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Ionic transport in sodium germanate glasses
320
Journal of Non-Crystalline Solids 84 (1986) 320-324 North-Holland, Amsterdam
IONIC TRANSPORT IN SODIUM GERMANATE GLASSES * J.N. M U N D Y , G.L. J I N and N.L. P E T E R S O N Materials Science and Technology Division, Argonne National Laboratory, Argonne, IL 60439, USA
Measurements of the electrical conductivity and tracer diffusion coefficient have been made for a series of XNa20 :(1 - X)GeO 2 glasses, where X = 0.01, 0.05, 0.10, 0.15, 0.19 and 0.29. The Haven ratios determined from these measurements show the same trends as earlier work. The dc conductivities of the present study also show the same minimum in sodium ion mobility (at X - 0.09) as found in the earlier studies. The minimum is shown to be an interplay between the pre-exponential and exponential terms. The activation enthalpy remains almost constant for X < 0.09 and then decreases rapidly with increasing X. These changes can be related to the average Ge-Ge separation which varies little below X - 0.08 but rapidly increases for larger X.
Over twenty years ago anomalies were f o u n d in the physical properties of sodium germanate glasses [1,2]. For example, the density has a m a x i m u m at a N a 2 0 concentration, X - 0 . 1 5 . This m a x i m u m leads to a m i n i m u m in the molar volume at X - 0 . 1 8 which is at the smallest X for which a stable crystalline sodium germanate ( 2 N a 2 0 : 9GeO2) has been found [3]. A structural model was postulated [1,2] based on the concept that additions of N a a O to germania glass convert some of the germanium from four-fold to six-fold coordination without breaking G e - O - G e bridging bonds. 22Na tracer diffusion measurements [4] show a m i n i m u m for X - 0.08-0.09; this value of X is clearly lower than that found for the a n o m a l y in the structural properties. Recent studies of sodium germanate glasses using R a m a n spectroscopy [5,6], neutron scattering [7] and E X A F S measurements [8] have confirmed the structural model. The neutron scattering data [7] showed that for X _< 0.2 each N a 2 0 molecule added to germania glass converts one g e r m a n i u m ion from tetrahedral to octahedral coordination without the formation of non-bridging oxygen ions; i.e., the concentration of G e O 6 octahedron structural units is given by C 6 = X / ( 1 - X ) . F o r X >_,0.2 non-bridging oxygen ions (NBOs) are formed. Only six glass compositions were examined b y neutron scattering and it appears likely that non-bridging oxygen ions begin to form for X >_ 0.18 [6], i.e., the composition of m i n i m u m molar volume. Tracer diffusion ( D x) and ionic conductivity ( o ) of dilute sodium germanate glasses have recently been measured by Kelly et al. [9]. Their measurements allowed a determination of the Haven ratio, H R, which for a single alkali glass * Work supported by the U.S. Department of Energy. 0022-3093/86/$03.50 © Elsevier Science Publishers B.V.
(North-Holland Physics Publishing Division)
J.N. Mundy et al. / Ionic transport in sodium germanate glasses
321
is defined as the ratio of D T to the diffusivity, D o, of the migrating alkali ion deduced from the Nernst-Einstein relation:
kT D~ = N e 2 . o ,
(1)
where k is the Boltzmann constant, T is the absolute temperature, N is the concentration of alkali ions per unit volume and e is the electronic charge. For the dilute sodium germanate glasses Kelly et al. [9] found H R - 1 and their analysis of the data of Evstrop'ev and Pavlovskii ( E - P ) [4] showed that H R decreased to - 0 . 3 for X>_ 0.15. Recent work by Thomas and Peterson [10] has confirmed the trend of H R ( X ) with somewhat lower values of H R for X >__0.05. The present measurements of H R at X = 0.10, 0.19 and 0.29 are in closer agreement to the results of E - P but the trend with X is the same in all studies. Thomas and Peterson [10] have satisfactorily explained the H R ( X ) data in terms of a single defect model for which diffusive j u m p correlation results from attractive interactions between the positive sodium ions and negative charge compensating centers (GeO6; germanium in octahedral coordination) in the glass. As X increases the average distance between sodium ions and GeO 6 units decreases and the attractive interaction betweeen the two results in a higher degree of correlation in j u m p direction and hence a lower value of H R. The present study has measured D x and o as a function of temperature for X = 0.01, 0.05, 0.10, 0.15, 0.19 and 0.29 in order to investigate why DT(X ) and Do(X) have minima at X - 0.09 [4,10] and why these minima are not related to the minimum in the molar volume or maximum of C 6 ( X - 0 . 