]OURNAL OF
I,I,II ELSEVIER
Journal of Non-Crystalline Solids 177 (1994) 9-25
Changes in air-exposed fracture surfaces of silicate glasses observed by atomic force microscopy Yoshihisa Watanabe a,* Yoshikazu Nakamura a J.T. Dickinson b, S.C. Langford b a
Department of Materials Science and Engineering, National Defense Academy, 1-10-20Hashirimizu, Yokosuka, Kanagawa 239, Japan b Department of Physics, Washington State University, Pullman, WA 99164-2814, USA
Abstract
Atomic force microscope images of fracture surfaces of soda-lime glass, barium-borosilicate glass, and fused silica, fractured in low vacuum and subsequently exposed to humid air are reported. The observations reveal that: (1) soda-lime glass fracture surfaces exposed to air develop swellings 50-70 nm high after three days, while vacuumstored samples show protrusions 10 nm high; with continued exposure to humid air, these swellings disappear and cone-like structures are formed; (2) barium-borosilicate fracture surfaces exposed to air develop relatively small numbers of crystalline protrusions typically 65 nm high after 3 days, while no similar features are observed on vacuum-stored material; and (3) fused silica fracture surfaces exposed to humid air for 3 days show no significant surface features compared with vacuum-stored material. The nm-scale structures observed on air-exposed fractured surfaces of soda-lime silica and barium-borosilicate are attributed to interactions between alkali and/or alkalineearth cations in the material and water from the air.
1. Introduction
Observations of fracture surface topography (fractography) have long played an important role in studies of fracture behavior [1,2]. M i c r o - m e ter-sized features can usually be studied by scanning electron microscopy (SEM). Both scanning tunneling microscopy (STM) and atomic force microscopy (AFM) have the potential to extend this type of characterization down to sub-nm scales, although surface roughness often limits the obtainable resolution.
* Corresponding author. Tel: +81-468 41 3810. Telefax: +81-468 44 5910.
In previous work, we have reported STM and A F M observations of metallic glasses [3-5] and silicate glasses [6] fractured under high-strain-energy conditions (rapid, unstable crack growth). STM images of fracture surfaces on as-cast metallic glasses showed nm-scale steps produced by the intersection of slip bands with the surface [4], as well as larger vein and groove features. By contrast, on fracture surfaces of annealed metallic glass, A F M revealed many pyramid-like features (not observed by SEM due to their small size), which we attribute to fracture along the edges of crystallites produced during heat treatment [5]. STM observations of gold-coated fractured surfaces of s o d a - l i m e glass and fused silica also showed a variety of nm-scale features in the mir-
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Y. Watanabe et al. / Journal of Non-CrystaUine Solids 177 (1994) 9-25
10
weight (~ 50 gm)
platform
sample
",4.
"d
Fig. 1. Schematic diagram of the double torsion specimen geometry for slow crack growth used in this study.
for region attributed to crack fingering and branching [6]. Differences in the local deformation behavior between soda-lime glass and fused
silica samples were clearly discerned in the STM images. In the present work, we describe AFM observations of soda-lime glass fracture surfaces exposed to high humidity. These surfaces show a variety of features which develop over the course of hours and days. Soda-lime glasses are known to interact with water and corrode in aqueous solutions [7-9]. Although the corrosion mechanisms are complex, it is well established that water leaches alkali cations from alkali-containing glasses, forming gel-like products on the surface [10]. Glass fracture surfaces represent reproducible, relatively 'pristine' surfaces on which to view the growth of features due to these interactions. Further, the fracture process itself may activate the surface for reactions with water vapor. For comparison purposes, we also show AFM images of barium-borosilicate glass and fused silica fracture surfaces exposed to air, and control samples of all three materials stored in vacuum.
¢0
Fig. 2. AFM image of the fracture surface of a soda-lime glass surface exposed to air for about 3.5 days, showing many swellings of various shapes.
