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Temperature dependence of ionic conductivity in (1 − x)ZrO2−(x − y)Sc2O3−yYb2O3 electrolyte material
SOLID STATE ELSEVIER
Solid State lonics 91 (1996) 249-256
IONICS
Temperature dependence of ionic conductivity in (1 - x)ZrO2-(x - y ) S c 2 0 3 - y Y b 2 0 3 electrolyte material Reiichi Chiba*, Takao Ishiil, Fumikatsu Yoshimura NTT Interdisciplinary Research Laboratories, Tokai, Ibaraki, 319-11, Japan Received 6 May 1996; accepted 24 June 1996
Abstract The temperature dependence of the ionic conductivity of (1 - x ) Z r O 2 - ( x - y)Sc203-yYb203 (x = 0.07-0.15, y = 0.000.03) was examined to clarify the origins of the ionic conductivity decrease at low temperature. For y = 0.02-0.03 in this system, the cubic phase was stabilized at room temperature and discontinuity in the ionic conductivity disappears. The Arrhenius plots of the ionic conductivity for the stabilized samples were curved. The grain boundary resistance for (1 - x ) Z r O 2 - ( x - 0.03)5c203-0.03Yb203 (x = 0.07-0.15) was separated from the total resistance with the AC impedance method. This allowed us to conclude that grain boundary resistance is not the cause of the curvature in the Arrhenius plots for this system. Keywords: Rare-earth ion-doped zirconia; Temperature dependence; Ionic conductivity; Grain boundary resistance; Solid oxide fuel cells; Electrolyte material
1. Introduction
Rare-earth ion-doped zirconia is thought to be practicable for use as the electrolyte for solid oxide fuel cells (SOFC), since its ionic transport number is 1.0 for a very wide range of oxygen partial pressures [ 1]. If higher ionic conductivity can be achieved, the operating temperature of the SOFC can be reduced from 1000°C to approximately 800°C, and restrictions regarding SOFC materials will be eased. When zirconia is doped with Sc 3÷ it exhibits a higher ionic conductivity than when doped with any other rare*Corresponding author. Tel.: (81-29) 287-7764; fax: (81-29) 287-7863; e-mail: [email protected] tPresent address: NTT LSI Laboratories, Atsugi-shi, Kanagawa 243-01, Japan.
earth ion, and this is thought to be because of the closeness of the ionic radii of Z r 4+ and Sc 3+ [2-6]. Therefore, zirconia doped with Sc 3+ is a good candidate as an electrolyte material for SOFC operating at reduced temperatures. The ionic radius of Yb 3÷ is also very close to that of Zr 4+, and so the conductivity of (1 - x)ZrO2-(x - y)SczO3-YYb203 is expected to be very high over a wide range of compositions. We investigated the temperature dependence of the ionic conductivity of this material. We also studied the mechanisms that limit its ionic conduction at relatively low temperatures.
2. Experimental The samples were prepared from high purity
0167-2738/96/$15.00 Copyright ©1996 Elsevier Science B.V. All rights reserved PII S0167-2738(96)00435-3
ZrO 2
250
R. Chiba et al. / Solid State lonics 91 (1996) 249-256
(99.9%), SczO 3 (99.9%) and Yb20 3 (99.9%) powders. The mixed powders were pressed into cylindrical pellets with a hydrostatic pressure of 100 MPa and sintered at 1620°C for 60 h in air. The crystal structure of the samples was characterized with an X-ray diffractometer using Cuket radiation at room temperature. The ionic conductivity of the samples was evaluated with the DC four-terminal method. The samples for this measurement were about 0.20 × 0.26 × 1.8 cm in size. Platinum wires were attached to the samples with platinum paste and fired in air at 1000°C for 1 h to form the current and voltage terminals. A constant current of 1.0-10 IxA was supplied by a current source (Keithley model 220). The current direction was reversed, (I+,I_), and the potential drop was measured for each direction, (V+,V_), with a digital multi-meter (Keithley model 195A). The conductivity, tr, was determined with those values as follows:
(l+/V+ + I_/V_) o- -
2
(1)
These measurements were performed at a temperature scanning rate of 2°/min in the range 4001100°C. The AC impedance method (two-terminal) was used to evaluate the boundary resistance. The samples for this measurement were about 0 . 2 0 x 0 . 6 0 × 0.60 cm in size. Platinum mesh was attached on two sides of the samples with platinum paste and fired in air at 1000°C for 1 h to form the electrodes. The measurements were performed in the 0.1-10 MHz frequency range from 200-600°C in air with an impedance analyzer (Schlumberger Technologies model SI1260).
3. R e s u l t s a n d d i s c u s s i o n
3. I. Crystal structure The X-ray diffraction pattems of the samples are shown in Figs. 1 and 2. 0.89ZrO2-0.11Sc203 are in the rhombohedral phase. They are in a mixture of the cubic phase and the rhombohedral phase when the y in the 0.89ZrO 2(0.89-y)Sc203-yYb203 is less than 0.20. The
I xloo ic.bic •~'~ ~
~__~ X=0.020 ~ cubic ~
x=001, I "~
3_4
__A x=ooos rhomhohedral
30
40 20
50 (deg.)
I
60
Fig. 1. X-ray diffraction patterns for 0.89ZrO2-(0.89-y)Sc203yYb203 (y=0, 0.005, 0.010, 0.015, 0.020 and 0.030) sintered at 1620°C for 60 h in air.
.=. t-
__1 X=0.170
cubic~
~__~ X= 0.150 t cubic X= 0.130 I cubic ~__
J xoo.,~ t c.b,c_L ~_~
~_
X = 0.090
,.__3.. x = 0'070 Jt 30
40
50 20
Fig. 2. X-ray diffraction patterns for (1 -x)ZrO2-(x0.03)Sc20~-0.03Yb203 (x=0.07, 0.09, 0.11, 0.13 and 0.15) sintered at 1620°C for 60 h in air.
samples are in a cubic phase when x is in the range 0.09-0.17 and y is in the range 0.02-0.03 in ( 1 x)ZrO2-(x-y)Sc203-yYb203 . They are in a mixture of the tetragonal and cubic phases when x is in the range 0.05-0.07 and y is in the range 0.02-0.03. The lattice constants, which were calculated from (222) peaks for (1 - x ) Z r O 2 - ( x - 0 . 0 3 ) S c 2 0 3 0.03Yb203, are listed in Table 1.
