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Chemical structure and the mixed mobile ion effect in silver-for-sodium ion exchange in silicate glasses
]OUXNALOF
ELSEVIER
Jotltllal of Non-CrystailineSolids 394 (1996) 85-92
Chemical structure and the mixed mobile ion effect in silver-for-sodium ion exchange in silicate glasses J.M. Inman, S.N. Houde-Walter *, B.L. Mclntyre, Z.M. Liao, R.S. Parker, V. Simmons The Institute of Optics, Universityof Rochester, Rochester, ICY 14627, USA
Received 20 December 1994; revised 5 June 3995
Abstract The relationship between chemical structure and ion transport in silver-for-sodium ion exchange in the endpoints of a series of sodium aluminosilicate glasses is examined. It is shown that the non-bridging oxygen (NBO) content of the glass has a major impact on both the local environments of the mobile cations and the mixed mobile ion effect (MMIE). X-ray absorption fine structure studies of the local environments of the mobile cations are used to help formulate a structural picture of ion exchange, in which interactions between the mobile cations affect ion transport rates. Studies of the diffusion coefficient using energy dispersive microanalysis and the modified quasi-chemical (MOC) diffusion coefficient are used to obtain quantitative values for MMIE. Parameter fits of the MQC diffusion coefficient to experimentally obtained values are used to extract self-diffusion coefficients, excess interaction energies and cation-cation coordination numbers. It is found that the NBO-rich glass has the highest excess interaction energy and exhibits the greatest MMIE, consistent with the structural model.
1. Introduction Ion exchange is an important method for fabricating photonics devices (e.g., waveguides and microoptics) which incorporate a variation of refractive index within a single glass component. Dopant diffusion rates in glass are generally dependent on the concentrations of the mobile cations. This concentration dependence of the diffusion coefficient is critical in determining the resultant dopant distributions (and therefore the refractive index profiles). This
* Corresponding author. Tel: + 3-736 275 7629. Telefax: + 3716 273 3027. E-mail: shw~optics.rochester.edu.
concentration dependence is another aspect of the long-studied mixed mobile ion effect (MMIE, also called the mixed alkali effect) [1-3]. Although the M M I E has been studied extensively in binary silicate glasses, these glasses are generally not useful for photonics technologies. Addition of alumina to the glass melt greatly improves the glass properties, resulting in increased durability [4] and diffusion rates [5] and a reduction of the tendency to form silver colloid during ion exchange [6]. These properties improve in aluminosilicate glasses as the ratio of alumina to alkali oxide in the glass (denoted by R = A l 2 0 3 / N a 2 0 ) approaches unity. Conflicting observations as to the behavior of the mixed mobile ion effect in aluminosilicate glasses
0022-3093/96/$35.00 © 3996 Elsevier Science B.V. All rights reserved SSDI 0022-3093(95)00462-9
86
J.M. Inman et al. / Journal of Non-Crystalline Solids 194 (1996) 85-92
have been reported. Burggraaf and Cornelissen's resuits for the diffusion coefficient of a potassium-forsodium exchange in sodium aluminosilicates show that the magnitude of the MMIE decreases as R --* 1 [7]. By contrast, Lapp and Shelby found from measurements of electrical conductivity in lithiumsodium aluminosilicate glasses that the MMIE increases with increasing alumina concentration [8]. Cao reported that simulated lithium/sodium aluminosilicates exhibit greater MMIE than the corresponding binary silicates in molecular dynamics studies of the self-diffusion coefficients [9]. Resolution of these apparently contradictory results would be beneficial to the understanding and prediction of ion transport properties in glass. Insight into the behavior of the MMIE can be had on examination of the chemical structure of glass. We have formulated a structural picture of ion exchange in aluminosilicate glasses based on studies of the local environments of the mobile cation species using X-ray absorption fine structure (XAFS) spectroscopy [10]. The role of the mobile cation environments is important as forces acting on the cations affect their transport properties. In the binary silicate glasses, the mobile cations are ionically bound to non-bridging oxygen (NBO). In these glasses it appears that the mobile cation species cluster, much as they do in their crystalline isomorphs [11-13]. The alkali-rich regions may form channels along which cation transport is expected to occur. This clustering leads to a strong electrostatic interaction between the mobile cations, which will vary with cation species. As a result, overall cation-cation interactions will change as an ion exchange progresses, leading to concentration dependence in the diffusion coefficient. In fully polymerized (R = 1) aluminosilicate glasses and crystals, the mobile cations sit in oxygen cages [10,14]. In these glasses the mobile cation is ionically bound to a single aluminum oxyanion [AIO4]-. Due to the greater cation-oxygen distance, the mobile cation is less tightly bound to the glass network, resulting in higher diffusion rates. In addition, there is no reason to expect cation-cation clustering, in which case the mobile cations should interact less. One would therefore expect less concentration dependence in glasses with higher R values (R ~ 1).
We have recently developed a new quantitative model that describes the concentration dependence in the diffusion coefficient as a result of cation-cation interaction energy, called the modified quasi-chemical (MQC) diffusion coefficient [15]. In this model, each mobile cation is surrounded by c other mobile cations and an excess interaction energy, et, t, is defined as ~Ag - Ag "~- E N a - N a
2
6int ~" ~ A g - N a - -
'
(I)
where ei_ j is the pair interaction energy for i,j cations. Then for a silver-sodium exchange performed at temperature, T, the diffusion coefficient as a function of normalized silver oxide concentration X = CAg/(CAg +
CNa) is
D(X)
/3' +1 1-x
'
(2)
where a = 1 -(DAg/DNa), D i is the self-diffusion coefficient of cation i and /3' is /31
~1 -- 4( X-- X0)[ 1 -- ( X - - X 0 ) ] [ 1 -- e2"inl//~T]
(3) The MQC diffusion coefficient expression can be viewed as having two terms: a mobility term, DAg/(1 --Xa), and the thermodynamic term in the square brackets in E~I. (2). This thermodynamic term can indicate strong concentration dependence and I has a maximum at X = ~ + X 0 - (X0 is a floating parameter that accounts for diffusion coefficient maxima that occur for X other than X = ~1 and is used to empirically account for varying total alkali content of the glass [7].) When •int "~- 0 , the thermodynamic term is 1 and ideal behavior is recovered. As a result, the MMIE is a consequence of the excess interaction between unlike mobile cations. In this study, we examine the dependence of the diffusion coefficient on silver concentration for silver-for-sodium ion exchange in sodium aluminosilicate glasses and observe how the mixed mobile ion effect changes with aluminum content. We use the MQC diffusion coefficient to observe changes in the
J.M. Inman et al. /Journal of Non-Crystalline Solids 194 (1996) 85-92 Table 1 Analyzed glass compositions (tool%) R
Na20
AI203
0.0
high-alkali; sodium tetrasilicate
19.3
-
0.91
high-alkali
22.2
20.3
B203
SiO 2 80.7
5.5
52.0
interaction energy with composition and the effect they have on the MMIE.