Y. Watanabe et al. / Journal of Non-Crystalline Solids 177 (1994) 9-25
The reaction of atmospheric water and other species with glass surfaces is of considerable practical importance in the durability of glass containers and other structures [11]. Under ambient conditions, a hydrated film is formed on the surface which can serve as a reservoir of chemical reactive species and can promote the growth of microcracks upon the application of stress [12]. Adhesion to glass surfaces is strongly influenced by surface reactions involving water [12], which is an important issue in the manufacture of fiber optic cables and automobile safety glass, among other products.
2. Experiment Three silicate glasses were studied: a soda-lime glass, a barium-borosilicate glass, and fused sil-
11
ica. Soda-lime glass samples were prepared from commercial plate glass. Barium-borosilicate samples were prepared from Corning No. 7059 glass; the nominal composition of this glass is (w%) SiO 2 48.6%, BaO 25.3%, B203 14.8% and A120 3 10.9%, with smaller amounts of Na20, CaO, and K20. Fused silica samples were prepared from Toshiba Ceramics T-4040 glass; the principle impurities in this material are A1 0.1 ppm, Fe 0.05 ppm, Na 0.05 ppm and K 0.05 ppm [13]. After the samples were cut to 75 x 25 × 1 mm 3, a 10 mm long notch was cut into one short edge of each sample with a diamond saw and a pre-crack was introduced in front of the notch. The samples were then loaded to failure in the double torsion specimen geometry, which allowed for controlled fracture at crack speeds of about 10 -3 m m / s . A schematic diagram of the apparatus is shown in Fig. 1. The samples were fractured in a vacuum
g C
0 0 0
6' 0 N
400
~
200
Fig. 3. Magnified AFM image of the region marked by the arrow in Fig. 2, focusingon an isolated, round bump, and an aggregate swelling.
12
Y. Watanabe et al. /Journal of Non-Crystalline Solids 177 (1994) 9-25
chamber maintained at a pressure of about 10 -1 Pa. This pressure is high enough to allow for controlled crack growth in fused silica and lowsodium borosilicate glasses, which require the presence of small amounts of water or other chemically active species. (Controlled crack growth in these materials is not generally observed at pressures < 10 - 3 Pa [14].) After fracture, half of each fractured sample was removed from the vacuum chamber and exposed to laboratory air. The other half was stored in vacuum until observation by AFM. The average humidity and temperature of the laboratory air was 50% and 293 K, respectively. After exposure to air, AFM observations were performed in air with a NanoScope III (Digital Instruments). Observations typically consisted of several scans at each of two widely separated areas of each surface. AFM observations of the samples stored in vacuum were completed within a few hours after removal from the vacuum system. As noted
I
150
I
I
s o d o - l i m e silico gloss
exposed to air . . . . stored in vacuurF
100 c-
50 0 0
iO0
200
300
(nm) Fig. 5. Cross-sectional profiles of the swellings observed on air-exposed soda-lime glass and the protrusion observed on the surface its vacuum-stored mate.
below, AFM images of soda-lime glass fracture surfaces stored in vacuum for long periods also show small features which appear to be due to water-glass interactions; however, these observations are complicated somewhat by possible water attack during scanning in air. The AFM was
V~
Fig. 4. AFM image of the fracture surface of a soda-lime glass surface stored in vacuum, showing many uniformly distributed protrusions.
Y. Watanabe et aL / Journal of Non-Crystalline Solids 177 (1994) 9-25
equipped with commercial silicon tips with a radius of curvature of 10-20 nm; the resolution of the resulting images was 5-10 nm in the xy plane and 0.1 nm in the z-direction.
3. Results
3.1. Soda-lime glass Fig. 2 is an AFM images of a smooth portion of a soda-lime glass fracture surface exposed to air for 3.5 days. This image shows many swellings on a relatively smooth surface. Some swellings are small, isolated and round, while others are much larger and appear to be composed of several swellings. The smaller swellings are typically on the order of 100 nm in diameter at the base of 20 nm in height. By contrast, the larger swellings are typically of the order of 300 nm in diameter
13
at the base and 70 nm in height. A magnified AFM image of the region marked by the arrow in Fig. 2 is shown in Fig. 3. The surfaces of both the small and large swellings appear to be quite smooth. These swellings are not observed on the mating soda-lime glass fracture surface stored in vacuum, as shown in Fig. 4. Instead, many minute protrusions can be seen. Note that the vertical scale of these protrusions is exaggerated in the plotted image; the relative dimensions of the protrusions on vacuum-stored versus air-exposed surfaces are shown in the cross-sections in Fig. 5. The solid line in Fig. 5 is a profile of a swelling on the air-exposed sample and the dashed line is a profile of a protrusion on the vacuum-stored sample. Although the protrusions are much smaller than the swellings, their shapes are quite similar. Further, the density of the protrusions on the vacuum-stored sample is comparable with the
IJN
Fig. 6. AFM image of a barium-borosilicate fracture surface exposed to air for about 3.5 days, showing many rectangular parallelepiped swellings.