3.2. Temperature dependence of the ionic conductivity The temperature dependence of the ionic conductivity for 0.89ZRO2-(0.11 - y ) S c 2 0 3 - Y Y b 2 0 3 (0.00--
251
R. Chiba et al. / Solid State lonics 91 (1996) 2 4 9 - 2 5 6
Table 1 Crystal structure and lattice constants for (1 - x ) Z r O 2 - ( x 0.03)Sc20 a-0.03Yb203
6.0
x
Crystal structure
Lattice constant (nm)
4.0
0.07 0.09 0.11 0.13 0.15 0.17 0.21
cubic ( + tetragonal) cubic cubic cubic cubic cubic cubic
(0.5112) 0.5106 0.5103 0.5098 0.5093 0.5089 0.5080
~ X
~2.o
t~-~.
=0.090
i ~ - x = oa3o
, . ~~
~0.0 C
-2.0 0.8
ii
1.4
1.6
0.03Yb203 (0.07-
1.0
1.2
1.4
1.6
1000/'1" (l/K) Fig. 3. Temperature dependence of ionic conductivity for 0.89ZrO2-(0.89-y)Sc203-YYb203 ( y = 0 , 0.005, 0.010, 0.015, 0.020 and 0.030).
conductivity, tr, generally depends on the temperature, as given by the following equation [1,2,7], o-= ( - - ~ ) e -ea/kBr.
1.2
Fig. 4. Temperature dependence of ionic conductivity for ( 1 x)ZrO2-(x-0.03)Sc203-0.03Yb203 (x=0.070, 0.090, 0.11, 0.13 and 0.15).
e-
0.8
1.0
1000/'1" (l/K)
(2)
C o, T, E a, k B indicate constants related to the frequency factor, temperature, activation energy and the Boltzmann constant, respectively. Here, In(o-T) is plotted against 1000/T and there should be a linear relation. An abrupt increase was observed in the conductivity around 650°C, which should correspond to a structural transition from the rhombohedral to the cubic phase. An increase in y in 0.89ZrO 2(0.11-y)Sc203-yYb203 lowers the transition temperature and reduces the conductivity change through the transition. When y is more than 0.02, no trace of the discontinuity was observed. This agrees well with the X-ray diffraction measurements. The temperature dependence of the ionic conductivity for ( 1 -x)ZrOz-(X - 0 . 0 3 ) S c 2 0 3 -
3.3. Composition dependence of the ionic conductivity To apply this material as an SOFC electrolyte, it should be a good conductor around 900°C [1]. The ionic conductivity at 1000°C and 800°C were plotted against the composition in Fig. 5. The highest value was obtained at x = 0.11, both at 800°C and 1000°C. 10°
(l-x)ZrOE-(X-0'03)Sc203-0"03Yb203 --~' 800°C 1000°C
"7.
10-I
106 ' '0108 " 0116 " 0:12 " 0]14 " 0.16 X
Fig. 5. Dependence of conductivity on composition for ( 1 x)ZrO2-(x-O.O3)Sc203-O.O3Yb203 (x=0.070, 0~090, 0.11, 0.13 and 0.15) at 800°C and 1000°C.
252
R. Chiba et al. / Solid State lonics 91 (1996) 249-256
The value is close to 0.1 S/cm, even at 800°C, which is necessary for practical use. 3.4. Fitting the ionic conductivity results to a trap model ln(trT) versus IO00/T is plotted in Fig. 4. When the temperature dependence of the ionic conductivity is described with Eq. (2), the plots should form straight lines. However, the temperature dependence shows a distinct curvature. If two activation processes are involved in the ionic conduction, the conductivity can be expressed by the following equation [7]: 1 O'tot - - -
Pl - + P2'
(3)
then,
curve converge with the lines. We fitted the equation to the data in Fig. 3 and estimated the activation energies and pre-exponential factors, which are listed in Table 2. E 2 is approximately twice as large as E 1. The curvature of the plots originates from the difference in the activation energy for the two processes (processes which determine the lower and higher temperature ranges). Two models were presented by Bauerle [7] to interpret the temperature dependence of the ionic conductivity which is expressed with two exponential terms. They are the grain boundary resistance model and the oxygen vacancy trapping model. In both models, conductivity in the higher temperature range is ruled by the conventional conducting mechanism expressed with Eq. (2). On the other hand, in the lower temperature range, they are ruled by the grain boundary resistance or by the oxygen ion trapping.
1
°'torT=
Ale-E1/knr + A2e _ e2/ksr .
(4)
Here, Pt, /72, El and E z indicate the resistivity and activation energy which correspond to each process. When E~ is smaller than E 2, E~ represents the activation energy in the higher temperature region and E 2 in the lower temperature region. A~ and A 2 indicate pre-exponential constants. We fitted this function to our measured results. One example is shown in Fig. 6. This equation fits our data well. The lines which represent the temperature dependence of each term (p~, P2) in the equation are also shown. The higher and lower parts of the
Y~
~
I/(oT )=Alexp[ Ea t /ksT ]
3.5. Grain boundary effect In order to clarify which model is appropriate in this case, we measured the grain boundary resistance in the lower temperature range. Fig. 7 shows impedance plots for (1 - x ) Z r O z - ( x - O . 0 3 ) S c 2 0 30.03Yb203 (0.07-
j o.o -2.0
'~ ~ " " ~ - ~ Ol).O.O8(ScaO~).O.03( 0e.89(Zr 89 . . . . . y bbzO~)
--
-4.0
'~,
~'~tL
\
I/(oT )=A t exp[Eaj /keTI + A: expl Ea2/ItsTI
1000/'r
(K"1)
Fig. 6. Temperature dependence of ionic conductivity for 0.89ZrO 2-o.08sc203-0.03Yb203.
