- Email: [email protected]
Ionic conductivity measurements of doped β-alumina compounds
Solid State Ionics 18 & 19 (198~) 608-61 I North-Holland. Amsterdam
608
IONIC CONDUCTIVITY MEASUREMENTS OF DOPED ;3-ALUMINA COMPOUNDS
D.R. WHITE,* S. CHEN,** M. SANKARARAMAN and H. SATO School of Materials Engineering, Purdue University, West Lafayette, IN 47907, USA
The temperature dependent conductivity of Co-stabilized tY'-alumina, Co and Ni-doped t3-aluminas, pure ;3-alumina, and K+--exchanged Ni-doped i3-alumina has been measured and compared betwen 25°C and 600°C. The analysis was made by means of phase-synehronous detection system in the frequency range 100 Hz to 10 MHz. From these measurements it was found that the doped ~3-alumina compounds had consistently higher conductivity than comparable undoped material, although still not quite as high as their stabilized ~"-alumina counterparts. It was also found that Co-stabilized/3"-aluminas displayed a break in the eonduetivity curve, previously reported only in Mg-stabilized ~T'-alumina. Doped /3-aluminas also displayed non-linear conductivity eurves showing a slight bending around 200°C.
1. I N T R O D U C T I O N The majority of investigations of the electrical pro-
perties of prt to further explore these properties in /3-aluminas, a series of first row transition metal ions has been added to prepare doped fl- and stabilized ;f'-alutnin~s. Although it has been possible to grow single crystals of most of these compounds, only those of cobalt and nickel have yielded large enough specimens for complete characterization. We have previ-
ously reported the results of the compositions and structures of these compounds. 3 5 Ilere, we conclude this work with their electrical characterizations. 2.
EXPERIMENTAL
Single crystals of cobalt and nickel-doped 3aluminas were prepared by means of skull melting technique as h~s been described in the previous publications. 3'4 Single crystals of ('o-stabilized 3"-abmfina.~ were prepared by a flux growth method following the procedure reported by Mc\Vhan, et al. s and were reported in detail by ('hen, et al. 5 Specimens cff pure (undoped) /~-ah)nlina were obtained froth the Oak Ridge National Laboratory. 7 Samples ['or c(mductivity Ineq.snrements were (.ui from large anti optically clear single crystals into a parallelepiped shape, and these were then pretreated in molten N a N O 3 to remove impurities from |he conduction planes (Note: a few samples were i,mexchanged in KNO 3 to prepare K+-,'~-alumina). Thin fihns of platinum were sputtered ( 25 ttm thickness) ()tit() the appropriale sides of the samples for ole(.trieal contacts. All specimens were stored in a vacuum desi<'ator prior to n l e a s u r e l n e n t .
*Present Address: l,anxide Corporation, Newark, Delaware 19711.
*'Present Address: Research Laboratories, Eastman-Kodak Company, Rochester, New York 1467D. 0 167-2738/86/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
609
D.R. White et aL / h)tlic conductivity measurements
Ionic conductivity measurements were made by means of phase synchronous d e t e c t i o n / c o m p u t e r modelling technique. 8-1° This data acquisition and analysis system is fully automated under the control of an ITP9836 mini-computer. The measurements are made by measuring the response {phase shift and amplitude difference) of the samples from an A C signal (100 ttz to l0 Mttz) by an HP3040A network analyzer. The system is calibrated to compensate for stray, real and imaginary, components unique to the test cell over the entire frequency band and over the temperature range 2 5 ° C - 6 0 0 ° C . All samples were allowed to bakeout in the test cell under a vacuum (10 mTorr) for three hours at 600°C prior to the measurement run. The data analysis for each temperature scan was carried out using a least squares fitting routine in which the DC resistance of the crystal is one of the fitting parameters. The fitting function is based, in part, on an equivalent circuit model representing the electrical response of the sample. The model giving the best fits consists of a resistor (R) and a non-Debye capacitor u C r in parallel with an Debye capacitor C {Figure l). In this model the resistor represents the DC resistance of the crystal, due primarily to the ionic motion in the conduction plane; while the non-Debye capacitor represents the combined dielectric response of the conduction plane and the electrode/electrolyte interface, m'12 The parallel capacitor represents the dielectric response of the spinel blocks which separate the conduction planes. The assumption that the spinel block's should be modelled as an ideal capacitor in parallel with the more common resistor-capacitor
C
ft v ---tllllll FI
C'
F I G U R E 1. Equivalent circuit for single crystalline fl-aluminas, consisting of a capacitor C in parallel with a resistor R, and a non-Debye capacitor C.
