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Interdiffusion of hydrogen and alkali ions in a glass surface
Journal of Non-Crystalline Solids 19 (1975) 137-144 © North-Holland Publishing Company
INTERDIFFUSION OF HYDROGEN AND ALKALI IONS IN A GLASS SURFACE R.H. DOREMUS Rensselaer Polytechnic Institute, Materials Engineering Department, Troy, New York 12181, USA
Experimental data on the interdiffusion of hydrogen and alkali ions in glass are examined using a concentration-dependent interdiffusion coefficient, taking into account surface dissolution. The comparisons between calculated and experimental concentration profiles and diffusion coefficients are more satisfactory than for a concentration-independent diffusion coefficient, and support the use of the interdiffusion coefficient.
1. Introduction Water reacts with the surfaces of silicate glasses to form a hydrated silica-rich layer. If the glass contains alkali, hydration is preceded by ion exchange between hydrogen (or hydronium) ions from the water and alkali ions in the glass Na + (glass) + H20 = H+ (glass) + NaOH.
(1)
Concentration profiles resulting from this exchange and subsequent interdiffusion have been measured in several different ways [ 1 - 6 ] . Boksay et al. [1 ] developed a theory to explain these profiles, but their theory fitted the observed profiles only for potassium silicate glasses. Their theory assumed a diffusion coefficient invariant with ionic concentration, and they attributed the discrepancies between theory and experiment for sodium silicate glasses to a diffusion coefficient dependent upon ionic concentration. Profiles in lithium silicate glasses, one of which is shown in fig. 1, are similar to those in sodium silicate glasses [5], and they also do not fit the simple theory of Boksay et al. In this paper the theory of Boksay et al. is extended by using a concentrationdependent diffusion coefficient. The profiles found for steady-state diffusion are consistent with those found experimentally. These and other experimental results on the reaction of water with glass are discussed in terms of the new theory, taking into account the structure of the hydrated layer as deduced from the work of Wikby [7]. 137
138
R.H. Doremus /Interdiffusion of hydrogen and alkali ions 1.0
o
0.8
0.6- _
o
o
E
"E 0 . 4 -
!
_ 02-
L
I
i
I
2
4
6
8
I0
12
I
14
ay/DH Fig. 1. Profile of lithium ion in a lithium silicate glass, measured from photon emission during sputtering. The glass was held 16 h in 0.1N H2SO4 at 50°C (curve g, fig. 5, ref. [5]). Points measured; line calculated from eq. (9) with b = 2600.
2.
Theory
The reaction o f water with an alkali silicate glass can be separated into two stages [8]. In the first the amount o f sodium and silica dissolved is proportional to the square root o f time, whereas in the second the amount dissolved is proportional to time. These dependencies suggest that the dissolution process is initially controlled by diffusion, and then b y a surface reaction. The dissolution of the glass surface means that diffusion in the glass must be considered with respect to a moving boundary. I f x is the distance o f a plane in the glass from its initial surface, then y , the distance from the actual surface, at time t is (2)
y = x - at,
where a is the rate of dissolution of the surface, which is assumed to be constant with time. Then the diffusion equation in x coordinates (ac/atx)
= (a/ax) D(ac/ax)t
,
(3)
where c is the concentration of diffusing material, can be transformed to y coordi-
R.H. Doremus / Interdiffusion of hydrogen and alkali ions
139
nates [1,2]
(ac/Bt)y : (a/By) D (Bc/BY)t + a(ac/OY)t .
(4)
Diffusion is assumed to occur in semi-infinite geometry with a constant concentration at the glass surface. For convenience it is assumed that the concentration c = 0 at y = 0 (the glass surface) and c = 1 far into the glass as y ~ oo. For these boundary conditions eq. (4) can be solved analytically when D is independent of concentration, but its solution is difficult for the concentration dependence of D desired here. Thus the equation will be solved for the steady-state Bc/Ot = 0. For this condition and the above boundary conditions [1,2] c : 1 - exp ( - a y / D ) .
