- Email: [email protected]
Sodium ion transport in high purity borosilicate glasses
Journal of Non-Crystalline Solids 51 (1982) 345-355 North-Holland Publishing Company
345
S O D I U M I O N T R A N S P O R T IN H I G H P U R I T Y B O R O S I L I C A T E GLASSES J o h n E. K E L L Y III * a n d M i n o r u T O M O Z A W A Materials Engineering Department, Rensselaer Polytechnic Institute, Troy, New York 12181, USA
Received 27 January 1982 Revised manuscript received 23 March 1982
22Na diffusion coefficients and dc electrical conductivity were measured in 0.7 B203.0.3 SiO2 (mole ratio) glasses containing small amounts of Na20 (111 ppm to 2.6 mol%). Correlation factors near unity were obtained from the Nernst-Einstein equation for these glasses. These values are in agreement with a previously proposed free "interstitial" alkali ion diffusion mechanism in low alkali content glasses. It is concluded from the low values of the sodium diffusion coefficients and dc conductivity in these glasses (relative to similar silicate and germanate glasses) that the Na ÷ are bound strongly to the borate-rich glass network and that the number of dissociated Na + at any given time is small.
1. Introduction Ionic transport in oxide glass influences m a n y of its i m p o r t a n t properties. The systematic alteration of a n y of these properties requires a basic u n d e r s t a n d i n g of the ionic transport m e c h a n i s m in the glass. A complete description of the transport process for alkali ions should include both the transport m e c h a n i s m and the n u m b e r of mobile ions. Single alkali glasses with low alkali c o n c e n t r a t i o n s provide a good starting p o i n t in the effort to u n d e r s t a n d these t r a n s p o r t p h e n o m e n a because the interaction of a n alkali ion with other alkali ions of the same or different type should be minimal. Earlier, the present authors measured s o d i u m diffusion [1] a n d electrical c o n d u c t i v i t y [2] in low s o d i u m c o n t e n t g e r m a n a t e glasses a n d observed experim e n t a l correlation factors or H a v e n ratios ( " f " from the N e r n s t - E i n s t e i n relation) near u n i t y for these glasses. F u r t h e r m o r e , a s u m m a r y of experimental correlation factor values for m a n y b i n a r y alkali oxide glasses indicated that at low alkali c o n t e n t s f = 1 a n d that increasing the alkali c o n t e n t in the glass reduced f to values near 0.2 to 0.5. However, it was f o u n d that the experimental data o n borate a n d borate-rich borosilicate glasses with low alkali conc e n t r a t i o n s is very limited [3,4]. The purpose of this research is to o b t a i n
* Now at International Business Machines Corporation, Poughkeepsie, New York 12602, USA. 0 0 2 2 - 3 0 9 3 / 8 2 / 0 0 0 0 - 0 0 0 0 / $ 0 2 . 7 5 © 1982 N o r t h - H o l l a n d
346
J.E. Kelly II1, M. Tomozawa / Na ion transport in borosilieate glasses
Table 1 Experimental correlation factors (fexperimental),water content and glass transition temperature of 0.7 B203-0.3 SiO2 glasses with low alkali content Na20 (ppm)
Tg ( ° C )
#c (cm
111 224 581 2330 4559 24,245
329 322 -
31.7 55.7 33.9 31.5 32.9 26.4
i) at 2 . 8 / ~ m
f(experimental) 0.99 1.02 1.07 0.73 a 0.75 a 1.13 a
a S o m e glass d e f o r m a t i o n w a s o b s e r v e d a f t e r electrical c o n d u c t i v i t y a n d d i f f u s i o n m e a s u r e m e n t s .
correlation factors, 22Na diffusion coefficients and electrical conductivities of low sodium content borate-rich glasses and to compare these results with various other high purity glasses. Preparation of low sodium content N a 2 0 - B 2 0 3 glasses is possible, but the low value of Tg ( = 230°C), the low value of the sodium diffusion coefficient ( D N a ~ I 0 -14 cm2/s at 300°C [3]) and the rapid attack of the glass by atmospheric water make this a difficult system to work with. The addition of silica to this system raises Tg making it possible to measure DNa at higher temperatures without encountering sample deformation (Tg values determined by a dilatometric method are shown for selected compositions in table 1) and it also increases the chemical durability. Phase separation in the 0.7 B203 • 0.3 SiO 2 glass system occurs only after prolonged heat treatment at 450-520°C [5], therefore, diffusion and electrical measurements at temperatures -~ 350°C will not be affected by phase separation. Thus 0.7 B203 • 0.3 SiO 2 glasses with low N a 2 0 contents were chosen for the present study.
2.
Theory
A basic understanding of alkali ion diffusion mechanisms in amorphous systems has been difficult to obtain due to the complexity of the random-network structure. However, the concept of a correlation factor ( f ) which is widely used for diffusion in crystalline systems has been applied with some success to many glass systems. The correlation factor results from the non-random motion of the diffusing atom, and, therefore, is a function of the diffusion mechanism. From a statistical model of diffusion, the correlation factor can be expressed as [6]: f = 1 + 2cos 0,.i+ l + 2 cos 8,.~+ 2 + ....