model is both consistent with the structure of the ,8aluminas and the dielectric behavior of spinels (i.e., low loss dielectric). 3. R E S U L T S A N D D I S C U S S I O N The results of the conductivity measurements are summarized in Figure 2. The activation energies, pre~ factors, and conductivity values at 25°C are given in Table 1. Note that the activation energies and prefactors for most of the materials are taken at high and Iow temperature regions due to the non-linearity of their conductivity curves. Table
1. Summary of data from conductivity
measurements of B-alumina compounds Compound "Pure B-alumina
0.142 + 0.002
ao [fFlcmqK) 2100 ___+13
Co2+-doped fl-alumina
0.139 + 0.001a 0.172 ~ 0.002b
4023 + 106a 9379-+- 626b
0.039
Ni2+-doped B-alumina
0.133 + 0.002a
3666 + 126a
0.028
0.203 ~ 0.001 b
22306"~ 857 b
Co2+-stabilized
0.060 + 0.003a
1816 __+90a
B'-alumina
0.154 + 0.001 b
15520 ~ 581 b
0.327 +_ ,002
14260 + 535
(K} Ni2+-doped B-alumina
•l
E~(eV)
¢r25.c l] rein l 0.028
0.131 ---
From high temperature data {-T>200°C}. From low temperature data (-T<200°C}.
As can be seen, the Co-stabilized f l ' - a l u m i n a sample had /he highest conductivity of the materials measured, with a value of 0.131 f] 1 cm-I at 25°C. This value is also one of the highest values reported for all /~-alumina type compounds. One of the most interesting features of this curve is its non-Arrhenius behavior, as is evident by the sharp hreak in the curve around 225°C-250°C (Fig. 3). This response is similar to that reported for Mg-stabilized /~"-alulnina l° and has been attributed to the development of ordering between ions and vacancies in the conduction plane.t3 16 Although the exact mechanism responsible for this hehavior is not understood, it is assumed that it is most likely the same in these two forms of fl"aluminas. Ni- and Co-doped fl-aluminas show the next highest conductivity values which are almost identical except for yet low temperature regions. As can be seen, these compounds exhibit " i m p r o v e d " conductivities over that of the undoped fl-alumina. This
610
D.R. Whit(, et al.
/ Ionic ('rmductirity measttr('nw~tts more "ol)en" path for ionic motion. Also at)parent from these curves is a gradual but distinct bending b(,giiming ar()un(t 200~'C-180°C as shown in Figures .I and 5. This curvature is most evident in Ni-dot)ed //alulnina, rausing its curve to intersect that of [lure /Calumina around 25%: in Figure :2. The reason for this non-Arrh('nius response is n(>t clear at. (his moment: however, it is most likely (lue (o (he deveh)pment ()f sh(~rt-range ()r(lering in the conduction plane with decreasing temperature. "].'he reason )hal this is ()bserved in the dol>e(l ~J-alumina samples and not in Áhe pure .)'-aluminas may I)e related (() (he "()p(,nn(,ss" ()f the c())lducti(m plane, which allows this ()r(h,ring phen()lll('n()n l ( ) ( ) c c u r ( o a greater ( , x l e n t ill t h e d ( , p e d
IEMPERRTURE (*C) ii
10
41~B
: ;t
_
• e
~19~
I
11~
f~
25
I
I
I
1
~I•AAA
A
x
~
&&
7 e 1~ ~
\ •,,
) , , . ' ~ .l l/ . tx .x.~i. ®
b,
x x
+"
•
1
b
2.0 1000/T (K -~)
3.0
('()Ill p ( ) l l II (t>;.
lrl(~I'I~ F 2. •
.
.
(
o +
.
.