1 8 ) . These questions are of particular interest to our present program which seeks to relate the ionic transport behavior to changes in the interaction between the alkali ion and charge compensating centers in alkali-oxide glasses. The values of D T (573 K) agree within experimental error with the previous studies [4,10] and further discussion will focus on the ionic conductivity measurements. The dc conductivity of alkali ion conductors may be expressed [11,12] as:
where c~ is a geometric factor which is the reciprocal of the number of possible j u m p directions from a given site (we assume a - ~- for the present glasses) and a is the ionic j u m p distance. The average j u m p rate of the alkali ion, ¢0p is given by % = v exp( S / k ) exp( - H / k T ) ,
(3)
where v is an appropriate attempt (vibration) frequency, S and H are the activation entropy and enthalpy for the ionic j u m p process. The term fiN expresses the concentration of mobile ions which may in some cases be
322
J.N. Mundy et al. / l o n i c transport in sodium germanate glasses
thermally activated and given by /3N = Ce e x p ( - H c / k T ) ,
(4)
where Ce is the effective carrier concentration at infinite temperature and H c is the enthalpy for the creation of the mobile ions. Although in an alkali oxide glass it might be expected that /3 = 1, Almond and West [12] show that deviations of 13 from unity may occur and will be evident when H 4: H c. Their work showed that while the slope of I n ( a T ) vs 1 / T gives ( H + Hc), the slope of ln(~op) vs 1 / T gives H alone. The present measurements of a were made as a function of both frequency (20-105 Hz) and temperature (100-500°C) and the results were analyzed by both complex impedance techniques in order to obtain the dc conductivities a( T) and by the method of Almond and West [12] in order to obtain ~0p(T). The activation enthalpies obtained from the o(T) and ~0p(T) data were the same within the standard deviations calculated from the fits of the data to eqs. (2) and (3); this suggests that/3 = 1 and all the alkali ions in the present glasses contribute to ionic transport. The intercepts at infinite temperature determine the values of a 0 and i, e x p ( S / k ) , respectively. The intercepts of u e x p ( S / k ) are poorly defined by the present measurements (3 + 2 × 1014 s - 1 ) but suggest for u = 1013 S-1 an entropy of S / k - 3. From eqs. (1-4) the diffusivity of the migrating alkali ions Do is given by
o0
exp(- )
where ao/N is a function of p, S and a. Measurements of the density of each sample, together with chemical analysis, allowed the determination of N for each of the glasses. The values of Do(X) for a temperature of 300°C are shown in fig. 1. The separated components of D o (pre-exponential and exponential) are shown as dashed lines. The separation of the present results suggests that the minimum in D o results largely from a minimum in the exponential term (maximum in H ) and that the decreasing of the pre-exponential term with X simply deepens the minimum and moves it to slightly higher X. The values of Do(X) agree within experimental error with the E - P data [4] with the exception of the value for X = 0.10; the present result is 25% smaller than the result in ref. [4]. The variations in the pre-exponential and exponential components are also. in reasonable agreement with those determined from the E - P data. However, in the recent work of Thomas and Peterson [10] the values of D o are twice the present values although the depth and position of the minimum in D O appear to be the same. Thomas and Peterson find little variation in H for X ~<0.09 and attribute the minimum in D o largely to the decrease in the pre-exponential term. It is important for our studies of the effect of systematically changing the attractive interaction between the alkali ions and the charge compensating centers that we resolve whether the minimum in D o results from the pre-exponential (ao/N) or exponential ( H ) component. -
J.N. Mundy et al. / Ionic transport in sodium germanate glasses
I
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323
-
I
I0
Z
~
20 tool % No20
30
i0-10
=1%
t~l z
~10-3
Fig. 1. Nernst-Einstein diffusivity (Do) and its pre-exponential and exponential components as a function of molecular concentration (X).