(la)
f = 1 + 2 ~ cosO~j+~,
(lb)
or
n=l
J.E. Kelly IIL M. Tornozawa / Na ion transport in borosilicate glasses
347
where Oi,i+,, is the angle between the two jump vectors i and i + n. If the motion of the diffusing ion is totally random in direction the sum in eq. (lb) is zero and f = 1. In crystalline materials it is possible to use the symmetry of the lattice to determine possible jump directions for various diffusion mechanisms and evaluate f theoretically [6,7]. However, in amorphous systems there is no long range symmetry and hence an exact evaluation of the sum of eq. (lb) is difficult (except for perfectly random motion as previously mentioned). Correlation factors ( f ) can be experimentally determined from a modified Nernst-Einstein equation: f(experimental) =
DCFZ,/°RT,
(2)
where D is the tracer diffusion coefficient of the charge carrier, C is the concentration of charge carriers, F is Faraday's constant, o is the resulting electrical conductivity, R is the gas constant and T is the absolute temperature. fexperi..... t a l ) = f for interstitial or vacancy type diffusion. (For a diffusion mechanism involving more than one atom per step fexperi .... tal) does not equal f [8,9].)fexpcrimental) is often referred to as the Haven ratio. Information about the correlation factor can also be obtained by using two different isotopes of the diffusing species [10,11]. Lim and Day have applied this technique to glass systems [12-15]. While the correlation factor contains information about the diffusion mechanism, it does not depend on the number of mobile ions. It has been suggested that only a small fraction of the alkali ions may be dissociated at any given time and, therefore, these glasses can be treated as weak electrolytes [16-19,2]. The dissociation constant ( K ) can be given by a modified Oswald Dilution Law
K -(a/ao)2C,
(3)
where A is the equivalent conductance (o/C) and A 0 is the equivalent conductance at infinite dilution. The assumptions made in the derivation of this expression are low dissociation and low charge carrier (alkali) content. Taking the logarithm of eq. (3) and rearranging yields log A = - ½ log C + ½ l o g ( A ~ K ) .
(4)
An equivalent expression for the alkali diffusion coefficient (D) can be obtained realizing that A is related to D via the Nernst-Einstein relation. The equivalent expression (if f = 1) is
log D = -
log c + ½ l o g ( D g K ) .
(5)
Evidence of partial dissociation (weak electrolyte) in low alkali glasses can, therefore, be obtained by plotting log A or log D versus log C and observing a slope of -- ½. Cordaro and Tomozawa [2] have compared eq. (4) with results on N a z O GeO 2 glass and obtained good agreement for N a 2 0 contents between 39 and 192 ppm N a 2 0 at 350°C.
348
J.E. Kelly I l L M. Tomozawa / Na ion transport in borosilieate glasses
3.1. Sample preparation Sodium borosilicate glasses were prepared by mixing either 99.9999% pure (for N a 2 0 contents ~<224 ppm) or 99.99% pure (for N a 2 0 contents ~>581 ppm) crystalline B203 powder with 99.999% pure SiO 2 and sodium carbonate. The molar ratio of B203 to SiO 2 was 70-30%. The glasses were melted in a 10% Rh-90% Pt covered crucible at 1600°C for 2 h, stirred with a Pt stirring tool, and melted for one additional hour in air. Following melting, the glass was poured into a graphite mold at room temperature. All glasses were also annealed at 350°C for 1 h in dry argon and furnace cooled to remove residual stress. The glass was stored in a vacuum dessicator to retard the attack of atmospheric water on the glass. Samples for diffusion measurments were cut into pieces approximately 1 cm × 1 cm × 1 mm. Samples for electrical measurements were approximately 2 c m diameter by 1 mm thick. All samples were polished to 1/tm diamond in oil.
3.2. :2Na diffusion measurements 22NaC1 was vapor deposited on one polished surface of each sample for diffusion measurement and two samples of each composition were placed together in a "sandwich" configuration with the radioisotope between them. The samples were then heat treated in a dry argon atmosphere allowing the 22Na to diffuse into the samples. Following this diffusion anneal, successive layers were etched off the samples using a 95% C 2 H s O H - 5 % H 2 0 solution. After each etching step the residual activity of the sample was measured and the etching depth was determined from the weight loss, surface area and density of the sample. The diffusion coefficient ( D ) was determined from the equation [21 ].
I( x, t) = !o erfc[ x / Z ( Dt ) l /2] •
(6)
where I(x, t) is the residual activity of the sample after etching to a distance x into the sample, I 0 is the initial residual activity and t is the diffusion anneal time.
3.3. Electrical conductivity measurements Gold electrodes were evaporated on the samples for electrical measurements in the three-electrode configuration given by Amey and Hamberger [22]. The external circuit used to measure the dc conductivity was similar to that of Namikawa [23].
3.4. Measurement of Na content and relative OH content Chemical analysis to determine Na concentrations in the glasses was performed using atomic absorption. The relative O H contents were determined
J.E. Kelly IlL M. Tomozawa / Na ion transport in borosilicate glasses
349
from the infrared absorption at 2.8 /~m corresponding to the fundamental wavelength for O - H stretching in these glasses. The extinction coefficient (/~) at this wavelength is not known for these glasses, therefore, an exact determination of the concentration of OH groups (c) can not be made. However, a comparison of (t~c) values gives the relative OH contents assuming (/z) does not change significantly with differing sodium contents.
4. Results
Fig. 1 is a typical residual activity (22 Na) profile from the sodium diffusion measurements. The small diffusion distances required great care in chemical sectioning, but the results were quite reproducible. Fig. 2 summarizes both the dc conductivity and 22Na diffusion coefficients at 350°C as a function of the Na 20 content in the glass. The 22Na diffusion coefficient decreases and the dc conductivity increases rapidly with the first additions of NazO. Beyond approximately 0.25 mol% N a 2 0 the change is less pronounced. Fig. 3 shows the dependence of the dc conductivity on temperature for the glasses containing 111 and 581 ppm Na20, The activation energies for conduction are (46.1 ± 1.2) and (48.1 -+ 4.2) kcal/mol, respectively.
4.0,i ~
3.0~ ~ { 0
b )
o
Da:3.41 x10 "14 Db:3.4g x10 -14
cm__ " 4 S
>.
.> o 2.0 o th rr
1.0 ~°~o I
~o
2,o
I
I
30
~,o
s0
X (~m) Fig. 1. Residual activity (22Na) versus penetration depth (x) for two different specimens of 0.7 B203-0.3 SiO2 glass containing 4559 ppm Na20.
0
-14
\
/
0 "~--. 0
I
.