Table 2 Activation energies estimated through fitting Eq. (2) to DC measurement data for (1-x)ZrO2-(x-0.03)Sc20~-0.03Yb203 x
E 1 (eV)
E z (eV)
0.07 0.09 0.11 0.13 0.15
0.630 0.634 0.728 0.879 0.879
1.13 1.28 1.42 1.59 1.62
253
R. Chiba et al. / Solid State lonics 91 (1996) 249-256
- 0.20 xl06
(a) X= 0.07
- 0.15 ~
- 0.05
o bulk
-s.o 104
o~
-6.0104
o.1
0.2
0.3
0.5
0.4
o°
0.6 xlO 6
-4.0104
x|O 6
-2.0104
X = 0.09
- 0.4
"0"5 I / - 0.3 -0.2
0"IH~ o
-1.0 lOs
+
I2"
YSZ (lOY angJe cry~d, [Ioo1)
-1.2 lOs
+
-O.lO[ . f
-1.4 i0 ~
0.0
L
i 1.0 l0 s 1.5 l0 s R e [f~]
5.0104
0.010 °
..
-0.1
(b) + 4 ,o'
O.
0.4
0 0.2 - 0.6 x106
•-
0.6
0.8
1.0
1.2 xlO 6
' x=o.ttI
~.0 lOs
-4,0 lOs ,
0 - 0.5 xlOs
,
0.4
0.8
1.6
1.2
÷
.
- 0.2
,
Fig.
8.
crystal
0.4
r
5.0 l0 s
(a) I m p e d a n c e sample
a
i
n
1.0106 1.5106 R e [D]
0.6
0.8
1.0
plots
at 3 0 0 ° C .
0.08Sc203-0.03Yb203 , i , 0.2
0
g
boundar 3
2.0106
2.5106
÷
2"
0
/" ~
0.010 c 0.0 10°
• *
-0.1
~ulk
-2,0 lOs
xiO6
X= 0.13 -- 00.3 .4 I
(0.89)ZrO ~-(0.05)ScaO~-(O.O~)Yb203
-I.O 106
"- 0.20"41, *" ÷" ,
2.5 l0 s
-1.2106
-8.0 l0 s
0
i
2,0 l0 s
for 0.90ZrOz-0.10Yb:O
(b) I m p e d a n c e
plots
3 single
for 0.89ZrO 2-
at 300°C.
1,2 xlO 6
-6.0 xl06
-2.0 10' . . . . . . . . . . . . . . . . . .
- ......
,
X= 0.15 ~---~-L5 10' ~
-2.
0
E
÷
.+ *
-L0 10'
4.0
8.0 R e [Z]
12.0
16.0xl06
(f2)
Fig. 7. Impedance plots for (1-x)ZrOz-(x-O.03)Sc2030.03Yb203 (x=0.070, 0.090, 0.11, 0.13 and 0.15). They were measured at 260°C. The frequency range is 0.1 Hz-10 MHz.
At very low frequency the plot rises in a straight line. This corresponds to the Warburg impedance and originates from the oxygen concentration gradient near the electrode/electrolyte interface. The diameters of the first and second loop correspond to the resistance of the grain and bulk, respectively. The impedance plots for 0.89ZrO:0.085c203-0.03Yb203 at various temperatures are shown in Fig. 9. The diameter of the second and first loops decrease with increases in temperature. However, the ratio of the first and second loop diameters
-5.0 lff o°oo ° ° ° o o o 300"C o
o °
80"C ~ io'
t 1o'
240"C
~a~°oooooo%~
o 260°C 2 to' ~ to' R e [Zl (f~)
4 lo 6
s 10'
Fig. 9. Impedance plots for 0.89ZrO2-0.08Sc203-0.03Yb203. The temperature was constant for each measurement. remains approximately the same through the experimental temperature range. Each element of the resistance evaluated with the AC impedance method is plotted against temperature in Fig. 10. The gradients of the slopes correspond to the activation energies, which are listed in Table 3. The activation energy for the grain boundary resistance is slightly smaller than that for the bulk. Since the former value is approximately 25% of the bulk value, the activation value for the total resistance is almost equal to
254
R. Chiba et al. / Solid State lonics 91 (1996) 249-256
(a)
10°
-. . . . . . . .
~.
~.~
q
• • , .... , .... , .... , ....
<,.internal
-.o,
I ~-to~
101
I
(b)
l
A
"
101.4
m"
"
1.5
1.6
%%.
lo0~
IJ
i o boundaryl~
~ `q
1.7
1.8
1.9
2.0
2.1
1.0
1.2
1.4
1000/'1" (l/K)
(c)
I÷tot=
-~,%
~
"]3-.
' .. ~ 10 IO=z ~
. . . . . . . . . . . . . . . . . . . ~i'nQ .... intemal
I
1.6
IO00/T
101
1 ;,;lj"
1.8 (l/K)
(d) 10. . . .
--=-total
,.~%
J~
~ 10-1 v
"~
2.2
J ~ boundary
"tz
I-e-total
"°' "O. "13
~10"2 I
10-2
2.0
¢ 10~ t 1-
10"3 10"4
b .
10" 1.2
1.4
1.6
1.8
1000/I"
(l/K)
(e)
2.0
2.2
" ~
t~
~
~" 10-1
1.4
........
101
100
1%,
m
1.6
1.8
looorr
(IlK)
2.0
2.2
j io.ou.ry I - * total
°m I-~-intemal
~¢ 10-2
re
u
10-3 10"* lO-S
lO~.
