Journal of Non-Crystalline Solids 49 (1982) 397-412 North-Holland Publishing Company
397
T H E E F F E C T S O F S U R F A C E AREA T O S O L U T I O N V O L U M E R A T I O AND SURFACE ROUGHNESS ON GLASS LEACHING * C.Q. B U C K W A L T E R , L.R. P E D E R S O N a n d G.L. M c V A Y
Pacific NorthwestLaboratory, Richland, Washington99352, U.S.A.
The effects of surface roughness on the leaching characteristics of both a simple borosilicate and a soda-lime-silicate glass were evaluated by using five different surface preparations with a constant sample surface area to leachate volume ratio (SA/V). For the borosilicate glass, corrosion rates were accelerated as a result of surface roughness by much more than the percentage increase in surface area, but they were approximately equal to the surface area increases for the soda-lime-silicate glass. Opposite trends in the amount of selective leaching with changes in surface roughness occurred with the two glasses, in which surface layer accumulation of insoluble components played a key role. The effects of varying SA/V on leaching characteristics were evaluated for a simple borosilicate glass by using five different SA/V values for one surface preparation. Except for Si, increasing SA/V ratios resulted in both an increase in the leachate pH and a decrease in the total elemental removal. The net effect was a thinner depletion layer with larger SA/V ratios. These results are compared to those for simple silicate glasses found in the literature.
1. Introduction The influence of the ratio of the sample surface area to the volume of solution into which it is immersed on the n a t u r e a n d rate of glass corrosion has been d e m o n s t r a t e d for several simple silicate glasses in previous studies [1-6]. These m e a s u r e m e n t s are useful in evaluating potential glass compositions for glass c o n t a i n e r a n d solar mirror applications where the glasses may be exposed to large volumes or to very thin films of water. Such data are also essential in assessing the d u r a b i l i t y of glasses designed for nuclear waste c o n t a i n m e n t . Surface area to solution volume ( S A / V ) in a geologic repository will be affected b y u n k n o w n water flow rates a n d b y possible cracking in the waste glass m o n o l i t h due to thermal stresses a n d other factors [7,8]. Thus, an u n d e r s t a n d i n g of the effects of variable S A / V ratios is i m p o r t a n t in predicting behavior over the full range of possible scenarios. U n d e r static corrosion conditions, the rate of silica dissolution from simple silicate glass has been r e p o r t e d to increase with the S A / V ratio due to increases in the p H of the leachate [1-4,6,9]. H y d r o g e n ion activity is proposed as being responsible for alkali dissolution, while hydroxyl ion activity promotes * Work supported by Basic Energy Science Division of the US Department of Energy under Contract No. DE-ACO6-76RLO 1830. 0 0 2 2 - 3 0 9 3 / 8 2 / 0 0 0 0 - 0 0 0 0 / $ 0 2 . 7 5 © 1982 N o r t h - H o l l a n d
398
c.Q. Buckwalteret al. / Effects of surface area to volume ratio on leaching
attack of the silicon-oxygen covalent bond [10]. At high S A / V ratios and their normally associated high pH values, glass corrosion is thought to proceed essentially congruently; while at low S A / V and pH values, selective alkali leaching is reported to be dominant [1-4,6]. Enhanced dissolution rates with increasing S A / V ratios have also been reported for silica powder even though high pH values are not involved [5]. This indicates that more is involved than pH considerations alone. Alkali release from K 2 0 . 3 SiO 2 glass was found to be insensitive to S A / V changes in spite of strongly affected silica dissolution rates [1], indicating that generalizations cannot be made from one glass composition to another. Surface roughness has been found to have a strong influence on the rate of glass corrosion [2,4,6,9]. Induced surface roughness not only increases the surface area of the glass, but it also leads to locally high S A / V ratios within surface scratches [9]. Sanders and Hench [9] have reported a positive correlation between the severity of an abraded surface and the increase in the dissolution rate. Dilmore [4] has determined that the increased rate of reaction due to surface scratches is directly proportional to the increase in surface area of the glass and is therefore proportional to the increase in the S A / V ratio. Most investigations of the effects of the S A / V ratio on glass leaching have used powders because of the wide range of particle sizes that can be produced [1,2,6], effectively yielding large S A / V ratio variations. Some disadvantages of powders include concentration cell effects, agglomeration of particles, difficulty of surface area determinations, and potentially significant particle dimension changes during leaching [2,6,11 ]. The present study assesses the effects of surface roughness and S A / V ratio changes on the leaching of a simple borosilicate and a soda-lime-silicate glass, which represents two important classes of glass. Borosilicate glasses are prime candidates for nuclear waste encapsulation. Soda-lime glasses have found wide commercial application and have been extensively characterized. Monolithic specimens were used to avoid the aforementioned difficulties associated with powders. Inductively coupled argon plasma spectroscopy (ICP) was used to analyze leachate solutions. Solid samples were depth-profiled using secondary ion mass spectroscopy (SIMS). Polished cross sections of the leached specimens were examined with SEM.
