- Email: [email protected]
A new experiment to measure the ionic charge-of-transport of a mixed conductor oxide
a+ .__ -
__ @I
SOLID STATE IONICS
Solid State Ionics 86-88 (1996) 757-760
ELSEVIER
A new experiment
to measure the ionic charge-of-transport mixed conductor oxide
of a
Ki-Chun Lee*, Han-Ill Yoo Department
of Inorganic Materials
Engineering,
Seoul National
University,
Seoul 151-742, South Korea
Abstract A new experiment has been designed on the basis of the polarization in an ion-blocking electrode condition, which allows one to simultaneously determine the ionic charge-of-transport (a:) and chemical diffusivity (8) of a mixed conductor compound, A,_,O, tested for the first time on the system of Co,-,O. The workability and promise is verified by the preliminary results, a: = 0.357 and B = 1.98 X lo-’ cm’/s at 1200°C and POz= 10m3” atm, which generally agree with reported values. Keywords:
Ionic charge-of-transport:
Mixed conductor;
Co, _,O
1. Introduction The linear transport theory [l] prescribes that, in a mixed conductor oxide, say, Co,_,0 with a practically rigid anion sub-lattice, a flow of mobile cations, may induce an electronic flow and vice versa, CO*+, i.e. the two flows interfere with each other. Efforts were intermittently made to verify this interference effect, but only with negative results [2-51. It has, thus, long been believed that the mobile cations and electrons migrate independently or that Kohlrausch’s law of independent migration be observed at least as a good approximation [2]. It is only recent that Yoo and coworkers [6,7], Janek [8] and Lee and Yoo [9] have experimentally verified the presence of the interference effect to a non-negligible degree in an electronic conductor oxide, Co,-, 0. As a measure of the cross effect,
*Corresponding
author
0167-2738/96/$15.00 Copyright PI1 SO167-2738(96)00168-3
01996
of the they introduced the “charges-of-transport” cations and electrons, c~f and (Y;, respectively, which phenomenologically correspond to the number ((Yy) of electrons dragged by a cation and vice versa, and designed three different types of experiments that eventually revealed the non-zero interference effect. The experimental details and results are already given elsewhere [6-lo]. We have designed a new experiment based on the polarization under an ion-blocking condition and have applied it to the model oxide Co, _,O to verify its workability. The rationale of the experiment and the preliminary results are reported.
2. Theoretical
background
According to irreversible thermodynamics [ 11, the thermodynamic equations of motion may be written for the mobile cations (A”) and electrons (e’) in a mixed conductor oxide A, _,O as
Elsevier Science B.V. All rights reserved
758
K. Lee, H. Yoo / Solid State lonics 86-88
J, = - LljVq, (ij = 1,2) ,
and subject straint +;
a; = L,,/L,, to an irreversible
(2) thermodynamic
< 1,
con-
(3)
where (Y: << 1, in general [7]. Eq. (1) may be rewritten in terms of the oxygen potential gradient, Vpo, instead of Vv,, due to the ionization equilibrium and the Gibbs-Duhem relation for the system as [ 111. J, =$L,,Vpo
+ L,,(z, - ff;)V% 3
J~=~L2,V~o-L22(l -z,a;)Vn,.
O&L
(1)
where Vvi represents the electrochemical potential gradient of the mobile species i (1 =A”‘; 2=e’) and L,, is the transport coefficient satisfying the reciprocity relation, L,, =L,,. The charges of transport are defined as [I I] a; = L,,IL,,;
(1996) 7S7- 760
(44
t4b)
It is noted that four variables, J,, J2, Vpo and Vqz are experimentally operable, i.e., measurable and controllable. By combining these variables in proper ways, one can, thus, determine the ionic charge-oftransport, cyT. Three different experiments have so far been carried out on the model oxide, Co,_,O; (i) the Chemla-type electrotransport experiment [6] in which J, is measured as a shift of a self-tracer profile in a finite VQ(- -FVP~,,, F being the Faraday constant and V’p;lppbeing the electric potential gradient applied) in a uniform oxygen potential atmosphere (Vpo = 0), (ii) the tensiovolumetric experiment [8] in which J,, driven by an electric field Vpapp, is measured tensiovolumetrically in an initially uniform oxygen potential atmosphere (VCL,= 0) and (iii) the electrochemical experiment [9] in which the ionic partial current z, FJ, and the total current F(z, J, J2) that are driven by an applied VP, are measured by an electrochemical means while keeping Vqapp= 0. The experimental results are exhaustively compiled in Ref. [12]. Let us now consider an electrochemical cell involving a mixed conductor A,-,0 and YSZ electrolytes as ionic probes,
P,,, Pr(
i) ( YSZ
YSZ ( Pt(4), P,? .