/--.,
I
I
l
i
I
i
20
X I0 "3
1.0 2.0 N~20 ( MOLE°/o )
15
I0
(PPM)
I
25
3.0
-12
-II
-I0
-%
('3
,-~ c~
to (9 0 .J
55
-12.5
~0-12.0
0
3=
i
-11.5
I
1,80 I000/T
I
°
I
1.70
581 PPM No20
(°K)-I
1.65
III PPM Na2:~
•
Fig. 3. Electrical conductivity (o) as a function of temperature in 0.7 B203-0.3 SiO 2 glasses containing 111 and 581 ppm Na20.
Fig. 2. 2~Na diffusion coefficient ( D ) and dc electrical conductivity (o) in 0.7 B203 0.3 SiO2 glasses as a function of N a 2 0 content at 350°C.
(.9 0 .-I
{:3 i...,
o
:E
rA- i O LLI (/)
-12
5
NQ20
1.75
,g
r,
.m
J.E. Kelly 111, M. Tomozawa / Na ion transport in borosilicate glasses
351
LOG [C (PPM Nq20)l
2
3
4
-5
-12
r o G'~
0-6
O
Z
0 ._J
e~e~
\ m (D
-14
-7 SLOPE
=
- I/2
II
-8
-15 - -
-5.5
I
-5.0
|
-4.5
I
-4.0
I
-3 . 5
I
-5.0
-2.5
LOG [C ( M O L E / C M 3 ) ]
Fig. 4. Equivalent conductance ( A ) and 22Na diffusion coefficient ( D ) in 0.7 B203-0.3 SiO 2 glasses with low alkali content as a function of sodium concentration (C) at 350°C.
Fig. 4 shows log D N a and log A versus log [Na] at 350°C for the glasses investigated. The slopes at [Na] below 581 ppm N a 2 0 are - 0 . 6 3 and - 0 . 6 8 for diffusion and conduction respectively in comparison with the value of - 0 . 5 predicted by the weak electrolyte theory. Table 1 lists the experimental correlation factors. Values near unity were found in most cases. The results for higher sodium content glasses are probably less reliable since the samples deformed slightly at the measuring temperature. Other sources of experimental error include difficulties in measuring DNa values of such small magnitude, measuring sodium contents and the possible effects of glass surface corrosion on electrical measurements. Table 1 also lists the relative water content in glasses. Although water in glass is known to influence the sodium transport property [24], the effect here, is considered small since variation of water content among different specimens is small.
5. Discussion
Correlation factors near unity indicate that Na ÷ diffusion occurs via a random process in the low sodium content sodium borosilicate glasses investi-
352
J.E. Kelly I l L M. Tomozawa / Na ion transport in borosilicate glasses
gated in this work. These results are in agreement with low sodium content silicate [12,25] and germanate glasses [1] where values o f f near unity have also been reported. An "interstitial" model of Na ÷ diffusion was previously proposed for these glasses [1] and appears to be valid for the glasses investigated in this study. According to this model, the Na + become thermally dissociated from their equilibrium positions and randomly diffuse through intermediate sites. Such intermediate sites must exist in low alkali content glasses because of the large distances between equilibrium Na sites assuming they are randomly distributed. These distances of -~ 20 to 100 ,~ in low alkali glasses would be too large for a single jump. The intermediate sites, are, therefore, similar to interstitial sites in crystalline materials in that they provide space through which atoms can diffuse in the absence of equilibrium positions (lattice positions in the case of crystalline materials). According to this free "interstitial" model of Na + diffusion in low alkali content glass, DNa should depend on the number of available intermediate sites, the "doorway size" between such sites and the number of dissociated ions moving. DN~ values for the borate rich glasses investigated here are much lower than values found in similar silicate and germanate glasses. Han et al. [4] made the same observation for Na20-B203 glasses. The dc conductivity decreases in the order GeO 2 > SiO 2 > 0.7 B203 • 0.3 SiO 2 as shown in fig. 5 and table2 (the slight difference in N a 2 0 content does not alter the order). Helium gas (which has approximately the same diameter as Na +) solubility for the three common glass formers decreases in the order [26,27] SiO 2 > B203 > G e O 2 . The diffusivities of helium gas decrease in the order B203 > SiO 2 > GeO 2 . Furthermore, the activation energy for He gas diffusion in B203 glass ~< that for SiO 2 or GeO 2 glass. However, the activation energy for Na diffusion (and electrical conduction) in borate rich glasses is much higher than for the other common glass forming oxide systems (cf. fig. 5 and table2). This seems to indicate that it is not the number of intermediate sites (pores) or the "doorway size" which is responsible for the low DN~ values observed in borate-rich glasses, but rather that the Na + are bound much more tightly to the borate glass structure than to the others. This view seems consistent with the observed trend of the high frequency dielectric constant, which attenuates the coulombic interaction energy. The smaller dielectric constant of 0.7 B203 • 0.3 SiO 2 glass is expected to produce stronger coulombic force between Na + and the adjacent non-bridging oxygen. The resulting large activation energy for dissociation permits fewer Na + to contribute to DN~ at any given time in borate rich glasses as compared to silicate and germanate glasses. Also, the value of a ( T = 300°C) for the sodium borosilicate glass containing 111 p p m N a 2 0 is
J.E. Kelly I11, M. Tomozawa / Na ion transport in borosilicate glasses
353
-8.0 _ ~0.04 B203 ~0.96
-9.0
S;O2 •
(28)
~E
_'2-"
'~ -I0.0 o k~ i.J
0._I -II.0
i
~
-12.0
Ge02(2)
~0.7 B
\ o.s,o -13.C
I 1.5 IO00/T
\
I 2.0 (OK)"l
I 2.5
Fig. 5. A comparison of electrical conductivity of low alkali oxide glasses. GeO 2 with 111 p p m N a 2 0 [2], 0.96 SIO2-0.04 B203 with 202 p p m N a 2 0 [28] and 0.7 B203-0.3 SiO 2 with 111 p p m Na20.
close to o ( T = 300°C) for B 2 0 3 glass (low in Na content) [3]. This indicates that additions of SiO 2 (up to 30 mol%) to B203 glass has little effect on the number of dissociated Na + or the mobility. Therefore, the majority of Na ÷ are most likely bound near B and diffusion is relatively unaffected by the existence Table 2 Electrical conductivity data for various low alkali oxide glasses (shown in fig. 5) Glass former (s)
Sodium content
Activation energy (kcal/ mol
log [o 0 ( ~ - c m ) - i ]
~o,
Ref.