TEMPERATURE
,,
('on(luctlvlt'¢ lih)t eolnparmg; (a) . (4)- -stabfl)zed ;4• , o+ ,)+ alununa, (b) ( o - -doped 3-alumlna, (c) Nl- -(Io~ed ;~-aluinina ((1) pure p'-alunlina (e) (pc)tassiuln) Ni "+doped /~-alumina behavior is, however, in agreement with other published values of doped /3-aluminas.''<17 As wz~s previously men(toned, this is thought to be due t() the removal of bridging oxygens in t h e c o n d u c t i o n p l a n e by a charge c()mpensation mechanism, which creates a
4~0
2~
[°E) I~8
lgg
\ 2.0
25
50
3.0
l~lal~/T
:4"4"..4. .
I
E
TEMPERFITURE {°El 2BRI
2S
I
"rue 10 ~ -.?
10 ~ 4,B0
50
I
(K -l}
I"I(',I 7I~l'; .l. • ,) +
"7 "7 E
.12 o
1182 b
N"I \
-I---~ 2.0
I
,
('(,I)(luctivity plot ()f Nl" -(I()i)((I ,>Lnlumin:t saml)h'. from skull melt gr(>wlh. Th(' p(>tassium-exchanged Ni-doped /:)-alumina samph!s gave the lowest conductivity values and Ill(, highest activati(m energies of all specimens. This dala is consistenl with other reports in the lileraturv for pot assium-ex changed /3-alulninas. 18,Lq
3.~
1000/T [K -~1
FIGITRE 3. Conduelivity plot of Coe+-stabilized /~'-alumina sample, from flux melt growth.
It should be pointed out Áhat, during (he course (,f the
nleasurelllPnts,
sev(,r31
att0iiipts
werP
ii/ade
to
c()mpare Ill(' lits ()blained from lhe equivah,nt circuit inodel shown in Fig. !, and that ()f the more c(unmon resistor and non-I)ebye capacitor 11 in series. Alth(mgb w'ry li(lh' (lifference in the abs(>lute c(mducli~ilv and
D.R. White et al. / Ionic conductivity measurements
TEMPERRTURE C°C] 41W
21~
llm
,~
25
611
of our team to develop the skull melting technique for the preparation of the wide variety of ~-Mumina compounds used in this work. REFERENCES
T
E U
T
10a
1.
W . L . Roth, F. Reidinger, and S. LaPlaca, "Stu(ties of Stabilization and Transport Mechanisms in /3 and y ' - A l u m i n a by Neutron Diffraction," in Superionic Conductors, 223, Ed. by G. D. Mahan and W. L. Roth, Plenum Press, New York, 1976.
2.
W. L. Roth, Trans. Am. Cryst. Assoc., 11, 51 (1975). I). R. White, S. Chen, ti. R. I~Iarrison and It. Sato, Solid State Ionics, 9-10, 225 (1983).
F tO I---
b
!
10
I
I 2.0
t
I
3.~
3.
1000/T (K-h
4. FIGURE 5. Conductivity plot of Co'°+-doped ¢~-alumina sample, from skull melt growth. 5. the activation energy values was found, the quality of the fits showed a marked improvement, especially at high frequencies ( > l Mllz), with the additional parallel capacitor. This may indicate that the often overlooked spinel blocks may influence, albeit slightly, the AC measurenlents of the fl-aluminas. (Note: the test cell calibration assumes a stray parallel capacitance due to the cell configuration and therefore is accounted for in the final conductivity analysis and is not related to the conductivity model described).
6.
7.
Courtesy of J. B. Bates.
8.
D. R. White, Ph.D. Thesis, Purdue University {19851. It. Engstrom and a. C. Wang, Solid State lonics, 1, 4:tl {1980).
9.
1O. II. Engstrom, J. B. Bates, W. E. Brundage, and J. C.. Wang, Solid State Ionics, 2, 265 (1981). ll.
A. K. Jonscher, J. Mat. Sei. ~ Phys. Stat. Sol. (a) ~ 665 (1975).
12.
J. P. Bates, Oak Ridge National Laboratory, private communication (January 1985).
13.
J . P . Boilot, G. Collin, P. tt. Collomban, and R. Comes, Phys. Rev., 1322, 5912 (1980).
14.