2. Experimental procedure The concentration dependence of the diffusion coefficient was examined in two glasses representative of the 'endpoints' of a series of sodium aluminosilicates with varying alumina/soda ratios. The mobile cation environments of these glasses were examined in our previous study [10]. The first glass was sodium tetrasilicate glass (batch composition Na2Si40 9) which has no alumina and R = 0 and the second glass was a high-alkali glass with R = 0.91 (batch composition Nao. 17AI o.15Bo.04Si 0.0900.56). The analyzed compositions are listed in Table 1. Although this second glass had a small amount of boron added to flux the glass and reduce crazing, it
87
is a minority component, so to a first approximation it can be viewed more simply as an aluminosilicate glass. The tetrasilicate glass was silver/sodium ion exchanged with silver for 2 days at 360°C in a 50 mol% AgNO 3, 50 mol% N a N O 3 salt melt, chosen to slow silver uptake to reduce colloid formation. The R = 0.91 aluminosilicate was exchanged in pure AgNO 3 for 3 days at 360°C. In both cases, the diffusions were performed into polished faces and the sample dimensions were large enough to assure that the diffusions were one-dimensional. The exchanged glasses were then cut in cross-sections to expose the diffusion profile and the resulting surfaces were polished for determination of the diffusion profile. The silver oxide concentration versus depth data was obtained using energy dispersive X-ray microanalysis (Cambridge $200 SEM) and reduced by the ZAF method of correcting for inter-element and matrix effects [ 16-18]. An accelerating voltage of 20 kV was used. The characteristic X-rays used in the analysis were the K-lines of oxygen, sodium, aluminum and silicon and the L-lines for silver. The glass samples were coated with approximately 10 nm of carbon to prevent charging of the sample surface. Composition standards were metallic silver and the undiffused base glasses analyzed by wet chemical
1.0
o~
o.8
e~
3 o (.)
0.6
~4
0
~
o.4
~ o
0.2
z
0.0 100
200
300
400
500
600
Depth [#am] Fig. 1. Normalized silver oxide concentration, X, versus depth profile for R = 0 glass.
J.M. lnman et al./Journal of Non-CrystaUine Solids 194 (1996) 85-92
88
Table 2 M Q C diffusion coefficient parameters
analysis. Multiple scans (at least five) were averaged for each data set. The diffusion coefficient as a function of silver c o n c e n t r a t i o n was d e t e r m i n e d using the Boltzmann-Matano method [19], which expresses the diffusion coefficient as a product of the derivative and the integral of the diffusion depth:
D( X= X1) =
(4)
where D is the diffusion coefficient evaluated at silver concentration X~, x ( X ) is the diffusion depth as a function of silver concentration and t is the duration of the diffusion. This method is valid when diffusion does not result in volumetric change to the sample, a condition nominally satisfied in the present study. A fifth degree polynomial was fit to the summed data and used to numerically evaluate this expression using a FORTRAN 77 program utilizing IMSL [20] routines. Using this procedure with a concentration profile obtained from a complementary error function, a worst-case error in the diffusion coefficient of 7% was obtained in the concentration range used in the analysis (0.2 < x < 1.0) when random noise of maximum amplitude of X~ois,= 0.05 was included. An IMSL non-linear regression routine
3.5
'
r
i
R = 0.91
- 0.061 2.4 0.61 8.5 × 1 0 - 10
- 0.023 3.5 0.57 2.3 × 1 0 - 9
DNa ( c m 2 / s ) :
1 . 4 X 10 - 9
4.1 X 10 - 9
X0: Dma x ( c m 2 / s ) :
0.26 3 . 2 X 10 - 9
0.20 5 . 8 X 10 - 9
MM1Ema x :
1.67
0.79
ei, t (eV): c: DAg/DNa: DAg ( c m 2 / s ) :
1 dx
2t d X f / ' x ( x ) d x ,
R = 0.00
was used to perform parameter fits of the resulting diffusion coefficients to the MQC model.
3. R e s u l t s
The results of the diffusion coefficient study are summarized in Table 2. Fig. 1 shows a typical normalized silver oxide concentration versus depth curve, that of the R = 0 glass. Fig. 2 shows the diffusion coefficient obtained from the profile, as well as the corresponding parameter fit. The quality of the R = 1 glass data and parameter fits is slightly better. In order to focus on the thermodynamic term,
i
J---,
Experimental ---- M Q C P a r a m e t e r Fit 3.0
I 2.5
o
i
L
!1
i
2.0 -
I
J
I
/ /
r
.....\ j
I I
! I i
I
I
0.7
0.8
1.5
J 1.0
L . . . .
0.5
0.1
0.2
j i
~ . . 0.3
L 0.4
. . , . 0.5
,. 0.6
.i
J
"l
•
i...L... 0.9
1.0
Normalized Silver Oxide Concentration, Fig. 2. Diffusion coefficient versus n o r m a l i z e d silver oxide c o n c e n t r a t i o n f o r R = 0 glass (solid line) a n d p a r a m e t e r fit to M Q C diffusion coefficient (dashed line).