0.7 B203-0.3 SiO 2
111 p p m N a 2 0
46.1
+4.64
3.6
0.96 SIO2-0.04 B203 GeO 2
202 pprn N a 2 0 111 p p m Na 20
29.2 23.7
--0.046 - 0.076
4.0
present work [28] [2]
5.5
354
J.E. Kelly HL M. Tomozawa / Na ion transport in borosilicate glasses
o f SiO 2 t e t r a h e d r a dispersed t h r o u g h o u t the B20 3 network. T h e qualitative a p p l i c a b i l i t y of the weak electrolyte m o d e l to these glasses r e m a i n s in question. T h e slopes in fig. 4 are s o m e w h a t larger than p r e d i c t e d b y this theory. However, this d a t a is o n l y at one t e m p e r a t u r e a n d the effects of s o d i u m c o n t e n t on the viscosity of the glass m a y influence these results.
6. Summary and conclusions E x p e r i m e n t a l m e a s u r e m e n t of correlation factors in low s o d i u m c o n t e n t s o d i u m borosilicate glasses yielded values n e a r unity. This suggests that N a ÷ ions diffuse via a r a n d o m j u m p i n g process. These results are in a g r e e m e n t with the free " i n t e r s t i t i a l " diffusion m e c h a n i s m previously p r o p o s e d for N a + diffusion in low alkali c o n t e n t glasses [1]. The low values of DNa a n d o, the high activation energy for c o n d u c t i o n in these glasses a n d the high helium gas diffusivity d a t a on B20 3 glass in c o m p a r i s o n with o t h e r low alkali glasses suggest that the N a + are b o n d e d very strongly to the b o r a t e - r i c h glass network. This is expected to result in only a few of the N a + being t h e r m a l l y d i s s o c i a t e d from their e q u i l i b r i u m positions at a n y one time. In view of these points, the weak electrolyte m o d e l should be a p p l i c a b l e to this glass system. However, the results p r e s e n t e d here are not conclusive enough to either verify or rule out its pertinence. T h e assistance of J.F. C o r d a r o with electrical m e a s u r e m e n t s is gratefully a p p r e c i a t e d . This w o r k was s u p p o r t e d b y N S F G r a n t D M R 81-00406.
References [1] J.E. Kelly, J.F. Cordaro and M. Tomozawa, J. Non-Crystalline Solids 41 (1980) 47. [2] J.F. Cordaro and M. Tomozawa, Phys. Chem. Glasses 21 (1980) 74. [3] K.S. Evstrop'ev and A.O. Ivanov, Advances in Glass Tech. Part 2, Proc. VI ICG, Washington, DC, July 1962 (1963) p. 79. [4] Y.H. Han, N.J. Kreidl and D.E. Day, J. Non-Crystalline Solids 30 (1979) 241. [5] R.J. Charles and F.E. Wagstaff, General Electric Tech. lnfo Series (1967). [6] K. Compaan and Y. Haven, Trans. Faraday Soc. 52 0956) 786. [7] K. Compaan and Y. Haven, Trans. Faraday Soc. 54 0958) 1498. [8] A.D. LeClaire, Physical Chemistry, An Advanced Treatise Vol. 10, ed., W. Jost (Academic Press, New York, 1970) p. 261. [9] L.R. Barr, J.N. Mundy and A.H. Rowe, Amorphous Materials eds., R.W. Douglas, B. Ellis (Wiley-Interscience, New York, 1972) p. 243. [10] A.H. Schoen, Phys. Rev. Lett. I (1958) 138. [1 l] J.R. Manning, Mass Transport in Oxide, eds., J.B. Eachtman, A.D. Franklin, National Bureau of Standards Special Publication 296 (1968). [12] C. Lim and D.E. Day, J. Am. Ceram. Soc. 61 (1978) 329. [13] C. Lim and D.E. Day, J. Am. Ceram. Soc. 60 (1977) 198. [14] C. Lira and D.E. Day, J. Am. Ceram. Soc. 60 (1977) 473. [15] C. Lim and D.E. Day, J. Am. Ceram. Soc. 61 (1978) 99.
J.E. Kelly I11, M. Tomozawa / Na ion transport in borosilicate glasses
355
[16] R.L. Myuller, Electrical Conductivity of Vitreous Substances (Consultants Bureau, New York, 1971) p. 93. [17] D. Ravaine and J.L. Souquet, Phys. Chem. Glasses 18 (1977) 27. [18] M. Tomozawa, Treatise on Materials Science and Technology: Glass I, Vol. 12, eds., M. Tomozawa, R.H. Doremus (Academic Press, New York, 1977). [19] M.O. Ingram, C.T. Moynihan and A.V. Lesikar, J. Non-Crystalline Solids 38-39 (1980) 371. [20] J. Bockris and A.K. Reddy, Modern Electrochemistry, Vol. 1 (Plenum, New York, 1970). [21] G.H. Frischat, Ionic Diffusion in Oxide Glasses, Trans. Tech. Publications (1975). [22] W.G. Amey and F. Hamberger, Proc. Am. Soc. Test Mat. 49 (1949) 1070. [23] H. Namikawa, J. Non-Crystalline Solids 14 (1974) 88. [24] J.F. Cordaro, J.E Kelly I11 and M. Tomozawa, Phys. Chem. Glasses 22 (1981) 90. [25] R.H. Doremus, Phys. Chem. Glasses 10 (1969) 28. [26] K.N. Woods and R.H. Doremus, Phys. Chem. Glasses 12 (1971) 69. [27] J.E. Shelby, J. Appl. Phys. 43 (1972) 3068. [28] J.H. Simmons, P.B. Elterman, C.J. Simmons and R.K. Mohr, J. Am. Ceram. Soc. 62 (1979) 158.