J. B. Bates, H. Engstrom, J. C. Wang, B. C. Lauson, N. J. Dudney, and W. E. Brundage, Solid State Ionies, 5, 159 (1981). J. C. Wang, J. B. Bates, N. J. Dudney, and H. Engstrom, Solid State lonics, 5, 35 (1981). H. Sato and R. Kikuchi, J. Physique, C7, 159 (1977).
ACKNOWLEDGEMENTS
We wish to thank Dr. Harold Harrison for his help in the preparation of materials. We would also like to thank Dr. J. B. Bates of Oak Ridge National Laboratories and Dr. Herbert Engstrom of Magnetic Peripherils, Inc. for their help in the development of the phase synchronous detection systems as well as many useful discussions and suggestions during the course of this work. The work was supported by NSF, MRL Grant DMR 80-20249.
15. 16.
553 (1978);
17.
A. Imai and M. Harata, Japan J. Appl. Phys., 11, [2] 180 (1972).
18.
M. S. Whittingham and R. A. Huggins, J. Electrochem. Sot., 118, 1 (1971).
19.
S. J. Allen, A. S. Cooper, F. DeRosa, J. P. Remeika, and S. K. Ulasi, Phys. Rev., B17, 10, 4031 (1978).
DEDICATION
This paper is dedicated to the memory of Dr. Haroid tlarrison who passed away unexpectedly on June 22, 1985. Dr. Harrison was a prime contributor in the area of crystal growth and was a key member
S. Chen, D. R. White, H. Sato, C. J. Sandburg, and H. R. Harrison, Proceedings of the Conference on High Temperature Solid Oxide Electrolytes, Brookhaven National Laboratory, Department of Applied Science, Vol. 2, 121 (1983). S. (-:hen, D. R. White, H. Sato, J. B. Lewis, and W. R. Robinson, J. Solid State Chem., in press. D . B . McWhan, P. D. Dernier, C. Vettier, A. S. Cooper, and J. P. Remeika, Phys. Rev., t317, 4043 (1978).
608
IONIC CONDUCTIVITY MEASUREMENTS OF DOPED ;3-ALUMINA COMPOUNDS
D.R. WHITE,* S. CHEN,** M. SANKARARAMAN and H. SATO School of Materials Engineering, Purdue University, West Lafayette, IN 47907, USA
The temperature dependent conductivity of Co-stabilized tY'-alumina, Co and Ni-doped t3-aluminas, pure ;3-alumina, and K+--exchanged Ni-doped i3-alumina has been measured and compared betwen 25°C and 600°C. The analysis was made by means of phase-synehronous detection system in the frequency range 100 Hz to 10 MHz. From these measurements it was found that the doped ~3-alumina compounds had consistently higher conductivity than comparable undoped material, although still not quite as high as their stabilized ~"-alumina counterparts. It was also found that Co-stabilized/3"-aluminas displayed a break in the eonduetivity curve, previously reported only in Mg-stabilized ~T'-alumina. Doped /3-aluminas also displayed non-linear conductivity eurves showing a slight bending around 200°C.
1. I N T R O D U C T I O N The majority of investigations of the electrical pro-
perties of p
ously reported the results of the compositions and structures of these compounds. 3 5 Ilere, we conclude this work with their electrical characterizations. 2.
EXPERIMENTAL
Single crystals of cobalt and nickel-doped 3aluminas were prepared by means of skull melting technique as h~s been described in the previous publications. 3'4 Single crystals of ('o-stabilized 3"-abmfina.~ were prepared by a flux growth method following the procedure reported by Mc\Vhan, et al. s and were reported in detail by ('hen, et al. 5 Specimens cff pure (undoped) /~-ah)nlina were obtained froth the Oak Ridge National Laboratory. 7 Samples ['or c(mductivity Ineq.snrements were (.ui from large anti optically clear single crystals into a parallelepiped shape, and these were then pretreated in molten N a N O 3 to remove impurities from |he conduction planes (Note: a few samples were i,mexchanged in KNO 3 to prepare K+-,'~-alumina). Thin fihns of platinum were sputtered ( 25 ttm thickness) ()tit() the appropriale sides of the samples for ole(.trieal contacts. All specimens were stored in a vacuum desi<'ator prior to n l e a s u r e l n e n t .