14
Y. Watanabe et aL /Journal of Non-Crystalline Solids 177 (1994) 9-25
density of swellings on the air-stored sample, assuming that the larger swellings account for several protrusions. This suggests that the swellings are formed by the growth and aggregation of protrusion-like structures.
3.2. Barium-borosilicate glass Fig. 6 shows an AFM image of the fracture surface of a barium-borosilicate glass exposed to air for about 3.5 days. Although swellings are also observed on this surface, they are much more sparsely distributed on the surface and more uniform in size and shape. A magnified AFM image of a typical swelling is shown in Fig. 7. These swellings show a distinct, rectangular parallelepiped form also evident in the cross-sectional views of Figs. 8. The bases of the swellings are roughly square, typically 100 nm on a edge; the tops are fairly flat and roughly square, but somewhat smaller than the bases (approximately 75
nm on a edge); the height of the larger swellings in Fig. 6 is typically about 65 nm. By contrast, the fracture surface of the same glass sample stored in a vacuum is much smoother. The AFM image of Fig. 9 shows no features which may be identified with obvious swellings. (Note the reduced vertical scale of Fig. 9 relative to the vacuum-stored soda-lime glass surface shown in Fig. 4.) However, small-area scans occasionally revealed rectangular, protrusion-like features, one of which is marked by the arrow in Fig. 10. The rectangular shape suggests that it may be the nucleus of a rectangular swelling.
3.3. Fused silica Figs. 11 and 12 show AFM images of two fused silica fracture surfaces, one of which was exposed to air for about 3.5 days (Fig. 11) and the other stored in vacuum (Fig. 12). No characteristic features are observed on either surface except for a minute protrusion on the air-exposed sample.
I)M
Fig. 7. Magnified view of one of the rectangular swellings marked by the arrow in the image in Fig. 6.
Y. Watanabe et al. / Journal of Non-Crystalline Solids 177 (1994) 9-25
3.4. Evolution of fracture surface morphology during air exposure As described above, small protrusions are observed on the soda-lime silica fracture surfaces stored in vacuum, while much larger swellings are observed on fracture surfaces exposed to air. To observe more clearly the evolution of these features with progressively longer exposure to air,
B Aw"m
/
"-A' B. A-A' !00
E c
(a)
0
v
-100 I
II
0
I00 E c
0
-
1
~-~ (nm)
B-B'
0
0
0
~
11
25O
500
(nm) Fig. 8. Cross-sectional views of the rectangular swelling: (a) obtained along the line A - A ' and (b) obtained along the line B-B'.
15
AFM observations were performed on soda-lime glass fracture surfaces exposed to laboratory air for approximately 5 h, 1 day, 12 days and 19 days. Fig. 13 displays an AFM image of a fracture surface exposed to air for approximately 5 h prior to imaging. Minute protrusions are already apparent on the surface. These protrusions are less than 10 nm in height similar in height to the protrusions observed on soda-lime glass samples stored in vacuum for much longer times. This is consistent with the hypothesis that the protrusions serve as precursors to the swellings. After exposure to air for 1 day, the fracture surface is covered with branched, amoebae-like features, 10-30 nm in height, as shown in Fig. 14. These structures look liquid-like, as if they poorly wet the substrate. The response of the AFM tip to these features during scanning was suggestive of a soft, sticky texture, accounting for the fuzzy appearance of the image. This behavior is consistent with a gel-like mechanical response. When the fracture surface is left in the atmosphere for 12 days prior to imaging, much larger, ~m-sized swellings are seen on the fracture surface. A typical AFM image is shown in Fig. 15. It is notable that some swellings (marked by arrows) appear to be eroded. A small-area scan of the eroded bump along the left side of Fig. 15 is shown in Fig. 16. The eroded features clearly show a dendritic structure branching from the edge of the swelling into the interior, suggesting that growth or erosion began near the edge of the swelling. A small-area scan along the edge of a dendritic feature is imaged in Fig. 17. This image shows the boundary between the smooth surface of the swelling and the rough, angular surface of the dendritic feature. The faceted surface of the dendritic feature is suggestive of a crystalline or polycrystalline structure. A remarkable, mountain-like structure is observed at the base of the dendritic feature, where it meets the fracture surface. Fig. 18 shows an AFM image of this region. This angular, mountain-like structure is located at the end of a long ridge, which forms the principle vein of the dendritic feature. The rest of the swelling (smooth surface) and the dendritic structure lie to the left of the image.