(S)
This exponential profile fits the data for a potassium silicate glass [ 1 ], but not for other glasses, an example of which is shown in fig, 1. Interdiffusion of two cations A and B can be described by an interdiffusion coefficient D of the form [9]
D =DADB/[CD A + (1 - C) DB] ,
(6)
where D A and D B are individual ionic diffusion coefficients and c is fhe atom fraction of A ions. This equation can also be written D = D A / [ 1 +c (DA/D B - 1] .
(7)
In interdiffusion of sodium and silver ions in a soda-lime glass at 378°C, eq. (7) was found to hold with D A and D B independent of ionic concentration [10]. There is some question as to whether or not a mixed alkali effect would cause D A and D B to vary with ionic concentration for other ionic pairs; however eq. (7) with constant D A and D B is at least consistent with interdiffusion of sodium and potassium in a soda-lime glass [ I 1 ]. Thus it is assumed that eq. (7) with D A and D B constant holds for interdiffusion of hydrogen (or hydronium) ions and alkali ions near room temperature. When eq. (7) for D is used for D in eq. (4), with Bc/ay = 0 and dc/dy ~ 0 a s y -+ o% then IDA/(1 + bc)] dc/dy = a(1 - c ) ,
(8)
where b = D A / D B - 1. A is the alkali ion initially in the glass, and c is its concentration. Solution of eq. (8) with the condition c = 0 when y = 0 gives c = [1 + e x p ( - a y / D B ) l/[1 + b exp (--ay/DB) ] .
(9)
When the ratio D A / D B = 1, b = 0 and D is independent of concentration. Then eq. (9) is the same as eq. (5).
R.H. Doremus / Interdiffusion of hydrogen and alkali ions
140
3. Comparison with experimental data and discussion Curves of concentration as a function of the dimensionless parameter ay/D B as calculated from eq. (9), are given in fig. 2 for various values of b (= D A / D B - 1). The curves are similar to that in fig. 1 and those in refs. [ 1 - 6 ] for sodium and lithium silicate glasses, showing that eq. (9) is superior to eq. (5) with constant D for describing the interdiffusion process. There are several difficulties in making a more detailed comparison between the experimental data and eq. (9), as outlined below. Baucke has found that the ratio of lithium to hydrogen mobilities in the same glass as used for fig. 1 is about 2600 at 50°C from electrolysis experiments [12]. The calculated curve for this mobility ratio gives a sharper increase of lithium concentration than the experimental data. This results because the resolution of the technique is limited to about 40 A, so an atomically sharp interface appears to be spread out about 70 A in width [5]. Since the total width of the surface layer shown in fig. 1 is about 300 ,/~, the lithium profile appears to be more spread out than it actually is. Baucke [5] found that the rate of dissolution of the glass was about 1.0 A/h at 50°C, so that a = 2.8 X 10 -12 cm/s. For the data in fig. 1 the concentration was 0.5 at a distance of 181 A from the glass surface. Since ay/D A = 7.9 at c = 0.5 for b = 2600, D H = 6.4 X 10 -19 cm2/s andDLi = 1.7 X 10-t5/cm2/s. The value of DLi can be compared with that calculated from the electrical resistivity p and the I.O IO
_
i
0.8--
0.6--
O
04--
0.2
Oo
2
4
6
8
IO
12
14
ay/D l,'ig. 2. Concentration profiles calculated from eq. (9) with different values of b (on curves).
141
R.H. Doremus /In terdiffusion of hydrogen and alkali ions outer surface
gel-glass interfoee
1.0
0.8 glass containing
gel 0.6
,er
s
,,Often ,ons
/
oo=,.,.g al~c i ~ s
"6 ~ o
0.4
8 0.2
I 0
Z
~ 4
I
1
1
I
6
8
I0
12
distance
Fig. 3. Model of the hydrated layers on the surface of alkali silicate glass.
Einstein equation DLi = RT/pF2CLi.