J.M. lnmanet aL/Journal of Non-CrystallineSolids194 (1996)85-92 the diffusion coefficient is normalized by the ideallimit diffusion coefficient (for which ~int = 0 ) . Therefore, we quantify the MMIE by MMIE D('int,X) D ( e i., = 0 , X )
2(
X/3'( X = 1) + (/3' 1-
X)#'( X= 0)
1 (5)
Fig. 3 shows the MMIE for the R = 0 sodium tetrasilicate glass (solid line) and for the R = 0.91 glass (dashed line). As can be seen from the figure, the glass with the most NBOs (the R = 0 sodium tetrasilicate) has the largest excess interaction energy and exhibits the greatest MMIE, with a maximum of 1.7. As a result of the short cation-oxygen separation, this glass also has the lowest self-diffusion coefficients for the mobile cations. Because of the form of the dependence of the MQC diffusion coefficient on excess interaction energy, ei, t, and cation-cation coordination, c, these two parameters have similar effects on the shape of
1.8
T
89
the diffusion coefficient. For instance, an increase in either one increases the magnitude of the MMIE, which causes an increase in the D(X) profile. It might be possible to arrive at the same or similar functional form with different values of these parameters. Therefore, the significance of any variation observed in ei~t and c for different glass compositions depends on how highly correlated these parameters are. This was investigated with the emt-C correlation maps shown in Fig. 4. For each glass, the bounded area contains the region for which the fit index of the MQC parameters to the experimental diffusion coefficient varies from its minimum by no more than 20%. The fit index used is the least-squares difference between the experimentally obtained diffusion coefficient and the parameter fit of the MQC diffusion coefficient, divided by the number of points, N:
1 iv FI=~
~., (DMQc(Xi)-Dexp(Xi)) 2.
As can be seen in Fig. 4, small changes in ~.t and c cause large increases in the fit index and there is no overlap of the regions (i.e., the degree of correlation between these parameters is extremely low). The
l R=0 Glass
1.4
"i'" R--'0.91 Glass
l.i
-i
I
J
i
_
o.o 0,0
0.2
0.3
(6)
i=l
0.5
~
i
0.7
0.8
",~ 1.0
Normalized Silver Oxide Concentration, Z Fig. 3. MMIE verses normalized silver oxide concentration for R = 0 (solid line) and R = 0.91 (dashed line) glasses.
90
J.M. Inman et al./ Journal of Non-Crystalline Solids 194 (1996) 85-92 2.50
o t~
I R=0 Glass
2.45
] ,
E Z
2.4O
i ]
' i
I, I
i ......
i
i
cation environments in these two glasses as determined by the M Q C model are therefore distinct.
(a)
4. Discussion
1
g
2.35
----~ .
_~ 2.30
t 1
7
U
1
2.25 . . . . .
-~
i
i 2.20 -0.0630
~
A
-0.0622
-0.0614
i
-0.0606
4).0598
-0.0590
Excess Interaction Energy, ~int [eV] 3.65
I
i
(b)
R--0.91 Glass I o
3.60
E 3.55
3.50
3.45
3.40
3.35 -0.0250
i -0.0242
-0.0234
, -0.0226
i I -0.0218
-0.0210
Excess Interaction Energy, £int [eV]
Fig. 4. Correlation maps of cation-cation coordination number versus excess interaction energy for MQC parameters fits to the experimental diffusion coefficients for the glasses listed in Table 1: (a) R = 0 and (b) R = 0.91. Note the different axes of the two maps.
Table 3 XAFS data [10] R Cation 0 0 0.91
Na Ag Ag
Comparison of the M M I E in these endpoint glasses reveals the impact of aluminum content on structure and transport properties. Prior XAFS results have shown that, in the presence of NBOs, the silver is able to alter the site formerly occupied by sodium so that the silver environment resembles that of A g 2 0 (see Table 3) [10]. Based on the sodium environments in R = 1 aluminosilicate crystals such as albite [14], the silver also alters the environment of the aluminum-associated site in the R "- 1 glass, although without the NBOs it cannot alter it enough to so strongly resemble A g 2 0 . The shorter A g - O distances imply that the silver cations are more tightly bound to the glass network than the sodium, which is consistent with the observation that the silver self-diffusion coefficients (and therefore mobility) are lower than for sodium (see Table 3). Also, as the structural picture indicates, the NBO-rich glass should have cation-cation clustering and therefore higher excess interaction energy and greater concentration dependence. This is borne out by the present experimental results and can be seen by overlaying the normalized M M I E for these two glasses (see Fig. 3) - the maximum M M I E for the NBO-rich glass is twice that of the NBO-poor glass. The cation-cation coordination number obtained from the fit for the R = 0 glass is close to 2. This is the expected value for a one-dimensional line of cation sites. This result is consistent with the picture of silver and sodium cations exchanging along ribbon-like channels, or a row of sites. It is also consis-
Exchangetemperature (°C)
Coordination number, N
Shell radius, r (,~,)
Debye-Waller factor, 2 o-2 (,~2)
360/400 360/400 535
4.3 2.1 2.5
2.32 2.08 2.23
0.017 0.012 0.036
J.M. lnman et aL / Journal of Non-Crystalline Solids 194 (1996) 85-92
tent with the view that the mobile cations interact largely through shared non-bridging oxygen. In the case where the electron from a mobile cation is distributed between two NBOs and the strongest cation-cation interaction occurs via those NBOs, each mobile cation would interact with exactly two other mobile cations. The MQC model considers only interacting cations and would therefore result in a value of c near 2 for this situation. The data in Table 3 and Fig. 2 corroborate this view. On the other hand, the larger cation-cation coordination in the R = 0.91 glass implies that the migration pathways are more three-dimensional in nature. This, too, was anticipated from the structural picture derived from the XAFS studies. As seen in the correlation maps of Fig. 4, the excess interaction energy and cation-cation coordination number have only a limited correlation when considered over a large concentration range, so that the values obtained for these parameters are clearly distinct for the two endpoint glasses. Examination of the role of these parameters in the MQC diffusion coefficient (Eq. (2)) shows why this difference is so. The thermodynamic term is driven by the energy through a non-linear dependence (Eq. (3)), whereas the cation-cation coordination is only a multiplicative factor. Therefore, these two parameters contribute to the shape of the D ( X ) profile differently, so that distinct values are obtained from a parameter fit. As can be seen from Fig. 3, these parameters can vary to result in extremely dissimilar diffusion coefficients so that the concentration profiles (and therefore refractive index profiles) will be very different. This is of paramount importance in the design of ion-exchanged micro-optic/photonic devices [21]. On reviewing earlier reports in the literature, we see that Burggraaf and Cornelissen [7] found, in a study of strengthening of aluminosilicate glasses by potassium-for-sodium ion exchange, that the concentration dependence of the diffusion coefficient was greater for a low-R glass than for a glass with R --- 1. This dependence is consistent with our results for silver-for-sodium ion exchange and with the predictions of the structural picture. A shift in the location of the maximum diffusion coefficient with alkali concentration was also observed ( X0 ~: 0). This shift is seen to a lesser extent in the present study, where the two glasses have different alkali contents and a