345
S O D I U M I O N T R A N S P O R T IN H I G H P U R I T Y B O R O S I L I C A T E GLASSES J o h n E. K E L L Y III * a n d M i n o r u T O M O Z A W A Materials Engineering Department, Rensselaer Polytechnic Institute, Troy, New York 12181, USA
Received 27 January 1982 Revised manuscript received 23 March 1982
22Na diffusion coefficients and dc electrical conductivity were measured in 0.7 B203.0.3 SiO2 (mole ratio) glasses containing small amounts of Na20 (111 ppm to 2.6 mol%). Correlation factors near unity were obtained from the Nernst-Einstein equation for these glasses. These values are in agreement with a previously proposed free "interstitial" alkali ion diffusion mechanism in low alkali content glasses. It is concluded from the low values of the sodium diffusion coefficients and dc conductivity in these glasses (relative to similar silicate and germanate glasses) that the Na ÷ are bound strongly to the borate-rich glass network and that the number of dissociated Na + at any given time is small.
1. Introduction Ionic transport in oxide glass influences m a n y of its i m p o r t a n t properties. The systematic alteration of a n y of these properties requires a basic u n d e r s t a n d i n g of the ionic transport m e c h a n i s m in the glass. A complete description of the transport process for alkali ions should include both the transport m e c h a n i s m and the n u m b e r of mobile ions. Single alkali glasses with low alkali c o n c e n t r a t i o n s provide a good starting p o i n t in the effort to u n d e r s t a n d these t r a n s p o r t p h e n o m e n a because the interaction of a n alkali ion with other alkali ions of the same or different type should be minimal. Earlier, the present authors measured s o d i u m diffusion [1] a n d electrical c o n d u c t i v i t y [2] in low s o d i u m c o n t e n t g e r m a n a t e glasses a n d observed experim e n t a l correlation factors or H a v e n ratios ( " f " from the N e r n s t - E i n s t e i n relation) near u n i t y for these glasses. F u r t h e r m o r e , a s u m m a r y of experimental correlation factor values for m a n y b i n a r y alkali oxide glasses indicated that at low alkali c o n t e n t s f = 1 a n d that increasing the alkali c o n t e n t in the glass reduced f to values near 0.2 to 0.5. However, it was f o u n d that the experimental data o n borate a n d borate-rich borosilicate glasses with low alkali conc e n t r a t i o n s is very limited [3,4]. The purpose of this research is to o b t a i n
* Now at International Business Machines Corporation, Poughkeepsie, New York 12602, USA. 0 0 2 2 - 3 0 9 3 / 8 2 / 0 0 0 0 - 0 0 0 0 / $ 0 2 . 7 5 © 1982 N o r t h - H o l l a n d
346
J.E. Kelly II1, M. Tomozawa / Na ion transport in borosilieate glasses
Table 1 Experimental correlation factors (fexperimental),water content and glass transition temperature of 0.7 B203-0.3 SiO2 glasses with low alkali content Na20 (ppm)
Tg ( ° C )
#c (cm
111 224 581 2330 4559 24,245
329 322 -
31.7 55.7 33.9 31.5 32.9 26.4
i) at 2 . 8 / ~ m
f(experimental) 0.99 1.02 1.07 0.73 a 0.75 a 1.13 a
a S o m e glass d e f o r m a t i o n w a s o b s e r v e d a f t e r electrical c o n d u c t i v i t y a n d d i f f u s i o n m e a s u r e m e n t s .
correlation factors, 22Na diffusion coefficients and electrical conductivities of low sodium content borate-rich glasses and to compare these results with various other high purity glasses. Preparation of low sodium content N a 2 0 - B 2 0 3 glasses is possible, but the low value of Tg ( = 230°C), the low value of the sodium diffusion coefficient ( D N a ~ I 0 -14 cm2/s at 300°C [3]) and the rapid attack of the glass by atmospheric water make this a difficult system to work with. The addition of silica to this system raises Tg making it possible to measure DNa at higher temperatures without encountering sample deformation (Tg values determined by a dilatometric method are shown for selected compositions in table 1) and it also increases the chemical durability. Phase separation in the 0.7 B203 • 0.3 SiO 2 glass system occurs only after prolonged heat treatment at 450-520°C [5], therefore, diffusion and electrical measurements at temperatures -~ 350°C will not be affected by phase separation. Thus 0.7 B203 • 0.3 SiO 2 glasses with low N a 2 0 contents were chosen for the present study.
2.
Theory
A basic understanding of alkali ion diffusion mechanisms in amorphous systems has been difficult to obtain due to the complexity of the random-network structure. However, the concept of a correlation factor ( f ) which is widely used for diffusion in crystalline systems has been applied with some success to many glass systems. The correlation factor results from the non-random motion of the diffusing atom, and, therefore, is a function of the diffusion mechanism. From a statistical model of diffusion, the correlation factor can be expressed as [6]: f = 1 + 2cos 0,.i+ l + 2 cos 8,.~+ 2 + ....
