics, Glasses, and Composites, eds. L.L. Hench and D.R. Ulrich (Wiley, New York, 1984) p. 27. [2] S.C. Park and L.L. Hench, in: Science of Ceramic Chemical Processing, eds. L.L. Hench and D.R. Ulrich (Wiley, New York, 1986) p. 168. [3] S.H. Wang, PhD dissertation, University of Florida (1988). [4] W.L. Vasconcelos, PhD dissertation, University of Florida (1989). [5] W.L Vasconcelos, R.T. DeHoff and L.L. Hench, in: Proc. 4th Int. Conf. on Ultrastructure Processing of Ceramics, Glasses and Composites, Tucson, AZ (Feb. 1989), eds. D. Uhlmann and D.R. Ulrich (Wiley, New York, 1990) in press. [6] W.L. Vasconcelos, R.T. DeHoff and L.L. Hench, Proc. 1st Florida-Brazil Seminar on Materials, Rio de Janeiro, Brazil (Aug. 1989). [7] W.L. Vasconcelos, R.T. DeHoff and L.L. Hench, these Proceedings p. 124. [8] F.N. Khines, R.T. DeHoff and J. Kronsbein, A Topological Study of the Sintering Process, Final Report for the US Atomic Energy Commission (University of Florida, Gainesville, 1969). [9] R.T. DeHoff, E.H. Aigeltinger and K.R. Craig, J. Microsc. 95 (1972) 69. [10] F.N. Rhines and R.T. DeHoff, in: Sintering and Homogeneous Catalysis, eds. G.C. Kuczynski, A.E. Miller and G.A. Sargent (Plenum, New York, 1984) p. 49. [11] R.T. DeHoff, in: Quantitative Microscopy, eds. R.T. DeHoff and F.N. Rhines (McGraw-Hill, New York, 1968) p. 291. [12] Testing Method for Flexural Strength, Japanese Industrial Standard, JIS R 1601-1981 (Japanese Standards Association, 1981). [13] M.F. Ashby and D.R.H. Jones, Engineering Materials 2 (Pergamon, Oxford, 1986). [14] F.L.L.B. Carneiro and A. Barcellos, Union of Testing and Research Laboratories for Materials and Structures, No. 13 (March, 1953). [15] A. Rudnick, A.R. Hunter and F.C. Holden, Mater. Res. Stand. 3 (1963) 283. [16] M.G. Lofthouse and P. Burroughs, J. Thermal Analysis 13 (1978) 439.
Journal of Non-Crystalline Solids 121 (1990) 132-135 North-Holland
MECHANICAL PROPERTIES EVOLUTION DURING SINTERING O F O P T I C A L S O L - G E L SILICA W.L. V A S C O N C E L O S a n d L.L. H E N C H Advanced Materials Research Center, University of Florida, One Progress Boulevard #14, Alachua, FL 32615 USA
As the densification of sol-gel derived optical silica monoliths proceeds, the mechanical properties of the material change continuously, corresponding to changes in structure. As shown by flexural, uniaxial compression, diametral-compression and dynamic mechanical testing, the evolution of mechanical properties can be divided into two regions: the first region corresponds to lower sintering temperatures and is characterized by relatively little increase in strength; in the second region, at higher densification temperatures, there is a pronounced increase in strength as densification proceeds. Changes in mechanical properties with densification are best described in terms of topological parameter, y, the relative genus.