1.2
1.4 1.6 1.8 lOOOrr ( l m )
2.0
2.2
Fig. 10. Arrhenius plots of internal, grain boundary and total ionic conductance, obtained with AC impedance measurement, for (1 -x)ZrO2-(x-0.03)Sc203-0.03Yb203 with (a) x=0.07, (b) x=0.09, (c) x=0.11, (d) x=0.13, and (e) x=0.15. Table 3 Activation energies estimated with AC impedance method for ( 1 -x)ZrO2-(x - 0.03)Sc 203-0.03Yb203 x
E,o, (eV)
Eb
(eV)
0.07 0.09 0.11 0.13 0.15
1.11 1.24 1.34 1.40 1.41
1.12 1.25 1.37 1.41 1.40
Es
(eV)
1.05 1.17 1.32 1.34 1.32
the bulk value. Because of this, the temperature dependence of the total resistance well represents the bulk one.
With the grain boundary model the boundary resistance must be much higher than the bulk resistance and Eg must be approximately twice as large as E b. Therefore, the grain boundary model can not explain the curvature in Fig. 5, and so the vacancy trap model is thought to be appropriate in this case. Here, E 2 (listed in Table 2) evaluated with DC measurements should be the same as E~ot (listed in Table 3) evaluated by AC impedance measurements. When x is between 0.07 and 0.11, both values agree well. However, Etot in Table 3 is approximately 15% larger than E 2 in Table 2. This seems to result from
255
R. Chiba et al. / Solid State lonics 91 (1996) 249-256
the different temperature ranges of the DC and AC measurements. The AC impedance measurements were performed in a lower temperature range than the DC measurements. In addition, the Arrhenius plots for x=0.13 and 0.15 in Fig. 3 have an S-shaped temperature dependence at the lower end of the temperature range, which might correspond to a phase change. This S-shaped temperature dependence reduces E 2 for x=0.13 and 0.15.
. . . . . .
x.....
2/.
0.6
i
.~
0.4}
'
f • 300
"// ~/
~
400
500
600
K = Ko ea~e-rs)/kBr,
(5)
C t = 2C 0,
where K is the equilibrium constant, C t is the trap concentration, C v is the free vacancy concentration, C O is the total vacancy concentration, k a is the Boltzmann constant, AE is the activation energy, T is the temperature and AS is the entropy. According to this model, the free vacancy fraction ( f = - C v / C o ) can be evaluated with the following equation [7] and the constants in Eq. (4), which can be determined through fitting. Cv f-
Co -
1 1 + ~ CoKoeaS/~be ae/kbr
1 -
1 + ( A l / A 2 ) e ~e2-e')/kBr"
i 1i
"/ ~/7
i 700
800 (°C)
900
1000
Fig. 11. Temperature dependence of free vacancy fraction calculated with the vacancy trap model.
According to the vacancy trap model, the oxygen ion vacancies are partially trapped near dopant ions (Sc 3÷, Yb 3+) because the dopant ions have smaller plus charges than zirconium ions (Zr 4÷) and statistically attract the oxygen ion vacancies. Because of charge neutrality, the concentration of the dopant (Sc 3+, Yb 3÷) is twice as high as that of the oxygen ion vacancies, and all vacancies should be trapped at low temperature. At high temperature, most of the vacancies are free and contribute to the ionic conduction. The free vacancy concentration (Cv) and free trap concentration ( C t - ( C o - C v ) ) is in equilibrium with the trapped vacancy concentration (C0 - Cv) as follows; C o - C v = K C v [ C , - (C o - Cv)],
=7
~
....f:;
temperature
3.6. F r e e v a c a n c y f r a c t i o n
^
(6)
With this procedure, we calculated the fraction for (1 - x ) Z r O 2 - ( x - 0.03)Sc203-0.03Yb203, which is shown in Fig. 11. The temperature-fraction plots are
on sigmoid curves. The temperature of the inflection point of the curves decreases with the dopant concentration. The highly doped samples have steeper slopes at the inflection point. This means that the binding energy of the association depends on the doping level. These results suggest that the association of trapping centers and vacancies is a kind of cooperative mechanism.
4. Conclusions
(1) For y =0.02-0.03 in (1 - x ) Z r O 2-(xy)Sc203-YYb203, the cubic phase was stabilized at room temperature and the discontinuity in the ionic conductivity disappeared. (2) Deviation from the Arrhenius equation was observed in the temperature dependence of the DC conductivity of the stabilized samples. (3) It was found that the curvature in the Arrhenius plots of the ionic conductivity can be described well with an equation with two exponential terms. (4) The grain boundary resistance was separated from the total resistance with an AC impedance method. The grain boundary resistance was approximately 25% of the total resistance. (5) The activation energy for the grain boundary resistance was very close to that of the bulk in our system. This revealed that the curvature of the Arrhenius plots can not be explained with the grain boundary model. (6) The temperature dependence of the free vacancy fraction for ( 1 - x ) Z r O 2 - ( x - 0 . 0 3 ) S c 2 0 3 -
256
R. Chiba et al. / Solid State lonics 91 (1996) 249-256
0 . 0 3 Y b 2 0 3 was evaluated based on the o x y g e n ion vacancy trap model. The sharp change of the free vacancy fraction was caused for samples highly doped with Sc 3÷.
Acknowledgments We express our gratitude to Dr. M i n o r u Suzuki and Dr. Yamaji for his constant e n c o u r a g e m e n t throughout this work. We also express thanks to Mr. T a m i o N a k a z a w a and Ms. Sanae Arai for their help with preparing samples and with measurements.
References [1] Nguyen Q. Minh, J. Am. Ceram. Soc. 76(30) (1993) 563. [2] S.P.S. Badwal, J. Mater. Sci. 22 (1987) 4125. [3] T. Takahashi, U. Suzuki and K. Esaki, 7th Symp. on Solid State Ionics in Japan, Extended Abstracts (1979) p. 29. [4] T. Ishii, T. Iwata and Y. Tajima, Proc. 3rd Int. Symp. on SOFC (The Electrochem. Soc.), Proc. Vol. 93(4) (1993) p. 59. [5] T. Ishii, Solid State Ionics 78 (1995) 333. [6] F.K. Moghadam, T. Yamashita, R. Sinclair and D.A. Stevenson, J. Am. Ceram. Soc. 66 (1983) 213. [7] J.E. Bauerle and J. Hrizo, J. Phys. Chem. Solids 30 (1969) 565.
