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Water diffusion into silica glass at a low temperature under high water vapor pressure
Journal of Non-Crystalline Solids 347 (2004) 211–219 www.elsevier.com/locate/jnoncrysol
Water diffusion into silica glass at a low temperature under high water vapor pressure Andrea Oehler 1, Minoru Tomozawa
*
Materials Science and Engineering Department, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY 12180-3590, USA Received 31 October 2003 Available online 22 October 2004
Abstract Water in glass has disproportionately large effects on various properties of oxide glasses, such as chemical durability and mechanical strength. Silica glass is the basis of many oxide glasses. Thus, there have been numerous studies on water diffusion into silica glasses. But most past research on water diffusion into silica glasses has been conducted at high temperatures, where water diffusion is accompanied by structural changes of the glass. In the present study, water diffusion into silica glass at low temperature, 250 C, was measured using IR spectroscopy as the main research tool. Saturated high water vapor pressure was used to increase the amount of water diffusing into the glass so that the water can be detected by the IR method after a reasonably short heat-treatment time. It was found that both water solubility and diffusion coefficient were time dependent. Furthermore, both hydroxyl and molecular water were detected in the glass. From the concentrations of hydroxyl and molecular water, an apparent equilibrium constant, K = [SiOH]n/[H2O] was evaluated. At high temperatures, water reacts with silica glass by Si–O–Si + H2O M 2SiOH, and the local reaction equilibrium has been established at the value of n being 2. In the present study of low temperature water diffusion in silica glass, unlike the local reaction equilibrium in high temperature studies, the value of n was found to be close to 1. This indicates that the two hydroxyls formed in the glass during the reaction are not independent of each other. 2004 Elsevier B.V. All rights reserved.
1. Introduction Water in glass has a disproportionately large influence on glass properties. It decreases viscosity, chemical durability and mechanical strength. Even when a glass is initially water-free, water can enter into a glass by diffusion. Silica glass (amorphous silica) is important in electronics, optics and microelectronic mechanical systems. Furthermore, it is a prototype of many silicate glasses and its properties can be used to predict properties of
* Corresponding author. Tel.: +1 518 276 6659; fax: +1 518 276 8554. E-mail address: [email protected] (M. Tomozawa). 1 Now at Intel Corp., Hillsboro, OR.
0022-3093/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2004.07.013
numerous other glasses. Also, the rate of water penetration into silicate glasses is being used as a means to determine the age of both archaeological and geological glasses [1,2]. Water diffusion coefficient in silica glass is small at low temperature, but still it can influence surface-sensitive properties of bulk glass and properties of amorphous thin films [3–5] and porous materials. Thus, it is useful to determine the water diffusion coefficient in silica glass. Most of the past research on water diffusion into silica glass was performed at high temperatures. In this study, the water diffusion coefficient into silica glass was measured at a low temperature of 250 C using infrared spectroscopy. In order to increase the signal intensity of infrared spectroscopy, the silica glass was exposed to high water vapor pressure using an autoclave.
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2. Experimental A high purity silica glass made by CVD (axial vapor deposition, AVD) for optical communication was used in the present experiment. This glass contains less than 1 ppm of water but approximately 1000 ppm of Cl. The glass samples were cut into pieces of approximately 20 mm · 20 mm · 1.3 mm using a cutting machine with a diamond blade. The 20 mm · 20 mm faces of the samples were polished using polishing papers with various grain sizes of SiC, starting with 240, 400 and 600 grit in water followed by 1000 grit SiC in oil and finally with CeO2 slurry. The polishing produces a slightly damaged surface layer [6], which was removed with etching by 10%HF–2.5%H2SO4 for 3 min at room temperature. Samples were then heat-treated with a saturated water vapor in a General Purpose Acid Digestion Bomb 4549 (Parr Instrument Company, Moline, IL), which is schematically shown in Fig. 1. The outside of the bomb is a stainless steel fixture designed to contain the high pressure. The inside of the bomb is a thick-walled Teflon vessel with a capacity of 45 ml. The bomb has a maximum operating temperature of 250 C and pressure of 122 atm. A Teflon stage held samples above the bomb floor as shown in Fig. 1. The stage allowed samples to be hydrated in saturated water vapor and not directly in the solution. The Teflon stage reduced the available volume for water and water vapor from 45 to 38.5 ml. Four milliliters of distilled water was placed in the bomb. This amount of water guaranteed that the water remains in equilibrium with saturated water vapor pressure of 39 atm at 250 C, and that water would not rise above the stage. Two or three glass samples were placed vertically in the bomb at one time and the bomb was
placed in an electric furnace kept at 250 ± 2 C. It took approximately 1 h for the contents of the bomb come up to the set temperature. After the heat-treatment for the specified period, the bomb was cooled by water for 10–15 min before it could be easily opened. The heattreatment time was 24–576 h, and the time to heat and cool the samples was less than 2% of the heat-treatment time. The samples were washed with ethanol after the hydration treatment. Infrared spectra of the samples were obtained using a Fourier transform-infrared (FTIR) spectrophotometer; the IR absorbance was obtained in nitrogen atmosphere as a function of heat-treatment time. The IR absorbance was converted to water concentration using BeerÕs law and the appropriate extinction coefficient. For many hydrated glass samples, the absorbance was measured as a function of the diffusion depth. For this purpose, IR absorbance was obtained after successive etching of the surface layer. Etching solutions used were 150 ml of 5%HF–2.5%H2SO4, 10%HF–2.5%H2SO4 at room temperature and 2 N NaOH at 80 C. Different etchants were used to make sure that the results are not artifacts of the etching procedure employed. The etched depth was estimated from the weight loss, surface area, and density of the glass specimen. The obtained residual absorbance vs. the etched depth was fitted with a polynomial and was differentiated to obtain the water concentration depth profile. The effective water diffusion coefficient, Deff, was obtained by two different methods. One was to compare the experimental concentration depth profile obtained after time, t, with the theoretical concentration profile given by pffiffiffiffiffiffiffiffiffi Cðx; tÞ ¼ C s ½erfcðx=2 Deff tÞ; ð1Þ where C(x, t) is the concentration at the depth x and heat-treatment time, t, and Cs is the surface concentration, which should be time independent. Erfc is a complementary error function. The values of Cs and Deff, which produce the best fit to the experimental concentration depth profiles, were obtained. The other method was to determine the diffusion coefficient from the time dependence of the water uptake, pffiffiffiffiffiffiffiffiffiffiffiffiffi pffi M t ¼ 2C s ð Deff =pÞ t; ð2Þ
Fig. 1. Schematic diagram of the Parr Acid Digestion Bomb used to heat-treat silica glass specimens at 250 C under 39 atm water vapor.
