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Inert gas solubility in binary germania–silica glasses
Journal of Non-Crystalline Solids 349 (2004) 209–214 www.elsevier.com/locate/jnoncrysol
Inert gas solubility in binary germania–silica glasses Christopher C. Tournour, James E. Shelby
*
HOGSE, New York State College of Ceramics, NYSCC at Alfred University, 2 Pine Street, Alfred, NY 14802, USA Available online 2 November 2004
Abstract Helium and neon solubility have been measured in vitreous silica, vitreous germania, and in a series of binary GeO2–SiO2 glasses. Measurements were made over a broad temperature range using a saturation-outgassing method. The enthalpy of solution of these gases is smaller for vitreous germania than for vitreous silica. Inert gas solubility decreases rapidly as silica is initially replaced by germania in the network, with a more gradual decrease in solubility with continued reduction in silica content. Solubility measurements at varying pressures establish that inert gas solubility in vitreous germania obeys HenryÕs Law up to 1 atm of gas pressure, as has already been established for vitreous silica. Additional helium solubility and diffusivity measurements were made using the permeation method at temperatures below 300 C. Helium diffusivity also decreases as silica is replaced by germania, with an approximately linear dependence on composition. The activation energy for diffusion increases as the germania concentration increases. Results of this study are attributed to changes in interstice size and/or distribution as a function of glass composition and experimental temperature. 2004 Elsevier B.V. All rights reserved. PACS: 61.43.Fs; 66.30.h
1. Introduction Inert gas migration measurements are excellent probes of the network structure of glasses and melts [1]. Unlike more chemically reactive gases, such as water vapor and carbon dioxide, inert gas atoms do not interact with the glass structure. These atoms reside in the interstitial spaces in the network. Gas solubility measurements can be used to reveal information regarding the amount and distribution of the free volume, while diffusion measurements can give information regarding the doorways between interstitial sites. Although helium migration has been studied extensively in vitreous silica [2–9], fewer studies have been re-
* Corresponding author. Tel.: +1 607 871 2470; fax: +1 607 871 2354. E-mail addresses: [email protected] (C.C. Tournour), [email protected] (J.E. Shelby).
0022-3093/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2004.08.144
ported for neon migration in this glassformer [6,8,10– 12]. Even less information is available for inert gas solubility and diffusion in vitreous germania [5,7]. It would appear that the ideas proposed for inert gas migration in vitreous silica could be confirmed by a similar study of helium and neon migration in vitreous germania, whose structure is similar to silica. Combinations of these two basic glassformers can also yield valuable information regarding how the free volume changes in a binary glass-forming system. In other systems, free volume changes can be complicated by changes in the basic nature of the glass structure, such as the formation of non-bridging oxygens upon addition of alkali oxides or changes in the network former co-ordination number in alkali borates or germanates when a specific concentration of alkali is reached [13]. Gas behavior can also be affected by phase separation, sometimes more so than by changes in the atomistic structure of the glass [1]. Binary germanosilicates are free of these effects because these glasses are believed to
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be isostructural with vitreous silica, with (GeO4 4 ) tetrahedral structural units randomly substituted for (SiO4 4 ) tetrahedra throughout the glass network [1]. In this case, any deviations from additivity observed in the gas solubility or diffusivity as silica is replaced by germania are due directly to changes in the free volume of the structure. This paper reports the results of helium and neon solubility and diffusivity measurements in vitreous silica, vitreous germania, and in a series of binary GeO2– SiO2 glasses. Results are discussed in terms of changes in the interstice size and/or distribution as a function of glass composition and experimental temperature.
The values reported for each glass in this study represent the average obtained for at least three separate measurements. The range of values for any given set of measurements varies from a few percent for glasses with high gas solubilities to 10–20% for glasses with low gas solubilities.