*Present Address: l,anxide Corporation, Newark, Delaware 19711.
*'Present Address: Research Laboratories, Eastman-Kodak Company, Rochester, New York 1467D. 0 167-2738/86/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
609
D.R. White et aL / h)tlic conductivity measurements
Ionic conductivity measurements were made by means of phase synchronous d e t e c t i o n / c o m p u t e r modelling technique. 8-1° This data acquisition and analysis system is fully automated under the control of an ITP9836 mini-computer. The measurements are made by measuring the response {phase shift and amplitude difference) of the samples from an A C signal (100 ttz to l0 Mttz) by an HP3040A network analyzer. The system is calibrated to compensate for stray, real and imaginary, components unique to the test cell over the entire frequency band and over the temperature range 2 5 ° C - 6 0 0 ° C . All samples were allowed to bakeout in the test cell under a vacuum (10 mTorr) for three hours at 600°C prior to the measurement run. The data analysis for each temperature scan was carried out using a least squares fitting routine in which the DC resistance of the crystal is one of the fitting parameters. The fitting function is based, in part, on an equivalent circuit model representing the electrical response of the sample. The model giving the best fits consists of a resistor (R) and a non-Debye capacitor u C r in parallel with an Debye capacitor C {Figure l). In this model the resistor represents the DC resistance of the crystal, due primarily to the ionic motion in the conduction plane; while the non-Debye capacitor represents the combined dielectric response of the conduction plane and the electrode/electrolyte interface, m'12 The parallel capacitor represents the dielectric response of the spinel blocks which separate the conduction planes. The assumption that the spinel block's should be modelled as an ideal capacitor in parallel with the more common resistor-capacitor
C
ft v ---tllllll FI
C'
F I G U R E 1. Equivalent circuit for single crystalline fl-aluminas, consisting of a capacitor C in parallel with a resistor R, and a non-Debye capacitor C.
model is both consistent with the structure of the ,8aluminas and the dielectric behavior of spinels (i.e., low loss dielectric). 3. R E S U L T S A N D D I S C U S S I O N The results of the conductivity measurements are summarized in Figure 2. The activation energies, pre~ factors, and conductivity values at 25°C are given in Table 1. Note that the activation energies and prefactors for most of the materials are taken at high and Iow temperature regions due to the non-linearity of their conductivity curves. Table
1. Summary of data from conductivity
measurements of B-alumina compounds Compound "Pure B-alumina
0.142 + 0.002
ao [fFlcmqK) 2100 ___+13
Co2+-doped fl-alumina
0.139 + 0.001a 0.172 ~ 0.002b
4023 + 106a 9379-+- 626b
0.039
Ni2+-doped B-alumina
0.133 + 0.002a
3666 + 126a
0.028
0.203 ~ 0.001 b
22306"~ 857 b
Co2+-stabilized
0.060 + 0.003a
1816 __+90a
B'-alumina
0.154 + 0.001 b
15520 ~ 581 b
0.327 +_ ,002
14260 + 535
(K} Ni2+-doped B-alumina
•l
E~(eV)
¢r25.c l] rein l 0.028
0.131 ---
From high temperature data {-T>200°C}. From low temperature data (-T<200°C}.
As can be seen, the Co-stabilized f l ' - a l u m i n a sample had /he highest conductivity of the materials measured, with a value of 0.131 f] 1 cm-I at 25°C. This value is also one of the highest values reported for all /~-alumina type compounds. One of the most interesting features of this curve is its non-Arrhenius behavior, as is evident by the sharp hreak in the curve around 225°C-250°C (Fig. 3). This response is similar to that reported for Mg-stabilized /~"-alulnina l° and has been attributed to the development of ordering between ions and vacancies in the conduction plane.t3 16 Although the exact mechanism responsible for this hehavior is not understood, it is assumed that it is most likely the same in these two forms of fl"aluminas. Ni- and Co-doped fl-aluminas show the next highest conductivity values which are almost identical except for yet low temperature regions. As can be seen, these compounds exhibit " i m p r o v e d " conductivities over that of the undoped fl-alumina. This
610
D.R. Whit(, et al.