A, _,O I W2)
I: PU)
(0
When a constant electric field, V(pdpp,is applied, via the electrodes Pt(3) and Pt(2), across the oxide that is initially equilibrated with a surrounding atmosphere (Po,), an ionic current, Eq. (4a) starts to flow along with an electronic current, Eq. (4b), eventually leading to an oxygen potential gradient across the system if the ionic flow is completely blocked at the YSZ/A, _,O interfaces. The local variation of the compostion of A, _,O due to the polarization current is given as
+$v.
J,
m
“$L,,V2&J
+ L,,(z, - “;)V2q*
(5)
if the polarization-induced VCL, is not so large that may be regarded as positionboth L,, and ~7 independent. In this equation, V, denotes the molar volume of the system. Under closed circuit conditions, as in our polarization cell, however, z,V.J,-V.J,=O
(6)
for the preservation of local charge neutrality. from Eqs. (4a) and (4b), )
v2v> = - +o
(7)
where t, stands for the ionic transference z1(z, t,
-
“TW,JL,,
+
z,tz,
-
number or
(8)
= 1 -z&I
Thus,
“:)L,,
&,’
By substituting Eq. (7) and the identity dS/dt= (dpoldt)(dSldpo), Eq. (5) may be rewritten as
-aA%= 13v2po at
Here, the chemical as [ll]
Lj&/TL 2 m ,,
diffusion
coefficient
(l-3+ )($ >-’ 0
D is defined
(10)
which one may notice reduces to the conventional, text-book expression for the chemical diffusivity of
K. Lee, H. Yoo I Solid State lonics 86-88
A,_,0 [13], if and only if (YT=O. For electronic conductor oxides like Co, -so, in particular, the chemical diffusivity is essentially the same (notwithstanding the non-zero interference effect or (YT #O) as the conventional diffusivity, simply because I, < 1, or
(11)
159
(1996) 757-760
A,_,O, ,&L,t)-&O,t) can be easily with the use of the YSZ-based oxygen shown in Cell (I), or /-G,(LJ) - /-&OJ) = 2F(E,,
monitored probes as
- E,,)
= 2FAE(t),
(16)
where E,, and E,, are the open-cell voltages measured from Pt(3) to Pt(4) and from Pt(2) Pt( l), respectively. From Eqs. (15,16),
as to
where the identity L,, = D,IV,RT (DA being the self-diffusivity of A) has been used. The system A, _ ,O is supposed to be equilibrated initially in a uniform oxygen potential atmosphere so that the initial condition is (17) /&o(x;t = 0) = &.
(12)
The boundary conditions are imposed by the ionblocking condition and a constant voltage, V, applied or
Obviously, AE(t)IV steady state.
approaches
(z,-cur>/z,
at the
J, (OJ) = J, (LJ) = 0;
(13a)
3. Experimental
rl,V+O - In,
(13b)
An actual cell was constructed in the configuration of Cell (I), as schematically illustrated in Fig. 1. A disk of Co metal, 11 mm dia. X 1.27 mm thick, was first placed concentrically inside an alumina ring, 12 mm ID X 17mm OD X 2.27 mm thick, and a 60-pm thick Pt-wire was placed diagonally upon each of the flat surfaces of the Co disk which was previously polished down to 1 pm. These two Pt wires were passed through the wall of the alumina ring to make external electrical connections. The whole assembly
= - FV.
These conditions can be translated into V/+,(O,t) and v,~o(L,t) via Eq. (4a). Inasmuch as the spatial variation of L,j (due to V,U~ or V6) is practically negligible, the applied electric field may be regarded as uniform or Vv2 = - FVIL, L being the length of the system. Thus, V,~o(o,t) =V,q,(L,t)
= 2(z, - a;)FV/z,L.
(14)
By solving Eq. (9) along with the initial boundary conditions, Eqs. (12,14), one obtains
procedures
and 4p
(ii) C
1TV
a0 xcos Xexp
1
(2n-
-i
1,7r;
-(2n-l)‘$L%
1
. (15) 11
As expected, ,uo(x,t) clearly carries the information of not only (_yF but also B. In principle, one could determine cy? from either Vpo(O,t) or V,uo(L,t) at any time, t, due to Eq. (14). In practice, however, the oxygen potential difference across the system
ld (iv)
Fig. 1. Cross-section of the cell constructed and the electrical circuitry: l-4 and a-d, Pt lead wires; (i) Co0 specimen; (ii) YSZ electrolyte disk; (iii) alumina ring; (iv) Pt ring; (v) Pt porous electrode.