3. Results The temperature dependence of helium and neon solubility in vitreous SiO2 and GeO2 is shown in Figs. 1 and 2. The solubility of helium and neon in GeO2 is less than SiO2 for any given temperature, with gas solubility
2. Experimental procedure Vitreous germania was prepared from 99.9% pure germania. The GeO2 powder was placed in a Pt/10Rh crucible and melted in an electric resistance furnace for 8 h at 1550 C. The glass was then annealed at its glass transformation temperature (Tg) of 500 C. Vitreous silica samples were obtained from a commercial source (Infrasil, which is manufactured by electrical fusion of quartz powder, and Suprasil, made by hydrolyzation of SiCl4 in an O2–H2 flame). Samples of the binary germanosilicates were supplied by Sandia National Laboratories, Bell Laboratories, and Corning Incorporated. Gas solubility samples were 1 mm thick plates cut from the bulk glasses. Diffusion measurements were carried out on samples in the form of 0.25 mm thick disks. All specimens were free of bubbles and had no visible striations. Solubility measurements were conducted using a saturation-outgassing technique developed by Jewell [14]. Details of this method have been discussed elsewhere [14–18] and will only be reviewed briefly here. Samples in the form of thin plates are exposed to the gas of interest at a known pressure and temperature for enough time to ensure equilibration with the surrounding atmosphere. The gas is frozen into the glass structure by rapidly removing the plates, which are contained in a small platinum crucible, from the saturation apparatus and quenching them in water. The sample is transferred to an outgassing system equipped with a residual gas analyzer (RGA) and reheated under vacuum to a temperature suitable to drive off the gas of interest in less than 1 h. The area under a measured curve is directly proportional to the amount of gas dissolved in the sample. Solubility values are determined by normalizing the amount of gas released from the glass by the sample mass and saturation pressure. Diffusion measurements were conducted using the more established permeation technique. Details of this method have been discussed in several studies by Shelby [7,12,19–21] and will not be repeated here.
Fig. 1. Effect of temperature on helium solubility in vitreous SiO2 and GeO2. Closed symbols are from this study while open symbols are literature values from Shelby [7,20].
Fig. 2. Effect of temperature on neon solubility in vitreous SiO2 and GeO2. Closed symbols are from this study while open symbols are literature values from Shelby [12].
C.C. Tournour, J.E. Shelby / Journal of Non-Crystalline Solids 349 (2004) 209–214
211
Table 1 Temperature dependence parameters for helium and neon solubility in vitreous silica and germania Glass
Gas
Temperature range (C)
S0 (·1016 atoms/gm-atm)
SiO2 (present study) SiO2 (Shelby) SiO2 (literature avg.)
He He He
69–861 103–636 25–1050
8.34 9.98 6.73
710 450 760
GeO2 (present study) GeO2 (Shelby) GeO2 (Doremus)
He He He
115–790 110–176 300–500
4.74 3.43 4.23
150 240 0a
SiO2 (present study) SiO2 (Shelby) SiO2 (literature avg.)
Ne Ne Ne
271–846 194–457 25–1050
3.77 3.80 3.16
1540 1320 1660
GeO2 (present study) GeO2 (Doremus)
Ne Ne
101–756 300–500
4.19 4.23
0 0a
DHS (cal/mol)
a
A value of zero essentially states that there is no slope to the defined curve (i.e. there is no enthalpy of solution for the gas atom to occupy the interstitial site).