(10)
From Baucke's data p = 7.7 X 109 ~2-cm at 50°C and CLi ~ 2.4 × 10 -2 mol/cm 3. Then from eq. (10) DLi = 1.6 × 10 -15 cm2/s, in fortuitously good agreement with the value from eq. (9) and the interdiffusion profile. This agreement at least shows that eq. (9) is consistent with other data on the glass of fig. 1. Another difficulty in comparing eq. (9) with experimental data results from the formation of a gel-like hydrated layer on glass surfaces. Wikby showed that the conductivity of such a layer is much greater than that of the dry glass containing alkali ions [7]. A simplified model of various layers on a glass surface after some ion exchange and hydration is shown in fig. 3. The outer surface of the glass is dissolving into the solution; this is the rate of dissolution measured by the rate of silica appearance in the solution. In the gel layer, ions are quite mobile [7, 13], and water can penetrate to the gel-glass interface. Both the outer surface and gel-glass surface are probably not as sharp as shown in fig. 3, but are rather spread out with a continuous change of properties over many atomic layers. The rate of interface motion a used in the above derivations of the diffusion equation should strictly be the rate at which the gel-glass interface moves relative to the original glass interface; this rate should be somewhat faster than the rate of movement of the outer surface. The transformation from the initial glass network of silicon-oxygen bonds to the looser gel structure results from the reaction of water with these bonds:
142
R.H. Doremus /lnterdiffusion o f hydrogen and alkali ions
H20 + S i - O - S i = SiOH HOSi.
(11)
This reaction breaks up the strong, rigid glass network to a more weakly bonded gel; however, the gel still contains enough primary Si-O bonds to hold it together and delay dissolution. The exact mechanism of this reaction is uncertain. It could result from a direct attack of water in the gel layer on the gel-glass interface. However, it is also possible that the hydrogen ions carry along water molecules in the form of hydronium ions (H30+). Once these water molecules are in the rigid glass they may react with the glass network by reaction [11], leading to a progressive deterioration of the network, making it more open. Then neutral water molecules could penetrate the partly hydrated layer and react with Si-O bonds, resulting in further hydration of the glass and eventual dissolution. With this mechanism the gel-glass interface may be quite diffuse. It is difficult to compare eq. (9) with the profiles of sodium in the surfaces of various glasses as measured by Boksay et al. [1, 2]. and Dobos [3] because of uncertainties in the position of the gel-glass interface and the ratios of alkali-to-hydrogen ion mobility in their glasses. The shapes of the profiles in fig. 1, ref. [1 ] (glasses 1 and 2, 28% Na20 , 4% BaO or SrO, 68% SiO2) are consistent with the curves of fig. 2 for high mobility ratios (104-105), and a gel layer about half the total thickness of the surface diffusion layer; a layer of about this thickness can be I.O
0.8
~ O.6 o
._~ 0.4
~O.2 0
I 0
I 0.4
I
i 0.8
distance
I
I 1.2
I
I 1.6
I 2.0
(micronsl
Fig. 4. Concentration profile of hydrogen ions in the surface of a natural obsidian [6] (points), compared to calculated profile for DA/D B = 100 from eq. (6) (line).
R.H. Doremus /lnterdiffusion of hydrogen and alkali ions
143
deduced for some of Wikby's sodium-calcium silicate glasses [7]. Profiles for glass No. 4 (20 mol% K20 , 12% SrO, 68% SiO2) in ref. [1], fig. 2, and ref. [3] indicate a potassium-to-hydrogen ion mobility ratio of perhaps about 10-1, with a thinner gel layer. This low ratio is possibly evidence for hydronium ion (H30+), rather than hydrogen ion, exchange. The radius of the hydronium ion (~1.4) is about the same as for potassium (1.33), although the former is more polarizable. Ehrmann et al. [14]. found a mobility ratio of 20-1 for potassium and hydrogen (hydronium) ions in a potash-lime glass (12.5% K20 , 12% CaO, 4.5% MgO, 70% SiO2). The concentration of hydrogen ions in a natural obsidian glass was measured from the 7-rays produced by bombarding the samples with the fluorine ions [6]. The smoothed profile is shown in fig. 4, where it is compared with the calculated profile for D from eq. (7) with DA/D B = 100. The comparison is close, indicating that the /) of eqs. (6) and (7) is consistent with the experimental data. From earlier data on obsidians [15], it can be estimated that the sample in fig. 4 was exposed to water for about 960 years. Then from the data and the calculated profile the diffusion coefficient of hydrogen (hydronium) ions in this obsidian at the variable ambient temperature is about 5 × 10 -20 cm2/s, about an order of magnitude below the value calculated for Baucke's data at 50°C, and about what one would expect at 25°C. Obsidians contain about 3.9 mol% Na20 and 2.85 mol% K20 [16], so ion exchange could be occurring with either of these ions, but presumably not with both, since in most cases there is no step in the profile of hydrogen ions. The concentration of H+ ions calculated for the sample of fig. 4 is about 6.6 × 10 -3 mol/cm 3, or more than twice the sodium or potassium ion concentration. This discrepancy suggests that some or all of the hydrogen ions are accompanied by water molecules, giving hydronium (H3 O+) ions. Equation (6) with concentration-independent diffusion coefficients is probably only an approximation to the true situation. Stress introduced into the glass by the interdiffusion, changes in activity coefficients with concentration and other unknown effects influencing the concentration dependence o f f have been neglected. Nevertheless, the above comparisons show that eq. (6) is superior to the assumption of a constant diffusion coefficient, and should stimulate further work to examine these other influences on D.