91
small difference in X0 is observed. The system Burggraaf and Cornelissen studied is perhaps one most similar to that of the present study due to the similar sizes of the potassium and silver ions. On the other hand, the results of the present study differ from those reported by Lapp and Shelby [8] and Cao [9]. Lapp and Shelby studied electrical conductivity in as-melted lithium aluminosilicates. The MMIE was defined as the departure from additivity of the single-alkali endpoints, without normalization for differences in conductivity with R. In Lapp and Shelby's work, the greatest MMIE was observed in glasses with R = l, which differs from the trend predicted from our XAFS studies and observed here in the present studies of the diffusion coefficient. Of course, Lapp and Shelby measured electrical conductivity (versus diffusion coefficient in the present study) in a different glass system, with a different definition of MMIE. Cao also used a 'departure from additivity' definition of MMIE and examined 'as-melted' lithium-sodium aluminosilicates. In his molecular dynamics simulation study of self-diffusion coefficients and their activation energies, he found greater MMIE for aluminosilicates than for the corresponding binary silicates, supporting Lapp and Shelby's results. This agreement indicates that either the trends observed in Burggraaf and Cornelissen's work and the present study are not general or that differences in quantifying MMIE can lead to different conclusions. As noted above, there are various ways to define MMIE. The definition used in this study (Eq. (5)) was chosen to allow direct examination of the thermodynamic term of the diffusion coefficient, which is the more physically interesting (and less understood) source of concentration dependence. Unlike many other definitions of MMIE, Eq. (5) has the effect of scaling for differences in ion transport rates that are not due to the thermodynamic term. For instance, even in the absence of MMIE, the ion-exchange rates of the glasses in the present study vary considerably, making direct comparison of diffusion coefficients for study of the MMIE difficult. A universal definition would allow greater insight into the similarities and differences observed in MMIE for different systems and manifestations (e.g., MMIE in ionic conductivity versus MMIE in the diffusion coefficient). The definition presented in Eq. (5) has
92
J.M. lnman et al./Journal of Non-CrystaUine Solids 194 (1996) 85-92
the advantage that it is based on physical grounds and is therefore the best choice for study of concentration dependence due to the thermodynamic term. It is encouraging that the trends in concentration dependence presented here are consistent with the simple structural view of ion exchange developed from XAFS studies. Needless to say, the elementary picture presented here may or may not account for all behavior in more complicated glass systems. Further studies are needed to gain complete understanding of the many aspects of the mixed mobile ion effect.
5. Conclusion We have investigated the relationship between chemical structure and concentration dependence of the diffusion coefficient in silver-for-sodium ion exchange in the endpoint glasses of a sodium aluminosilicate series. Through XAFS studies and the use of the MQC diffusion coefficient, we have shown that the mixed mobile ion effect can be attributed in large part to proximity effects between nearestneighbor mobile cations in a sodium silicate glass and a sodium aluminosilicate glass. We found that our non-bridging oxygen-rich R---0 glass had the largest excess interaction energy and exhibited the largest mixed mobile ion effect. A glass with nearly no NBOs had lower excess interaction and less MMIE.
Acknowledgements This work has been supported by the National Science Foundation (ECE-9403013) and the ARO
URI. One of the authors (J.M.I.) is on a fellowship from the National Science Foundation.
References [1] D.E. Day, J. Non-Cryst. Solids 21 (1976) 343. [2] G.H. Frischat and R. Kirchmeyer, J. Am. Ceram. Soc. 56 (1973) 552. [3] R. Terai, J. Non-Cryst. Solids 6 (1971) 121. [4] M. Volf, Chemical Approach to Glass (Elsevier, Amsterdam, 1984) oh. 14. [5] R. Terai, Phys. Chem. Glasses 10 (1969) 146. [6] R. Aranjo, Appl. Opt. 31 (1992) 5221. [7] A.J. Burggraaf and J. Cornelissen, Phys. Chem. Glasses 5 (1964) 123. [8] J.C. Lapp and J.E. Shelby J. Non-Cryst. Solids 95&96 (1987) 889. [9] Y. Cao, doctoral thesis, Alfred University (Sept. 1994) oh. 6. [10] S.N. Houde-Walter, J.M. lnman, A.J. Dent and G.N. Greaves, J. Phys. Chem. 97 (1993) 9330. [11] G.N. Greaves, J. Non-Cryst. Solids 71 (1985) 203. [12] B. Vessal, G.N. Greaves, P.T. Martin, A.V. Chadwick, R. Mole and S.N. Houde-Walter, Nature 356 (1992) 504. [13] C. Huang and A.N. Cormack, J. Chem. Phys. 93 (1990) 8180. [14] P.H. Ribbe, H.D. Megaw and W.H. Taylor, Acta Crystallogr. B25 (1969) 1503. [15] J.M. Inman, J.L. Bentley and S.N. Houde-Walter, J. NonCryst. Solids 191 (1995) 209. [16] J.I. Goldstein, D.E. Newbury, P. Echlin, D.C. Joy, C. Fiori and E. Lifshin, Scanning Electron Microscopy and X-Ray Microanalysis (Plenum, New York, 1981) p. 306. [17] M. von Heimendahl, Electron Microscopy of Materials (Academic, New York, 1980) p. 42. [18] L.E. Murr, Electron and Ion Microscopy and Microanalysis, 2nd Ed. (Dekker, New York, 1991) p. 191. [19] J. Crank, The Mathematics of Diffusion (Clarendon, Oxford, 1975) p. 230. [20] IMSL MATH/LIBRARY, Version 1.1, Jan. 1989, IMSL, Inc. [21] J.L. Bentley, manuscript in preparation.