2. Experimental This study consisted of two principal parts: (1) The surface roughness of the glasses was varied while the S A / V ratio was held constant; and (2) the S A / V ratio was varied while the surface roughness was held constant. Monolithic samples with an average geometric surface area of 3 X 10 -4 m 2, but whose surface areas were each carefully measured, were prepared from commerically obtained borosilicate and soda-lime-silicate glass. Compositions of the glasses are listed in table 1. Samples were leached under static conditions for 1, 3, 7,
C.Q. Buckwalter et al. / Effects of surface area to volume ratio on leaching
399
Table 1 Glass composition in wt% oxide Borosilicate SiO 2 B20 K 20 Na20 Li 2° A1203
Soda-lime-silicate 67.4 17.0 8.0 3.0 0.7 3.6 99.7
SiO 2 Na 20 CaO MgO
72.7 15.1 8.4 4.0
100.2
and 14 days in teflon containers at (70 -4- 1)oC. Where possible, glass specimens were suspended in solution using a teflon string, such that solution access to all sides of the sample was equivalent. The leachant was deionized water with an initial pH of 5.5 - 0 . 2 . Five different types of surfaces were prepared to examine the effects of surface roughness on glass corrosion. The specimens were either (1) abraded with 100-grit SiC sandpaper, (2) abraded with 600-grit SiC sandpaper, (3) polished with 7/~m diamond paste, (4) polished with 1/xm diamond paste, or (5) fractured. All specimens were ultrasonically cleaned in absolute ethanol to remove adhering fine glass particles. The degree of surface roughness was evaluated by using both a stylus profilometer* and an SEM ** photomicrograph of the sample cross section and a planimeter. The influence of surface area to leachate volume on glass corrosion was examined using five SA/V ratios at a constant surface roughness. Glasses polished with 7/~m diamond paste were static-leached at SA/V values of 1, 10, 50, 4000, and 16000 m - i . The high SA/V ratios were attained by sandwiching 1.25 X 1 0 - a m and 5.0 X 1 0 - 4 m platinum wire spacers between two glass samples for the 16000 m - i and 4000 m - i surface areas, respectively. After leaching for specified time periods, samples were removed and air dried for SIMS *** analysis. After pH determinations, the leachate was acidified and I C P t analysis performed. The p H values of the 4000 and 16000m - l SA/V samples were obtained with p H paper since solution volumes were too small for a pH probe. SIMS analyses were also performed on unleached samples to cheek for contamination and surface depletion of alkali ions. Neither effect was significant. SIMS analyses were performed using a rastered 5 keV argon ion gun.
* ** *** t
Sloan Dektak. Jarrell-Ash Model 975 Atom Comp. SIMS I, Physical Electronics 550 System. JEOL JSMU-3.