Acknowledgement This work was supported by the Office of Naval Research, Contract No. NOOO 14-67-A-0117, NR 032-531.
References l 1] Z. Boksay,G. Bouquet and S. Dobos, Phys. Chem. Glasses 8 (1967) 140. [2] Z. Boksay, G. Bouquet and S. Dobos, Phys. Chem. Glasses 9 (1968) 69. [3] S. Dobos, Acad. Sci. Hung. 68 (1971) 371; 69 (1971) 43, 49.
144
R.H. Doremus /Interdiffusion of hydrogen and alkali ions
[4] H. Bach and F.G.K. Baucke, Electrochim. Acta 16 (1971) 1311. [5] F.G.K. Baucke, 1. Non-Crystalline Solids 14 (1974) 13. [6] R.R. Lee, D.A. Leich, J.A. Tombrello, J.E. Ericson and I. Friedman, Nature 250 (1974) 44. [7] A. Wikby, Electrochim. Acta 19 (1974) 329. [8] M. A. Rana and R.W. Douglas, Phys. Chem. Glasses 2 (1961) 179,196. [9] R.H. Doremus, Glass Science (Wiley, New York, 1973) pp. 164 ff. [10] R.H. Doremus, J. Phys. Chem. 68 (1964) 2212. [11] R.H. Doremus, J. Am. Ceram. Soc. 57 (1974) 478. [12] F.G.K. Baucke, in: Proc. 9th Univ. Conf. Ceramic Science, eds. A.H. Heuer and A.R. Cooper, held in Cleveland, Ohio 3 - 6 June 1974, to be published, [13] G. Eisenman, ed., in: Glass electrodes for hydrogen and other cations (Dekker, New York, 1967) oh. 5. [14] P. Ehrmann, M. deBilly and J. Zarzycki, Verres Refract. 15 (1961) 61. [15] I. Friedman, K.L. Pierce, J.D. Obradovich and W.D. Long, Science 180 (1973) 733. [16] J.E. Ericson, A. Makishima, J.D. Mackenzie and R. Berger, J. Non-Crystalline Solids 17 (1975) 129.
INTERDIFFUSION OF HYDROGEN AND ALKALI IONS IN A GLASS SURFACE R.H. DOREMUS Rensselaer Polytechnic Institute, Materials Engineering Department, Troy, New York 12181, USA
Experimental data on the interdiffusion of hydrogen and alkali ions in glass are examined using a concentration-dependent interdiffusion coefficient, taking into account surface dissolution. The comparisons between calculated and experimental concentration profiles and diffusion coefficients are more satisfactory than for a concentration-independent diffusion coefficient, and support the use of the interdiffusion coefficient.
1. Introduction Water reacts with the surfaces of silicate glasses to form a hydrated silica-rich layer. If the glass contains alkali, hydration is preceded by ion exchange between hydrogen (or hydronium) ions from the water and alkali ions in the glass Na + (glass) + H20 = H+ (glass) + NaOH.