K. Lee, H. Yoo I Solid State Ionics 86-88
760
was fired for oxidation of the metal disk at 1200°C in air initially for two days. Then, two YSZ disks with porous Pt-electrodes and lead wires attached were placed each one on each side of the alumina ring and oxidation firing was continued for another five days, to complete oxidation. By this procedure, the YSZ disks were made to adhere very intimately to the newly formed COO. Futhermore, the increased volume of the Co0 filled up the original gap between the metal disk and the alumina ring to secure a perfect air-tight seal and the two Pt wires became embedded 1.27 mm apart within the oxide to make the inner potential probes (indicated by “a” and “b” in Fig. 1). In order to further secure the air-tightness, the circumferential seam between each of the YSZ disks and the alumina ring was sealed with a high temperature ceramic sealant. A constant voltage was applied via the Pt lead wires “c” and “d” in Fig. 1 and the actual voltage drop, V, across the system Co0 was determined by the two implanted probes “a” and “b”. The oxygen chemical potentials at both of the YSZ/CoO interfaces were monitored by measuring the open-cell voltages across the two YSZ electrolytes, E,, and
(1996) 757-760
T = 12OO“C
1
D = 1.98x1 O”cm’/s
Fig. 2. A typical example of the time evolution of the oxygen chemical potential difference, Al?(t), from the moment of switching on a voltage, V= 8.92 mV, across the specimen. Solid line is that calculated from Eq. (17) in the text.
Acknowledgments This work has been financially supported by the Research Centre for Thin Film Fabrication and Crystal Growing of Advanced Materials at the Seoul National University.
References 4. Preliminary
results
Fig. 2 shows a typical evolution of the oxygen chemical potential difference across the specimen, AE(= E,, -E,, ) from the moment of switching on a polarization potential of V=8.92 mV (the resulting current was 0.36 A) at 1200°C in an initial atmosphere of PO, = 10p3’63 atm. The data could be satisfactorily fitted upto the 25th term of Eq. (17), as delineated by the solid line in the figure, yielding as the fitting parameters (Y; = 0.357?0.006;
D = (1.98?0.05)
X
10P6cm2/s.
The value for the charge-of-transport turns out to be highly consistent with that reported previously [9,12] and the chemical diffusivity is in reasonable agreement with that calculated from Dieckmann [14], 4.4X 10m6 cm’/s, strongly supporting the workability and promise of this new experiment.
[1] S.R. de Groot, Thermodynamics of Irreversible Processes (North-Holland, Amsterdam, 195 1). [2] S. Miyatani, Solid State Comm. 38 (1981) 257. [3] F. Morin, J. Electrochem. Sot. 126 (1979) 760. [4] F. Millot, N. Ait-Younes and P Gerdanian, High Temp. High Press. 14 (1982) 725. [5] N. Ait-Younes, F. Millot and P. Gerdanian, Solid State Ionics 12 (1984) 431. [6] H.-I. Yoo and M. Martin, Ceram. Trans. 24 (1991) 103. [7] H.-I. Yoo. J.-H. Lee, M. Martin, J. Janek and H. Schmalzried, Solid State Ionics 67 ( 1994) 3 17. [8] J. Janek, Ber. Bunsenges. Phys. Chem. 98 (1994) 1213. [9] J.-H. Lee and H.-I. Yoo, J. Electrochem. Sot. 141 (1994) 2789. [lo] J.-I. Yoo, Proc. 2nd Intemat. Symp. on Ionic and Mixed Conducting Ceramics, eds. T.A. Ramanarayanan, W.L. Worrell and H.L. TuIler,Vol. 94-12 (The Electrochem. Sot., New Jersey, 1994) pp. 353-365. [ 1 l] H.-I. Yoo, H. Schmalzried, M. Martin and J. Janek, Z. Phys. Chem. (NF) 168 (1990) 129. [12] H.-I. Yoo and J.-H. Lee, J. Phys. Chem. Solids, 57 (1996) 65. [13] C. Wagner, Z. Physik. Chem. B21 (1933) 25; in: Atom Movements (ASM, Cleveland, 1951) p. 15 1. [ 141 R. Dieckmann, Z. Phys. Chem. (NF) -107 (1977) 189
__ @I
SOLID STATE IONICS
Solid State Ionics 86-88 (1996) 757-760
ELSEVIER
A new experiment
to measure the ionic charge-of-transport mixed conductor oxide
of a
Ki-Chun Lee*, Han-Ill Yoo Department
of Inorganic Materials
Engineering,
Seoul National
University,
Seoul 151-742, South Korea