ELSEVIER
Jotltllal of Non-CrystailineSolids 394 (1996) 85-92
Chemical structure and the mixed mobile ion effect in silver-for-sodium ion exchange in silicate glasses J.M. Inman, S.N. Houde-Walter *, B.L. Mclntyre, Z.M. Liao, R.S. Parker, V. Simmons The Institute of Optics, Universityof Rochester, Rochester, ICY 14627, USA
Received 20 December 1994; revised 5 June 3995
Abstract The relationship between chemical structure and ion transport in silver-for-sodium ion exchange in the endpoints of a series of sodium aluminosilicate glasses is examined. It is shown that the non-bridging oxygen (NBO) content of the glass has a major impact on both the local environments of the mobile cations and the mixed mobile ion effect (MMIE). X-ray absorption fine structure studies of the local environments of the mobile cations are used to help formulate a structural picture of ion exchange, in which interactions between the mobile cations affect ion transport rates. Studies of the diffusion coefficient using energy dispersive microanalysis and the modified quasi-chemical (MOC) diffusion coefficient are used to obtain quantitative values for MMIE. Parameter fits of the MQC diffusion coefficient to experimentally obtained values are used to extract self-diffusion coefficients, excess interaction energies and cation-cation coordination numbers. It is found that the NBO-rich glass has the highest excess interaction energy and exhibits the greatest MMIE, consistent with the structural model.
1. Introduction Ion exchange is an important method for fabricating photonics devices (e.g., waveguides and microoptics) which incorporate a variation of refractive index within a single glass component. Dopant diffusion rates in glass are generally dependent on the concentrations of the mobile cations. This concentration dependence of the diffusion coefficient is critical in determining the resultant dopant distributions (and therefore the refractive index profiles). This
* Corresponding author. Tel: + 3-736 275 7629. Telefax: + 3716 273 3027. E-mail: shw~optics.rochester.edu.
concentration dependence is another aspect of the long-studied mixed mobile ion effect (MMIE, also called the mixed alkali effect) [1-3]. Although the M M I E has been studied extensively in binary silicate glasses, these glasses are generally not useful for photonics technologies. Addition of alumina to the glass melt greatly improves the glass properties, resulting in increased durability [4] and diffusion rates [5] and a reduction of the tendency to form silver colloid during ion exchange [6]. These properties improve in aluminosilicate glasses as the ratio of alumina to alkali oxide in the glass (denoted by R = A l 2 0 3 / N a 2 0 ) approaches unity. Conflicting observations as to the behavior of the mixed mobile ion effect in aluminosilicate glasses
0022-3093/96/$35.00 © 3996 Elsevier Science B.V. All rights reserved SSDI 0022-3093(95)00462-9
86
J.M. Inman et al. / Journal of Non-Crystalline Solids 194 (1996) 85-92
have been reported. Burggraaf and Cornelissen's resuits for the diffusion coefficient of a potassium-forsodium exchange in sodium aluminosilicates show that the magnitude of the MMIE decreases as R --* 1 [7]. By contrast, Lapp and Shelby found from measurements of electrical conductivity in lithiumsodium aluminosilicate glasses that the MMIE increases with increasing alumina concentration [8]. Cao reported that simulated lithium/sodium aluminosilicates exhibit greater MMIE than the corresponding binary silicates in molecular dynamics studies of the self-diffusion coefficients [9]. Resolution of these apparently contradictory results would be beneficial to the understanding and prediction of ion transport properties in glass. Insight into the behavior of the MMIE can be had on examination of the chemical structure of glass. We have formulated a structural picture of ion exchange in aluminosilicate glasses based on studies of the local environments of the mobile cation species using X-ray absorption fine structure (XAFS) spectroscopy [10]. The role of the mobile cation environments is important as forces acting on the cations affect their transport properties. In the binary silicate glasses, the mobile cations are ionically bound to non-bridging oxygen (NBO). In these glasses it appears that the mobile cation species cluster, much as they do in their crystalline isomorphs [11-13]. The alkali-rich regions may form channels along which cation transport is expected to occur. This clustering leads to a strong electrostatic interaction between the mobile cations, which will vary with cation species. As a result, overall cation-cation interactions will change as an ion exchange progresses, leading to concentration dependence in the diffusion coefficient. In fully polymerized (R = 1) aluminosilicate glasses and crystals, the mobile cations sit in oxygen cages [10,14]. In these glasses the mobile cation is ionically bound to a single aluminum oxyanion [AIO4]-. Due to the greater cation-oxygen distance, the mobile cation is less tightly bound to the glass network, resulting in higher diffusion rates. In addition, there is no reason to expect cation-cation clustering, in which case the mobile cations should interact less. One would therefore expect less concentration dependence in glasses with higher R values (R ~ 1).
We have recently developed a new quantitative model that describes the concentration dependence in the diffusion coefficient as a result of cation-cation interaction energy, called the modified quasi-chemical (MQC) diffusion coefficient [15]. In this model, each mobile cation is surrounded by c other mobile cations and an excess interaction energy, et, t, is defined as ~Ag - Ag "~- E N a - N a
2
6int ~" ~ A g - N a - -
'
(I)
where ei_ j is the pair interaction energy for i,j cations. Then for a silver-sodium exchange performed at temperature, T, the diffusion coefficient as a function of normalized silver oxide concentration X = CAg/(CAg +
CNa) is
D(X)
/3' +1 1-x
'
(2)
where a = 1 -(DAg/DNa), D i is the self-diffusion coefficient of cation i and /3' is /31
~1 -- 4( X-- X0)[ 1 -- ( X - - X 0 ) ] [ 1 -- e2"inl//~T]
(3) The MQC diffusion coefficient expression can be viewed as having two terms: a mobility term, DAg/(1 --Xa), and the thermodynamic term in the square brackets in E~I. (2). This thermodynamic term can indicate strong concentration dependence and I has a maximum at X = ~ + X 0 - (X0 is a floating parameter that accounts for diffusion coefficient maxima that occur for X other than X = ~1 and is used to empirically account for varying total alkali content of the glass [7].) When •int "~- 0 , the thermodynamic term is 1 and ideal behavior is recovered. As a result, the MMIE is a consequence of the excess interaction between unlike mobile cations. In this study, we examine the dependence of the diffusion coefficient on silver concentration for silver-for-sodium ion exchange in sodium aluminosilicate glasses and observe how the mixed mobile ion effect changes with aluminum content. We use the MQC diffusion coefficient to observe changes in the
J.M. Inman et al. /Journal of Non-Crystalline Solids 194 (1996) 85-92 Table 1 Analyzed glass compositions (tool%) R
Na20
AI203
0.0
high-alkali; sodium tetrasilicate
19.3
-
0.91
high-alkali
22.2
20.3
B203
SiO 2 80.7
5.5
52.0
interaction energy with composition and the effect they have on the MMIE.