in silica decreasing with increasing temperature while gas solubility in germania does not show any significant temperature dependence over the temperature range measured. The temperature dependence of the solubility is expressed by the vanÕt Hoff equation S ¼ S 0 expðDH S =RT Þ;
ð1Þ
where S is the solubility, S0 is the solubility at infinite temperature, DHS is the enthalpy of solution, R is the gas constant, and T is the absolute temperature. The values of S0 and DHS determined from this equation, along with some published values for comparison, are listed in Table 1. These results show both a lower enthalpy of solution and S0 for vitreous germania in comparison to vitreous silica. It is also worth noting that the present study uses a saturation-outgassing technique to directly measure solubility whereas past studies primarily used the permeation method in which solubilities were calculated by dividing a measured permeability by a measured diffusivity. It has been previously shown that helium and neon solubility in vitreous silica obey HenryÕs Law up to 1 atm of gas pressure [8]. Such a trend, however, has yet to be established for vitreous germania. The pressure dependence of the gas solubilities shown in Fig. 3 for helium both confirms the previous data for SiO2 and demonstrates that helium solubility in GeO2 does indeed increase linearly as a function of the helium partial pressure, i.e., it obeys HenryÕs Law. Neon solubility as a function of pressure, as shown in Fig. 4, has also been found to increase linearly with increasing partial pressure of the gas for both silica and germania. The solubility of helium and neon in binary germanosilicate glasses approaches the solubility of these gases in pure vitreous GeO2 as silica is replaced in the network. This relationship is illustrated in Figs. 5 and 6, which show the compositional dependence of helium and neon solubility at 500 C, respectively. Both helium
Fig. 3. Effect of saturation pressure on the concentration of helium in vitreous SiO2 and GeO2 at 500 C.
Fig. 4. Effect of saturation pressure on the concentration of neon in vitreous SiO2 and GeO2 at 500 C.
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Fig. 5. Effect of replacing silica with germania on helium solubility in a series of GeO2–SiO2 glasses. Closed symbols are from saturationoutgassing measurements while open symbols are from permeation measurements.
Fig. 7. Effect of temperature on helium diffusion in a series of GeO2– SiO2 glasses with the mol% germania indicated in the legend above. Error bars are of the size of the symbols in the figure.
Fig. 6. Effect of replacing silica with germania on helium and neon solubility in a series of GeO2–SiO2 glasses.
Fig. 8. Effect of replacing silica with germania on helium diffusivity in a series of GeO2–SiO2 glasses. Error bars are of the size of the symbols in the figure.
Table 2 Temperature dependence parameters for helium diffusion in a series of GeO2–SiO2 glasses D0 (·104 cm2/s)
ED (cal/mol)
Glass
Gas
Temperature range (C)
SiO2 (present study) SiO2 (Shelby) SiO2 (literature avg.)
He He He
124–235 90–171 –
3.7 3.8 5.5
5610 5510 6200
2.5GeO2–97.5SiO2 13.5GeO2–86.5SiO2 31.0GeO2–69.0SiO2
He He He
110–227 103–222 101–208
3.4 3.9 4.9
5590 5750 6235
GeO2 (present study) GeO2 (Shelby) GeO2 (literature avg.)
He He He
133–219 110–176 –
9.4 12.3 15.2
7800 7770 8020
C.C. Tournour, J.E. Shelby / Journal of Non-Crystalline Solids 349 (2004) 209–214
and neon solubility decrease rapidly with initial replacement of SiO2 by GeO2 in these glasses, followed by a more gradual decrease in solubility with continued replacement of silica in the network. Diffusivity measurements were made using a permeation method at temperatures below 300 C and are shown in Fig. 7 as a function of temperature. Isothermal helium diffusivity is shown in Fig. 8 as a function of increasing germania concentration at 200 C. Helium diffusivity also decreases as silica is replaced by germania, approaching the diffusivity of vitreous germania with decreasing silica concentration. Temperature dependence parameters were determined from an Arrhenius fit to the diffusivity data and are listed in Table 2. The activation energy for diffusion increases as the germania concentration increases.