(1)
Concentration profiles resulting from this exchange and subsequent interdiffusion have been measured in several different ways [ 1 - 6 ] . Boksay et al. [1 ] developed a theory to explain these profiles, but their theory fitted the observed profiles only for potassium silicate glasses. Their theory assumed a diffusion coefficient invariant with ionic concentration, and they attributed the discrepancies between theory and experiment for sodium silicate glasses to a diffusion coefficient dependent upon ionic concentration. Profiles in lithium silicate glasses, one of which is shown in fig. 1, are similar to those in sodium silicate glasses [5], and they also do not fit the simple theory of Boksay et al. In this paper the theory of Boksay et al. is extended by using a concentrationdependent diffusion coefficient. The profiles found for steady-state diffusion are consistent with those found experimentally. These and other experimental results on the reaction of water with glass are discussed in terms of the new theory, taking into account the structure of the hydrated layer as deduced from the work of Wikby [7]. 137
138
R.H. Doremus /Interdiffusion of hydrogen and alkali ions 1.0
o
0.8
0.6- _
o
o
E
"E 0 . 4 -
!
_ 02-
L
I
i
I
2
4
6
8
I0
12
I
14
ay/DH Fig. 1. Profile of lithium ion in a lithium silicate glass, measured from photon emission during sputtering. The glass was held 16 h in 0.1N H2SO4 at 50°C (curve g, fig. 5, ref. [5]). Points measured; line calculated from eq. (9) with b = 2600.
2.
Theory
The reaction o f water with an alkali silicate glass can be separated into two stages [8]. In the first the amount o f sodium and silica dissolved is proportional to the square root o f time, whereas in the second the amount dissolved is proportional to time. These dependencies suggest that the dissolution process is initially controlled by diffusion, and then b y a surface reaction. The dissolution of the glass surface means that diffusion in the glass must be considered with respect to a moving boundary. I f x is the distance o f a plane in the glass from its initial surface, then y , the distance from the actual surface, at time t is (2)
y = x - at,
where a is the rate of dissolution of the surface, which is assumed to be constant with time. Then the diffusion equation in x coordinates (ac/atx)
= (a/ax) D(ac/ax)t
,
(3)
where c is the concentration of diffusing material, can be transformed to y coordi-
R.H. Doremus / Interdiffusion of hydrogen and alkali ions
139
nates [1,2]
(ac/Bt)y : (a/By) D (Bc/BY)t + a(ac/OY)t .
(4)
Diffusion is assumed to occur in semi-infinite geometry with a constant concentration at the glass surface. For convenience it is assumed that the concentration c = 0 at y = 0 (the glass surface) and c = 1 far into the glass as y ~ oo. For these boundary conditions eq. (4) can be solved analytically when D is independent of concentration, but its solution is difficult for the concentration dependence of D desired here. Thus the equation will be solved for the steady-state Bc/Ot = 0. For this condition and the above boundary conditions [1,2] c : 1 - exp ( - a y / D ) .
(S)
This exponential profile fits the data for a potassium silicate glass [ 1 ], but not for other glasses, an example of which is shown in fig, 1. Interdiffusion of two cations A and B can be described by an interdiffusion coefficient D of the form [9]
D =DADB/[CD A + (1 - C) DB] ,
(6)
where D A and D B are individual ionic diffusion coefficients and c is fhe atom fraction of A ions. This equation can also be written D = D A / [ 1 +c (DA/D B - 1] .
(7)
In interdiffusion of sodium and silver ions in a soda-lime glass at 378°C, eq. (7) was found to hold with D A and D B independent of ionic concentration [10]. There is some question as to whether or not a mixed alkali effect would cause D A and D B to vary with ionic concentration for other ionic pairs; however eq. (7) with constant D A and D B is at least consistent with interdiffusion of sodium and potassium in a soda-lime glass [ I 1 ]. Thus it is assumed that eq. (7) with D A and D B constant holds for interdiffusion of hydrogen (or hydronium) ions and alkali ions near room temperature. When eq. (7) for D is used for D in eq. (4), with Bc/ay = 0 and dc/dy ~ 0 a s y -+ o% then IDA/(1 + bc)] dc/dy = a(1 - c ) ,
(8)
where b = D A / D B - 1. A is the alkali ion initially in the glass, and c is its concentration. Solution of eq. (8) with the condition c = 0 when y = 0 gives c = [1 + e x p ( - a y / D B ) l/[1 + b exp (--ay/DB) ] .
(9)
When the ratio D A / D B = 1, b = 0 and D is independent of concentration. Then eq. (9) is the same as eq. (5).