Solid State lonics 91 (1996) 249-256
IONICS
Temperature dependence of ionic conductivity in (1 - x)ZrO2-(x - y ) S c 2 0 3 - y Y b 2 0 3 electrolyte material Reiichi Chiba*, Takao Ishiil, Fumikatsu Yoshimura NTT Interdisciplinary Research Laboratories, Tokai, Ibaraki, 319-11, Japan Received 6 May 1996; accepted 24 June 1996
Abstract The temperature dependence of the ionic conductivity of (1 - x ) Z r O 2 - ( x - y)Sc203-yYb203 (x = 0.07-0.15, y = 0.000.03) was examined to clarify the origins of the ionic conductivity decrease at low temperature. For y = 0.02-0.03 in this system, the cubic phase was stabilized at room temperature and discontinuity in the ionic conductivity disappears. The Arrhenius plots of the ionic conductivity for the stabilized samples were curved. The grain boundary resistance for (1 - x ) Z r O 2 - ( x - 0.03)5c203-0.03Yb203 (x = 0.07-0.15) was separated from the total resistance with the AC impedance method. This allowed us to conclude that grain boundary resistance is not the cause of the curvature in the Arrhenius plots for this system. Keywords: Rare-earth ion-doped zirconia; Temperature dependence; Ionic conductivity; Grain boundary resistance; Solid oxide fuel cells; Electrolyte material
1. Introduction
Rare-earth ion-doped zirconia is thought to be practicable for use as the electrolyte for solid oxide fuel cells (SOFC), since its ionic transport number is 1.0 for a very wide range of oxygen partial pressures [ 1]. If higher ionic conductivity can be achieved, the operating temperature of the SOFC can be reduced from 1000°C to approximately 800°C, and restrictions regarding SOFC materials will be eased. When zirconia is doped with Sc 3÷ it exhibits a higher ionic conductivity than when doped with any other rare*Corresponding author. Tel.: (81-29) 287-7764; fax: (81-29) 287-7863; e-mail: [email protected] tPresent address: NTT LSI Laboratories, Atsugi-shi, Kanagawa 243-01, Japan.
earth ion, and this is thought to be because of the closeness of the ionic radii of Z r 4+ and Sc 3+ [2-6]. Therefore, zirconia doped with Sc 3+ is a good candidate as an electrolyte material for SOFC operating at reduced temperatures. The ionic radius of Yb 3÷ is also very close to that of Zr 4+, and so the conductivity of (1 - x)ZrO2-(x - y)SczO3-YYb203 is expected to be very high over a wide range of compositions. We investigated the temperature dependence of the ionic conductivity of this material. We also studied the mechanisms that limit its ionic conduction at relatively low temperatures.
2. Experimental The samples were prepared from high purity
0167-2738/96/$15.00 Copyright ©1996 Elsevier Science B.V. All rights reserved PII S0167-2738(96)00435-3
ZrO 2
250
R. Chiba et al. / Solid State lonics 91 (1996) 249-256
(99.9%), SczO 3 (99.9%) and Yb20 3 (99.9%) powders. The mixed powders were pressed into cylindrical pellets with a hydrostatic pressure of 100 MPa and sintered at 1620°C for 60 h in air. The crystal structure of the samples was characterized with an X-ray diffractometer using Cuket radiation at room temperature. The ionic conductivity of the samples was evaluated with the DC four-terminal method. The samples for this measurement were about 0.20 × 0.26 × 1.8 cm in size. Platinum wires were attached to the samples with platinum paste and fired in air at 1000°C for 1 h to form the current and voltage terminals. A constant current of 1.0-10 IxA was supplied by a current source (Keithley model 220). The current direction was reversed, (I+,I_), and the potential drop was measured for each direction, (V+,V_), with a digital multi-meter (Keithley model 195A). The conductivity, tr, was determined with those values as follows:
(l+/V+ + I_/V_) o- -
2
(1)
These measurements were performed at a temperature scanning rate of 2°/min in the range 4001100°C. The AC impedance method (two-terminal) was used to evaluate the boundary resistance. The samples for this measurement were about 0 . 2 0 x 0 . 6 0 × 0.60 cm in size. Platinum mesh was attached on two sides of the samples with platinum paste and fired in air at 1000°C for 1 h to form the electrodes. The measurements were performed in the 0.1-10 MHz frequency range from 200-600°C in air with an impedance analyzer (Schlumberger Technologies model SI1260).
3. R e s u l t s a n d d i s c u s s i o n
3. I. Crystal structure The X-ray diffraction pattems of the samples are shown in Figs. 1 and 2. 0.89ZrO2-0.11Sc203 are in the rhombohedral phase. They are in a mixture of the cubic phase and the rhombohedral phase when the y in the 0.89ZrO 2(0.89-y)Sc203-yYb203 is less than 0.20. The
I xloo ic.bic •~'~ ~
~__~ X=0.020 ~ cubic ~
x=001, I "~
3_4
__A x=ooos rhomhohedral
30
40 20
50 (deg.)
I
60
Fig. 1. X-ray diffraction patterns for 0.89ZrO2-(0.89-y)Sc203yYb203 (y=0, 0.005, 0.010, 0.015, 0.020 and 0.030) sintered at 1620°C for 60 h in air.
.=. t-
__1 X=0.170
cubic~
~__~ X= 0.150 t cubic X= 0.130 I cubic ~__
J xoo.,~ t c.b,c_L ~_~
~_
X = 0.090
,.__3.. x = 0'070 Jt 30
40
50 20
Fig. 2. X-ray diffraction patterns for (1 -x)ZrO2-(x0.03)Sc20~-0.03Yb203 (x=0.07, 0.09, 0.11, 0.13 and 0.15) sintered at 1620°C for 60 h in air.
samples are in a cubic phase when x is in the range 0.09-0.17 and y is in the range 0.02-0.03 in ( 1 x)ZrO2-(x-y)Sc203-yYb203 . They are in a mixture of the tetragonal and cubic phases when x is in the range 0.05-0.07 and y is in the range 0.02-0.03. The lattice constants, which were calculated from (222) peaks for (1 - x ) Z r O 2 - ( x - 0 . 0 3 ) S c 2 0 3 0.03Yb203, are listed in Table 1.