2. Experimental procedure The concentration dependence of the diffusion coefficient was examined in two glasses representative of the 'endpoints' of a series of sodium aluminosilicates with varying alumina/soda ratios. The mobile cation environments of these glasses were examined in our previous study [10]. The first glass was sodium tetrasilicate glass (batch composition Na2Si40 9) which has no alumina and R = 0 and the second glass was a high-alkali glass with R = 0.91 (batch composition Nao. 17AI o.15Bo.04Si 0.0900.56). The analyzed compositions are listed in Table 1. Although this second glass had a small amount of boron added to flux the glass and reduce crazing, it
87
is a minority component, so to a first approximation it can be viewed more simply as an aluminosilicate glass. The tetrasilicate glass was silver/sodium ion exchanged with silver for 2 days at 360°C in a 50 mol% AgNO 3, 50 mol% N a N O 3 salt melt, chosen to slow silver uptake to reduce colloid formation. The R = 0.91 aluminosilicate was exchanged in pure AgNO 3 for 3 days at 360°C. In both cases, the diffusions were performed into polished faces and the sample dimensions were large enough to assure that the diffusions were one-dimensional. The exchanged glasses were then cut in cross-sections to expose the diffusion profile and the resulting surfaces were polished for determination of the diffusion profile. The silver oxide concentration versus depth data was obtained using energy dispersive X-ray microanalysis (Cambridge $200 SEM) and reduced by the ZAF method of correcting for inter-element and matrix effects [ 16-18]. An accelerating voltage of 20 kV was used. The characteristic X-rays used in the analysis were the K-lines of oxygen, sodium, aluminum and silicon and the L-lines for silver. The glass samples were coated with approximately 10 nm of carbon to prevent charging of the sample surface. Composition standards were metallic silver and the undiffused base glasses analyzed by wet chemical
1.0
o~
o.8
e~
3 o (.)
0.6
~4
0
~
o.4
~ o
0.2
z
0.0 100
200
300
400
500
600
Depth [#am] Fig. 1. Normalized silver oxide concentration, X, versus depth profile for R = 0 glass.
J.M. lnman et al./Journal of Non-CrystaUine Solids 194 (1996) 85-92
88
Table 2 M Q C diffusion coefficient parameters
analysis. Multiple scans (at least five) were averaged for each data set. The diffusion coefficient as a function of silver c o n c e n t r a t i o n was d e t e r m i n e d using the Boltzmann-Matano method [19], which expresses the diffusion coefficient as a product of the derivative and the integral of the diffusion depth:
D( X= X1) =
(4)
where D is the diffusion coefficient evaluated at silver concentration X~, x ( X ) is the diffusion depth as a function of silver concentration and t is the duration of the diffusion. This method is valid when diffusion does not result in volumetric change to the sample, a condition nominally satisfied in the present study. A fifth degree polynomial was fit to the summed data and used to numerically evaluate this expression using a FORTRAN 77 program utilizing IMSL [20] routines. Using this procedure with a concentration profile obtained from a complementary error function, a worst-case error in the diffusion coefficient of 7% was obtained in the concentration range used in the analysis (0.2 < x < 1.0) when random noise of maximum amplitude of X~ois,= 0.05 was included. An IMSL non-linear regression routine
3.5
'
r
i
R = 0.91
- 0.061 2.4 0.61 8.5 × 1 0 - 10
- 0.023 3.5 0.57 2.3 × 1 0 - 9
DNa ( c m 2 / s ) :
1 . 4 X 10 - 9
4.1 X 10 - 9
X0: Dma x ( c m 2 / s ) :
0.26 3 . 2 X 10 - 9
0.20 5 . 8 X 10 - 9
MM1Ema x :
1.67
0.79
ei, t (eV): c: DAg/DNa: DAg ( c m 2 / s ) :
1 dx
2t d X f / ' x ( x ) d x ,
R = 0.00
was used to perform parameter fits of the resulting diffusion coefficients to the MQC model.
3. R e s u l t s
The results of the diffusion coefficient study are summarized in Table 2. Fig. 1 shows a typical normalized silver oxide concentration versus depth curve, that of the R = 0 glass. Fig. 2 shows the diffusion coefficient obtained from the profile, as well as the corresponding parameter fit. The quality of the R = 1 glass data and parameter fits is slightly better. In order to focus on the thermodynamic term,
i
J---,
Experimental ---- M Q C P a r a m e t e r Fit 3.0
I 2.5
o
i
L
!1
i
2.0 -
I
J
I
/ /
r
.....\ j
I I
! I i
I
I
0.7
0.8
1.5
J 1.0
L . . . .
0.5
0.1
0.2
j i
~ . . 0.3
L 0.4
. . , . 0.5
,. 0.6
.i
J
"l
•
i...L... 0.9
1.0
Normalized Silver Oxide Concentration, Fig. 2. Diffusion coefficient versus n o r m a l i z e d silver oxide c o n c e n t r a t i o n f o r R = 0 glass (solid line) a n d p a r a m e t e r fit to M Q C diffusion coefficient (dashed line).