R.H. Doremus / Interdiffusion of hydrogen and alkali ions
140
3. Comparison with experimental data and discussion Curves of concentration as a function of the dimensionless parameter ay/D B as calculated from eq. (9), are given in fig. 2 for various values of b (= D A / D B - 1). The curves are similar to that in fig. 1 and those in refs. [ 1 - 6 ] for sodium and lithium silicate glasses, showing that eq. (9) is superior to eq. (5) with constant D for describing the interdiffusion process. There are several difficulties in making a more detailed comparison between the experimental data and eq. (9), as outlined below. Baucke has found that the ratio of lithium to hydrogen mobilities in the same glass as used for fig. 1 is about 2600 at 50°C from electrolysis experiments [12]. The calculated curve for this mobility ratio gives a sharper increase of lithium concentration than the experimental data. This results because the resolution of the technique is limited to about 40 A, so an atomically sharp interface appears to be spread out about 70 A in width [5]. Since the total width of the surface layer shown in fig. 1 is about 300 ,/~, the lithium profile appears to be more spread out than it actually is. Baucke [5] found that the rate of dissolution of the glass was about 1.0 A/h at 50°C, so that a = 2.8 X 10 -12 cm/s. For the data in fig. 1 the concentration was 0.5 at a distance of 181 A from the glass surface. Since ay/D A = 7.9 at c = 0.5 for b = 2600, D H = 6.4 X 10 -19 cm2/s andDLi = 1.7 X 10-t5/cm2/s. The value of DLi can be compared with that calculated from the electrical resistivity p and the I.O IO
_
i
0.8--
0.6--
O
04--
0.2
Oo
2
4
6
8
IO
12
14
ay/D l,'ig. 2. Concentration profiles calculated from eq. (9) with different values of b (on curves).
141
R.H. Doremus /In terdiffusion of hydrogen and alkali ions outer surface
gel-glass interfoee
1.0
0.8 glass containing
gel 0.6
,er
s
,,Often ,ons
/
oo=,.,.g al~c i ~ s
"6 ~ o
0.4
8 0.2
I 0
Z
~ 4
I
1
1
I
6
8
I0
12
distance
Fig. 3. Model of the hydrated layers on the surface of alkali silicate glass.
Einstein equation DLi = RT/pF2CLi.
(10)
From Baucke's data p = 7.7 X 109 ~2-cm at 50°C and CLi ~ 2.4 × 10 -2 mol/cm 3. Then from eq. (10) DLi = 1.6 × 10 -15 cm2/s, in fortuitously good agreement with the value from eq. (9) and the interdiffusion profile. This agreement at least shows that eq. (9) is consistent with other data on the glass of fig. 1. Another difficulty in comparing eq. (9) with experimental data results from the formation of a gel-like hydrated layer on glass surfaces. Wikby showed that the conductivity of such a layer is much greater than that of the dry glass containing alkali ions [7]. A simplified model of various layers on a glass surface after some ion exchange and hydration is shown in fig. 3. The outer surface of the glass is dissolving into the solution; this is the rate of dissolution measured by the rate of silica appearance in the solution. In the gel layer, ions are quite mobile [7, 13], and water can penetrate to the gel-glass interface. Both the outer surface and gel-glass surface are probably not as sharp as shown in fig. 3, but are rather spread out with a continuous change of properties over many atomic layers. The rate of interface motion a used in the above derivations of the diffusion equation should strictly be the rate at which the gel-glass interface moves relative to the original glass interface; this rate should be somewhat faster than the rate of movement of the outer surface. The transformation from the initial glass network of silicon-oxygen bonds to the looser gel structure results from the reaction of water with these bonds:
142
R.H. Doremus /lnterdiffusion o f hydrogen and alkali ions
H20 + S i - O - S i = SiOH HOSi.