where Mt is the uptake at time t from one side of the specimen. The slope of the water uptake vs. square root of time curve gives the product of the surface concentration and the square root of the diffusion coefficient. From the surface concentration obtained by the etching method described above, the diffusion coefficient was obtained. For some samples, the concentration depth profiles were obtained only near the surface of the specimen to evaluate the surface concentration, Cs, without obtaining the complete depth profiles. Therefore more
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data of Cs and Deff were obtained using the second method. Many of the experimental data did not follow the above theoretical predictions precisely. The surface concentration, Cs, increased with the heat-treatment time instead of staying a constant, and, consequently, the uptake, Mt, did not increase proportionately with the square root of time. Yet, the above equations (1) and (2) were applied at each heat-treatment time and the apparent diffusion coefficients were evaluated by the method described above. Namely, the concentration pffi profile was fitted to Eq. (1) and the slope of Mt vs. t at each heat-treatment time was equated to the corresponding expression of Eq. (2) with the surface concentration at the time, Cs.
3. Results The glass samples were transparent even after the hydration. Fig. 2 shows the IR spectra, absorbance vs. wavenumber, for silica glass samples heat-treated in water vapor at 39 atm and 250 C as a function of hydration time. It was observed that the absorbance increased monotonically with the hydration time as expected. The observed base line increase of the absorbance with the heat-treatment time is probably due to the surface roughening resulting in reduced transmission. The unhydrated specimen, on the other hand, exhibited a background absorbance that can be approximated by a straight line between 5000 and 2000 cm1. Since the main interest in this research is to investigate the water diffusion, the background absorbance values were sub-
Fig. 2. Infrared spectra, absorbance vs. wavenumber for silica glass samples heat-treated in water vapor at 39 atm and 250 C.
Fig. 3. Corrected infrared spectra, absorbance vs. wavenumber, for silica glass samples heat-treated in water vapor at 39 atm and 250 C.
tracted to obtain the absorbance data shown in Fig. 3. Two main absorbance peaks appeared in the measured range of the IR wavenumber: 3670 and 3425 cm1. Additionally, a shoulder was observed at 3600 cm1. The peak at 3670 cm1 is attributed to hydroxyl (–OH) and the peak at 3425 cm1 to molecular water (H2O) by a detailed peak separation method [3]. A peak near 3600 cm1 has been attributed to hydrogen-bonded hydroxyls [3,7–9]. In addition, free-molecular water is known to give rise to a IR peak at 3225 cm1. Therefore, even though there was no clear peak observed in the present data, the absorbance at 3225 cm1 was measured to obtain the trend of the free molecular water concentration. The heat-treatment time dependence of the absorbance at three wavenumbers, 3670, 3425 and 3225 cm1, is shown in Fig. 4. Davis showed [3,10] earlier that these water-related IR peak wavenumbers remained unchanged with the hydration temperature when the temperature is higher than 650 C but that they decreased with decreasing hydration temperature below 650 C. Consistently, the current data showed the IR peaks at slightly lower wavenumbers than the wavenumbers quoted. It is believed that the IR peak at 3425 cm1 represents the total amount of molecular water including free molecular water, which is responsible for the peak at 3225 cm1 [3,10,11]. The absorbance value corresponds to eCd where e is extinction coefficient, C is the concentration of species responsible for the vibration and d is the specimen thickness. The concentrations of hydroxyl and molecular water, therefore, were evaluated from the absorbance at 3670 and 3425 cm1 using the extinction coefficient values of 155 and 81 l/molH2O cm, respectively
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Fig. 4. One-half absorbance vs. heat-treatment time for silica glass samples heat-treated in water vapor at 39 atm and 250 C. The maximum error ranges of absorbance are indicated.
Fig. 6. Concentration profile of hydroxyl for silica glass samples heattreated at 250 C and at 39 atm for various length of time. (.) Sample A (24 h); ( ) sample B (72 h); ( ) sample B 0 (72 h); (m) sample C (144 h); (>) sample C 0 (144 h); (n) sample C00 (144 h); () sample D (336 h); (h) sample D 0 (336 h); () sample E (576 h).
[3,10,11]. (The extinction coefficient for 3225 cm1 peak is not known but would probably be close to the value 81 l/molH2O cm, for 3425 cm1.) The total amount of water was obtained by adding the water concentrations obtained from the two peaks. Fig. 5 shows the one-half of the residual absorbance of the hydroxyl peak as a function of the etched depth.
One-half of the absorbance was used since water diffuses into the specimen from two surfaces. One specimen, sample C00 , heat-treated for 144 h (shown as open triangles in the figure) exhibited higher values than two other specimens heat-treated for the same time for the depth less than 10 lm. This anomalous specimen may have
Fig. 5. One-half residual absorbance at 3670 cm1 vs. depth removed for silica glass samples heat-treated at 250 C and 39 atm for various length of time. (.) Sample A (24 h); ( ) sample B (72 h); ( ) sample B 0 (72 h); (m) sample C (144 h); (>) sample C 0 (144 h); (n) sample C00 (144 h); () sample D (336 h); (h) sample D 0 (336 h); () sample E (576 h).
Fig. 7. One-half residual absorbance at 3425 cm1 vs. depth removed for silica glass samples heat-treated at 250 C and 39 atm for various length of time. (.) Sample A (24 h); ( ) sample B (72 h); ( ) sample B 0 (72 h); (m) sample C (144 h); (>) sample C 0 (144 h); (n) sample C00 (144 h); () sample D (336 h); (h) sample D 0 (336 h); (): sample E (576 h).
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Fig. 8. Concentration profile of molecular water for silica glass samples heat-treated at 250 C and at 39 atm for various length of time. (.) Sample A (24 h); ( ) sample B (72 h); ( ) sample B 0 (72 h); (m) sample C (144 h); (>) sample C 0 (144 h); (n) sample C00 (144 h); () sample D (336 h); (h) sample D 0 (336 h); () sample E (576 h).
been immersed accidentally in liquid water during the hydration treatment. The deviated data were eliminated from the subsequent analysis. Fig. 6 shows the corresponding hydroxyl concentration profiles obtained by differentiating the data in Fig. 5. Fig. 7 shows the residual absorbance of the molecular water peak as a function of the etched depth. Again the same sample C00 exhibited anomalous behavior below 10 lm and the data were eliminated from the subsequent analysis. Fig. 8 shows the corresponding molecular water concentration profiles. Fig. 9 summarizes the surface concentration, Cs, for hydroxyl, molecular water and the total water. The anomalous data (sample C00 ) are marked by filled symbols. The surface concentration increased with increasing the heat-treatment time. The maximum total
215
Fig. 9. Surface concentration of hydroxyl, molecular water and total water for silica glass samples heat-treated at 250 C and at 39 atm as a function of heat-treatment time.