16
Y. Watanabe et al. /Journal of Non-Crystalline Solids 177 (1994) 9-25
Fig. 19 shows an AFM image of a fracture surface exposed to air for 19 days prior to imaging. Most of the swellings have disappeared, apparently replaced by sharp cone-shaped protrusions. The distribution of the cone-shaped protrusions is not unlike that of the larger swellings observed at earlier times. We suspect that these cones are crystallites produced by the growth of mountain-like features, such as that shown in Fig. 18; the swellings are apparently consumed in the process. This possibility is suggested by the topview of Fig. 19 shown in Fig. 20, which shows ~m-sized, island-like features whose size and shape (as viewed from above) are consistent with that of the swellings observed after 12 days in air. Further, many of the island-like features are associated with one or more cones. Thus the size, shape, and distribution of these islands are consistent with identification as the remnants of the swellings. In summary, minute protrusions are created
after exposure to air for a few hours. After exposure to air for 1 day, soft, sticky structures are formed. These sticky structures become swellings after 12 days exposure to the atmosphere, and can developed dendritic features suggestive of an erosive process. Finally, the swellings disappear after 19 days exposure to the atmosphere, leaving behind cone-like structures.
4. Discussion
Immediately after fracture, air-borne water condenses onto the fresh fracture surface and will accumulate until the equilibrium rate of evaporation matches the rate of condensation. Although water condenses on the surface in a relatively pure state, it accumulates Na and other species from the glass. These impurities lower the equilibrium vapor pressure of water above the solution and thus promote further condensation. Sub-
IJN
Fig. 9. A F M image of a barium-borosilicate fracture surface stored in vacuum.
Y. Watanabe et al. / Journal of Non-Crystalline Solids 177 (1994) 9-25
17
nM
Fig. 10. Magnified A F M image of Fig. 9. The arrow indicates a protrusion-like feature suggesting a nucleus to be a rectangular parallelepiped swelling.
¢q
UN
Fig. 11. A F M image of a fused silica fracture surface exposed to air for about 3.5 days.
Y. Watanabe et al. /Journal of Non-Crystalline Solids 177 (1994) 9-25
18
sequent exchange between H ÷ ions from the water and alkali in the glass disrupts the structure of the silica network leaves the surface water enriched in O H - . In some glasses, this process produces a H-rich surface layer (a 'hydrogen glass') in which the alkali is merely replaced by H. However, in typical soda-lime silicates, the resuiting O H - ions react with dangling Si bonds to form additional silanol species [12]. Hydroxyl ions also attack intact Si-O-Si bonds, further disrupting the silica network. This process is apparently limited by the formation of a silica-rich surface layer along with a Ca-rich subsurface layer, the latter acting as a barrier to further alkali transport from the bulk. During prolonged exposure to air, reactions with atmospheric CO 2 will tend to neutralize the basic surface material, forming carbonates and
acid carbonates. Carbonates and acid salts have been observed on air-exposed surfaces of sodalime glass by X-ray photoelectron spectroscopy (XPS) [15]. As the rate of alkali incorporation into the adsorbed water drops, these reactions should reduce the pH of the adsorbed water (1) further slowing the dissolution of the silicate network by O H - and (2) promoting gel formation in the dissolved silicate material. The AFM results show a gel-like phase concentrated in patches along the surface. This non-uniformity was suggested by early XPS results on weathered sodalime silicate glasses; although lacking the spatial resolution to observe the non-uniformity directly, the intensity of the Si signals suggested that portions of the glass surface were bare [15]. The appearance of the protrusions and swellings indicate that this gel phase does not perfectly wet the
Z o o o
e~ N
IJM Fig. 12. AFM image of a fused silica fracture surface stored in vacuum, showing no characteristic features.