(la)
f = 1 + 2 ~ cosO~j+~,
(lb)
or
n=l
J.E. Kelly IIL M. Tornozawa / Na ion transport in borosilicate glasses
347
where Oi,i+,, is the angle between the two jump vectors i and i + n. If the motion of the diffusing ion is totally random in direction the sum in eq. (lb) is zero and f = 1. In crystalline materials it is possible to use the symmetry of the lattice to determine possible jump directions for various diffusion mechanisms and evaluate f theoretically [6,7]. However, in amorphous systems there is no long range symmetry and hence an exact evaluation of the sum of eq. (lb) is difficult (except for perfectly random motion as previously mentioned). Correlation factors ( f ) can be experimentally determined from a modified Nernst-Einstein equation: f(experimental) =
DCFZ,/°RT,
(2)
where D is the tracer diffusion coefficient of the charge carrier, C is the concentration of charge carriers, F is Faraday's constant, o is the resulting electrical conductivity, R is the gas constant and T is the absolute temperature. fexperi..... t a l ) = f for interstitial or vacancy type diffusion. (For a diffusion mechanism involving more than one atom per step fexperi .... tal) does not equal f [8,9].)fexpcrimental) is often referred to as the Haven ratio. Information about the correlation factor can also be obtained by using two different isotopes of the diffusing species [10,11]. Lim and Day have applied this technique to glass systems [12-15]. While the correlation factor contains information about the diffusion mechanism, it does not depend on the number of mobile ions. It has been suggested that only a small fraction of the alkali ions may be dissociated at any given time and, therefore, these glasses can be treated as weak electrolytes [16-19,2]. The dissociation constant ( K ) can be given by a modified Oswald Dilution Law
K -(a/ao)2C,
(3)
where A is the equivalent conductance (o/C) and A 0 is the equivalent conductance at infinite dilution. The assumptions made in the derivation of this expression are low dissociation and low charge carrier (alkali) content. Taking the logarithm of eq. (3) and rearranging yields log A = - ½ log C + ½ l o g ( A ~ K ) .
(4)
An equivalent expression for the alkali diffusion coefficient (D) can be obtained realizing that A is related to D via the Nernst-Einstein relation. The equivalent expression (if f = 1) is
log D = -
log c + ½ l o g ( D g K ) .
(5)
Evidence of partial dissociation (weak electrolyte) in low alkali glasses can, therefore, be obtained by plotting log A or log D versus log C and observing a slope of -- ½. Cordaro and Tomozawa [2] have compared eq. (4) with results on N a z O GeO 2 glass and obtained good agreement for N a 2 0 contents between 39 and 192 ppm N a 2 0 at 350°C.
348
J.E. Kelly I l L M. Tomozawa / Na ion transport in borosilieate glasses
3.1. Sample preparation Sodium borosilicate glasses were prepared by mixing either 99.9999% pure (for N a 2 0 contents ~<224 ppm) or 99.99% pure (for N a 2 0 contents ~>581 ppm) crystalline B203 powder with 99.999% pure SiO 2 and sodium carbonate. The molar ratio of B203 to SiO 2 was 70-30%. The glasses were melted in a 10% Rh-90% Pt covered crucible at 1600°C for 2 h, stirred with a Pt stirring tool, and melted for one additional hour in air. Following melting, the glass was poured into a graphite mold at room temperature. All glasses were also annealed at 350°C for 1 h in dry argon and furnace cooled to remove residual stress. The glass was stored in a vacuum dessicator to retard the attack of atmospheric water on the glass. Samples for diffusion measurments were cut into pieces approximately 1 cm × 1 cm × 1 mm. Samples for electrical measurements were approximately 2 c m diameter by 1 mm thick. All samples were polished to 1/tm diamond in oil.
3.2. :2Na diffusion measurements 22NaC1 was vapor deposited on one polished surface of each sample for diffusion measurement and two samples of each composition were placed together in a "sandwich" configuration with the radioisotope between them. The samples were then heat treated in a dry argon atmosphere allowing the 22Na to diffuse into the samples. Following this diffusion anneal, successive layers were etched off the samples using a 95% C 2 H s O H - 5 % H 2 0 solution. After each etching step the residual activity of the sample was measured and the etching depth was determined from the weight loss, surface area and density of the sample. The diffusion coefficient ( D ) was determined from the equation [21 ].
I( x, t) = !o erfc[ x / Z ( Dt ) l /2] •
(6)
where I(x, t) is the residual activity of the sample after etching to a distance x into the sample, I 0 is the initial residual activity and t is the diffusion anneal time.
3.3. Electrical conductivity measurements Gold electrodes were evaporated on the samples for electrical measurements in the three-electrode configuration given by Amey and Hamberger [22]. The external circuit used to measure the dc conductivity was similar to that of Namikawa [23].
3.4. Measurement of Na content and relative OH content Chemical analysis to determine Na concentrations in the glasses was performed using atomic absorption. The relative O H contents were determined
J.E. Kelly IlL M. Tomozawa / Na ion transport in borosilicate glasses
349
from the infrared absorption at 2.8 /~m corresponding to the fundamental wavelength for O - H stretching in these glasses. The extinction coefficient (/~) at this wavelength is not known for these glasses, therefore, an exact determination of the concentration of OH groups (c) can not be made. However, a comparison of (t~c) values gives the relative OH contents assuming (/z) does not change significantly with differing sodium contents.
4. Results
Fig. 1 is a typical residual activity (22 Na) profile from the sodium diffusion measurements. The small diffusion distances required great care in chemical sectioning, but the results were quite reproducible. Fig. 2 summarizes both the dc conductivity and 22Na diffusion coefficients at 350°C as a function of the Na 20 content in the glass. The 22Na diffusion coefficient decreases and the dc conductivity increases rapidly with the first additions of NazO. Beyond approximately 0.25 mol% N a 2 0 the change is less pronounced. Fig. 3 shows the dependence of the dc conductivity on temperature for the glasses containing 111 and 581 ppm Na20, The activation energies for conduction are (46.1 ± 1.2) and (48.1 -+ 4.2) kcal/mol, respectively.
4.0,i ~
3.0~ ~ { 0
b )
o
Da:3.41 x10 "14 Db:3.4g x10 -14
cm__ " 4 S
>.
.> o 2.0 o th rr
1.0 ~°~o I
~o
2,o
I
I
30
~,o
s0
X (~m) Fig. 1. Residual activity (22Na) versus penetration depth (x) for two different specimens of 0.7 B203-0.3 SiO2 glass containing 4559 ppm Na20.
0
-14
\
/
0 "~--. 0
I
.
/--.,
I
I
l
i
I
i
20
X I0 "3
1.0 2.0 N~20 ( MOLE°/o )
15
I0
(PPM)
I
25
3.0
-12
-II
-I0
-%
('3
,-~ c~
to (9 0 .J
55
-12.5
~0-12.0
0
3=
i
-11.5
I
1,80 I000/T
I
°
I
1.70
581 PPM No20
(°K)-I
1.65
III PPM Na2:~
•
Fig. 3. Electrical conductivity (o) as a function of temperature in 0.7 B203-0.3 SiO 2 glasses containing 111 and 581 ppm Na20.