1. Introduction T h e e v a l u a t i o n o f m e c h a n i c a l p r o p e r t i e s is very i m p o r t a n t in the d e v e l o p m e n t of s o l - g e l d e r i v e d p r o d u c t s [1-3]. H o w e v e r , o n l y recently have relationships between mechanical properties and structural properties, including topological parameters, been e x p l o r e d [4-7]. T o p o l o g i c a l p a r a m e t e r s yield structural inform a t i o n n o t a v a i l a b l e f r o m the m o r e c o m m o n l y used metric p a r a m e t e r s such as v o l u m e fraction a n d surface a r e a p e r unit volume. F o r a given p o r e n e t w o r k , the c o n v e n i e n t t o p o l o g i c a l p a r a m e t e r s used to c h a r a c t e r i z e the structure are the n u m b e r of n o d e s b e t w e e n p o r e s N v, the n u m b e r of p o r e b r a n c h e s B v, the n u m b e r of s e p a r a t e p a r t s Pv a n d the genus G v [8-10]. T h e genus can be d e f i n e d as " t h e m a x i m u m n u m b e r of n o n s e l f - r e e n t r a n t closed curves which m a y b e c o n s t r u c t e d on the surface w i t h o u t d i v i d i n g it i n t o two s e p a r a t e p a r t s " [11]. Based on gas a d s o r p t i o n m e a s u r e m e n t s a n d g e o m e t r i c m o d e l i n g , t o p o l o g i c a l p a r a m e t e r s such as Bv, N v, G v a n d Pv of the p o r e structure c a n be e s t i m a t e d [4]. In o r d e r to facilitate c o m p a r i s o n s b e t w e e n different s t r u c t u r a l c o n d i t i o n s , the conc e p t of relative genus ), is i n t r o d u c e d as follows
[4]: Gv 3 ' - Go , where G ° is the genus of a d r i e d sample.
(1)
T h e s t r u c t u r a l e v o l u t i o n of s o l - g e l silica m o n o liths d u r i n g sintering c a n be d i v i d e d i n t o two d i s t i n c t regions: in the first region, c o r r e s p o n d i n g to low d e n s i f i c a t i o n t e m p e r a t u r e s , the s t r u c t u r a l p a r a m e t e r s c h a n g e relatively little with the increase in d e n s i f i c a t i o n t e m p e r a t u r e , while in the s e c o n d higher t e m p e r a t u r e region the s t r u c t u r a l t r a n s f o r m a t i o n s are very t e m p e r a t u r e d e p e n d e n t [1]. T h e objective of this w o r k is to a n a l y z e the m e c h a n i c a l p r o p e r t i e s of s o l - g e l silica m o n o l i t h s a n d to d e v e l o p r e l a t i o n s h i p s b e t w e e n those p r o p erties a n d the t o p o l o g i c a l p a r a m e t e r s .
2. Experimental procedure S o l - g e l silica m o n o l i t h s were p r e p a r e d b y acid catalysis (HNO3) of tetramethylorthosilicate (TMOS) and deionized-water (DI-water). The m o l a r r a t i o T M O S / D I - w a t e r was 1 / 1 6 . T h e samples were aged at 60 ° C for two d a y s a n d d r i e d at 1 8 0 ° C in T e f l o n ® containers. T h e s a m p l e s were d e n s i f i e d using c o n t r o l l e d h e a t i n g rates (average o f 20 ° C / h ) , a n d the m a x i m u m d e n s i f i c a t i o n temp e r a t u r e s were in the r a n g e of 5 0 0 - 1 1 0 0 ° C in a d r y - a i r ( D A ) a t m o s p h e r e , in a c h l o r i n e a t m o sphere at 1 1 5 0 ° C . F o r all s a m p l e s the h e a t i n g schedule was the s a m e a n d the h o l d i n g time at the m a x i m u m t e m p e r a t u r e was 1 h. These s a m p l e s are t e r m e d ' t y p e A s a m p l e s ' in this work. A set of silica gel s a m p l e s was p r e p a r e d in a similar
0022-3093/89/$03.50 © 1990 - Elsevier Science Publishers B.V. (North-Holland)
W.L Vasconcelos, L L
Hench / Sintering of optical sol-gel silica
manner, but the densification took place in a furnace with no flow of dry-air and open to the ambient atmosphere (OF). A third set of samples was prepared using H F as the catalyzer. This third set of samples is referred to as ' t y p e B samples'. Four-point bending tests [12] were performed in a MTS 810/442 testing machine at a cross-heat speed of 0.016 m m / m i n in ambient air. F r o m these tests the flexural modulus E b w a s calculated as follows [4]:
-
-
32Awt3 ,
(2)
where P is the load of fracture, L is the distance between the lower supporting points, A is the m a x i m u m displacement on the center of the specimen, w is the width and t is the thickness of a tested sample. Uniaxial compression [13] and Brazilian tests (or diametral-compression test) [14,15] were carried out in a MTS 810/458 testing machine at a cross-head speed of 0.02 m m / m i n in ambient air. F r o m the uniaxial compression tests, the compression modulus ( E c) was calculated as follows [4]: Ec-
Aoc &,
140"
120100 80 0
60 40
x
20
W
0
200
400
600
800
1000 1 2 0 0
TEMPERATURE(°C)
7PL 3 Eb
133
(3)
where A% is the variation of stress and Ac is the variation in the strain. F r o m the Brazilian testing, a value for tension strength o t was obtained using [151
Fig. 1. Variation of the flexural modulus as a function of densification t e m p e r a t u r e f o r t y p e A silica gels.