3.2. Temperature dependence of the ionic conductivity The temperature dependence of the ionic conductivity for 0.89ZRO2-(0.11 - y ) S c 2 0 3 - Y Y b 2 0 3 (0.00--
251
R. Chiba et al. / Solid State lonics 91 (1996) 2 4 9 - 2 5 6
Table 1 Crystal structure and lattice constants for (1 - x ) Z r O 2 - ( x 0.03)Sc20 a-0.03Yb203
6.0
x
Crystal structure
Lattice constant (nm)
4.0
0.07 0.09 0.11 0.13 0.15 0.17 0.21
cubic ( + tetragonal) cubic cubic cubic cubic cubic cubic
(0.5112) 0.5106 0.5103 0.5098 0.5093 0.5089 0.5080
~ X
~2.o
t~-~.
=0.090
i ~ - x = oa3o
, . ~~
~0.0 C
-2.0 0.8
ii
1.4
1.6
0.03Yb203 (0.07-
1.0
1.2
1.4
1.6
1000/'1" (l/K) Fig. 3. Temperature dependence of ionic conductivity for 0.89ZrO2-(0.89-y)Sc203-YYb203 ( y = 0 , 0.005, 0.010, 0.015, 0.020 and 0.030).
conductivity, tr, generally depends on the temperature, as given by the following equation [1,2,7], o-= ( - - ~ ) e -ea/kBr.
1.2
Fig. 4. Temperature dependence of ionic conductivity for ( 1 x)ZrO2-(x-0.03)Sc203-0.03Yb203 (x=0.070, 0.090, 0.11, 0.13 and 0.15).
e-
0.8
1.0
1000/'1" (l/K)
(2)
C o, T, E a, k B indicate constants related to the frequency factor, temperature, activation energy and the Boltzmann constant, respectively. Here, In(o-T) is plotted against 1000/T and there should be a linear relation. An abrupt increase was observed in the conductivity around 650°C, which should correspond to a structural transition from the rhombohedral to the cubic phase. An increase in y in 0.89ZrO 2(0.11-y)Sc203-yYb203 lowers the transition temperature and reduces the conductivity change through the transition. When y is more than 0.02, no trace of the discontinuity was observed. This agrees well with the X-ray diffraction measurements. The temperature dependence of the ionic conductivity for ( 1 -x)ZrOz-(X - 0 . 0 3 ) S c 2 0 3 -
3.3. Composition dependence of the ionic conductivity To apply this material as an SOFC electrolyte, it should be a good conductor around 900°C [1]. The ionic conductivity at 1000°C and 800°C were plotted against the composition in Fig. 5. The highest value was obtained at x = 0.11, both at 800°C and 1000°C. 10°
(l-x)ZrOE-(X-0'03)Sc203-0"03Yb203 --~' 800°C 1000°C
"7.
10-I
106 ' '0108 " 0116 " 0:12 " 0]14 " 0.16 X
Fig. 5. Dependence of conductivity on composition for ( 1 x)ZrO2-(x-O.O3)Sc203-O.O3Yb203 (x=0.070, 0~090, 0.11, 0.13 and 0.15) at 800°C and 1000°C.
252
R. Chiba et al. / Solid State lonics 91 (1996) 249-256
The value is close to 0.1 S/cm, even at 800°C, which is necessary for practical use. 3.4. Fitting the ionic conductivity results to a trap model ln(trT) versus IO00/T is plotted in Fig. 4. When the temperature dependence of the ionic conductivity is described with Eq. (2), the plots should form straight lines. However, the temperature dependence shows a distinct curvature. If two activation processes are involved in the ionic conduction, the conductivity can be expressed by the following equation [7]: 1 O'tot - - -
Pl - + P2'
(3)
then,
curve converge with the lines. We fitted the equation to the data in Fig. 3 and estimated the activation energies and pre-exponential factors, which are listed in Table 2. E 2 is approximately twice as large as E 1. The curvature of the plots originates from the difference in the activation energy for the two processes (processes which determine the lower and higher temperature ranges). Two models were presented by Bauerle [7] to interpret the temperature dependence of the ionic conductivity which is expressed with two exponential terms. They are the grain boundary resistance model and the oxygen vacancy trapping model. In both models, conductivity in the higher temperature range is ruled by the conventional conducting mechanism expressed with Eq. (2). On the other hand, in the lower temperature range, they are ruled by the grain boundary resistance or by the oxygen ion trapping.
1
°'torT=
Ale-E1/knr + A2e _ e2/ksr .
(4)
Here, Pt, /72, El and E z indicate the resistivity and activation energy which correspond to each process. When E~ is smaller than E 2, E~ represents the activation energy in the higher temperature region and E 2 in the lower temperature region. A~ and A 2 indicate pre-exponential constants. We fitted this function to our measured results. One example is shown in Fig. 6. This equation fits our data well. The lines which represent the temperature dependence of each term (p~, P2) in the equation are also shown. The higher and lower parts of the
Y~
~
I/(oT )=Alexp[ Ea t /ksT ]
3.5. Grain boundary effect In order to clarify which model is appropriate in this case, we measured the grain boundary resistance in the lower temperature range. Fig. 7 shows impedance plots for (1 - x ) Z r O z - ( x - O . 0 3 ) S c 2 0 30.03Yb203 (0.07-
j o.o -2.0
'~ ~ " " ~ - ~ Ol).O.O8(ScaO~).O.03( 0e.89(Zr 89 . . . . . y bbzO~)
--
-4.0
'~,
~'~tL
\
I/(oT )=A t exp[Eaj /keTI + A: expl Ea2/ItsTI
1000/'r
(K"1)
Fig. 6. Temperature dependence of ionic conductivity for 0.89ZrO 2-o.08sc203-0.03Yb203.