In order to examine how the activation enthalpy ( H ) varies with X, we have plotted in fig. 2 values from six different studies. The values of H are plotted as a function of the average sodium-Ge (octahedrally coordinated) separation. The overall evidence suggests that H shows a marginal increase when proceeding from large separations of 100 A ( X - 1 . 5 × 10 -5) to a separation of - 5 . 4 A ( X - 0 . 0 9 ) , but for smaller separations (X>__ 0.1) H rapidly decreases. It should be noted that the maximum in H occurs near X = 0.08, a composition considerably smaller than X = 0.18 where a saturation in C 6 or the formation of NBOs should occur. Although the variation in H R ( X ) is related to the N a - G e (oct.) separation [10] the activation enthalpy shows no obvious correlation with this separation. The variation of H appears however to correlate well with the average G e - G e separation decreases marginally from low soda concentration (3.63 A) to a minimum of 3.58 A at X - 0.08 and rapidly increases at higher X thus mirroring the changes in the migration enthalpy. The weight of evidence in fig. 2 would suggest that the minimum in D o is largely a result of o o / N decreasing with increasing X up to X - 0.08 at which point the sharp decrease in H compensates for any further decrease in % / N
324
J.N. Mundy et al. / l o n i c transport in sodium germanate glasses
I
I
::!t ?o 5.58
1.2--
I
I
I
Ge-Ge SEPARATION (,,~)
3"I,, I
A >
t I dl~.~,,
^
A
A
~
I
--
I.O--
v
-1-
~i
~ MAGRUDER
T
[] C0RDAR0 AND TOMOZAWA (1982) ll4j
I
z~ THOMAS AND PETERSON (1984) [10] - • EVSTROP'EV AND PAVLOVSKII (1966)[4]
0.8
etel. (1984)[131
. .
-
o PRESENT WORK 0.6-2
I
5
I
I0
I
20
I
50
I00
Na-Ge (Oct) SEPARATION (A)
I 0.3
I
I
I
I
0.1 0.03 0.01 3xlO -3
I
I
3 x l O -4
3x IO -5
Fig. 2. Activation enthalpy ( H ) as a function of N a - G e O 6 separation and molecular concentration (X).
and causes Do to increase. If oo/N ( X ) is to be the dominant cause for the decrease in D o at low values of X, then the value of oo/N ( X ) must decrease by a factor of > 5 between X = 0 and 0.09. This decrease must result from changes in u, S a n d / o r a. References
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15]
A.O. Ivanov and K.S. Evstrop'ev, Dokl. Akad. Nauk. SSSR 145 (1962) 797. M.K. Murthy and J. Ip, Nature 201 (1964) 285. N. Ingri and G. Lundgren, Acta Chem. Scand. 17 (1963) 617. K.K. Evstrop'ev and V.K. Pavlovskii, Inorg. Mat. 3 (1967) 592. H. Verweij and J.H.J.M. Buster, J. Non-Cryst. Solids 34 (1979) 81. T. Furukawa and W.B. White, J. Mat. Sci. 15 (1980) 1648. M. Ueno, M. Misawa and K. Suzuki, Physica 120B (1983) 347. S. Sakka and K. Kamiya, J. Non-Cryst. Solids 49 (1982) 103. J.E. Kelly III, J.F. Cordaro and M. Tomozawa, J. Non-Cryst. Solids 41 (1980) 47. M.P. Thomas and N.L. Peterson, Solid State Ionics 14 (1984) 297. R.A. Huggins, in: Diffusion in Solids, Recent Developments, eds. A.S. Nowick and J.J. Burton (Academic Press, New York, 1975) p. 445. D.P. Almond and A.R. West, Solid St. Ionics 9 & 10 (1983) 277. R.H. Magruder III, D.L. Kinser, R.A. Weeks and J.M. Jackson, J. Appl. Phys. 57 (1985) 345. J.F. Cordaro and M. Tomozawa, J. Am. Ceram. Soc. 65 (1982) C-50. E.E. Khawaja, M.A. Khan, A.S.W. Li and J.S. Hwang, J. Mat. Sci. Lett. 3 (1984) 593.