water content in silica glass obtained in the present study was 1 mole H2O/l of silica glass 2.6 mol% H2O 0.8 wt% H2O. Table 1 summarizes the surface concentrations, Cs(OH), and effective diffusion coefficient, Deff(OH), obtained from the hydroxyl data. Table 2 shows the corresponding data for molecular water, Cs(H2O) and Deff(H2O). Fig. 10 shows the obtained effective diffusion coefficients as a function of heat-treatment time. Within experimental error, diffusion coefficients obtained using hydroxyl concentration profiles and hydroxyl uptake time dependence as well as those obtained using molecular water concentration profiles and molecular water uptake time dependence are the same. Fig. 11 compares the present diffusion data with the diffusion coefficients obtained under lower water vapor pressure, 355 Torr water vapor [12].
Table 1 Surface concentration, Cs(OH), and apparent effective diffusion coefficients for hydroxyl, Deff(OH), at 250 C in water vapor pressure 39 atm Sample
Heat-treatment time, t (h)
From uptake Cs(OH) (moles of H2O/l of SiO2)
A B B0 C C0 D D0 E
24 72 72 144 144 336 336 576
0.25 0.41 0.42 0.45 0.46 0.54 0.56 0.64
From profile 2
Deff(OH) (cm /s)
Cs(OH) (moles of H2O/l of SiO2)
Deff(OH) (cm2/s)
0.43
4.5 · 1012
0.47 0.55 0.57
4.3 · 1012 3.9 · 1012 2.8 · 1012
12
7.8 · 10 3.8 · 1012 3.8 · 1012 3.9 · 1012 3.7 · 1012 3.3 · 1012 3.1 · 1012 2.7 · 1012
These parameters were determined by two methods: (1) Total uptake of hydroxyl vs. hydration time, together with the measured surface concentration were substituted in Eq. (2). (2) Concentration profiles were fit with Eq. (1). A typical error range of Cs is ±0.05 moles of H2O/l of SiO2 and that for Deff is ±0.5 · 1012 cm2/s.
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Table 2 Surface concentration, Cs(H2O) and apparent effective diffusion coefficients for molecular water, Deff(H2O), at 250 C in water vapor pressure 39 atm Sample
Heat-treatment time, t (h)
A B B0 C C0 D D0 E
24 72 72 144 144 336 336 576
From uptake
From profile 2
Cs(H2O) (moles of H2O/l of SiO2)
Deff(H2O) (cm /s)
0.17 0.24 0.24 0.42 0.30 0.38 0.45 0.44
9.9 · 1012 6.4 · 1012 6.0 · 1012 2.3 · 1012 4.5 · 1012 3.2 · 1012 2.2 · 1012 2.6 · 1012
Cs(H2O) (moles of H2O/l of SiO2)
Deff(H2O) (cm2/s)
0.27
6.3 · 1012
0.31 0.38 0.46
4.5 · 1012 3.3 · 1012 1.9 · 1012
These parameters were obtained by two methods: (1) Total uptake of molecular water vs. hydration time, together with the measured surface concentration were substituted in Eq. (2). (2) Concentration profiles were fit with Eq. (1). A typical error range of Cs is ±0.05 moles of H2O/l of SiO2 and that for Deff is ±0.5 · 1012 cm2/s.
-11
Effective Diffusioin Coefficient, Deff (cm /s)
10 2
From OH uptake From OH profile From H2O uptake From H2O profile
-12
10
0
100
200
300
400
500
600
Time (hrs) Fig. 10. Effective diffusion coefficient of water into silica glass at 250 C under 39 atm water vapor pressure as a function of heattreatment time.
The possible relationship between hydroxyl concentration and molecular water concentration was examined by plotting the two concentrations in log–log scale in Fig. 12. The majority of the data fall on a single line with the slope close to unity (1.16). The absorbance ratio of hydroxyl/molecular water is plotted against the heat-treatment time in Fig. 13. It appears that the absorbance ratio approaches a constant value of 3.
4. Discussion The background of IR absorption spectra increasing with increasing hydration time is considered to be caused by increasing surface roughness. Alternatively, a porous structure formation by the hydration treatment was observed in some glasses [13–15]. But these glasses
Fig. 11. Comparison of the present water diffusion coefficient with the previous data by Davis and Tomozawa [12].
contained the components which can be selectively leached by water or ion-exchanged with proton or hydronium ions, resulting in glasses with extremely high water contents by the hydration. In the present silica glass sample, such selective leaching or ion-exchange does not occur. Additionally, the Raman and IR spectra of the porous glasses showed predominantly peaks due to molecular water [16–18], in contrast of high hydroxyl concentration in the present sample. Therefore, surface porous layer formation is unlikely in the present sample. The contribution of the surface adsorbed water to the present IR spectra is minimal since the samples were washed with ethanol after the hydration treatment and IR spectra were obtained in nitrogen atmosphere. The obtained water concentration profiles in the present samples are also indicative of diffusion profiles without any accumulated concentration on the specimen surface.
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Total Absorbance Ratio OH/H2O
5
4
3
2
1
0
0
100
200
300
400
500
600
Time (hrs)
Fig. 12. Relation between hydroxyl concentration and molecular water concentration in silica glass heat-treated at 250 C under 39 atm water vapor pressure.
Therefore, all the water-related species observed in the present work were treated as obtained by the water diffusion process. Water in silica glass reacts with the glass network by H2 O þ SiOSi $ SiOH þ HOSi
ð3Þ
Under low water vapor pressure at high temperature, water in silica glass exists mainly as hydroxyl and the concentration of molecular water is so low that it cannot be usually detected. Yet it is postulated that diffusion of water takes place by the motion of molecular water and hydroxyl is considered immobile [19]. It is usually assumed [19] that the above reaction is rapid at high temperature and a local equilibrium is established with the equilibrium constant 2
K 1 ¼ ½SiOH =½H2 O;
ð4Þ
where [SiOH] and [H2O] are activities or concentration of hydroxyl and molecular water, respectively and the activity of silica is assumed to be unity when the concentration of water is low. Then the effective diffusion coefficient of water obtained by following the hydroxyl concentration is given by [10,12,19,20] Deff ðOHÞ ¼ 4½SiOHDH2 O =K 1 ;
ð5Þ
where DH2O is the diffusion coefficient of molecular water when it does not react with the glass network. The equilibrium constant, K1, has not been determined for cases when the total water concentration is low, which is the case when the water vapor pressure is low. For some geological glasses with a high water concentration, both hydroxyl and molecular water have
Fig. 13. Ratio of the hydroxyl concentration to molecular water concentration, as a function of the heat-treatment time at 250 C under 39 atm water vapor pressure. A typical error range of ±0.2 in the ratio is indicated.