Y. Watanabe et al. /Journal of Non-CrystaUine Solids 177 (1994) 9-25
glass surface and pulls into droplets, forming small protrusions in the early stages of condensation and subsequently growing into micrometersized 'swellings'. As the concentration of carbonates in the adsorbed water increases, the solution may become supersaturated with respect to alkaline earths and perhaps alkalis as well. (CaCO 3 and MgCO 3, in particular, have low solubilities in water.) Assuming that nucleation sites for the precipitation or crystallization of these materials are relatively rare, significant supersaturation can result. The mountain-like feature at the base of the dendritic vein in Fig. 18 appears to be the 'seed' which initiated crystallization throughout the rest of the swelling. Subsequent AFM observations suggest that the gel-like swellings eventually collapse to form the island-like structures of Fig. 20, and that the mountain-like features continue to grow. Silicate gels typically collapse when dehydrated due
19
to the mechanical weakness of the silicate network relative to the surface tension of the fluid phase. In the present case, the crystallization of alkaline earth (and perhaps alkali) species may dehydrate the gel by removing substantial amounts of anion and cation species; the vapor pressure of the aqueous phase of the gel will then increase, leading to evaporation and dehydration. Rapid crystallization will often form dendritic structures, such as the one shown in Fig. 16, when the crystallization 'front' grows faster than the crystallizing species can diffuse through the aqueous phase. This process is responsible for dendritic patterns of crystal growth in lava flows, for instance, where the cooling lava becomes highly supersaturated in one or more species [16]. Mathematically, the process is similar to formation of branching structures during the dissolution of porous materials and during the electrical breakdown of dielectrics [17]. The observation of
|
IJM
Fig. 13. AFM imageof a soda-lime glass fracture surface exposed to air for approximately5 h prior to imaging.Minute protrusions are already apparent on the surface.
Y. Watanabe et al. /Journal of Non-Crystalline Solids 177 (1994) 9-25
20
dendritic structures suggests that the initial stages of crystallization can be quite rapid. However, depending on the kinetics of CO 2 incorporation into the adsorbed water, the subsequent collapse the gel-like structures and the deposition of carbonates at the cone-like structures may continue for days. Soda-lime glass fracture surfaces typically display enhanced alkali concentrations (relative to melt surfaces, etc.), which may contribute to the size and dramatic evolution of the surface features reported above. While melt surfaces are often depleted of alkali (and consequently are more resistant to hydration than fracture surfaces), soda-lime glass fracture surfaces typically display alkali concentrations in excess of bulk values, as verified by Auger electron spectroscopy [19] and ion scattering spectrometry [20]. Enhanced alkali concentrations increase the amount of silica that can be incorporated into the adsorbed aqueous film. Molecular dynamics simula-
tions suggest that part of this excess is due to surface restructuring. However, the intense Na emissions from soda-lime glass during the first few milliseconds after fracture in vacuum (at leat 1012 Na atoms/cm 2) indicate that significant amounts of Na are transported from the bulk to the surface [21]. Fracture-induced detects (e.g. dangling or strained bonds) may also render fracture surfaces more vulnerable to water attack. In any case, the composition and structure of newly formed fracture surfaces are strong non-equilibrium, which would enhance the surface reactivity well above what one would expect on the basis of bulk composition. Hydration in barium-borosilicate and fused silica glasses is much less extensive than hydration in soda-lime silica. Secondary ion mass spectrometry depth profiles of melt surfaces prepared in air show that the glass composition has a strong effect on the extent of surface hydration [12]. In fused silica melt surfaces prepared in air,
!
IJM
Fig. 14. AFM image of a soda-lime glass fracture surface exposed to air for approximately 1 day prior to imaging.