J.M. lnmanet aL/Journal of Non-CrystallineSolids194 (1996)85-92 the diffusion coefficient is normalized by the ideallimit diffusion coefficient (for which ~int = 0 ) . Therefore, we quantify the MMIE by MMIE D('int,X) D ( e i., = 0 , X )
2(
X/3'( X = 1) + (/3' 1-
X)#'( X= 0)
1 (5)
Fig. 3 shows the MMIE for the R = 0 sodium tetrasilicate glass (solid line) and for the R = 0.91 glass (dashed line). As can be seen from the figure, the glass with the most NBOs (the R = 0 sodium tetrasilicate) has the largest excess interaction energy and exhibits the greatest MMIE, with a maximum of 1.7. As a result of the short cation-oxygen separation, this glass also has the lowest self-diffusion coefficients for the mobile cations. Because of the form of the dependence of the MQC diffusion coefficient on excess interaction energy, ei, t, and cation-cation coordination, c, these two parameters have similar effects on the shape of
1.8
T
89
the diffusion coefficient. For instance, an increase in either one increases the magnitude of the MMIE, which causes an increase in the D(X) profile. It might be possible to arrive at the same or similar functional form with different values of these parameters. Therefore, the significance of any variation observed in ei~t and c for different glass compositions depends on how highly correlated these parameters are. This was investigated with the emt-C correlation maps shown in Fig. 4. For each glass, the bounded area contains the region for which the fit index of the MQC parameters to the experimental diffusion coefficient varies from its minimum by no more than 20%. The fit index used is the least-squares difference between the experimentally obtained diffusion coefficient and the parameter fit of the MQC diffusion coefficient, divided by the number of points, N:
1 iv FI=~
~., (DMQc(Xi)-Dexp(Xi)) 2.
As can be seen in Fig. 4, small changes in ~.t and c cause large increases in the fit index and there is no overlap of the regions (i.e., the degree of correlation between these parameters is extremely low). The
l R=0 Glass
1.4
"i'" R--'0.91 Glass
l.i
-i
I
J
i
_
o.o 0,0
0.2
0.3
(6)
i=l
0.5
~
i
0.7
0.8
",~ 1.0
Normalized Silver Oxide Concentration, Z Fig. 3. MMIE verses normalized silver oxide concentration for R = 0 (solid line) and R = 0.91 (dashed line) glasses.
90
J.M. Inman et al./ Journal of Non-Crystalline Solids 194 (1996) 85-92 2.50
o t~
I R=0 Glass
2.45
] ,
E Z
2.4O
i ]
' i
I, I
i ......
i
i
cation environments in these two glasses as determined by the M Q C model are therefore distinct.
(a)
4. Discussion
1
g
2.35
----~ .
_~ 2.30
t 1
7
U
1
2.25 . . . . .
-~
i
i 2.20 -0.0630
~
A
-0.0622
-0.0614
i
-0.0606
4).0598
-0.0590
Excess Interaction Energy, ~int [eV] 3.65
I
i
(b)
R--0.91 Glass I o
3.60
E 3.55
3.50
3.45
3.40
3.35 -0.0250
i -0.0242
-0.0234
, -0.0226
i I -0.0218
-0.0210
Excess Interaction Energy, £int [eV]
Fig. 4. Correlation maps of cation-cation coordination number versus excess interaction energy for MQC parameters fits to the experimental diffusion coefficients for the glasses listed in Table 1: (a) R = 0 and (b) R = 0.91. Note the different axes of the two maps.
Table 3 XAFS data [10] R Cation 0 0 0.91
Na Ag Ag
Comparison of the M M I E in these endpoint glasses reveals the impact of aluminum content on structure and transport properties. Prior XAFS results have shown that, in the presence of NBOs, the silver is able to alter the site formerly occupied by sodium so that the silver environment resembles that of A g 2 0 (see Table 3) [10]. Based on the sodium environments in R = 1 aluminosilicate crystals such as albite [14], the silver also alters the environment of the aluminum-associated site in the R "- 1 glass, although without the NBOs it cannot alter it enough to so strongly resemble A g 2 0 . The shorter A g - O distances imply that the silver cations are more tightly bound to the glass network than the sodium, which is consistent with the observation that the silver self-diffusion coefficients (and therefore mobility) are lower than for sodium (see Table 3). Also, as the structural picture indicates, the NBO-rich glass should have cation-cation clustering and therefore higher excess interaction energy and greater concentration dependence. This is borne out by the present experimental results and can be seen by overlaying the normalized M M I E for these two glasses (see Fig. 3) - the maximum M M I E for the NBO-rich glass is twice that of the NBO-poor glass. The cation-cation coordination number obtained from the fit for the R = 0 glass is close to 2. This is the expected value for a one-dimensional line of cation sites. This result is consistent with the picture of silver and sodium cations exchanging along ribbon-like channels, or a row of sites. It is also consis-
Exchangetemperature (°C)
Coordination number, N
Shell radius, r (,~,)
Debye-Waller factor, 2 o-2 (,~2)
360/400 360/400 535
4.3 2.1 2.5
2.32 2.08 2.23
0.017 0.012 0.036
J.M. lnman et aL / Journal of Non-Crystalline Solids 194 (1996) 85-92
tent with the view that the mobile cations interact largely through shared non-bridging oxygen. In the case where the electron from a mobile cation is distributed between two NBOs and the strongest cation-cation interaction occurs via those NBOs, each mobile cation would interact with exactly two other mobile cations. The MQC model considers only interacting cations and would therefore result in a value of c near 2 for this situation. The data in Table 3 and Fig. 2 corroborate this view. On the other hand, the larger cation-cation coordination in the R = 0.91 glass implies that the migration pathways are more three-dimensional in nature. This, too, was anticipated from the structural picture derived from the XAFS studies. As seen in the correlation maps of Fig. 4, the excess interaction energy and cation-cation coordination number have only a limited correlation when considered over a large concentration range, so that the values obtained for these parameters are clearly distinct for the two endpoint glasses. Examination of the role of these parameters in the MQC diffusion coefficient (Eq. (2)) shows why this difference is so. The thermodynamic term is driven by the energy through a non-linear dependence (Eq. (3)), whereas the cation-cation coordination is only a multiplicative factor. Therefore, these two parameters contribute to the shape of the D ( X ) profile differently, so that distinct values are obtained from a parameter fit. As can be seen from Fig. 3, these parameters can vary to result in extremely dissimilar diffusion coefficients so that the concentration profiles (and therefore refractive index profiles) will be very different. This is of paramount importance in the design of ion-exchanged micro-optic/photonic devices [21]. On reviewing earlier reports in the literature, we see that Burggraaf and Cornelissen [7] found, in a study of strengthening of aluminosilicate glasses by potassium-for-sodium ion exchange, that the concentration dependence of the diffusion coefficient was greater for a low-R glass than for a glass with R --- 1. This dependence is consistent with our results for silver-for-sodium ion exchange and with the predictions of the structural picture. A shift in the location of the maximum diffusion coefficient with alkali concentration was also observed ( X0 ~: 0). This shift is seen to a lesser extent in the present study, where the two glasses have different alkali contents and a