4. Discussion Doremus [5,22] suggests that the solubilities of various gases in glass are a measure of the free volume of the network structure. His model proposes that inert gas dissolution is a simple physical process where the gas atoms occupy empty interstices within the network. Using this model, the observed decrease in solubility as silica is replaced by germania in a series of GeO2–SiO2 glasses can be due to either inaccessible interstices caused by too small a doorway between adjacent solubility sites or to a change in the size distribution of interstitial sites. A significant change in the doorway size between sites would result in a corresponding change in the activation energy for diffusion due to the additional energy necessary to further dilate the doorway to the size of the diffusing atom for the more compact structure. Similarly, a change in the size distribution of interstitial sites leads to changes in S0 and the enthalpy of solution [23]. Results of the present study indicate only a small increase in the activation energy for diffusion as germania replaces silica, leading to the conclusion that changes in doorway size in this series of glasses is small. The lower solubility of helium and neon in germania must therefore be due to differences in the distribution of interstices, meaning that GeO2 contains a smaller concentration of appropriately sized interstices available to atoms of the size of helium and neon. Kurkjian and Douglas [24] found that, although the [RO4 4 ] tetrahedron for vitreous GeO2 has a larger volume than that of vitreous SiO2, the smaller R–O–R bond angle of the germania network leads to a more dense packing of these tetrahedral structural units. Assuming the interstitial size distribution for both of these glass-forming oxides is lognormal, as proposed by Shackelford [25,26], the mean of this distribution must be less for vitreous germania than for vitreous silica. This decrease in the mean interstitial size essentially
213
shifts the entire distribution to the left, yielding a smaller number of interstices capable of accommodating helium or neon atoms. The solubility values determined in the present study generally support this view. More specifically, the negative deviation from additivity observed in the compositional dependence of helium and neon solubility in GeO2–SiO2 glasses is due to an increase in packing efficiency as the concentration of the more compact (GeO4 4 ) tetrahedra increases. The replacement of silica by germania in the network results in either a decreasing number of accessible interstices or a decreasing average size of the solubility sites. A decrease in the concentration of accessible sites is reflected by a decrease in S0, whereas a decrease in the average interstice size results in an increase in the enthalpy of solution [23]. The scatter in the solubility data as well as the relatively small changes in S0 and DHS, shown in Table 1, make it impossible to distinguish between these two mechanisms. It is likely that both mechanisms are acting simultaneously to affect the gas solubility in the glasses.
5. Conclusions Helium and neon solubility are affected by changes in interstice size and/or distribution as a function of glass composition and experimental temperature. Gas solubilities approach those of vitreous germania as the concentration of GeO2 increases in binary GeO2–SiO2 glasses, with initial replacement of silica by germania causing a more dramatic decrease in the solubility than further replacement. This trend is due to a shifting interstice distribution as the mean interstice size decreases, resulting in fewer sites large enough to accommodate a helium or neon atom. Similarly, helium diffusion in these glasses is affected by changes in the free volume of the structure. Activation energies for diffusion indicate that the size of the doorways between interstitial sites are similar for vitreous silica and germania, but GeO2 has been shown to have a more compact network [24], and therefore, lower diffusion coefficient than vitreous silica. Both the solubility and diffusivity of helium and neon in germanosilicate glasses are temperature dependent. Solubility decreases as a function of increasing temperature, with vitreous silica displaying a small temperature dependence for gas solubility while vitreous germania shows little, if any, dependence upon temperature. Helium diffusion increases with increasing temperature over the limited temperature region of this study.
References [1] J.E. Shelby, Handbook of Gas Diffusion in Solids and Melts, ASM International, Materials Park, OH, 1996. [2] D.E. Swets, R.W. Lee, R.C. Frank, J. Chem. Phys. 34 (1961) 17.
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[3] V.H.-O. Mulfinger, H. Scholze, Glastech. Ber. 35 (1962) 466. [4] H. Scholze, H.-O. Mulfinger, H. Franz, 6th International Congress on Glass, 1962. [5] R.H. Doremus, J. Am. Ceram. Soc. 49 (1966) 461. [6] J.F. Shackelford, P.L. Studt, R.M. Fulrath, J. Appl. Phys. 43 (1972) 1619. [7] J.E. Shelby, J. Appl. Phys. 43 (1972) 3068. [8] J.E. Shelby, J. Appl. Phys. 47 (1976) 135. [9] E. Papanikolau, J. Non-Cryst. Solids 38&39 (1980) 563. [10] R.C. Frank, D.E. Swets, R.W. Lee, J. Chem. Phys. 35 (1961) 1451. [11] W.G. Perkins, D.R. Begeal, J. Chem. Phys. 54 (1971) 1683. [12] J.E. Shelby, Phys. Chem. Glasses 13 (1972) 167. [13] J.E. Shelby, Introduction to Glass Science and Technology, The Royal Society of Chemistry, Cambridge, UK, 1997. [14] J.M. Jewell, PhD thesis, Alfred University, 1986.