Journal of Non-Crystalline Solids 84 (1986) 320-324 North-Holland, Amsterdam
IONIC TRANSPORT IN SODIUM GERMANATE GLASSES * J.N. M U N D Y , G.L. J I N and N.L. P E T E R S O N Materials Science and Technology Division, Argonne National Laboratory, Argonne, IL 60439, USA
Measurements of the electrical conductivity and tracer diffusion coefficient have been made for a series of XNa20 :(1 - X)GeO 2 glasses, where X = 0.01, 0.05, 0.10, 0.15, 0.19 and 0.29. The Haven ratios determined from these measurements show the same trends as earlier work. The dc conductivities of the present study also show the same minimum in sodium ion mobility (at X - 0.09) as found in the earlier studies. The minimum is shown to be an interplay between the pre-exponential and exponential terms. The activation enthalpy remains almost constant for X < 0.09 and then decreases rapidly with increasing X. These changes can be related to the average Ge-Ge separation which varies little below X - 0.08 but rapidly increases for larger X.
Over twenty years ago anomalies were f o u n d in the physical properties of sodium germanate glasses [1,2]. For example, the density has a m a x i m u m at a N a 2 0 concentration, X - 0 . 1 5 . This m a x i m u m leads to a m i n i m u m in the molar volume at X - 0 . 1 8 which is at the smallest X for which a stable crystalline sodium germanate ( 2 N a 2 0 : 9GeO2) has been found [3]. A structural model was postulated [1,2] based on the concept that additions of N a a O to germania glass convert some of the germanium from four-fold to six-fold coordination without breaking G e - O - G e bridging bonds. 22Na tracer diffusion measurements [4] show a m i n i m u m for X - 0.08-0.09; this value of X is clearly lower than that found for the a n o m a l y in the structural properties. Recent studies of sodium germanate glasses using R a m a n spectroscopy [5,6], neutron scattering [7] and E X A F S measurements [8] have confirmed the structural model. The neutron scattering data [7] showed that for X _< 0.2 each N a 2 0 molecule added to germania glass converts one g e r m a n i u m ion from tetrahedral to octahedral coordination without the formation of non-bridging oxygen ions; i.e., the concentration of G e O 6 octahedron structural units is given by C 6 = X / ( 1 - X ) . F o r X >_,0.2 non-bridging oxygen ions (NBOs) are formed. Only six glass compositions were examined b y neutron scattering and it appears likely that non-bridging oxygen ions begin to form for X >_ 0.18 [6], i.e., the composition of m i n i m u m molar volume. Tracer diffusion ( D x) and ionic conductivity ( o ) of dilute sodium germanate glasses have recently been measured by Kelly et al. [9]. Their measurements allowed a determination of the Haven ratio, H R, which for a single alkali glass * Work supported by the U.S. Department of Energy. 0022-3093/86/$03.50 © Elsevier Science Publishers B.V.
(North-Holland Physics Publishing Division)
J.N. Mundy et al. / Ionic transport in sodium germanate glasses
321
is defined as the ratio of D T to the diffusivity, D o, of the migrating alkali ion deduced from the Nernst-Einstein relation:
kT D~ = N e 2 . o ,
(1)
where k is the Boltzmann constant, T is the absolute temperature, N is the concentration of alkali ions per unit volume and e is the electronic charge. For the dilute sodium germanate glasses Kelly et al. [9] found H R - 1 and their analysis of the data of Evstrop'ev and Pavlovskii ( E - P ) [4] showed that H R decreased to - 0 . 3 for X>_ 0.15. Recent work by Thomas and Peterson [10] has confirmed the trend of H R ( X ) with somewhat lower values of H R for X >__0.05. The present measurements of H R at X = 0.10, 0.19 and 0.29 are in closer agreement to the results of E - P but the trend with X is the same in all studies. Thomas and Peterson [10] have satisfactorily explained the H R ( X ) data in terms of a single defect model for which diffusive j u m p correlation results from attractive interactions between the positive sodium ions and negative charge compensating centers (GeO6; germanium in octahedral coordination) in the glass. As X increases the average distance between sodium ions and GeO 6 units decreases and the attractive interaction betweeen the two results in a higher degree of correlation in j u m p direction and hence a lower value of H R. The present study has measured D x and o as a function of temperature for X = 0.01, 0.05, 0.10, 0.15, 0.19 and 0.29 in order to investigate why DT(X ) and Do(X) have minima at X - 0.09 [4,10] and why these minima are not related to the minimum in the molar volume or maximum of C 6 ( X - 0 . 1 8 ) . These questions are of particular interest to our present program which seeks to relate the ionic transport behavior to changes in the interaction between the alkali ion and charge compensating centers in alkali-oxide glasses. The values of D T (573 K) agree within experimental error with the previous studies [4,10] and further discussion will focus on the ionic conductivity measurements. The dc conductivity of alkali ion conductors may be expressed [11,12] as:
where c~ is a geometric factor which is the reciprocal of the number of possible j u m p directions from a given site (we assume a - ~- for the present glasses) and a is the ionic j u m p distance. The average j u m p rate of the alkali ion, ¢0p is given by % = v exp( S / k ) exp( - H / k T ) ,
(3)
where v is an appropriate attempt (vibration) frequency, S and H are the activation entropy and enthalpy for the ionic j u m p process. The term fiN expresses the concentration of mobile ions which may in some cases be
322
J.N. Mundy et al. / l o n i c transport in sodium germanate glasses
thermally activated and given by /3N = Ce e x p ( - H c / k T ) ,
(4)
where Ce is the effective carrier concentration at infinite temperature and H c is the enthalpy for the creation of the mobile ions. Although in an alkali oxide glass it might be expected that /3 = 1, Almond and West [12] show that deviations of 13 from unity may occur and will be evident when H 4: H c. Their work showed that while the slope of I n ( a T ) vs 1 / T gives ( H + Hc), the slope of ln(~op) vs 1 / T gives H alone. The present measurements of a were made as a function of both frequency (20-105 Hz) and temperature (100-500°C) and the results were analyzed by both complex impedance techniques in order to obtain the dc conductivities a( T) and by the method of Almond and West [12] in order to obtain ~0p(T). The activation enthalpies obtained from the o(T) and ~0p(T) data were the same within the standard deviations calculated from the fits of the data to eqs. (2) and (3); this suggests that/3 = 1 and all the alkali ions in the present glasses contribute to ionic transport. The intercepts at infinite temperature determine the values of a 0 and i, e x p ( S / k ) , respectively. The intercepts of u e x p ( S / k ) are poorly defined by the present measurements (3 + 2 × 1014 s - 1 ) but suggest for u = 1013 S-1 an entropy of S / k - 3. From eqs. (1-4) the diffusivity of the migrating alkali ions Do is given by
o0
exp(- )
where ao/N is a function of p, S and a. Measurements of the density of each sample, together with chemical analysis, allowed the determination of N for each of the glasses. The values of Do(X) for a temperature of 300°C are shown in fig. 1. The separated components of D o (pre-exponential and exponential) are shown as dashed lines. The separation of the present results suggests that the minimum in D o results largely from a minimum in the exponential term (maximum in H ) and that the decreasing of the pre-exponential term with X simply deepens the minimum and moves it to slightly higher X. The values of Do(X) agree within experimental error with the E - P data [4] with the exception of the value for X = 0.10; the present result is 25% smaller than the result in ref. [4]. The variations in the pre-exponential and exponential components are also. in reasonable agreement with those determined from the E - P data. However, in the recent work of Thomas and Peterson [10] the values of D o are twice the present values although the depth and position of the minimum in D O appear to be the same. Thomas and Peterson find little variation in H for X ~<0.09 and attribute the minimum in D o largely to the decrease in the pre-exponential term. It is important for our studies of the effect of systematically changing the attractive interaction between the alkali ions and the charge compensating centers that we resolve whether the minimum in D o results from the pre-exponential (ao/N) or exponential ( H ) component. -
J.N. Mundy et al. / Ionic transport in sodium germanate glasses
I
'
', 1
I
/ ,d
°°I
io-9!
//
/
b
-
/
10-7
/
•.r i...
I
'o- ' ° o
-,o-8 ,I=
/
-
:
/
Io -9
-:_110 -2 ---i
---i
i
0
o
323
-
I
I0
Z
~
20 tool % No20
30
i0-10
=1%
t~l z
~10-3
Fig. 1. Nernst-Einstein diffusivity (Do) and its pre-exponential and exponential components as a function of molecular concentration (X).