Abstract A new experiment has been designed on the basis of the polarization in an ion-blocking electrode condition, which allows one to simultaneously determine the ionic charge-of-transport (a:) and chemical diffusivity (8) of a mixed conductor compound, A,_,O, tested for the first time on the system of Co,-,O. The workability and promise is verified by the preliminary results, a: = 0.357 and B = 1.98 X lo-’ cm’/s at 1200°C and POz= 10m3” atm, which generally agree with reported values. Keywords:
Ionic charge-of-transport:
Mixed conductor;
Co, _,O
1. Introduction The linear transport theory [l] prescribes that, in a mixed conductor oxide, say, Co,_,0 with a practically rigid anion sub-lattice, a flow of mobile cations, may induce an electronic flow and vice versa, CO*+, i.e. the two flows interfere with each other. Efforts were intermittently made to verify this interference effect, but only with negative results [2-51. It has, thus, long been believed that the mobile cations and electrons migrate independently or that Kohlrausch’s law of independent migration be observed at least as a good approximation [2]. It is only recent that Yoo and coworkers [6,7], Janek [8] and Lee and Yoo [9] have experimentally verified the presence of the interference effect to a non-negligible degree in an electronic conductor oxide, Co,-, 0. As a measure of the cross effect,
*Corresponding
author
0167-2738/96/$15.00 Copyright PI1 SO167-2738(96)00168-3
01996
of the they introduced the “charges-of-transport” cations and electrons, c~f and (Y;, respectively, which phenomenologically correspond to the number ((Yy) of electrons dragged by a cation and vice versa, and designed three different types of experiments that eventually revealed the non-zero interference effect. The experimental details and results are already given elsewhere [6-lo]. We have designed a new experiment based on the polarization under an ion-blocking condition and have applied it to the model oxide Co, _,O to verify its workability. The rationale of the experiment and the preliminary results are reported.
2. Theoretical
background
According to irreversible thermodynamics [ 11, the thermodynamic equations of motion may be written for the mobile cations (A”) and electrons (e’) in a mixed conductor oxide A, _,O as
Elsevier Science B.V. All rights reserved
758
K. Lee, H. Yoo / Solid State lonics 86-88
J, = - LljVq, (ij = 1,2) ,
and subject straint +;
a; = L,,/L,, to an irreversible
(2) thermodynamic
< 1,
con-
(3)
where (Y: << 1, in general [7]. Eq. (1) may be rewritten in terms of the oxygen potential gradient, Vpo, instead of Vv,, due to the ionization equilibrium and the Gibbs-Duhem relation for the system as [ 111. J, =$L,,Vpo
+ L,,(z, - ff;)V% 3
J~=~L2,V~o-L22(l -z,a;)Vn,.
O&L
(1)
where Vvi represents the electrochemical potential gradient of the mobile species i (1 =A”‘; 2=e’) and L,, is the transport coefficient satisfying the reciprocity relation, L,, =L,,. The charges of transport are defined as [I I] a; = L,,IL,,;
(1996) 7S7- 760
(44
t4b)
It is noted that four variables, J,, J2, Vpo and Vqz are experimentally operable, i.e., measurable and controllable. By combining these variables in proper ways, one can, thus, determine the ionic charge-oftransport, cyT. Three different experiments have so far been carried out on the model oxide, Co,_,O; (i) the Chemla-type electrotransport experiment [6] in which J, is measured as a shift of a self-tracer profile in a finite VQ(- -FVP~,,, F being the Faraday constant and V’p;lppbeing the electric potential gradient applied) in a uniform oxygen potential atmosphere (Vpo = 0), (ii) the tensiovolumetric experiment [8] in which J,, driven by an electric field Vpapp, is measured tensiovolumetrically in an initially uniform oxygen potential atmosphere (VCL,= 0) and (iii) the electrochemical experiment [9] in which the ionic partial current z, FJ, and the total current F(z, J, J2) that are driven by an applied VP, are measured by an electrochemical means while keeping Vqapp= 0. The experimental results are exhaustively compiled in Ref. [12]. Let us now consider an electrochemical cell involving a mixed conductor A,-,0 and YSZ electrolytes as ionic probes,
P,,, Pr(
i) ( YSZ
YSZ ( Pt(4), P,? .