been observed and the equilibrium constant has been determined as a function of temperature [21,22]. In the present experiment of water diffusion at low temperature, the above equilibrium constant, Eq. (4), was not observed. If the above equilibrium constant, Eq. (4), is observed, the slope of the line in Fig. 12 should be 2. The slope of the data was much closer to unity than two. Thus, the equilibrium constant is closer to K 2 ¼ ½SiOH=½H2 O:
ð6Þ
With the absorbance ratio of the hydroxyl band to the molecular water band being 3, this equilibrium constant, K2, can be obtained using the extinction coefficients, eOH = 77.5 l/molOH cm for the hydroxyl band and eH2O = 81 l/molH2O cm for the molecular water band, as [OH]/[H2O] 3. FickÕs law of diffusion for water in silica glass with these two water species can be given by ofð1=2Þ½SiOHg=ot þ o½H2 O=ot ¼ o½DOH ofð1=2Þ½SiOHg=ox=ox þ o½DH2 O o½H2 O=ox=ox: Here the factor 1/2 in front of [SiOH] is needed since two [SiOH] are created from one [H2O] and for the same amount of water, [SiOH] is twice [H2O]. DOH is the diffusion coefficient of hydroxyl [SiOH] and is zero since hydroxyl is immobile. Then, ofð1=2Þ½OHg=ot þ o½H2 O=ot ¼ o½DH2 O o½H2 O=ox=ox: ð7Þ Using the equilibrium constant given by Eq. (6) to replace the molecular concentration with the hydroxyl concentration,
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ofð1=2Þ½OHg=ot þ of½OH=K 2 g=ot
-6
Present data Doremus
¼ o½DH2 O of½OH=K 2 g=ox=ox; -7
The effective diffusion coefficient of water determined from the hydroxyl distribution is Deff ðOHÞ ¼ DH2 O =fK 2 ½ð1=2Þ þ ð1=K 2 Þg ¼ DH2 O =½ð1=2ÞK 2 þ 1:
ð8Þ
Using Eq. (6) to replace the hydroxyl concentration with the molecular water concentration, Eq. (7) becomes
-8 -9
2
¼ o½DH2 O of½OH=K 2 g=ox=ox:
log DH O (cm2/s)
ofðð1=2Þ þ ð1=K 2 ÞÞ½OHg=ot
-10 -11 -12 0.5
1.0
ofð1=2ÞK 2 ½H2 Og=ot þ o½H2 O=ot
1.5
2.0
2.5
1000/T
¼ o½DH2 O o½H2 O=ox=ox;
Fig. 14. Diffusion coefficient of molecular water, DH2O, as a function of temperature, estimated by Doremus [23] compared with the present data. The arrow in the figure indicates the direction of increasing heattreatment time.
ofðð1=2ÞK 2 þ 1Þ½H2 Og=ot ¼ o½DH2 O o½H2 O=ox=ox: The effective diffusion coefficient of water determined from the molecular water distribution is Deff ðH2 OÞ ¼ DH2 O =½ð1=2ÞK 2 þ 1;
ð9Þ
which is identical with Eq. (8). This is consistent with the current experimental results, which showed that the effective diffusion coefficient derived from [SiOH] profile is the same as that derived from [H2O] profile, within experimental error. From Eq. (8) or (9), the diffusion coefficient of molecular water is given by DH2 O ¼ ½ð1=2ÞK 2 þ 1Deff ;
ð10Þ
where Deff is the effective water diffusion coefficient obtained from [SiOH] profile or [H2O] profile. The diffusion coefficients of molecular water evaluated by applying this relation to the present data at various heat-treatment times are shown in Fig. 14, together with the previous data estimated by Doremus [23]. The value obtained here appears to be in the same range as those at lower water vapor pressures. In the present study, the equilibrium constant given by Eq. (6) rather than the traditional one given by Eq. (4) appears to apply to the low temperature water diffusion. This implies that two hydroxyls produced by the chemical reaction given by Eq. (3) are not entirely independent. The reaction of water with silica glass at a low temperature should be represented by H2 O þ SiOSi $ ðSiOHÞ2
ð30 Þ
while at high temperatures, the reaction represented by Eq. (3) would apply. If this equilibrium reaction (30 ) is applicable, the equilibrium constant will be given by K 3 ¼ ½ðSiOHÞ2 =½H2 O ¼ K 2 =2:
ð11Þ
Analyzing FickÕs law of diffusion in the same manner as in the previous paragraph, the following equations can be obtained. Deff ðOHÞ ¼ DH2 O =ðK 3 þ 1Þ;
ð12Þ
Deff ðH2 OÞ ¼ DH2 O =ðK 3 þ 1Þ;
ð13Þ
DH2 O ¼ ðK 3 þ 1ÞDeff :
ð14Þ
These Eqs. (12)–(14) become the same Eqs. (8)–(10) with the use of Eq. (11). Recently, Plotnichenko et al. [24] showed theoretically that the IR peak at 3565 ± 14 cm1, which is close to our observed shoulder position at 3600 cm1, was due to a strongly hydrogen bonded hydroxyls in which two hydroxyls are connected with a cyclic configuration. This interpretation is consistent with our model of the pair formation of two hydroxyls, shown by Eq. (30 ). Another unique feature of low temperature water diffusion is the time dependence of both the surface concentration (or water solubility) and diffusion coefficient: while the surface concentration increased with increasing heat-treatment time, the diffusion coefficient decreased with increasing heat-treatment time. The phenomenon has been observed earlier at 350 and 650 C under lower vapor pressure [12,25]. The time dependence at these temperatures was attributed to the local stress, structural relaxation and the progress of reaction (3) and changing value of the equilibrium constant. In view of the present observation, the possibility of the changing equilibrium constant of reaction (3Õ) has to be added.
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5. Conclusions Water diffusion into a high purity silica glass was measured at 250 C under 39 atm water vapor pressure. Both hydroxyl and molecular water were observed to exist in the hydrated glasses. From the ratio of hydroxyl and molecular water we suggest that the two hydroxyls produced by the reaction of a water molecule with a silica network are not independent and the reaction should be represented by H2 O þ SiOSi $ ðSiOHÞ2 The diffusion coefficient of water was evaluated using both hydroxyl and molecular water profiles. The diffusion coefficient decreased with increasing heat-treatment time, while the surface concentration (or solubility) of water increased with increasing heat-treatment time.