[15] J. T. Kohli, PhD thesis, Alfred University, 1987. [16] M.G. Mesko, K. Newton, J.E. Shelby, Phys. Chem. Glasses 41 (2000) 111. [17] M.G. Mesko, B.E. Kenyon, J.E. Shelby, Glastech. Ber. 73 (2000) 33. [18] M.G. Mesko, J.E. Shelby, Phys. Chem. Glasses 43 (2002) 91. [19] J.E. Shelby, Phys. Rev. 4 (1971) 2681. [20] J.E. Shelby, J. Am. Ceram. Soc. 55 (1972) 61. [21] J.E. Shelby, S.C. Keeton, J. Am. Ceram. Soc. 57 (1974) 45. [22] R.H. Doremus, Phys. Chem. Glasses 3 (1962) 127. [23] J.E. Shelby, J. Appl. Phys. 46 (1975) 4510. [24] C.R. Kurkjian, R.W. Douglas, Phys. Chem. Glasses 1 (1960) 19. [25] J.F. Shackelford, J.S. Masaryk, J. Non-Cryst. Solids 30 (1978) 127. [26] J.F. Shackelford, B.D. Brown, J. Am. Ceram. Soc. 63 (1980) 562.
Inert gas solubility in binary germania–silica glasses Christopher C. Tournour, James E. Shelby
*
HOGSE, New York State College of Ceramics, NYSCC at Alfred University, 2 Pine Street, Alfred, NY 14802, USA Available online 2 November 2004
Abstract Helium and neon solubility have been measured in vitreous silica, vitreous germania, and in a series of binary GeO2–SiO2 glasses. Measurements were made over a broad temperature range using a saturation-outgassing method. The enthalpy of solution of these gases is smaller for vitreous germania than for vitreous silica. Inert gas solubility decreases rapidly as silica is initially replaced by germania in the network, with a more gradual decrease in solubility with continued reduction in silica content. Solubility measurements at varying pressures establish that inert gas solubility in vitreous germania obeys HenryÕs Law up to 1 atm of gas pressure, as has already been established for vitreous silica. Additional helium solubility and diffusivity measurements were made using the permeation method at temperatures below 300 C. Helium diffusivity also decreases as silica is replaced by germania, with an approximately linear dependence on composition. The activation energy for diffusion increases as the germania concentration increases. Results of this study are attributed to changes in interstice size and/or distribution as a function of glass composition and experimental temperature. 2004 Elsevier B.V. All rights reserved. PACS: 61.43.Fs; 66.30.h
1. Introduction Inert gas migration measurements are excellent probes of the network structure of glasses and melts [1]. Unlike more chemically reactive gases, such as water vapor and carbon dioxide, inert gas atoms do not interact with the glass structure. These atoms reside in the interstitial spaces in the network. Gas solubility measurements can be used to reveal information regarding the amount and distribution of the free volume, while diffusion measurements can give information regarding the doorways between interstitial sites. Although helium migration has been studied extensively in vitreous silica [2–9], fewer studies have been re-
* Corresponding author. Tel.: +1 607 871 2470; fax: +1 607 871 2354. E-mail addresses: [email protected] (C.C. Tournour), [email protected] (J.E. Shelby).