A, _,O I W2)
I: PU)
(0
When a constant electric field, V(pdpp,is applied, via the electrodes Pt(3) and Pt(2), across the oxide that is initially equilibrated with a surrounding atmosphere (Po,), an ionic current, Eq. (4a) starts to flow along with an electronic current, Eq. (4b), eventually leading to an oxygen potential gradient across the system if the ionic flow is completely blocked at the YSZ/A, _,O interfaces. The local variation of the compostion of A, _,O due to the polarization current is given as
+$v.
J,
m
“$L,,V2&J
+ L,,(z, - “;)V2q*
(5)
if the polarization-induced VCL, is not so large that may be regarded as positionboth L,, and ~7 independent. In this equation, V, denotes the molar volume of the system. Under closed circuit conditions, as in our polarization cell, however, z,V.J,-V.J,=O
(6)
for the preservation of local charge neutrality. from Eqs. (4a) and (4b), )
v2v> = - +o
(7)
where t, stands for the ionic transference z1(z, t,
-
“TW,JL,,
+
z,tz,
-
number or
(8)
= 1 -z&I
Thus,
“:)L,,
&,’
By substituting Eq. (7) and the identity dS/dt= (dpoldt)(dSldpo), Eq. (5) may be rewritten as
-aA%= 13v2po at
Here, the chemical as [ll]
Lj&/TL 2 m ,,
diffusion
coefficient
(l-3+ )($ >-’ 0
D is defined
(10)
which one may notice reduces to the conventional, text-book expression for the chemical diffusivity of
K. Lee, H. Yoo I Solid State lonics 86-88
A,_,0 [13], if and only if (YT=O. For electronic conductor oxides like Co, -so, in particular, the chemical diffusivity is essentially the same (notwithstanding the non-zero interference effect or (YT #O) as the conventional diffusivity, simply because I, < 1, or
(11)
159
(1996) 757-760
A,_,O, ,&L,t)-&O,t) can be easily with the use of the YSZ-based oxygen shown in Cell (I), or /-G,(LJ) - /-&OJ) = 2F(E,,
monitored probes as
- E,,)
= 2FAE(t),
(16)
where E,, and E,, are the open-cell voltages measured from Pt(3) to Pt(4) and from Pt(2) Pt( l), respectively. From Eqs. (15,16),
as to
where the identity L,, = D,IV,RT (DA being the self-diffusivity of A) has been used. The system A, _ ,O is supposed to be equilibrated initially in a uniform oxygen potential atmosphere so that the initial condition is (17) /&o(x;t = 0) = &.
(12)
The boundary conditions are imposed by the ionblocking condition and a constant voltage, V, applied or
Obviously, AE(t)IV steady state.
approaches
(z,-cur>/z,
at the
J, (OJ) = J, (LJ) = 0;
(13a)
3. Experimental
rl,V+O - In,
(13b)
An actual cell was constructed in the configuration of Cell (I), as schematically illustrated in Fig. 1. A disk of Co metal, 11 mm dia. X 1.27 mm thick, was first placed concentrically inside an alumina ring, 12 mm ID X 17mm OD X 2.27 mm thick, and a 60-pm thick Pt-wire was placed diagonally upon each of the flat surfaces of the Co disk which was previously polished down to 1 pm. These two Pt wires were passed through the wall of the alumina ring to make external electrical connections. The whole assembly
= - FV.
These conditions can be translated into V/+,(O,t) and v,~o(L,t) via Eq. (4a). Inasmuch as the spatial variation of L,j (due to V,U~ or V6) is practically negligible, the applied electric field may be regarded as uniform or Vv2 = - FVIL, L being the length of the system. Thus, V,~o(o,t) =V,q,(L,t)
= 2(z, - a;)FV/z,L.
(14)
By solving Eq. (9) along with the initial boundary conditions, Eqs. (12,14), one obtains
procedures
and 4p
(ii) C
1TV
a0 xcos Xexp
1
(2n-
-i
1,7r;
-(2n-l)‘$L%
1
. (15) 11
As expected, ,uo(x,t) clearly carries the information of not only (_yF but also B. In principle, one could determine cy? from either Vpo(O,t) or V,uo(L,t) at any time, t, due to Eq. (14). In practice, however, the oxygen potential difference across the system
ld (iv)
Fig. 1. Cross-section of the cell constructed and the electrical circuitry: l-4 and a-d, Pt lead wires; (i) Co0 specimen; (ii) YSZ electrolyte disk; (iii) alumina ring; (iv) Pt ring; (v) Pt porous electrode.