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Water diffusion into silica glass at a low temperature under high water vapor pressure Andrea Oehler 1, Minoru Tomozawa
*
Materials Science and Engineering Department, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY 12180-3590, USA Received 31 October 2003 Available online 22 October 2004
Abstract Water in glass has disproportionately large effects on various properties of oxide glasses, such as chemical durability and mechanical strength. Silica glass is the basis of many oxide glasses. Thus, there have been numerous studies on water diffusion into silica glasses. But most past research on water diffusion into silica glasses has been conducted at high temperatures, where water diffusion is accompanied by structural changes of the glass. In the present study, water diffusion into silica glass at low temperature, 250 C, was measured using IR spectroscopy as the main research tool. Saturated high water vapor pressure was used to increase the amount of water diffusing into the glass so that the water can be detected by the IR method after a reasonably short heat-treatment time. It was found that both water solubility and diffusion coefficient were time dependent. Furthermore, both hydroxyl and molecular water were detected in the glass. From the concentrations of hydroxyl and molecular water, an apparent equilibrium constant, K = [SiOH]n/[H2O] was evaluated. At high temperatures, water reacts with silica glass by Si–O–Si + H2O M 2SiOH, and the local reaction equilibrium has been established at the value of n being 2. In the present study of low temperature water diffusion in silica glass, unlike the local reaction equilibrium in high temperature studies, the value of n was found to be close to 1. This indicates that the two hydroxyls formed in the glass during the reaction are not independent of each other. 2004 Elsevier B.V. All rights reserved.
1. Introduction Water in glass has a disproportionately large influence on glass properties. It decreases viscosity, chemical durability and mechanical strength. Even when a glass is initially water-free, water can enter into a glass by diffusion. Silica glass (amorphous silica) is important in electronics, optics and microelectronic mechanical systems. Furthermore, it is a prototype of many silicate glasses and its properties can be used to predict properties of
* Corresponding author. Tel.: +1 518 276 6659; fax: +1 518 276 8554. E-mail address: [email protected] (M. Tomozawa). 1 Now at Intel Corp., Hillsboro, OR.
0022-3093/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2004.07.013
numerous other glasses. Also, the rate of water penetration into silicate glasses is being used as a means to determine the age of both archaeological and geological glasses [1,2]. Water diffusion coefficient in silica glass is small at low temperature, but still it can influence surface-sensitive properties of bulk glass and properties of amorphous thin films [3–5] and porous materials. Thus, it is useful to determine the water diffusion coefficient in silica glass. Most of the past research on water diffusion into silica glass was performed at high temperatures. In this study, the water diffusion coefficient into silica glass was measured at a low temperature of 250 C using infrared spectroscopy. In order to increase the signal intensity of infrared spectroscopy, the silica glass was exposed to high water vapor pressure using an autoclave.
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2. Experimental A high purity silica glass made by CVD (axial vapor deposition, AVD) for optical communication was used in the present experiment. This glass contains less than 1 ppm of water but approximately 1000 ppm of Cl. The glass samples were cut into pieces of approximately 20 mm · 20 mm · 1.3 mm using a cutting machine with a diamond blade. The 20 mm · 20 mm faces of the samples were polished using polishing papers with various grain sizes of SiC, starting with 240, 400 and 600 grit in water followed by 1000 grit SiC in oil and finally with CeO2 slurry. The polishing produces a slightly damaged surface layer [6], which was removed with etching by 10%HF–2.5%H2SO4 for 3 min at room temperature. Samples were then heat-treated with a saturated water vapor in a General Purpose Acid Digestion Bomb 4549 (Parr Instrument Company, Moline, IL), which is schematically shown in Fig. 1. The outside of the bomb is a stainless steel fixture designed to contain the high pressure. The inside of the bomb is a thick-walled Teflon vessel with a capacity of 45 ml. The bomb has a maximum operating temperature of 250 C and pressure of 122 atm. A Teflon stage held samples above the bomb floor as shown in Fig. 1. The stage allowed samples to be hydrated in saturated water vapor and not directly in the solution. The Teflon stage reduced the available volume for water and water vapor from 45 to 38.5 ml. Four milliliters of distilled water was placed in the bomb. This amount of water guaranteed that the water remains in equilibrium with saturated water vapor pressure of 39 atm at 250 C, and that water would not rise above the stage. Two or three glass samples were placed vertically in the bomb at one time and the bomb was
placed in an electric furnace kept at 250 ± 2 C. It took approximately 1 h for the contents of the bomb come up to the set temperature. After the heat-treatment for the specified period, the bomb was cooled by water for 10–15 min before it could be easily opened. The heattreatment time was 24–576 h, and the time to heat and cool the samples was less than 2% of the heat-treatment time. The samples were washed with ethanol after the hydration treatment. Infrared spectra of the samples were obtained using a Fourier transform-infrared (FTIR) spectrophotometer; the IR absorbance was obtained in nitrogen atmosphere as a function of heat-treatment time. The IR absorbance was converted to water concentration using BeerÕs law and the appropriate extinction coefficient. For many hydrated glass samples, the absorbance was measured as a function of the diffusion depth. For this purpose, IR absorbance was obtained after successive etching of the surface layer. Etching solutions used were 150 ml of 5%HF–2.5%H2SO4, 10%HF–2.5%H2SO4 at room temperature and 2 N NaOH at 80 C. Different etchants were used to make sure that the results are not artifacts of the etching procedure employed. The etched depth was estimated from the weight loss, surface area, and density of the glass specimen. The obtained residual absorbance vs. the etched depth was fitted with a polynomial and was differentiated to obtain the water concentration depth profile. The effective water diffusion coefficient, Deff, was obtained by two different methods. One was to compare the experimental concentration depth profile obtained after time, t, with the theoretical concentration profile given by pffiffiffiffiffiffiffiffiffi Cðx; tÞ ¼ C s ½erfcðx=2 Deff tÞ; ð1Þ where C(x, t) is the concentration at the depth x and heat-treatment time, t, and Cs is the surface concentration, which should be time independent. Erfc is a complementary error function. The values of Cs and Deff, which produce the best fit to the experimental concentration depth profiles, were obtained. The other method was to determine the diffusion coefficient from the time dependence of the water uptake, pffiffiffiffiffiffiffiffiffiffiffiffiffi pffi M t ¼ 2C s ð Deff =pÞ t; ð2Þ
Fig. 1. Schematic diagram of the Parr Acid Digestion Bomb used to heat-treat silica glass specimens at 250 C under 39 atm water vapor.
where Mt is the uptake at time t from one side of the specimen. The slope of the water uptake vs. square root of time curve gives the product of the surface concentration and the square root of the diffusion coefficient. From the surface concentration obtained by the etching method described above, the diffusion coefficient was obtained. For some samples, the concentration depth profiles were obtained only near the surface of the specimen to evaluate the surface concentration, Cs, without obtaining the complete depth profiles. Therefore more
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data of Cs and Deff were obtained using the second method. Many of the experimental data did not follow the above theoretical predictions precisely. The surface concentration, Cs, increased with the heat-treatment time instead of staying a constant, and, consequently, the uptake, Mt, did not increase proportionately with the square root of time. Yet, the above equations (1) and (2) were applied at each heat-treatment time and the apparent diffusion coefficients were evaluated by the method described above. Namely, the concentration pffi profile was fitted to Eq. (1) and the slope of Mt vs. t at each heat-treatment time was equated to the corresponding expression of Eq. (2) with the surface concentration at the time, Cs.