(11)
This reaction breaks up the strong, rigid glass network to a more weakly bonded gel; however, the gel still contains enough primary Si-O bonds to hold it together and delay dissolution. The exact mechanism of this reaction is uncertain. It could result from a direct attack of water in the gel layer on the gel-glass interface. However, it is also possible that the hydrogen ions carry along water molecules in the form of hydronium ions (H30+). Once these water molecules are in the rigid glass they may react with the glass network by reaction [11], leading to a progressive deterioration of the network, making it more open. Then neutral water molecules could penetrate the partly hydrated layer and react with Si-O bonds, resulting in further hydration of the glass and eventual dissolution. With this mechanism the gel-glass interface may be quite diffuse. It is difficult to compare eq. (9) with the profiles of sodium in the surfaces of various glasses as measured by Boksay et al. [1, 2]. and Dobos [3] because of uncertainties in the position of the gel-glass interface and the ratios of alkali-to-hydrogen ion mobility in their glasses. The shapes of the profiles in fig. 1, ref. [1 ] (glasses 1 and 2, 28% Na20 , 4% BaO or SrO, 68% SiO2) are consistent with the curves of fig. 2 for high mobility ratios (104-105), and a gel layer about half the total thickness of the surface diffusion layer; a layer of about this thickness can be I.O
0.8
~ O.6 o
._~ 0.4
~O.2 0
I 0
I 0.4
I
i 0.8
distance
I
I 1.2
I
I 1.6
I 2.0
(micronsl
Fig. 4. Concentration profile of hydrogen ions in the surface of a natural obsidian [6] (points), compared to calculated profile for DA/D B = 100 from eq. (6) (line).
R.H. Doremus /lnterdiffusion of hydrogen and alkali ions
143
deduced for some of Wikby's sodium-calcium silicate glasses [7]. Profiles for glass No. 4 (20 mol% K20 , 12% SrO, 68% SiO2) in ref. [1], fig. 2, and ref. [3] indicate a potassium-to-hydrogen ion mobility ratio of perhaps about 10-1, with a thinner gel layer. This low ratio is possibly evidence for hydronium ion (H30+), rather than hydrogen ion, exchange. The radius of the hydronium ion (~1.4) is about the same as for potassium (1.33), although the former is more polarizable. Ehrmann et al. [14]. found a mobility ratio of 20-1 for potassium and hydrogen (hydronium) ions in a potash-lime glass (12.5% K20 , 12% CaO, 4.5% MgO, 70% SiO2). The concentration of hydrogen ions in a natural obsidian glass was measured from the 7-rays produced by bombarding the samples with the fluorine ions [6]. The smoothed profile is shown in fig. 4, where it is compared with the calculated profile for D from eq. (7) with DA/D B = 100. The comparison is close, indicating that the /) of eqs. (6) and (7) is consistent with the experimental data. From earlier data on obsidians [15], it can be estimated that the sample in fig. 4 was exposed to water for about 960 years. Then from the data and the calculated profile the diffusion coefficient of hydrogen (hydronium) ions in this obsidian at the variable ambient temperature is about 5 × 10 -20 cm2/s, about an order of magnitude below the value calculated for Baucke's data at 50°C, and about what one would expect at 25°C. Obsidians contain about 3.9 mol% Na20 and 2.85 mol% K20 [16], so ion exchange could be occurring with either of these ions, but presumably not with both, since in most cases there is no step in the profile of hydrogen ions. The concentration of H+ ions calculated for the sample of fig. 4 is about 6.6 × 10 -3 mol/cm 3, or more than twice the sodium or potassium ion concentration. This discrepancy suggests that some or all of the hydrogen ions are accompanied by water molecules, giving hydronium (H3 O+) ions. Equation (6) with concentration-independent diffusion coefficients is probably only an approximation to the true situation. Stress introduced into the glass by the interdiffusion, changes in activity coefficients with concentration and other unknown effects influencing the concentration dependence o f f have been neglected. Nevertheless, the above comparisons show that eq. (6) is superior to the assumption of a constant diffusion coefficient, and should stimulate further work to examine these other influences on D.
Acknowledgement This work was supported by the Office of Naval Research, Contract No. NOOO 14-67-A-0117, NR 032-531.
References l 1] Z. Boksay,G. Bouquet and S. Dobos, Phys. Chem. Glasses 8 (1967) 140. [2] Z. Boksay, G. Bouquet and S. Dobos, Phys. Chem. Glasses 9 (1968) 69. [3] S. Dobos, Acad. Sci. Hung. 68 (1971) 371; 69 (1971) 43, 49.
144
R.H. Doremus /Interdiffusion of hydrogen and alkali ions
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