400
C.Q. Buckwalter et al. / Effects of surface area to volume ratio on leaching
Sputter rates are based on SiO 2 determined from calibration on standard films. All specimens were cooled with liquid nitrogen to limit alkali mobility during analysis. Sample charging was compensated using a rastered and defocused 1.5 keV electron beam. The SIMS signal was at least 50% raster-gated tc minimize unwanted influence from the edges of the sputter crater.
I I I0~
Fig. 1. SEM micrograh of soda-lime-silicate cross sections show: (a) 100-grit abrasion; (b) 600-grit abrasion; (c) fractured surface; (d) 7/~m polish; (e) I #m polish.
C.Q. Buckwalter el aL / Effects of surface area to volume ratio on &aching
401
3. E x p e r i m e n t a l results 3.1. Surface roughness
D i s s o l u t i o n rates for b o t h b o r o s i l i c a t e a n d s o d a - l i m e - s i l i c a t e glasses generally i n c r e a s e d w i t h i n c r e a s i n g s u r f a c e r o u g h n e s s . I n all cases, glasses a b r a d e d BOROSILICATE GLASS -
K
12
8
4
8
0 Si
•
: "
100 GRIT 600 GRIT 7MICRON 1 MICRON
_
0
1
3
g---
I
I
7
14
LEACHTIME, DAYS
Fig. 2. ICP leachate analysis on borosilicate glass samples. Abraded surfaces show fastest release and polished surfaces appear somewhat passivated when compared to fractured surface.
402
C Q. Buckwalter et ul. / Effects of surface area to volume ratio on leaching
with 100-grit sandpaper had the greatest corrosion rates, while the polished glasses reacted the slowest. Fractured surfaces dissolved at a rate intermediate between the 600-grit abraded and the 7#m polished samples. A strong correlation between leachate pH and dissolution rate was observed for both glasses. The extent of surface roughness induced by abrasion and polishing was determined from surface profilometer measurements and tracing SEM micrograph perimeters with a planimeter. Characteristic scratch depths were 15 #m, 3 #m, 0.06 #m and 0.008 #m for the 100-grit and 600-grit abraded, and 7/~m and 1/~m polished glasses, respectively. Cross sections of SEM micrographs of representative unleached samples are given in fig. I. Average surface area increases over those calculated from macroscopic measurements were 33% and 17% for the 100-grit and 600-grit abraded glasses, respectively. Imperceptibly small surface area increases were obtained for the polished specimens. The release of all major components of the borosilicate glass increased with increasing surface roughness. These results, normalized to the bulk composition of the glass, are given in fig. 2 for sodium, potassium, boron, and silicon. The dissolution rate of silicon varied most as a function of surface roughness with the 100-grit glasses resulting in approximately a six-fold increase over fractured samples. The leachate pH also correlated with the relative surface roughness and dissolution rates. As shown in fig. 3, the roughest surfaces resulted in the highest leachate pH values, while the fracture surfaces resulted in the lowest pH values. The spread in pH values after 14 days of leaching was approximately one unit. The most extensive selective leaching for the borosilicate glass occurred with the fractured and polished samples as shown in the SIMS depth profiles in fig. 4. Samples abraded with 600- and 100-grit sandpaper showed progressively
pH
10
8
~
~7
I
L
I
C
6
5 -4
A
T
E
•
100 GRIT
O
600 GRIT
•
7U
A
1/~
[]
FRACTURE
I
I
I
I
0 1
3
7 TIME, days
14
Fig. 3. pH of leachatesfromborosilicateglassesshowshighervalues for roughersurfaces.
C.Q. Buckwalter et al. / Effects of surface area to volume ratio BOROSILICATE
o,I
leaching
403
GLASS
K
5.0 2.0 1.0
V
0.5 0.2 0. I
r-
i0.0
--
.....
600 GRIT
------
IMICRON
.......