0022-3093/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2004.08.144
ported for neon migration in this glassformer [6,8,10– 12]. Even less information is available for inert gas solubility and diffusion in vitreous germania [5,7]. It would appear that the ideas proposed for inert gas migration in vitreous silica could be confirmed by a similar study of helium and neon migration in vitreous germania, whose structure is similar to silica. Combinations of these two basic glassformers can also yield valuable information regarding how the free volume changes in a binary glass-forming system. In other systems, free volume changes can be complicated by changes in the basic nature of the glass structure, such as the formation of non-bridging oxygens upon addition of alkali oxides or changes in the network former co-ordination number in alkali borates or germanates when a specific concentration of alkali is reached [13]. Gas behavior can also be affected by phase separation, sometimes more so than by changes in the atomistic structure of the glass [1]. Binary germanosilicates are free of these effects because these glasses are believed to
210
C.C. Tournour, J.E. Shelby / Journal of Non-Crystalline Solids 349 (2004) 209–214
be isostructural with vitreous silica, with (GeO4 4 ) tetrahedral structural units randomly substituted for (SiO4 4 ) tetrahedra throughout the glass network [1]. In this case, any deviations from additivity observed in the gas solubility or diffusivity as silica is replaced by germania are due directly to changes in the free volume of the structure. This paper reports the results of helium and neon solubility and diffusivity measurements in vitreous silica, vitreous germania, and in a series of binary GeO2– SiO2 glasses. Results are discussed in terms of changes in the interstice size and/or distribution as a function of glass composition and experimental temperature.
The values reported for each glass in this study represent the average obtained for at least three separate measurements. The range of values for any given set of measurements varies from a few percent for glasses with high gas solubilities to 10–20% for glasses with low gas solubilities.
3. Results The temperature dependence of helium and neon solubility in vitreous SiO2 and GeO2 is shown in Figs. 1 and 2. The solubility of helium and neon in GeO2 is less than SiO2 for any given temperature, with gas solubility
2. Experimental procedure Vitreous germania was prepared from 99.9% pure germania. The GeO2 powder was placed in a Pt/10Rh crucible and melted in an electric resistance furnace for 8 h at 1550 C. The glass was then annealed at its glass transformation temperature (Tg) of 500 C. Vitreous silica samples were obtained from a commercial source (Infrasil, which is manufactured by electrical fusion of quartz powder, and Suprasil, made by hydrolyzation of SiCl4 in an O2–H2 flame). Samples of the binary germanosilicates were supplied by Sandia National Laboratories, Bell Laboratories, and Corning Incorporated. Gas solubility samples were 1 mm thick plates cut from the bulk glasses. Diffusion measurements were carried out on samples in the form of 0.25 mm thick disks. All specimens were free of bubbles and had no visible striations. Solubility measurements were conducted using a saturation-outgassing technique developed by Jewell [14]. Details of this method have been discussed elsewhere [14–18] and will only be reviewed briefly here. Samples in the form of thin plates are exposed to the gas of interest at a known pressure and temperature for enough time to ensure equilibration with the surrounding atmosphere. The gas is frozen into the glass structure by rapidly removing the plates, which are contained in a small platinum crucible, from the saturation apparatus and quenching them in water. The sample is transferred to an outgassing system equipped with a residual gas analyzer (RGA) and reheated under vacuum to a temperature suitable to drive off the gas of interest in less than 1 h. The area under a measured curve is directly proportional to the amount of gas dissolved in the sample. Solubility values are determined by normalizing the amount of gas released from the glass by the sample mass and saturation pressure. Diffusion measurements were conducted using the more established permeation technique. Details of this method have been discussed in several studies by Shelby [7,12,19–21] and will not be repeated here.
Fig. 1. Effect of temperature on helium solubility in vitreous SiO2 and GeO2. Closed symbols are from this study while open symbols are literature values from Shelby [7,20].
Fig. 2. Effect of temperature on neon solubility in vitreous SiO2 and GeO2. Closed symbols are from this study while open symbols are literature values from Shelby [12].
C.C. Tournour, J.E. Shelby / Journal of Non-Crystalline Solids 349 (2004) 209–214
211
Table 1 Temperature dependence parameters for helium and neon solubility in vitreous silica and germania Glass
Gas
Temperature range (C)
S0 (·1016 atoms/gm-atm)
SiO2 (present study) SiO2 (Shelby) SiO2 (literature avg.)
He He He
69–861 103–636 25–1050
8.34 9.98 6.73
710 450 760
GeO2 (present study) GeO2 (Shelby) GeO2 (Doremus)
He He He
115–790 110–176 300–500
4.74 3.43 4.23
150 240 0a
SiO2 (present study) SiO2 (Shelby) SiO2 (literature avg.)