clamps the sample, k is the spring constant of the flexure pivots of the clamp arms, L v is the clamping distance, H is the sample width, D is the sample length and B is the sample thickness.
3. Results and discussion As the densification temperature increases the flexural modulus increases, as shown in fig. 1. For lower densification temperatures the increase in modulus is relatively small, but for higher temperatures the modulus increases more sharply. The variation of compression modulus with densification temperature is depicted in fig 2, for samples densified in a dry-air (DA) atmosphere and in a furnace with no flow of dry-air (OF). As seen in
2P ot- vDH'
(4)
where here P is the applied load, D is the diameter of the specimen and H is the length of the specimen. Dynamic mechanical tests were performed in a dynamic mechanical analyzer type DMA-982 (Dupont Instruments). The resonant frequency f0 of the mechanical system formed by the D M A and the sample is related to the Young's modulus E of the sample as follows [16]:
(4"~2f2Jo-k) ('~D 3 E= 2H( D / 2 + L v ) t - B ' ] '
a'~" .
o~ •
where Jo is the moment of inertia of the arm that
O F
,-I
20 O Z
o_ ¢/)
10
tll gt.
O o
(5)
30
.
0
,
200
.
.
.
,
.
,
400 600 800 TEMPERATURE(°C)
•
.
.
1000 1200
Fig. 2. Variation of compression modulus as a function of densification temperature for type A samples densified in dry-air (DA) and ambient (OF) atmospheres.
134
W.L Vasconcelos, L.L. Hench / Sintering of optical sol-gel silica 100
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o
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80' 60
,-I
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400
,
i
600
•
i
800
TEMPERATURE
M.
•
0
1000 1200
•
0.0
.
0.2
(°C)
Fig. 3. Variation of tensile strength (Brazilian test) as a function of densification temperature for type A and B samples. FQ represents fused quartz samples.
fig. 2, the use of dry-air or ambient atmosphere seems to have little influence on the compression modulus of sol-gel silica in the temperature range explored. The tensile strength obtained from the Brazilian tests for type A silica gels densified in the range of 180-1150 o C is shown in fig. 3. The tensile strength increases relatively very little as the densification temperature increases from 1 8 0 ° C to about 900 o C, and increases sharply at 1150 o C. Figure 3 also shows that the tensile strength of type B silica gel samples (average pore radius of 82 .~) is smaller than for type A samples (average pore radius of 12 A). Tensile strength values of fused quartz samples are comparable to the values of type A sol-gel samples sintered at 1150 o C.
-
i
,
i
•
.
0.4
0.6 0.8 R E L A T I V E GENUS
•
.
1.0
,
1.2
Fig. 5. Variation of the flexural modulus as a function of relative genus 7.
The variation of tensile modulus (DMA) measured in the temperature range 25-400 o C for type A samples densified in the range 1 8 0 - 1 0 0 0 ° C is shown in fig. 4. As the testing temperature increases, the tensile modulus decreases for all samples. At a given testing temperature the tensile modulus increases continuously with increasing densification temperature, and that increase is more pronounced for temperatures > 700 o C. The experimental results depicted in figs. 1 - 4 show that the strength of sol-gel silica increases as densification proceeds. Also, we suggest the presence of two distinct regions of mechanical properties behavior. In the first region, which corresponds to low densification temperatures, there is a relatively minor increase in strength with increasing sintering temperature. The strength increases considerably in the second region, at high
30 ~"
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Fig. 4. Variation of the tensile modulus (DMA) as a function of densification temperature for type A samples. The key indicates the testing temperatures.