I MICRON
- . . . . . . . . FRACTURE I
I
I
I
I
I
I
I
I
/
~ y _~: ~ ..~:~:.:
I---
,,z, I',"
~~E Z
."'" ..y/.'."
-
2
2.0
"
1.0
~
,,z,
~
0.5 I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
Na
2.0 1.0 0.5 0.2 O.l 0.05
I
0
20
40
60
80
I00
SPUTTER TIME, MINUTES (40 nm PER MINUTE, BASED ON SiO2)
Fig. 4. SIMS depth profiles for 14-day leached borosilicate glass showing a larger depletion layer for alkalis and boron on the smoother surfaces indicating selective leaching.
less selective leaching. Boron was the most completely removed c o m p o n e n t within the leached layer, although the depletion depths of boron, sodium, and potassium were similar. Effects were similar for the s o d a - l i m e - s i l i c a t e glass in that all major c o m p o n e n t s except magnesium had e n h a n c e d release with increasing surface roughness. These components leached at essentially identical rates as shown in
404
c Q. Buckwalter et aL / Effects of surface area to volume ratio on leaching
fig. 5. The concentration of magnesium in solution was constant after approximately three days of leaching from glasses abraded with 100-grit sandpaper in spite of continued release of other components. Normalized magnesium release from 600-grit abraded samples was lower than that for silicon but greater than the magnesium release from the 100-grit abraded sample. Magnesium enrichment on the sample surface is evident from the SIMS
SODA LIME SILICATEGLASS
Na
50 40 30 20 10
Ca
50 40
~E
30
2o
~.
o
N
50
_~
40
Mg
• 100 GRIT o 600 GRIT • 7 MICRON 1 MICRON a FRACIIJRE
30 20 I0 0
Si
50
40 30 20
10
O
I
3
7
14
LEACHTIME, DAYS
Fig. 5. ICP leachate analysis on soda-lime-silicate glass samples. Abraded surfaces show significantly larger release except for magnesium, which exhibits resorption.
C.Q. Buckwalter et al. / Effects of surface area to volume ratio on leaching
405
depth profiles in fig. 6 on both the 100-grit and 600-grit abraded samples, which is in good agreement with the solution data. The SIMS data also indicate essentially congruent glass dissolution for the polished and fractured glasses. Unlike the borosilicate glass, the thickest leach layers were formed on the roughest surfaces. Calcium was depleted to much smaller depths than sodium, whereas magnesium showed no depletion from any of the samples
SODA LIME SILICATEGLASS
Na
20.0 I0.0 5.0 2.0 1.0 0.5
I
A Z LIJ (,~ p,,,
~E O I-Z O
I
I
I
I
I
t
I
I
I
I
I
I
I
I
I
I
Ca
10.0 5.0 2.0
I--(Z
1.0
z
Z
0.5
0 0
I
Mg - -
20.0 I0.0
100 GRIT 7 MICRON 1 MICRON FRACTURE
5.0 2.0 1.0
m
I
0
0
I 20
I
I
40
I
I
60
I
I 80
I 100
SPUTTERTIME, MINUTES (40 nm PER MINUTE, BASEDON SiO2)
Fig. 6. SIMS depth profiles for 14-day leached soda-lime-silicate glass showing near-congruent dissolution for smoother surfaces and magnesiumenrichment for rougher surfaces.
C.Q. Buckwalter et al. / Effects of surface area to volume ratio on leaching
406
leached 14 days. Some selective leaching of magnesium was found at shorter leaching times, however. The pH of the leachate solution generally increased with surface roughness for the soda-lime-silicate glass as is shown in fig. 7. The leachate pH of the 1 # m and 7 # m polished samples, however, rose more slowly with leaching time than did either the other soda-lime-silicate glasses or analogous borosilicate glass samples. The elemental losses follow curves clearly related to the pHversus-time dependence as can be seen in the solution data of fig. 5.