Table 2 Activation energies estimated through fitting Eq. (2) to DC measurement data for (1-x)ZrO2-(x-0.03)Sc20~-0.03Yb203 x
E 1 (eV)
E z (eV)
0.07 0.09 0.11 0.13 0.15
0.630 0.634 0.728 0.879 0.879
1.13 1.28 1.42 1.59 1.62
253
R. Chiba et al. / Solid State lonics 91 (1996) 249-256
- 0.20 xl06
(a) X= 0.07
- 0.15 ~
- 0.05
o bulk
-s.o 104
o~
-6.0104
o.1
0.2
0.3
0.5
0.4
o°
0.6 xlO 6
-4.0104
x|O 6
-2.0104
X = 0.09
- 0.4
"0"5 I / - 0.3 -0.2
0"IH~ o
-1.0 lOs
+
I2"
YSZ (lOY angJe cry~d, [Ioo1)
-1.2 lOs
+
-O.lO[ . f
-1.4 i0 ~
0.0
L
i 1.0 l0 s 1.5 l0 s R e [f~]
5.0104
0.010 °
..
-0.1
(b) + 4 ,o'
O.
0.4
0 0.2 - 0.6 x106
•-
0.6
0.8
1.0
1.2 xlO 6
' x=o.ttI
~.0 lOs
-4,0 lOs ,
0 - 0.5 xlOs
,
0.4
0.8
1.6
1.2
÷
.
- 0.2
,
Fig.
8.
crystal
0.4
r
5.0 l0 s
(a) I m p e d a n c e sample
a
i
n
1.0106 1.5106 R e [D]
0.6
0.8
1.0
plots
at 3 0 0 ° C .
0.08Sc203-0.03Yb203 , i , 0.2
0
g
boundar 3
2.0106
2.5106
÷
2"
0
/" ~
0.010 c 0.0 10°
• *
-0.1
~ulk
-2,0 lOs
xiO6
X= 0.13 -- 00.3 .4 I
(0.89)ZrO ~-(0.05)ScaO~-(O.O~)Yb203
-I.O 106
"- 0.20"41, *" ÷" ,
2.5 l0 s
-1.2106
-8.0 l0 s
0
i
2,0 l0 s
for 0.90ZrOz-0.10Yb:O
(b) I m p e d a n c e
plots
3 single
for 0.89ZrO 2-
at 300°C.
1,2 xlO 6
-6.0 xl06
-2.0 10' . . . . . . . . . . . . . . . . . .
- ......
,
X= 0.15 ~---~-L5 10' ~
-2.
0
E
÷
.+ *
-L0 10'
4.0
8.0 R e [Z]
12.0
16.0xl06
(f2)
Fig. 7. Impedance plots for (1-x)ZrOz-(x-O.03)Sc2030.03Yb203 (x=0.070, 0.090, 0.11, 0.13 and 0.15). They were measured at 260°C. The frequency range is 0.1 Hz-10 MHz.
At very low frequency the plot rises in a straight line. This corresponds to the Warburg impedance and originates from the oxygen concentration gradient near the electrode/electrolyte interface. The diameters of the first and second loop correspond to the resistance of the grain and bulk, respectively. The impedance plots for 0.89ZrO:0.085c203-0.03Yb203 at various temperatures are shown in Fig. 9. The diameter of the second and first loops decrease with increases in temperature. However, the ratio of the first and second loop diameters
-5.0 lff o°oo ° ° ° o o o 300"C o
o °
80"C ~ io'
t 1o'
240"C
~a~°oooooo%~
o 260°C 2 to' ~ to' R e [Zl (f~)
4 lo 6
s 10'
Fig. 9. Impedance plots for 0.89ZrO2-0.08Sc203-0.03Yb203. The temperature was constant for each measurement. remains approximately the same through the experimental temperature range. Each element of the resistance evaluated with the AC impedance method is plotted against temperature in Fig. 10. The gradients of the slopes correspond to the activation energies, which are listed in Table 3. The activation energy for the grain boundary resistance is slightly smaller than that for the bulk. Since the former value is approximately 25% of the bulk value, the activation value for the total resistance is almost equal to
254
R. Chiba et al. / Solid State lonics 91 (1996) 249-256
(a)
10°
-. . . . . . . .
~.
~.~
q
• • , .... , .... , .... , ....
<,.internal
-.o,
I ~-to~
101
I
(b)
l
A
"
101.4
m"
"
1.5
1.6
%%.
lo0~
IJ
i o boundaryl~
~ `q
1.7
1.8
1.9
2.0
2.1
1.0
1.2
1.4
1000/'1" (l/K)
(c)
I÷tot=
-~,%
~
"]3-.
' .. ~ 10 IO=z ~
. . . . . . . . . . . . . . . . . . . ~i'nQ .... intemal
I
1.6
IO00/T
101
1 ;,;lj"
1.8 (l/K)
(d) 10. . . .
--=-total
,.~%
J~
~ 10-1 v
"~
2.2
J ~ boundary
"tz
I-e-total
"°' "O. "13
~10"2 I
10-2
2.0
¢ 10~ t 1-
10"3 10"4
b .
10" 1.2
1.4
1.6
1.8
1000/I"
(l/K)
(e)
2.0
2.2
" ~
t~
~
~" 10-1
1.4
........
101
100
1%,
m
1.6
1.8
looorr
(IlK)
2.0
2.2
j io.ou.ry I - * total
°m I-~-intemal
~¢ 10-2
re
u
10-3 10"* lO-S
lO~.