Ne Ne Ne
271–846 194–457 25–1050
3.77 3.80 3.16
1540 1320 1660
GeO2 (present study) GeO2 (Doremus)
Ne Ne
101–756 300–500
4.19 4.23
0 0a
DHS (cal/mol)
a
A value of zero essentially states that there is no slope to the defined curve (i.e. there is no enthalpy of solution for the gas atom to occupy the interstitial site).
in silica decreasing with increasing temperature while gas solubility in germania does not show any significant temperature dependence over the temperature range measured. The temperature dependence of the solubility is expressed by the vanÕt Hoff equation S ¼ S 0 expðDH S =RT Þ;
ð1Þ
where S is the solubility, S0 is the solubility at infinite temperature, DHS is the enthalpy of solution, R is the gas constant, and T is the absolute temperature. The values of S0 and DHS determined from this equation, along with some published values for comparison, are listed in Table 1. These results show both a lower enthalpy of solution and S0 for vitreous germania in comparison to vitreous silica. It is also worth noting that the present study uses a saturation-outgassing technique to directly measure solubility whereas past studies primarily used the permeation method in which solubilities were calculated by dividing a measured permeability by a measured diffusivity. It has been previously shown that helium and neon solubility in vitreous silica obey HenryÕs Law up to 1 atm of gas pressure [8]. Such a trend, however, has yet to be established for vitreous germania. The pressure dependence of the gas solubilities shown in Fig. 3 for helium both confirms the previous data for SiO2 and demonstrates that helium solubility in GeO2 does indeed increase linearly as a function of the helium partial pressure, i.e., it obeys HenryÕs Law. Neon solubility as a function of pressure, as shown in Fig. 4, has also been found to increase linearly with increasing partial pressure of the gas for both silica and germania. The solubility of helium and neon in binary germanosilicate glasses approaches the solubility of these gases in pure vitreous GeO2 as silica is replaced in the network. This relationship is illustrated in Figs. 5 and 6, which show the compositional dependence of helium and neon solubility at 500 C, respectively. Both helium
Fig. 3. Effect of saturation pressure on the concentration of helium in vitreous SiO2 and GeO2 at 500 C.
Fig. 4. Effect of saturation pressure on the concentration of neon in vitreous SiO2 and GeO2 at 500 C.
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Fig. 5. Effect of replacing silica with germania on helium solubility in a series of GeO2–SiO2 glasses. Closed symbols are from saturationoutgassing measurements while open symbols are from permeation measurements.
Fig. 7. Effect of temperature on helium diffusion in a series of GeO2– SiO2 glasses with the mol% germania indicated in the legend above. Error bars are of the size of the symbols in the figure.
Fig. 6. Effect of replacing silica with germania on helium and neon solubility in a series of GeO2–SiO2 glasses.
Fig. 8. Effect of replacing silica with germania on helium diffusivity in a series of GeO2–SiO2 glasses. Error bars are of the size of the symbols in the figure.
Table 2 Temperature dependence parameters for helium diffusion in a series of GeO2–SiO2 glasses D0 (·104 cm2/s)
ED (cal/mol)
Glass
Gas
Temperature range (C)
SiO2 (present study) SiO2 (Shelby) SiO2 (literature avg.)
He He He
124–235 90–171 –
3.7 3.8 5.5
5610 5510 6200
2.5GeO2–97.5SiO2 13.5GeO2–86.5SiO2 31.0GeO2–69.0SiO2
He He He
110–227 103–222 101–208
3.4 3.9 4.9
5590 5750 6235
GeO2 (present study) GeO2 (Shelby) GeO2 (literature avg.)