In order to examine how the activation enthalpy ( H ) varies with X, we have plotted in fig. 2 values from six different studies. The values of H are plotted as a function of the average sodium-Ge (octahedrally coordinated) separation. The overall evidence suggests that H shows a marginal increase when proceeding from large separations of 100 A ( X - 1 . 5 × 10 -5) to a separation of - 5 . 4 A ( X - 0 . 0 9 ) , but for smaller separations (X>__ 0.1) H rapidly decreases. It should be noted that the maximum in H occurs near X = 0.08, a composition considerably smaller than X = 0.18 where a saturation in C 6 or the formation of NBOs should occur. Although the variation in H R ( X ) is related to the N a - G e (oct.) separation [10] the activation enthalpy shows no obvious correlation with this separation. The variation of H appears however to correlate well with the average G e - G e separation decreases marginally from low soda concentration (3.63 A) to a minimum of 3.58 A at X - 0.08 and rapidly increases at higher X thus mirroring the changes in the migration enthalpy. The weight of evidence in fig. 2 would suggest that the minimum in D o is largely a result of o o / N decreasing with increasing X up to X - 0.08 at which point the sharp decrease in H compensates for any further decrease in % / N
324
J.N. Mundy et al. / l o n i c transport in sodium germanate glasses
I
I
::!t ?o 5.58
1.2--
I
I
I
Ge-Ge SEPARATION (,,~)
3"I,, I
A >
t I dl~.~,,
^
A
A
~
I
--
I.O--
v
-1-
~i
~ MAGRUDER
T
[] C0RDAR0 AND TOMOZAWA (1982) ll4j
I
z~ THOMAS AND PETERSON (1984) [10] - • EVSTROP'EV AND PAVLOVSKII (1966)[4]
0.8
etel. (1984)[131
. .
-
o PRESENT WORK 0.6-2
I
5
I
I0
I
20
I
50
I00
Na-Ge (Oct) SEPARATION (A)
I 0.3
I
I
I
I
0.1 0.03 0.01 3xlO -3
I
I
3 x l O -4
3x IO -5
Fig. 2. Activation enthalpy ( H ) as a function of N a - G e O 6 separation and molecular concentration (X).
and causes Do to increase. If oo/N ( X ) is to be the dominant cause for the decrease in D o at low values of X, then the value of oo/N ( X ) must decrease by a factor of > 5 between X = 0 and 0.09. This decrease must result from changes in u, S a n d / o r a. References
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15]
A.O. Ivanov and K.S. Evstrop'ev, Dokl. Akad. Nauk. SSSR 145 (1962) 797. M.K. Murthy and J. Ip, Nature 201 (1964) 285. N. Ingri and G. Lundgren, Acta Chem. Scand. 17 (1963) 617. K.K. Evstrop'ev and V.K. Pavlovskii, Inorg. Mat. 3 (1967) 592. H. Verweij and J.H.J.M. Buster, J. Non-Cryst. Solids 34 (1979) 81. T. Furukawa and W.B. White, J. Mat. Sci. 15 (1980) 1648. M. Ueno, M. Misawa and K. Suzuki, Physica 120B (1983) 347. S. Sakka and K. Kamiya, J. Non-Cryst. Solids 49 (1982) 103. J.E. Kelly III, J.F. Cordaro and M. Tomozawa, J. Non-Cryst. Solids 41 (1980) 47. M.P. Thomas and N.L. Peterson, Solid State Ionics 14 (1984) 297. R.A. Huggins, in: Diffusion in Solids, Recent Developments, eds. A.S. Nowick and J.J. Burton (Academic Press, New York, 1975) p. 445. D.P. Almond and A.R. West, Solid St. Ionics 9 & 10 (1983) 277. R.H. Magruder III, D.L. Kinser, R.A. Weeks and J.M. Jackson, J. Appl. Phys. 57 (1985) 345. J.F. Cordaro and M. Tomozawa, J. Am. Ceram. Soc. 65 (1982) C-50. E.E. Khawaja, M.A. Khan, A.S.W. Li and J.S. Hwang, J. Mat. Sci. Lett. 3 (1984) 593.