Y. Watanabe et al. / Journal of Non-Crystalline Solids 177 (1994) 9-25
hydration may be limited to the surface monolayer, while in typical alumina-borosilicate glasses the hydrated layer extends a few tens of nm although the degree of alkali depletion in the subsurface region can be quite dramatic. By contrast, sub-surface alkali depletion in E-glass (with a relatively high Na concentration) can extend hundreds of nm; substantial interactions of this sort are required to account for the micrometer-sized swellings observed on the soda-lime glass discussed above. Conversely, less extensive interactions on barium-borosilicate surfaces would account for the small number of swellinglike features, as well as their apparently crystalline, as opposed to gel-like, nature. (The small amount of O H - produced in surface reactions
21
would be rapidly neutralized by atmospheric CO2, producing a crystalline phase much earlier after exposure to the atmosphere; this crystalline phase is probably composed principally of barium carbonate.) Fused silica is very resistant to water attack, consistent with the apparent lack of characteristic surface features. Recent AFM observations water adsorption on soda-lime glass and silica films by Sato and Tsukamoto show that the film roughness increases with increasing relative humidity [18]. They also report localized corrosion on soda-lime silica glass in regions with extensive water adsorption. These results are consistent with our AFM observations of the soda-lime silica fracture surfaces.
O O o
IJN
Fig. 15. AFM image of a soda-lime glass fracture surface exposed to air for approximately 12 days prior to imaging. These swellings here are much larger than those after 1 day.
Y. Watanabe et aL /Journal of Non-Crystalline Solids 177 (1994) 9-25
22
5. Conclusions
Atomic force microscopy observations were performed of the fracture surfaces of soda-lime glass, barium-borosilicate glass, and fused silica samples. Nanometer-scale swellings were found on soda-lime glass and barium-borosilicate fracture surfaces exposed to air. Swellings on the soda-lime glass appear to involve a gel-like product, while the swellings on barium-borosilicate appear to be crystalline. No characteristic features were observed on the fused silica fracture surfaces, whether exposed to air or stored in vacuum. We attribute the nucleation and growth of surface features on the soda-lime glass fracture surface to: (1) water adsorption onto the glass and hydrogen/alkali exchange in the nearsurface region; (2) the reaction of solvated silanol
species to form a gel-like material which forms droplet-like swellings on the surface; and (3) the nucleation and growth of a crystalline phase or phases. The formation of these features is facilitated by the non-equilibrium composition of the fracture surface. Crystallite growth in the barium-borosilicate occurs without the formation of obvious gel-like droplet features, presumably due to the limited amount of surface hydration in this material. The limited transport of ionic species from the glass to the adsorbed water limits the amount of water which accumulates on the surface. Nevertheless, the thin hydration layer is sufficient for material transport to crystallites nucleated on the surface. Again, the non-equilibrium composition of fracture surfaces may enhance surface hydration relative to melt-formed surfaces. The lack of alkali
z c o o o
o
N
0M
Fig. 16. A magnified image of one of the swellings in Fig. 15, showing a dendritic pattern.
23
o o o ~0
JJN
Fig. 17. A small-area scan of the boundary between the dendritic feature and the swelling imaged in Fig. 16.
z t-
eD ¢D ¢D o
,ml
IJM Fig. 18. A small-area scan of the base of the dendritic structure shown in Fig. 16.
Y. Watanabe et al. /Journal of Non-Crystalline Solids 177 (1994) 9-25
24 Z
pN
Fig. 19. AFM image of a soda-lime glass fracture surface exposed to air for 19 days prior to imaging, showing sharp, cone-shaped protrusions.
•3 0 , 0
,20.0
10,0
0 0
10,0
20,0
30,0
Fig. 20. A top-view of the image in Fig. 19, showing the outline of the cone-shaped protrusions as well as what appear to be the remains of the swellings.