Fig. 2. 2~Na diffusion coefficient ( D ) and dc electrical conductivity (o) in 0.7 B203 0.3 SiO2 glasses as a function of N a 2 0 content at 350°C.
(.9 0 .-I
{:3 i...,
o
:E
rA- i O LLI (/)
-12
5
NQ20
1.75
,g
r,
.m
J.E. Kelly 111, M. Tomozawa / Na ion transport in borosilicate glasses
351
LOG [C (PPM Nq20)l
2
3
4
-5
-12
r o G'~
0-6
O
Z
0 ._J
e~e~
\ m (D
-14
-7 SLOPE
=
- I/2
II
-8
-15 - -
-5.5
I
-5.0
|
-4.5
I
-4.0
I
-3 . 5
I
-5.0
-2.5
LOG [C ( M O L E / C M 3 ) ]
Fig. 4. Equivalent conductance ( A ) and 22Na diffusion coefficient ( D ) in 0.7 B203-0.3 SiO 2 glasses with low alkali content as a function of sodium concentration (C) at 350°C.
Fig. 4 shows log D N a and log A versus log [Na] at 350°C for the glasses investigated. The slopes at [Na] below 581 ppm N a 2 0 are - 0 . 6 3 and - 0 . 6 8 for diffusion and conduction respectively in comparison with the value of - 0 . 5 predicted by the weak electrolyte theory. Table 1 lists the experimental correlation factors. Values near unity were found in most cases. The results for higher sodium content glasses are probably less reliable since the samples deformed slightly at the measuring temperature. Other sources of experimental error include difficulties in measuring DNa values of such small magnitude, measuring sodium contents and the possible effects of glass surface corrosion on electrical measurements. Table 1 also lists the relative water content in glasses. Although water in glass is known to influence the sodium transport property [24], the effect here, is considered small since variation of water content among different specimens is small.
5. Discussion
Correlation factors near unity indicate that Na ÷ diffusion occurs via a random process in the low sodium content sodium borosilicate glasses investi-
352
J.E. Kelly I l L M. Tomozawa / Na ion transport in borosilicate glasses
gated in this work. These results are in agreement with low sodium content silicate [12,25] and germanate glasses [1] where values o f f near unity have also been reported. An "interstitial" model of Na ÷ diffusion was previously proposed for these glasses [1] and appears to be valid for the glasses investigated in this study. According to this model, the Na + become thermally dissociated from their equilibrium positions and randomly diffuse through intermediate sites. Such intermediate sites must exist in low alkali content glasses because of the large distances between equilibrium Na sites assuming they are randomly distributed. These distances of -~ 20 to 100 ,~ in low alkali glasses would be too large for a single jump. The intermediate sites, are, therefore, similar to interstitial sites in crystalline materials in that they provide space through which atoms can diffuse in the absence of equilibrium positions (lattice positions in the case of crystalline materials). According to this free "interstitial" model of Na + diffusion in low alkali content glass, DNa should depend on the number of available intermediate sites, the "doorway size" between such sites and the number of dissociated ions moving. DN~ values for the borate rich glasses investigated here are much lower than values found in similar silicate and germanate glasses. Han et al. [4] made the same observation for Na20-B203 glasses. The dc conductivity decreases in the order GeO 2 > SiO 2 > 0.7 B203 • 0.3 SiO 2 as shown in fig. 5 and table2 (the slight difference in N a 2 0 content does not alter the order). Helium gas (which has approximately the same diameter as Na +) solubility for the three common glass formers decreases in the order [26,27] SiO 2 > B203 > G e O 2 . The diffusivities of helium gas decrease in the order B203 > SiO 2 > GeO 2 . Furthermore, the activation energy for He gas diffusion in B203 glass ~< that for SiO 2 or GeO 2 glass. However, the activation energy for Na diffusion (and electrical conduction) in borate rich glasses is much higher than for the other common glass forming oxide systems (cf. fig. 5 and table2). This seems to indicate that it is not the number of intermediate sites (pores) or the "doorway size" which is responsible for the low DN~ values observed in borate-rich glasses, but rather that the Na + are bound much more tightly to the borate glass structure than to the others. This view seems consistent with the observed trend of the high frequency dielectric constant, which attenuates the coulombic interaction energy. The smaller dielectric constant of 0.7 B203 • 0.3 SiO 2 glass is expected to produce stronger coulombic force between Na + and the adjacent non-bridging oxygen. The resulting large activation energy for dissociation permits fewer Na + to contribute to DN~ at any given time in borate rich glasses as compared to silicate and germanate glasses. Also, the value of a ( T = 300°C) for the sodium borosilicate glass containing 111 p p m N a 2 0 is
J.E. Kelly I11, M. Tomozawa / Na ion transport in borosilicate glasses
353
-8.0 _ ~0.04 B203 ~0.96
-9.0
S;O2 •
(28)
~E
_'2-"
'~ -I0.0 o k~ i.J
0._I -II.0
i
~
-12.0
Ge02(2)
~0.7 B
\ o.s,o -13.C
I 1.5 IO00/T
\
I 2.0 (OK)"l
I 2.5
Fig. 5. A comparison of electrical conductivity of low alkali oxide glasses. GeO 2 with 111 p p m N a 2 0 [2], 0.96 SIO2-0.04 B203 with 202 p p m N a 2 0 [28] and 0.7 B203-0.3 SiO 2 with 111 p p m Na20.
close to o ( T = 300°C) for B 2 0 3 glass (low in Na content) [3]. This indicates that additions of SiO 2 (up to 30 mol%) to B203 glass has little effect on the number of dissociated Na + or the mobility. Therefore, the majority of Na ÷ are most likely bound near B and diffusion is relatively unaffected by the existence Table 2 Electrical conductivity data for various low alkali oxide glasses (shown in fig. 5) Glass former (s)
Sodium content
Activation energy (kcal/ mol
log [o 0 ( ~ - c m ) - i ]
~o,
Ref.