1.2
1.4 1.6 1.8 lOOOrr ( l m )
2.0
2.2
Fig. 10. Arrhenius plots of internal, grain boundary and total ionic conductance, obtained with AC impedance measurement, for (1 -x)ZrO2-(x-0.03)Sc203-0.03Yb203 with (a) x=0.07, (b) x=0.09, (c) x=0.11, (d) x=0.13, and (e) x=0.15. Table 3 Activation energies estimated with AC impedance method for ( 1 -x)ZrO2-(x - 0.03)Sc 203-0.03Yb203 x
E,o, (eV)
Eb
(eV)
0.07 0.09 0.11 0.13 0.15
1.11 1.24 1.34 1.40 1.41
1.12 1.25 1.37 1.41 1.40
Es
(eV)
1.05 1.17 1.32 1.34 1.32
the bulk value. Because of this, the temperature dependence of the total resistance well represents the bulk one.
With the grain boundary model the boundary resistance must be much higher than the bulk resistance and Eg must be approximately twice as large as E b. Therefore, the grain boundary model can not explain the curvature in Fig. 5, and so the vacancy trap model is thought to be appropriate in this case. Here, E 2 (listed in Table 2) evaluated with DC measurements should be the same as E~ot (listed in Table 3) evaluated by AC impedance measurements. When x is between 0.07 and 0.11, both values agree well. However, Etot in Table 3 is approximately 15% larger than E 2 in Table 2. This seems to result from
255
R. Chiba et al. / Solid State lonics 91 (1996) 249-256
the different temperature ranges of the DC and AC measurements. The AC impedance measurements were performed in a lower temperature range than the DC measurements. In addition, the Arrhenius plots for x=0.13 and 0.15 in Fig. 3 have an S-shaped temperature dependence at the lower end of the temperature range, which might correspond to a phase change. This S-shaped temperature dependence reduces E 2 for x=0.13 and 0.15.
. . . . . .
x.....
2/.
0.6
i
.~
0.4}
'
f • 300
"// ~/
~
400
500
600
K = Ko ea~e-rs)/kBr,
(5)
C t = 2C 0,
where K is the equilibrium constant, C t is the trap concentration, C v is the free vacancy concentration, C O is the total vacancy concentration, k a is the Boltzmann constant, AE is the activation energy, T is the temperature and AS is the entropy. According to this model, the free vacancy fraction ( f = - C v / C o ) can be evaluated with the following equation [7] and the constants in Eq. (4), which can be determined through fitting. Cv f-
Co -
1 1 + ~ CoKoeaS/~be ae/kbr
1 -
1 + ( A l / A 2 ) e ~e2-e')/kBr"
i 1i
"/ ~/7
i 700
800 (°C)
900
1000
Fig. 11. Temperature dependence of free vacancy fraction calculated with the vacancy trap model.
According to the vacancy trap model, the oxygen ion vacancies are partially trapped near dopant ions (Sc 3÷, Yb 3+) because the dopant ions have smaller plus charges than zirconium ions (Zr 4÷) and statistically attract the oxygen ion vacancies. Because of charge neutrality, the concentration of the dopant (Sc 3+, Yb 3÷) is twice as high as that of the oxygen ion vacancies, and all vacancies should be trapped at low temperature. At high temperature, most of the vacancies are free and contribute to the ionic conduction. The free vacancy concentration (Cv) and free trap concentration ( C t - ( C o - C v ) ) is in equilibrium with the trapped vacancy concentration (C0 - Cv) as follows; C o - C v = K C v [ C , - (C o - Cv)],
=7
~
....f:;
temperature
3.6. F r e e v a c a n c y f r a c t i o n
^
(6)
With this procedure, we calculated the fraction for (1 - x ) Z r O 2 - ( x - 0.03)Sc203-0.03Yb203, which is shown in Fig. 11. The temperature-fraction plots are
on sigmoid curves. The temperature of the inflection point of the curves decreases with the dopant concentration. The highly doped samples have steeper slopes at the inflection point. This means that the binding energy of the association depends on the doping level. These results suggest that the association of trapping centers and vacancies is a kind of cooperative mechanism.
4. Conclusions
(1) For y =0.02-0.03 in (1 - x ) Z r O 2-(xy)Sc203-YYb203, the cubic phase was stabilized at room temperature and the discontinuity in the ionic conductivity disappeared. (2) Deviation from the Arrhenius equation was observed in the temperature dependence of the DC conductivity of the stabilized samples. (3) It was found that the curvature in the Arrhenius plots of the ionic conductivity can be described well with an equation with two exponential terms. (4) The grain boundary resistance was separated from the total resistance with an AC impedance method. The grain boundary resistance was approximately 25% of the total resistance. (5) The activation energy for the grain boundary resistance was very close to that of the bulk in our system. This revealed that the curvature of the Arrhenius plots can not be explained with the grain boundary model. (6) The temperature dependence of the free vacancy fraction for ( 1 - x ) Z r O 2 - ( x - 0 . 0 3 ) S c 2 0 3 -
256
R. Chiba et al. / Solid State lonics 91 (1996) 249-256
0 . 0 3 Y b 2 0 3 was evaluated based on the o x y g e n ion vacancy trap model. The sharp change of the free vacancy fraction was caused for samples highly doped with Sc 3÷.
Acknowledgments We express our gratitude to Dr. M i n o r u Suzuki and Dr. Yamaji for his constant e n c o u r a g e m e n t throughout this work. We also express thanks to Mr. T a m i o N a k a z a w a and Ms. Sanae Arai for their help with preparing samples and with measurements.
References [1] Nguyen Q. Minh, J. Am. Ceram. Soc. 76(30) (1993) 563. [2] S.P.S. Badwal, J. Mater. Sci. 22 (1987) 4125. [3] T. Takahashi, U. Suzuki and K. Esaki, 7th Symp. on Solid State Ionics in Japan, Extended Abstracts (1979) p. 29. [4] T. Ishii, T. Iwata and Y. Tajima, Proc. 3rd Int. Symp. on SOFC (The Electrochem. Soc.), Proc. Vol. 93(4) (1993) p. 59. [5] T. Ishii, Solid State Ionics 78 (1995) 333. [6] F.K. Moghadam, T. Yamashita, R. Sinclair and D.A. Stevenson, J. Am. Ceram. Soc. 66 (1983) 213. [7] J.E. Bauerle and J. Hrizo, J. Phys. Chem. Solids 30 (1969) 565.