3.2. Surface area of glass to leachant volume A significant decrease in the amounts of sodium, boron, and potassium released occurred with an increase in S A / V ratio for the borosilicate glass shown in fig. 8. In contrast, the dissolution of silicon increased with increasing S A / V ratio as did the tendency toward congruent dissolution. Because of the very small volume of solution, ICP analysis was not possible for leachates from the 4000m i and 16000m i experiments. Measurements of the pH values were conducted, however, for all five S A / V ratios as shown in fig. 9. A general increase in pH with an increasing S A / V ratio occurred over the time span of these experiments. Greatest selective leaching of boron and alkali resulted when the smallest S A / V ratios were used, as revealed by the SIMS depth profiles in fig. 10. The thickness of the leached layer decreased with increased S A / V ratio, which is in agreement with solution data. The extent of depletion of sodium and boron was similar, while a lower percentage of potassium was extracted from the leached layer, although all had similar depletion depths. More than an order of magnitude difference in leached layer thickness was evident between glasses leached at the lowest and highest S A / V ratios.
11 10
SODA LIME SILICA ,1¢
O~--"
'==
6 ~_~lr
]
s
•
100 GRIT
A 10 [3 FRACTURE I
3
7 14 TIME, days Fig. 7. pH of |eachatcs from soda-lime-silicate glasses showing higher values for
rougher surfaces.
C.Q. Buckwalter et al.
/ Effects of surface area to volume ratio on leaching
407
BOROSILICATEGLASS i0
K
•
lm_1
8
o 10m- 1 ~
6
o 50m - ~ . ~
4
2 0 15
I
I
L
I
I
I
i
I
I
3
7
14
Na
12 9
N
6
z
0 B
._.i
12
3 I
Si 1.5 1.0 0.5 I
1
LEACHTIME, DAYS Fig. 8. ICP leachate analysis of S A / V borosilicate samples showing alkali and boron dissolution favored in low SA / V ratio and silicon dissolution favored in high SA / V ratios.
4.
Discussion
The dissolution of b o t h a simplified borosilicate a n d a soda-lime-silicate glass generally increased with increasing surface roughness, which is in agree-
408
C.Q, Buckwalter et al. / Effects of surface area to volume ratio on leaching BOROSILICAIE 10
o
I
I~ 50m-I
5
~
l
-
3
•
1
'100~-1
14
TIME, days
Fig. 9. pH of S A / V borosilicate data shows higher pH values at high S A / V ratios.
ment with previous studies on simple silicate glasses [2,4,6,9]. However, some differences from the literature were also found. These differences include the relation of an increase in surface area from surface scratches to the magnitude of glass corrosion, the dependence of selective leaching on the degree of surface roughness, and the suitability of 600-grid abrasion as the best surface preparation for glass durability studies. Surface scratches on the borosilicate glass led to a dissolution rate that was much higher than could be explained by an increase in surface area alone, which was in contrast to previous work [4]. An increase of 33% in surface area on samples abraded with 100-grit sandpaper resulted in a silicon dissolution increase of 600% over that of fractured samples. Similarly, a 17% increase in surface area produced by 600-grit sandpaper abrasion resulted in more than twice as much silicon in solution as was found for the fracture surface. More moderate increases were determined for the soda-lime-silicate glass. Abrasion with 100-grit sandpaper led to silicon dissolution approximately double that of the fracture surface. Samples abraded with 600-grid sandpaper showed an increase in dissolution that was no greater than the increase in surface area. The increase in dissolution resulting from rough surfaces can potentially be explained by higher pH values in the surface scratches than in the bulk solution. Sample abrasion leads to both an increase in the surface area and in the concentration of high energy and reactive sites. These can both result in enhanced and increased pH values. High localized pH values within the scratches should lead to a locally high dissolution rate of the silicate network, which has previously been observed for alkali silicate glasses [9]. The extent of magnesium enhancement on the surface of soda-lime-silicate glass as surface roughness increases (fig. 6) is an indication of increasing local pH values in support of the above arguments. These high localized pH values should then control the magnesium solubility [12].