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Fig. 6. Variation of the compression modulus as a function of relative genus %
W.L. Vasconcelos, LL. Hench / Sintering of optical sol-gel silica
densification temperatures. Previous studies [1-4] show that the structural evolution of sol-silica can also be divided into two regions, similar to the variation of mechanical properties. As the connectivity (as indicated by the relative genus, ~,) of the pore network decreases, the flexural modulus increases, as shown in fig. 5. Similarly, as the relative genus (T) decreases, the compression modulus increases, as depicted in fig. 6. Figures 5 and 6 indicate a relationship between the genus of the pore network and mechanical properties. It is possible that such a relationship is associated with decreasing levels of stress concentration as the number of pore branches associated with the pore nodes (pore coordination number) decreases.
4. Conclusions
With densification, the strength of optical solgel silica monoliths increases continuously, as shown by flexural, uniaxial compression, diametral-compression and dynamic mechanical testing. The evolution of mechanical properties can be divided into two regions: the first region corresponds to low sintering temperatures and is characterized by a relatively small increase in strength; in the second re#on, at high densification temperatures, there is a pronounced increase in strength as densification proceeds. We suggest that the relationship between mechanical properties and relative genus T shows that sol-gel silica strength depends on the local stress concentration associated with pore connectivity. The authors acknowledge the support of the US-AFOSR (contract no; F49620-88-C-0073). One of the authors (W.L.V.) is indebted to the support of U F M G (Federal University of Minas Gerais) and CAPES (Brazilian Agency of Post-Graduation).
135
References [1] J. Zarzycki, in: Ultrastructure Processing of Ceramics, Glasses, and Composites, eds. L.L. Hench and D.R. Ulrich (Wiley, New York, 1984) p. 27. [2] S.C. Park and L.L. Hench, in: Science of Ceramic Chemical Processing, eds. L.L. Hench and D.R. Ulrich (Wiley, New York, 1986) p. 168. [3] S.H. Wang, PhD dissertation, University of Florida (1988). [4] W.L. Vasconcelos, PhD dissertation, University of Florida (1989). [5] W.L Vasconcelos, R.T. DeHoff and L.L. Hench, in: Proc. 4th Int. Conf. on Ultrastructure Processing of Ceramics, Glasses and Composites, Tucson, AZ (Feb. 1989), eds. D. Uhlmann and D.R. Ulrich (Wiley, New York, 1990) in press. [6] W.L. Vasconcelos, R.T. DeHoff and L.L. Hench, Proc. 1st Florida-Brazil Seminar on Materials, Rio de Janeiro, Brazil (Aug. 1989). [7] W.L. Vasconcelos, R.T. DeHoff and L.L. Hench, these Proceedings p. 124. [8] F.N. Khines, R.T. DeHoff and J. Kronsbein, A Topological Study of the Sintering Process, Final Report for the US Atomic Energy Commission (University of Florida, Gainesville, 1969). [9] R.T. DeHoff, E.H. Aigeltinger and K.R. Craig, J. Microsc. 95 (1972) 69. [10] F.N. Rhines and R.T. DeHoff, in: Sintering and Homogeneous Catalysis, eds. G.C. Kuczynski, A.E. Miller and G.A. Sargent (Plenum, New York, 1984) p. 49. [11] R.T. DeHoff, in: Quantitative Microscopy, eds. R.T. DeHoff and F.N. Rhines (McGraw-Hill, New York, 1968) p. 291. [12] Testing Method for Flexural Strength, Japanese Industrial Standard, JIS R 1601-1981 (Japanese Standards Association, 1981). [13] M.F. Ashby and D.R.H. Jones, Engineering Materials 2 (Pergamon, Oxford, 1986). [14] F.L.L.B. Carneiro and A. Barcellos, Union of Testing and Research Laboratories for Materials and Structures, No. 13 (March, 1953). [15] A. Rudnick, A.R. Hunter and F.C. Holden, Mater. Res. Stand. 3 (1963) 283. [16] M.G. Lofthouse and P. Burroughs, J. Thermal Analysis 13 (1978) 439.