K. Lee, H. Yoo I Solid State Ionics 86-88
760
was fired for oxidation of the metal disk at 1200°C in air initially for two days. Then, two YSZ disks with porous Pt-electrodes and lead wires attached were placed each one on each side of the alumina ring and oxidation firing was continued for another five days, to complete oxidation. By this procedure, the YSZ disks were made to adhere very intimately to the newly formed COO. Futhermore, the increased volume of the Co0 filled up the original gap between the metal disk and the alumina ring to secure a perfect air-tight seal and the two Pt wires became embedded 1.27 mm apart within the oxide to make the inner potential probes (indicated by “a” and “b” in Fig. 1). In order to further secure the air-tightness, the circumferential seam between each of the YSZ disks and the alumina ring was sealed with a high temperature ceramic sealant. A constant voltage was applied via the Pt lead wires “c” and “d” in Fig. 1 and the actual voltage drop, V, across the system Co0 was determined by the two implanted probes “a” and “b”. The oxygen chemical potentials at both of the YSZ/CoO interfaces were monitored by measuring the open-cell voltages across the two YSZ electrolytes, E,, and
(1996) 757-760
T = 12OO“C
1
D = 1.98x1 O”cm’/s
Fig. 2. A typical example of the time evolution of the oxygen chemical potential difference, Al?(t), from the moment of switching on a voltage, V= 8.92 mV, across the specimen. Solid line is that calculated from Eq. (17) in the text.
Acknowledgments This work has been financially supported by the Research Centre for Thin Film Fabrication and Crystal Growing of Advanced Materials at the Seoul National University.
References 4. Preliminary
results
Fig. 2 shows a typical evolution of the oxygen chemical potential difference across the specimen, AE(= E,, -E,, ) from the moment of switching on a polarization potential of V=8.92 mV (the resulting current was 0.36 A) at 1200°C in an initial atmosphere of PO, = 10p3’63 atm. The data could be satisfactorily fitted upto the 25th term of Eq. (17), as delineated by the solid line in the figure, yielding as the fitting parameters (Y; = 0.357?0.006;
D = (1.98?0.05)
X
10P6cm2/s.
The value for the charge-of-transport turns out to be highly consistent with that reported previously [9,12] and the chemical diffusivity is in reasonable agreement with that calculated from Dieckmann [14], 4.4X 10m6 cm’/s, strongly supporting the workability and promise of this new experiment.
[1] S.R. de Groot, Thermodynamics of Irreversible Processes (North-Holland, Amsterdam, 195 1). [2] S. Miyatani, Solid State Comm. 38 (1981) 257. [3] F. Morin, J. Electrochem. Sot. 126 (1979) 760. [4] F. Millot, N. Ait-Younes and P Gerdanian, High Temp. High Press. 14 (1982) 725. [5] N. Ait-Younes, F. Millot and P. Gerdanian, Solid State Ionics 12 (1984) 431. [6] H.-I. Yoo and M. Martin, Ceram. Trans. 24 (1991) 103. [7] H.-I. Yoo. J.-H. Lee, M. Martin, J. Janek and H. Schmalzried, Solid State Ionics 67 ( 1994) 3 17. [8] J. Janek, Ber. Bunsenges. Phys. Chem. 98 (1994) 1213. [9] J.-H. Lee and H.-I. Yoo, J. Electrochem. Sot. 141 (1994) 2789. [lo] J.-I. Yoo, Proc. 2nd Intemat. Symp. on Ionic and Mixed Conducting Ceramics, eds. T.A. Ramanarayanan, W.L. Worrell and H.L. TuIler,Vol. 94-12 (The Electrochem. Sot., New Jersey, 1994) pp. 353-365. [ 1 l] H.-I. Yoo, H. Schmalzried, M. Martin and J. Janek, Z. Phys. Chem. (NF) 168 (1990) 129. [12] H.-I. Yoo and J.-H. Lee, J. Phys. Chem. Solids, 57 (1996) 65. [13] C. Wagner, Z. Physik. Chem. B21 (1933) 25; in: Atom Movements (ASM, Cleveland, 1951) p. 15 1. [ 141 R. Dieckmann, Z. Phys. Chem. (NF) -107 (1977) 189