He He He
133–219 110–176 –
9.4 12.3 15.2
7800 7770 8020
C.C. Tournour, J.E. Shelby / Journal of Non-Crystalline Solids 349 (2004) 209–214
and neon solubility decrease rapidly with initial replacement of SiO2 by GeO2 in these glasses, followed by a more gradual decrease in solubility with continued replacement of silica in the network. Diffusivity measurements were made using a permeation method at temperatures below 300 C and are shown in Fig. 7 as a function of temperature. Isothermal helium diffusivity is shown in Fig. 8 as a function of increasing germania concentration at 200 C. Helium diffusivity also decreases as silica is replaced by germania, approaching the diffusivity of vitreous germania with decreasing silica concentration. Temperature dependence parameters were determined from an Arrhenius fit to the diffusivity data and are listed in Table 2. The activation energy for diffusion increases as the germania concentration increases.
4. Discussion Doremus [5,22] suggests that the solubilities of various gases in glass are a measure of the free volume of the network structure. His model proposes that inert gas dissolution is a simple physical process where the gas atoms occupy empty interstices within the network. Using this model, the observed decrease in solubility as silica is replaced by germania in a series of GeO2–SiO2 glasses can be due to either inaccessible interstices caused by too small a doorway between adjacent solubility sites or to a change in the size distribution of interstitial sites. A significant change in the doorway size between sites would result in a corresponding change in the activation energy for diffusion due to the additional energy necessary to further dilate the doorway to the size of the diffusing atom for the more compact structure. Similarly, a change in the size distribution of interstitial sites leads to changes in S0 and the enthalpy of solution [23]. Results of the present study indicate only a small increase in the activation energy for diffusion as germania replaces silica, leading to the conclusion that changes in doorway size in this series of glasses is small. The lower solubility of helium and neon in germania must therefore be due to differences in the distribution of interstices, meaning that GeO2 contains a smaller concentration of appropriately sized interstices available to atoms of the size of helium and neon. Kurkjian and Douglas [24] found that, although the [RO4 4 ] tetrahedron for vitreous GeO2 has a larger volume than that of vitreous SiO2, the smaller R–O–R bond angle of the germania network leads to a more dense packing of these tetrahedral structural units. Assuming the interstitial size distribution for both of these glass-forming oxides is lognormal, as proposed by Shackelford [25,26], the mean of this distribution must be less for vitreous germania than for vitreous silica. This decrease in the mean interstitial size essentially
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shifts the entire distribution to the left, yielding a smaller number of interstices capable of accommodating helium or neon atoms. The solubility values determined in the present study generally support this view. More specifically, the negative deviation from additivity observed in the compositional dependence of helium and neon solubility in GeO2–SiO2 glasses is due to an increase in packing efficiency as the concentration of the more compact (GeO4 4 ) tetrahedra increases. The replacement of silica by germania in the network results in either a decreasing number of accessible interstices or a decreasing average size of the solubility sites. A decrease in the concentration of accessible sites is reflected by a decrease in S0, whereas a decrease in the average interstice size results in an increase in the enthalpy of solution [23]. The scatter in the solubility data as well as the relatively small changes in S0 and DHS, shown in Table 1, make it impossible to distinguish between these two mechanisms. It is likely that both mechanisms are acting simultaneously to affect the gas solubility in the glasses.
5. Conclusions Helium and neon solubility are affected by changes in interstice size and/or distribution as a function of glass composition and experimental temperature. Gas solubilities approach those of vitreous germania as the concentration of GeO2 increases in binary GeO2–SiO2 glasses, with initial replacement of silica by germania causing a more dramatic decrease in the solubility than further replacement. This trend is due to a shifting interstice distribution as the mean interstice size decreases, resulting in fewer sites large enough to accommodate a helium or neon atom. Similarly, helium diffusion in these glasses is affected by changes in the free volume of the structure. Activation energies for diffusion indicate that the size of the doorways between interstitial sites are similar for vitreous silica and germania, but GeO2 has been shown to have a more compact network [24], and therefore, lower diffusion coefficient than vitreous silica. Both the solubility and diffusivity of helium and neon in germanosilicate glasses are temperature dependent. Solubility decreases as a function of increasing temperature, with vitreous silica displaying a small temperature dependence for gas solubility while vitreous germania shows little, if any, dependence upon temperature. Helium diffusion increases with increasing temperature over the limited temperature region of this study.
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