0.7 B203-0.3 SiO 2
111 p p m N a 2 0
46.1
+4.64
3.6
0.96 SIO2-0.04 B203 GeO 2
202 pprn N a 2 0 111 p p m Na 20
29.2 23.7
--0.046 - 0.076
4.0
present work [28] [2]
5.5
354
J.E. Kelly HL M. Tomozawa / Na ion transport in borosilicate glasses
o f SiO 2 t e t r a h e d r a dispersed t h r o u g h o u t the B20 3 network. T h e qualitative a p p l i c a b i l i t y of the weak electrolyte m o d e l to these glasses r e m a i n s in question. T h e slopes in fig. 4 are s o m e w h a t larger than p r e d i c t e d b y this theory. However, this d a t a is o n l y at one t e m p e r a t u r e a n d the effects of s o d i u m c o n t e n t on the viscosity of the glass m a y influence these results.
6. Summary and conclusions E x p e r i m e n t a l m e a s u r e m e n t of correlation factors in low s o d i u m c o n t e n t s o d i u m borosilicate glasses yielded values n e a r unity. This suggests that N a ÷ ions diffuse via a r a n d o m j u m p i n g process. These results are in a g r e e m e n t with the free " i n t e r s t i t i a l " diffusion m e c h a n i s m previously p r o p o s e d for N a + diffusion in low alkali c o n t e n t glasses [1]. The low values of DNa a n d o, the high activation energy for c o n d u c t i o n in these glasses a n d the high helium gas diffusivity d a t a on B20 3 glass in c o m p a r i s o n with o t h e r low alkali glasses suggest that the N a + are b o n d e d very strongly to the b o r a t e - r i c h glass network. This is expected to result in only a few of the N a + being t h e r m a l l y d i s s o c i a t e d from their e q u i l i b r i u m positions at a n y one time. In view of these points, the weak electrolyte m o d e l should be a p p l i c a b l e to this glass system. However, the results p r e s e n t e d here are not conclusive enough to either verify or rule out its pertinence. T h e assistance of J.F. C o r d a r o with electrical m e a s u r e m e n t s is gratefully a p p r e c i a t e d . This w o r k was s u p p o r t e d b y N S F G r a n t D M R 81-00406.
References [1] J.E. Kelly, J.F. Cordaro and M. Tomozawa, J. Non-Crystalline Solids 41 (1980) 47. [2] J.F. Cordaro and M. Tomozawa, Phys. Chem. Glasses 21 (1980) 74. [3] K.S. Evstrop'ev and A.O. Ivanov, Advances in Glass Tech. Part 2, Proc. VI ICG, Washington, DC, July 1962 (1963) p. 79. [4] Y.H. Han, N.J. Kreidl and D.E. Day, J. Non-Crystalline Solids 30 (1979) 241. [5] R.J. Charles and F.E. Wagstaff, General Electric Tech. lnfo Series (1967). [6] K. Compaan and Y. Haven, Trans. Faraday Soc. 52 0956) 786. [7] K. Compaan and Y. Haven, Trans. Faraday Soc. 54 0958) 1498. [8] A.D. LeClaire, Physical Chemistry, An Advanced Treatise Vol. 10, ed., W. Jost (Academic Press, New York, 1970) p. 261. [9] L.R. Barr, J.N. Mundy and A.H. Rowe, Amorphous Materials eds., R.W. Douglas, B. Ellis (Wiley-Interscience, New York, 1972) p. 243. [10] A.H. Schoen, Phys. Rev. Lett. I (1958) 138. [1 l] J.R. Manning, Mass Transport in Oxide, eds., J.B. Eachtman, A.D. Franklin, National Bureau of Standards Special Publication 296 (1968). [12] C. Lim and D.E. Day, J. Am. Ceram. Soc. 61 (1978) 329. [13] C. Lim and D.E. Day, J. Am. Ceram. Soc. 60 (1977) 198. [14] C. Lira and D.E. Day, J. Am. Ceram. Soc. 60 (1977) 473. [15] C. Lim and D.E. Day, J. Am. Ceram. Soc. 61 (1978) 99.
J.E. Kelly I11, M. Tomozawa / Na ion transport in borosilicate glasses
355
[16] R.L. Myuller, Electrical Conductivity of Vitreous Substances (Consultants Bureau, New York, 1971) p. 93. [17] D. Ravaine and J.L. Souquet, Phys. Chem. Glasses 18 (1977) 27. [18] M. Tomozawa, Treatise on Materials Science and Technology: Glass I, Vol. 12, eds., M. Tomozawa, R.H. Doremus (Academic Press, New York, 1977). [19] M.O. Ingram, C.T. Moynihan and A.V. Lesikar, J. Non-Crystalline Solids 38-39 (1980) 371. [20] J. Bockris and A.K. Reddy, Modern Electrochemistry, Vol. 1 (Plenum, New York, 1970). [21] G.H. Frischat, Ionic Diffusion in Oxide Glasses, Trans. Tech. Publications (1975). [22] W.G. Amey and F. Hamberger, Proc. Am. Soc. Test Mat. 49 (1949) 1070. [23] H. Namikawa, J. Non-Crystalline Solids 14 (1974) 88. [24] J.F. Cordaro, J.E Kelly I11 and M. Tomozawa, Phys. Chem. Glasses 22 (1981) 90. [25] R.H. Doremus, Phys. Chem. Glasses 10 (1969) 28. [26] K.N. Woods and R.H. Doremus, Phys. Chem. Glasses 12 (1971) 69. [27] J.E. Shelby, J. Appl. Phys. 43 (1972) 3068. [28] J.H. Simmons, P.B. Elterman, C.J. Simmons and R.K. Mohr, J. Am. Ceram. Soc. 62 (1979) 158.