C.Q. Buckwalter et al. / Effects of surface area to volume ratio on leaching
409
BOROSILICATE GLASS 5.0 2.0
Im -I
1.0
.....
0.5
--
0.2 0.I
I
A
I
--
I0 m'l --
.....
4,000m - I
......
16,000m-I
I
I
o
I0.0
~o
5.0
j.lil," //.i /,/,/,,.."
z
2.0 t
ii
--
1.0
o
/"
50 m-I
I
I
I
I
,'
"/
tad
0
c~
0.2
i
a
I
i
i
t
I
I
I
I
I
I
I
I
I
Na 2.0 [i '1
1.0
I: I"
/
/ ff
,"
/, i
0.5
p
0.2 0.1 0.05
I
0
I
40
I
80
120
160
200
SPUTTERTIME, MINUTES (40 nm PERMINUTE, BASEDON SiO2)
Fig. 10. SIMS depth profiles on 14-day leached borosilicate glass showing that low SA/V ratios have larger depletion depth than high SA/V ratios.
The extent of selective leaching as a function of surface roughness varied in opposite directions for the two glasses tested. Depletion layers, determined by S I M S on the borosilicate glass, decreased with increased surface roughness while leached layers on s o d a - l i m e - s i l i c a t e glass increased as a function of surface roughness. The borosilicate glass results m a y be explained by the effects of higher solution p H values which occur for rough surfaces. Higher
410
C Q . Buckwalter et aL / Effects of surface area to volume ratio on leaching
hydroxide concentrations in solution lead to enhanced silicon dissolution at the expense of the thickness of the leached layer. However, magnesium enhancement on the roughest soda-lime-silicate glass surfaces apparently slows the rate of silicon dissolution by imposing a barrier to hydroxide attack which leads to a thicker depletion layer. Assuming that leaching results for freshly fractured surfaces can be considered as the standard, abrasion by 600-grit sandpaper introduced artifacts into the leaching results. This surface treatment has been suggested as the method of choice because of the ease of sample preparation and reproducibility of results [2,6,9]. Considerably greater magnesium resorption on the abraded soda-lime-silicate surfaces than on fractured surfaces was found after leaching. In addition, dissolution rates for 600-grit abraded samples were generally larger than for fractured surfaces on both soda-lime-silicate and borosilicate glasses. Artifacts were also observed for the 1 ~m and 7 ~ m polished sodalime-silicate samples. Polishing appeared to passivate these samples tO aqueous corrosion in the beginning stages of exposure - an effect which later disappeared. These latter effects were not observed for the borosilicate glass. Effects of varying the SA/V ratio found in the present experiments on borosilicate monolithic samples are in general agreement with those of earlier investigations on simple silicate glass powders [1-4,6]. Aqueous corrosion of the simplified borosilicate glass using low SA/V ratios resulted in predominantly selective leaching, while the use of high SA/V ratios caused a tendency toward congruent glass dissolution due to increases in silica release and decreases in release of the other elements (fig. 8 and 10). Greatly accelerated corrosion rates for monolithic soda-lime-silicate glass have also been reported in a reaction chamber which maintained a thin water film on the glass [13]. These conditions, which correspond to a relatively high SA/V value, were intended to be representative of conditions that might prevail in an assembly of solar mirror panels. Based on the results from the simplified borosilicate glass used in this investigation, the effects of high SA/V conditions (such as cracks or thin films of water) would be small compared to the effects of having large volumes of water present. This is a particularly important consideration for cracks which develop in waste containment borosilicate glasses. It means that surface area increases due to cracking of a waste glass monolith do not have to be considered at full value. However, the effects of SA/V ratio variations on complex borosilicate waste glasses need to be verified since different surface layer development might occur that could alter the results. Elemental removal from the simplified borosilicate glass was strongly dependent upon SA/V ratios. However, potassium leaching from a K2 ° . 3 SiO2 glass was unaffected by varying SA/V ratios [1], while sodium and calcium dissolution from a soda-lime-silicate glass powder increased with an increase in the SA/V ratio [6]. Consideration of present and previous [1,6] results demonstrates the importance of exercising caution about using leaching results, from one glass to make generic statements about glass corrosion. Aqueous
C.Q. Buckwalteret aL / lfffects of surface area to volume ratio on leaching
411
corrosion of the latter, generally less durable soda-lime and potassium-silicate glasses tends toward congruent.dissolution even at fairly low S A / V values yielding relatively thin alkali-deficient surface zones when compared to the borosilicate glass of the present study. Thus, elevated pH values that occur at the high S A / V ratios would merely speed the rate of matrix dissolution, resulting in nearly equivalent increases in the release rates for all components, including alkalis.