3. Results The glass samples were transparent even after the hydration. Fig. 2 shows the IR spectra, absorbance vs. wavenumber, for silica glass samples heat-treated in water vapor at 39 atm and 250 C as a function of hydration time. It was observed that the absorbance increased monotonically with the hydration time as expected. The observed base line increase of the absorbance with the heat-treatment time is probably due to the surface roughening resulting in reduced transmission. The unhydrated specimen, on the other hand, exhibited a background absorbance that can be approximated by a straight line between 5000 and 2000 cm1. Since the main interest in this research is to investigate the water diffusion, the background absorbance values were sub-
Fig. 2. Infrared spectra, absorbance vs. wavenumber for silica glass samples heat-treated in water vapor at 39 atm and 250 C.
Fig. 3. Corrected infrared spectra, absorbance vs. wavenumber, for silica glass samples heat-treated in water vapor at 39 atm and 250 C.
tracted to obtain the absorbance data shown in Fig. 3. Two main absorbance peaks appeared in the measured range of the IR wavenumber: 3670 and 3425 cm1. Additionally, a shoulder was observed at 3600 cm1. The peak at 3670 cm1 is attributed to hydroxyl (–OH) and the peak at 3425 cm1 to molecular water (H2O) by a detailed peak separation method [3]. A peak near 3600 cm1 has been attributed to hydrogen-bonded hydroxyls [3,7–9]. In addition, free-molecular water is known to give rise to a IR peak at 3225 cm1. Therefore, even though there was no clear peak observed in the present data, the absorbance at 3225 cm1 was measured to obtain the trend of the free molecular water concentration. The heat-treatment time dependence of the absorbance at three wavenumbers, 3670, 3425 and 3225 cm1, is shown in Fig. 4. Davis showed [3,10] earlier that these water-related IR peak wavenumbers remained unchanged with the hydration temperature when the temperature is higher than 650 C but that they decreased with decreasing hydration temperature below 650 C. Consistently, the current data showed the IR peaks at slightly lower wavenumbers than the wavenumbers quoted. It is believed that the IR peak at 3425 cm1 represents the total amount of molecular water including free molecular water, which is responsible for the peak at 3225 cm1 [3,10,11]. The absorbance value corresponds to eCd where e is extinction coefficient, C is the concentration of species responsible for the vibration and d is the specimen thickness. The concentrations of hydroxyl and molecular water, therefore, were evaluated from the absorbance at 3670 and 3425 cm1 using the extinction coefficient values of 155 and 81 l/molH2O cm, respectively
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Fig. 4. One-half absorbance vs. heat-treatment time for silica glass samples heat-treated in water vapor at 39 atm and 250 C. The maximum error ranges of absorbance are indicated.
Fig. 6. Concentration profile of hydroxyl for silica glass samples heattreated at 250 C and at 39 atm for various length of time. (.) Sample A (24 h); ( ) sample B (72 h); ( ) sample B 0 (72 h); (m) sample C (144 h); (>) sample C 0 (144 h); (n) sample C00 (144 h); () sample D (336 h); (h) sample D 0 (336 h); () sample E (576 h).
[3,10,11]. (The extinction coefficient for 3225 cm1 peak is not known but would probably be close to the value 81 l/molH2O cm, for 3425 cm1.) The total amount of water was obtained by adding the water concentrations obtained from the two peaks. Fig. 5 shows the one-half of the residual absorbance of the hydroxyl peak as a function of the etched depth.
One-half of the absorbance was used since water diffuses into the specimen from two surfaces. One specimen, sample C00 , heat-treated for 144 h (shown as open triangles in the figure) exhibited higher values than two other specimens heat-treated for the same time for the depth less than 10 lm. This anomalous specimen may have
Fig. 5. One-half residual absorbance at 3670 cm1 vs. depth removed for silica glass samples heat-treated at 250 C and 39 atm for various length of time. (.) Sample A (24 h); ( ) sample B (72 h); ( ) sample B 0 (72 h); (m) sample C (144 h); (>) sample C 0 (144 h); (n) sample C00 (144 h); () sample D (336 h); (h) sample D 0 (336 h); () sample E (576 h).
Fig. 7. One-half residual absorbance at 3425 cm1 vs. depth removed for silica glass samples heat-treated at 250 C and 39 atm for various length of time. (.) Sample A (24 h); ( ) sample B (72 h); ( ) sample B 0 (72 h); (m) sample C (144 h); (>) sample C 0 (144 h); (n) sample C00 (144 h); () sample D (336 h); (h) sample D 0 (336 h); (): sample E (576 h).
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Fig. 8. Concentration profile of molecular water for silica glass samples heat-treated at 250 C and at 39 atm for various length of time. (.) Sample A (24 h); ( ) sample B (72 h); ( ) sample B 0 (72 h); (m) sample C (144 h); (>) sample C 0 (144 h); (n) sample C00 (144 h); () sample D (336 h); (h) sample D 0 (336 h); () sample E (576 h).
been immersed accidentally in liquid water during the hydration treatment. The deviated data were eliminated from the subsequent analysis. Fig. 6 shows the corresponding hydroxyl concentration profiles obtained by differentiating the data in Fig. 5. Fig. 7 shows the residual absorbance of the molecular water peak as a function of the etched depth. Again the same sample C00 exhibited anomalous behavior below 10 lm and the data were eliminated from the subsequent analysis. Fig. 8 shows the corresponding molecular water concentration profiles. Fig. 9 summarizes the surface concentration, Cs, for hydroxyl, molecular water and the total water. The anomalous data (sample C00 ) are marked by filled symbols. The surface concentration increased with increasing the heat-treatment time. The maximum total
215
Fig. 9. Surface concentration of hydroxyl, molecular water and total water for silica glass samples heat-treated at 250 C and at 39 atm as a function of heat-treatment time.
water content in silica glass obtained in the present study was 1 mole H2O/l of silica glass 2.6 mol% H2O 0.8 wt% H2O. Table 1 summarizes the surface concentrations, Cs(OH), and effective diffusion coefficient, Deff(OH), obtained from the hydroxyl data. Table 2 shows the corresponding data for molecular water, Cs(H2O) and Deff(H2O). Fig. 10 shows the obtained effective diffusion coefficients as a function of heat-treatment time. Within experimental error, diffusion coefficients obtained using hydroxyl concentration profiles and hydroxyl uptake time dependence as well as those obtained using molecular water concentration profiles and molecular water uptake time dependence are the same. Fig. 11 compares the present diffusion data with the diffusion coefficients obtained under lower water vapor pressure, 355 Torr water vapor [12].