91
small difference in X0 is observed. The system Burggraaf and Cornelissen studied is perhaps one most similar to that of the present study due to the similar sizes of the potassium and silver ions. On the other hand, the results of the present study differ from those reported by Lapp and Shelby [8] and Cao [9]. Lapp and Shelby studied electrical conductivity in as-melted lithium aluminosilicates. The MMIE was defined as the departure from additivity of the single-alkali endpoints, without normalization for differences in conductivity with R. In Lapp and Shelby's work, the greatest MMIE was observed in glasses with R = l, which differs from the trend predicted from our XAFS studies and observed here in the present studies of the diffusion coefficient. Of course, Lapp and Shelby measured electrical conductivity (versus diffusion coefficient in the present study) in a different glass system, with a different definition of MMIE. Cao also used a 'departure from additivity' definition of MMIE and examined 'as-melted' lithium-sodium aluminosilicates. In his molecular dynamics simulation study of self-diffusion coefficients and their activation energies, he found greater MMIE for aluminosilicates than for the corresponding binary silicates, supporting Lapp and Shelby's results. This agreement indicates that either the trends observed in Burggraaf and Cornelissen's work and the present study are not general or that differences in quantifying MMIE can lead to different conclusions. As noted above, there are various ways to define MMIE. The definition used in this study (Eq. (5)) was chosen to allow direct examination of the thermodynamic term of the diffusion coefficient, which is the more physically interesting (and less understood) source of concentration dependence. Unlike many other definitions of MMIE, Eq. (5) has the effect of scaling for differences in ion transport rates that are not due to the thermodynamic term. For instance, even in the absence of MMIE, the ion-exchange rates of the glasses in the present study vary considerably, making direct comparison of diffusion coefficients for study of the MMIE difficult. A universal definition would allow greater insight into the similarities and differences observed in MMIE for different systems and manifestations (e.g., MMIE in ionic conductivity versus MMIE in the diffusion coefficient). The definition presented in Eq. (5) has
92
J.M. lnman et al./Journal of Non-CrystaUine Solids 194 (1996) 85-92
the advantage that it is based on physical grounds and is therefore the best choice for study of concentration dependence due to the thermodynamic term. It is encouraging that the trends in concentration dependence presented here are consistent with the simple structural view of ion exchange developed from XAFS studies. Needless to say, the elementary picture presented here may or may not account for all behavior in more complicated glass systems. Further studies are needed to gain complete understanding of the many aspects of the mixed mobile ion effect.
5. Conclusion We have investigated the relationship between chemical structure and concentration dependence of the diffusion coefficient in silver-for-sodium ion exchange in the endpoint glasses of a sodium aluminosilicate series. Through XAFS studies and the use of the MQC diffusion coefficient, we have shown that the mixed mobile ion effect can be attributed in large part to proximity effects between nearestneighbor mobile cations in a sodium silicate glass and a sodium aluminosilicate glass. We found that our non-bridging oxygen-rich R---0 glass had the largest excess interaction energy and exhibited the largest mixed mobile ion effect. A glass with nearly no NBOs had lower excess interaction and less MMIE.
Acknowledgements This work has been supported by the National Science Foundation (ECE-9403013) and the ARO
URI. One of the authors (J.M.I.) is on a fellowship from the National Science Foundation.
References [1] D.E. Day, J. Non-Cryst. Solids 21 (1976) 343. [2] G.H. Frischat and R. Kirchmeyer, J. Am. Ceram. Soc. 56 (1973) 552. [3] R. Terai, J. Non-Cryst. Solids 6 (1971) 121. [4] M. Volf, Chemical Approach to Glass (Elsevier, Amsterdam, 1984) oh. 14. [5] R. Terai, Phys. Chem. Glasses 10 (1969) 146. [6] R. Aranjo, Appl. Opt. 31 (1992) 5221. [7] A.J. Burggraaf and J. Cornelissen, Phys. Chem. Glasses 5 (1964) 123. [8] J.C. Lapp and J.E. Shelby J. Non-Cryst. Solids 95&96 (1987) 889. [9] Y. Cao, doctoral thesis, Alfred University (Sept. 1994) oh. 6. [10] S.N. Houde-Walter, J.M. lnman, A.J. Dent and G.N. Greaves, J. Phys. Chem. 97 (1993) 9330. [11] G.N. Greaves, J. Non-Cryst. Solids 71 (1985) 203. [12] B. Vessal, G.N. Greaves, P.T. Martin, A.V. Chadwick, R. Mole and S.N. Houde-Walter, Nature 356 (1992) 504. [13] C. Huang and A.N. Cormack, J. Chem. Phys. 93 (1990) 8180. [14] P.H. Ribbe, H.D. Megaw and W.H. Taylor, Acta Crystallogr. B25 (1969) 1503. [15] J.M. Inman, J.L. Bentley and S.N. Houde-Walter, J. NonCryst. Solids 191 (1995) 209. [16] J.I. Goldstein, D.E. Newbury, P. Echlin, D.C. Joy, C. Fiori and E. Lifshin, Scanning Electron Microscopy and X-Ray Microanalysis (Plenum, New York, 1981) p. 306. [17] M. von Heimendahl, Electron Microscopy of Materials (Academic, New York, 1980) p. 42. [18] L.E. Murr, Electron and Ion Microscopy and Microanalysis, 2nd Ed. (Dekker, New York, 1991) p. 191. [19] J. Crank, The Mathematics of Diffusion (Clarendon, Oxford, 1975) p. 230. [20] IMSL MATH/LIBRARY, Version 1.1, Jan. 1989, IMSL, Inc. [21] J.L. Bentley, manuscript in preparation.