Y. Watanabe et aL / Journal of Non-Crystalline Solids 177 (1994) 9-25
a n d alkaline earths in the fused silica m a t e r i a l p r e v e n t s the f o r m a t i o n of gel-like or crystalline features o n fracture surfaces u n d e r the conditions of this experiment. Glass surfaces - especially fracture surfaces display u n i q u e , chemically active surfaces which are strongly reactive to a t m o s p h e r i c water. O n e may a p p r e c i a t e the difficulty of f o r m i n g a strong adhesive b o n d to a surface covered by semi-liquid droplets, such as those observed after 24 h exposure to air. Conversely, the high reactivity of these surfaces may be a d v a n t a g e o u s to b o n d form a t i o n if w a t e r reactions can be avoided or mitigated. V a l u a b l e clues as to the n a t u r e of these reactions can now be o b t a i n e d by nm-scale observations of the evolving surface morphology with p r o b e microscopies. T h e a u t h o r s t h a n k Carlos P a n t a n o for helpful discussions. This work was s u p p o r t e d by the Air Force Office of Scientific R e s e a r c h u n d e r Contract A F O S R - F 4 9 6 2 0 - 9 1 - C - 0 0 9 3 , the Ceramics a n d Electronics Materials Division of the National Science F o u n d a t i o n u n d e r G r a n t D M R 8912179, a n d the W a s h i n g t o n T e c h n o l o g y Center.
References [1] R.W. Rice, in: Fractography of Glasses and Ceramics, ed. J.R. Varner and V.D. Frechette (American Ceramic Society, Westerville, OH, 1988) p. 3. [2] R.W. Rice, in: Fractography of Ceramic and Metal Failures, ed. J.J. Mecholsky Jr. and S.R. Powell Jr. (Ameri-
25
can Society for Testing and Materials, Philadelphia, PA, 1984) p. 5. [3] Y. Watanabe, J.T. Dickinson, D.M. Kulawansa and S.C. Langford, Memo. Nat. Defense Acad. Jpn. 31 (1992) 53. [4] D.M. Kulawansa, J.T. Dickinson, S.C. Langford and Y. Watanabe, J. Mater. Res. 8 (1993) 2543. [5] Y. Watanabe, Y. Nakamura, J.T. Dickinson, D.M. Kulawansa and S.C. Langford, Mater. Sci. and Eng. A. A 176 (1994) 411. [6] D.M. Kulawansa, L.C. Jensen, S.C. Langford, J.T. Dickinson and Y. Watanabe, J. Mater. Res. 9 (1994) 476. [7] L.R. Pederson, D.R. Baer, G.L. McVay and M.H. Engelhard, J. Non-Cryst. Solids 86 (1986) 369. [8] B.C. Bunker, G.W. Arnold, E.K. Beauchamp and D.E. Day, J. Non-Cryst. Solids 58 (1983) 295. [9] D.E. Clark, M.F. Dilmore, E.C. Ethridge and L.L. Hench, J. Am. Ceram. Soc. 59 (1976) 62. [10] H. Schodze, J. Non-Cryst. Solids 102 (1988) 1. [11] L.L. Hench and D.E. Clark, J. Non-Cryst. Solids 28 (1978) 83. [12] C.G. Pantano, in: Strength of Inorganic Glass, ed. C.R. Kurkjian (Plenum, New York, 1985) 37. [13] Toshiba Ceramics catalog. [14] S.M. Wiederhorn, H. Johnson, A.M. Diness and A.H. Heuer, J. Am. Ceram. Soc. 57 (1974) 336. [15] C.G. Pantano, Am. Ceram. Soc. Bull. 60 (1981) 1154. [16] A.D. Fowler, H.E. Stanley and G. Daccord, Nature 341 (1989) 134. [17] Paul Meakin, Phase Trans. Crit. Phenom. 12 (1998) 365. [18] A. Sato and Y. Tsukamoto, J. Ceram. Soc. Jpn. 101 (1993) 400. [19] J.P. Lacharme, P. Champion and D. L6ger, Scan. Electron Microsc. (1981) 237. [20] C.G. Pantano, J.F. Kelso and M.J. Suscavage, in: Advances in Materials Characterization, ed. D.R. Rossington, R.A. Condrate and R.L. Snyder (Plenum, New York, 1983) p. 1. [21] S.C. Langford, L.C. Jensen, J.T. Dickinson and L.R. Pederson, J. Mater. Res. 6 (1991) 1358.