5. Summary and conclusions Surface roughness leads to an increase in glass corrosion in excess of the associated increase in surface area. S A / V ratio increases within scratches in the glass caused by abrasion result in locally elevated pH values and enhanced silicon dissolution. The extent of selective leaching as a function of surface roughness is composition-dependent. A borosilicate glass had smaller amounts of selective leaching with increased surface roughness, while a soda-lime-silicate glass followed an opposite trend. Results on the latter glass are attributable to an enrichment of magnesium on the surface scratches. The effect of S A / V ratio variations on leaching characteristics of a simplified borosilicate glass was to exhibit selective leaching at low S A / V values and a tendency toward congruent dissolution at high S A / V ratios. The net effect was less leaching and a smaller reaction layer at high S A / V values. This implies that for situations involving both high and low S A / V ratios, such as cracks in a monolithic leach sample, the relative contribution from the high S A / V conditions could be small. The total alkali release from borosilicate glass decreased and the silicon release increased with increasing S A / V ratio, which is in contrast to results from soda-lime-silica glass The authors thank Allen Lautensleger for solution analysis, James Coleman for the SEM micrographs, and Valerie Coburn for experimental assistance. This work was sponsored by the Basic Energy Science Division of the U.S. Department of Energy under contract KC-02-01-03-80170.
References [1] T.M. El-Shamyand R.W. Douglas, Glass Tech. (1972) 77. [2] L.L. Hench, J. Non-CrystallineSolids 25 (1977) 343. [3] E.C. Ethridge, PhD Dissertation, University of Florida (1977). [4] M.F. Dilmore, PhD Dissertation, University of Florida (1977). [5] R.J. Charles, J. Am. Ceram. Soc. 47 (1964) 154. [6] D.E. Clark, C.G. Pantano, Jr., and L.L. Hench, Corrosion of glass (Magazines for Industry, New York, 1979) p. 37. [7] C.C. Chapman, J.L. Buelt, S.C. Slate, Y.B. Katayama and L.R. Bunnell, PNL-2904, BattellePacific Northwest Laboratory, Richland, Washington (1979).
412
C.Q. Buckwalter et al. / Effects of surface area to volume ratio on leaching
[8] S.C. Slate et al., Proc. Conf. High-level radioactive solid waste forms, NUREG/CP-0005 Nuclear Regulatory Commission, Washington, D.C., 1978. [9] D.M. Sanders and L.L. Hench, J. Am. Ceram. Soc. 52 (1973) 666. [10] C.R. Das, Theoretical aspects of the corrosion of glass (The Glass Industry, 1969) p. 422. [11] G.L. McVay and C.Q. Buckwalter, Nucl. Techn. 51 (December, 1980). [12] M. Pourbaix, Atlas of electrochemical equilibria in aqueous solutions (Cebekor, Brussels, 1974). [13] J.E. Shelby, J. Vitko, Jr., and C.G. Pantano, Solar Energy Mat. 3 (1980) 97.