Table 1 Surface concentration, Cs(OH), and apparent effective diffusion coefficients for hydroxyl, Deff(OH), at 250 C in water vapor pressure 39 atm Sample
Heat-treatment time, t (h)
From uptake Cs(OH) (moles of H2O/l of SiO2)
A B B0 C C0 D D0 E
24 72 72 144 144 336 336 576
0.25 0.41 0.42 0.45 0.46 0.54 0.56 0.64
From profile 2
Deff(OH) (cm /s)
Cs(OH) (moles of H2O/l of SiO2)
Deff(OH) (cm2/s)
0.43
4.5 · 1012
0.47 0.55 0.57
4.3 · 1012 3.9 · 1012 2.8 · 1012
12
7.8 · 10 3.8 · 1012 3.8 · 1012 3.9 · 1012 3.7 · 1012 3.3 · 1012 3.1 · 1012 2.7 · 1012
These parameters were determined by two methods: (1) Total uptake of hydroxyl vs. hydration time, together with the measured surface concentration were substituted in Eq. (2). (2) Concentration profiles were fit with Eq. (1). A typical error range of Cs is ±0.05 moles of H2O/l of SiO2 and that for Deff is ±0.5 · 1012 cm2/s.
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Table 2 Surface concentration, Cs(H2O) and apparent effective diffusion coefficients for molecular water, Deff(H2O), at 250 C in water vapor pressure 39 atm Sample
Heat-treatment time, t (h)
A B B0 C C0 D D0 E
24 72 72 144 144 336 336 576
From uptake
From profile 2
Cs(H2O) (moles of H2O/l of SiO2)
Deff(H2O) (cm /s)
0.17 0.24 0.24 0.42 0.30 0.38 0.45 0.44
9.9 · 1012 6.4 · 1012 6.0 · 1012 2.3 · 1012 4.5 · 1012 3.2 · 1012 2.2 · 1012 2.6 · 1012
Cs(H2O) (moles of H2O/l of SiO2)
Deff(H2O) (cm2/s)
0.27
6.3 · 1012
0.31 0.38 0.46
4.5 · 1012 3.3 · 1012 1.9 · 1012
These parameters were obtained by two methods: (1) Total uptake of molecular water vs. hydration time, together with the measured surface concentration were substituted in Eq. (2). (2) Concentration profiles were fit with Eq. (1). A typical error range of Cs is ±0.05 moles of H2O/l of SiO2 and that for Deff is ±0.5 · 1012 cm2/s.
-11
Effective Diffusioin Coefficient, Deff (cm /s)
10 2
From OH uptake From OH profile From H2O uptake From H2O profile
-12
10
0
100
200
300
400
500
600
Time (hrs) Fig. 10. Effective diffusion coefficient of water into silica glass at 250 C under 39 atm water vapor pressure as a function of heattreatment time.
The possible relationship between hydroxyl concentration and molecular water concentration was examined by plotting the two concentrations in log–log scale in Fig. 12. The majority of the data fall on a single line with the slope close to unity (1.16). The absorbance ratio of hydroxyl/molecular water is plotted against the heat-treatment time in Fig. 13. It appears that the absorbance ratio approaches a constant value of 3.
4. Discussion The background of IR absorption spectra increasing with increasing hydration time is considered to be caused by increasing surface roughness. Alternatively, a porous structure formation by the hydration treatment was observed in some glasses [13–15]. But these glasses
Fig. 11. Comparison of the present water diffusion coefficient with the previous data by Davis and Tomozawa [12].
contained the components which can be selectively leached by water or ion-exchanged with proton or hydronium ions, resulting in glasses with extremely high water contents by the hydration. In the present silica glass sample, such selective leaching or ion-exchange does not occur. Additionally, the Raman and IR spectra of the porous glasses showed predominantly peaks due to molecular water [16–18], in contrast of high hydroxyl concentration in the present sample. Therefore, surface porous layer formation is unlikely in the present sample. The contribution of the surface adsorbed water to the present IR spectra is minimal since the samples were washed with ethanol after the hydration treatment and IR spectra were obtained in nitrogen atmosphere. The obtained water concentration profiles in the present samples are also indicative of diffusion profiles without any accumulated concentration on the specimen surface.
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Total Absorbance Ratio OH/H2O
5
4
3
2
1
0
0
100
200
300
400
500
600
Time (hrs)
Fig. 12. Relation between hydroxyl concentration and molecular water concentration in silica glass heat-treated at 250 C under 39 atm water vapor pressure.
Therefore, all the water-related species observed in the present work were treated as obtained by the water diffusion process. Water in silica glass reacts with the glass network by H2 O þ SiOSi $ SiOH þ HOSi
ð3Þ
Under low water vapor pressure at high temperature, water in silica glass exists mainly as hydroxyl and the concentration of molecular water is so low that it cannot be usually detected. Yet it is postulated that diffusion of water takes place by the motion of molecular water and hydroxyl is considered immobile [19]. It is usually assumed [19] that the above reaction is rapid at high temperature and a local equilibrium is established with the equilibrium constant 2
K 1 ¼ ½SiOH =½H2 O;
ð4Þ
where [SiOH] and [H2O] are activities or concentration of hydroxyl and molecular water, respectively and the activity of silica is assumed to be unity when the concentration of water is low. Then the effective diffusion coefficient of water obtained by following the hydroxyl concentration is given by [10,12,19,20] Deff ðOHÞ ¼ 4½SiOHDH2 O =K 1 ;
ð5Þ
where DH2O is the diffusion coefficient of molecular water when it does not react with the glass network. The equilibrium constant, K1, has not been determined for cases when the total water concentration is low, which is the case when the water vapor pressure is low. For some geological glasses with a high water concentration, both hydroxyl and molecular water have
Fig. 13. Ratio of the hydroxyl concentration to molecular water concentration, as a function of the heat-treatment time at 250 C under 39 atm water vapor pressure. A typical error range of ±0.2 in the ratio is indicated.
been observed and the equilibrium constant has been determined as a function of temperature [21,22]. In the present experiment of water diffusion at low temperature, the above equilibrium constant, Eq. (4), was not observed. If the above equilibrium constant, Eq. (4), is observed, the slope of the line in Fig. 12 should be 2. The slope of the data was much closer to unity than two. Thus, the equilibrium constant is closer to K 2 ¼ ½SiOH=½H2 O:
ð6Þ
With the absorbance ratio of the hydroxyl band to the molecular water band being 3, this equilibrium constant, K2, can be obtained using the extinction coefficients, eOH = 77.5 l/molOH cm for the hydroxyl band and eH2O = 81 l/molH2O cm for the molecular water band, as [OH]/[H2O] 3. FickÕs law of diffusion for water in silica glass with these two water species can be given by ofð1=2Þ½SiOHg=ot þ o½H2 O=ot ¼ o½DOH ofð1=2Þ½SiOHg=ox=ox þ o½DH2 O o½H2 O=ox=ox: Here the factor 1/2 in front of [SiOH] is needed since two [SiOH] are created from one [H2O] and for the same amount of water, [SiOH] is twice [H2O]. DOH is the diffusion coefficient of hydroxyl [SiOH] and is zero since hydroxyl is immobile. Then, ofð1=2Þ½OHg=ot þ o½H2 O=ot ¼ o½DH2 O o½H2 O=ox=ox: ð7Þ Using the equilibrium constant given by Eq. (6) to replace the molecular concentration with the hydroxyl concentration,
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ofð1=2Þ½OHg=ot þ of½OH=K 2 g=ot
-6
Present data Doremus
¼ o½DH2 O of½OH=K 2 g=ox=ox; -7
The effective diffusion coefficient of water determined from the hydroxyl distribution is Deff ðOHÞ ¼ DH2 O =fK 2 ½ð1=2Þ þ ð1=K 2 Þg ¼ DH2 O =½ð1=2ÞK 2 þ 1:
ð8Þ
Using Eq. (6) to replace the hydroxyl concentration with the molecular water concentration, Eq. (7) becomes
-8 -9
2
¼ o½DH2 O of½OH=K 2 g=ox=ox:
log DH O (cm2/s)
ofðð1=2Þ þ ð1=K 2 ÞÞ½OHg=ot
-10 -11 -12 0.5
1.0
ofð1=2ÞK 2 ½H2 Og=ot þ o½H2 O=ot
1.5
2.0
2.5
1000/T
¼ o½DH2 O o½H2 O=ox=ox;
Fig. 14. Diffusion coefficient of molecular water, DH2O, as a function of temperature, estimated by Doremus [23] compared with the present data. The arrow in the figure indicates the direction of increasing heattreatment time.
ofðð1=2ÞK 2 þ 1Þ½H2 Og=ot ¼ o½DH2 O o½H2 O=ox=ox: The effective diffusion coefficient of water determined from the molecular water distribution is Deff ðH2 OÞ ¼ DH2 O =½ð1=2ÞK 2 þ 1;
ð9Þ
which is identical with Eq. (8). This is consistent with the current experimental results, which showed that the effective diffusion coefficient derived from [SiOH] profile is the same as that derived from [H2O] profile, within experimental error. From Eq. (8) or (9), the diffusion coefficient of molecular water is given by DH2 O ¼ ½ð1=2ÞK 2 þ 1Deff ;
ð10Þ
where Deff is the effective water diffusion coefficient obtained from [SiOH] profile or [H2O] profile. The diffusion coefficients of molecular water evaluated by applying this relation to the present data at various heat-treatment times are shown in Fig. 14, together with the previous data estimated by Doremus [23]. The value obtained here appears to be in the same range as those at lower water vapor pressures. In the present study, the equilibrium constant given by Eq. (6) rather than the traditional one given by Eq. (4) appears to apply to the low temperature water diffusion. This implies that two hydroxyls produced by the chemical reaction given by Eq. (3) are not entirely independent. The reaction of water with silica glass at a low temperature should be represented by H2 O þ SiOSi $ ðSiOHÞ2
ð30 Þ
while at high temperatures, the reaction represented by Eq. (3) would apply. If this equilibrium reaction (30 ) is applicable, the equilibrium constant will be given by K 3 ¼ ½ðSiOHÞ2 =½H2 O ¼ K 2 =2:
ð11Þ
Analyzing FickÕs law of diffusion in the same manner as in the previous paragraph, the following equations can be obtained. Deff ðOHÞ ¼ DH2 O =ðK 3 þ 1Þ;
ð12Þ
Deff ðH2 OÞ ¼ DH2 O =ðK 3 þ 1Þ;
ð13Þ
DH2 O ¼ ðK 3 þ 1ÞDeff :
ð14Þ
These Eqs. (12)–(14) become the same Eqs. (8)–(10) with the use of Eq. (11). Recently, Plotnichenko et al. [24] showed theoretically that the IR peak at 3565 ± 14 cm1, which is close to our observed shoulder position at 3600 cm1, was due to a strongly hydrogen bonded hydroxyls in which two hydroxyls are connected with a cyclic configuration. This interpretation is consistent with our model of the pair formation of two hydroxyls, shown by Eq. (30 ). Another unique feature of low temperature water diffusion is the time dependence of both the surface concentration (or water solubility) and diffusion coefficient: while the surface concentration increased with increasing heat-treatment time, the diffusion coefficient decreased with increasing heat-treatment time. The phenomenon has been observed earlier at 350 and 650 C under lower vapor pressure [12,25]. The time dependence at these temperatures was attributed to the local stress, structural relaxation and the progress of reaction (3) and changing value of the equilibrium constant. In view of the present observation, the possibility of the changing equilibrium constant of reaction (3Õ) has to be added.
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5. Conclusions Water diffusion into a high purity silica glass was measured at 250 C under 39 atm water vapor pressure. Both hydroxyl and molecular water were observed to exist in the hydrated glasses. From the ratio of hydroxyl and molecular water we suggest that the two hydroxyls produced by the reaction of a water molecule with a silica network are not independent and the reaction should be represented by H2 O þ SiOSi $ ðSiOHÞ2 The diffusion coefficient of water was evaluated using both hydroxyl and molecular water profiles. The diffusion coefficient decreased with increasing heat-treatment time, while the surface concentration (or solubility) of water increased with increasing heat-treatment time.
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