/ Ionic ('rmductirity measttr('nw~tts more "ol)en" path for ionic motion. Also at)parent from these curves is a gradual but distinct bending b(,giiming ar()un(t 200~'C-180°C as shown in Figures .I and 5. This curvature is most evident in Ni-dot)ed //alulnina, rausing its curve to intersect that of [lure /Calumina around 25%: in Figure :2. The reason for this non-Arrh('nius response is n(>t clear at. (his moment: however, it is most likely (lue (o (he deveh)pment ()f sh(~rt-range ()r(lering in the conduction plane with decreasing temperature. "].'he reason )hal this is ()bserved in the dol>e(l ~J-alumina samples and not in Áhe pure .)'-aluminas may I)e related (() (he "()p(,nn(,ss" ()f the c())lducti(m plane, which allows this ()r(h,ring phen()lll('n()n l ( ) ( ) c c u r ( o a greater ( , x l e n t ill t h e d ( , p e d
IEMPERRTURE (*C) ii
10
41~B
: ;t
_
• e
~19~
I
11~
f~
25
I
I
I
1
~I•AAA
A
x
~
&&
7 e 1~ ~
\ •,,
) , , . ' ~ .l l/ . tx .x.~i. ®
b,
x x
+"
•
1
b
2.0 1000/T (K -~)
3.0
('()Ill p ( ) l l II (t>;.
lrl(~I'I~ F 2. •
.
.
(
o +
.
.
TEMPERATURE
,,
('on(luctlvlt'¢ lih)t eolnparmg; (a) . (4)- -stabfl)zed ;4• , o+ ,)+ alununa, (b) ( o - -doped 3-alumlna, (c) Nl- -(Io~ed ;~-aluinina ((1) pure p'-alunlina (e) (pc)tassiuln) Ni "+doped /~-alumina behavior is, however, in agreement with other published values of doped /3-aluminas.''<17 As wz~s previously men(toned, this is thought to be due t() the removal of bridging oxygens in t h e c o n d u c t i o n p l a n e by a charge c()mpensation mechanism, which creates a
4~0
2~
[°E) I~8
lgg
\ 2.0
25
50
3.0
l~lal~/T
:4"4"..4. .
I
E
TEMPERFITURE {°El 2BRI
2S
I
"rue 10 ~ -.?
10 ~ 4,B0
50
I
(K -l}
I"I(',I 7I~l'; .l. • ,) +
"7 "7 E
.12 o
1182 b
N"I \
-I---~ 2.0
I
,
('(,I)(luctivity plot ()f Nl" -(I()i)((I ,>Lnlumin:t saml)h'. from skull melt gr(>wlh. Th(' p(>tassium-exchanged Ni-doped /:)-alumina samph!s gave the lowest conductivity values and Ill(, highest activati(m energies of all specimens. This dala is consistenl with other reports in the lileraturv for pot assium-ex changed /3-alulninas. 18,Lq
3.~
1000/T [K -~1
FIGITRE 3. Conduelivity plot of Coe+-stabilized /~'-alumina sample, from flux melt growth.
It should be pointed out Áhat, during (he course (,f the
nleasurelllPnts,
sev(,r31
att0iiipts
werP
ii/ade
to
c()mpare Ill(' lits ()blained from lhe equivah,nt circuit inodel shown in Fig. !, and that ()f the more c(unmon resistor and non-I)ebye capacitor 11 in series. Alth(mgb w'ry li(lh' (lifference in the abs(>lute c(mducli~ilv and
D.R. White et al. / Ionic conductivity measurements
TEMPERRTURE C°C] 41W
21~
llm
,~
25
611
of our team to develop the skull melting technique for the preparation of the wide variety of ~-Mumina compounds used in this work. REFERENCES
T
E U
T
10a
1.
W . L . Roth, F. Reidinger, and S. LaPlaca, "Stu(ties of Stabilization and Transport Mechanisms in /3 and y ' - A l u m i n a by Neutron Diffraction," in Superionic Conductors, 223, Ed. by G. D. Mahan and W. L. Roth, Plenum Press, New York, 1976.
2.
W. L. Roth, Trans. Am. Cryst. Assoc., 11, 51 (1975). I). R. White, S. Chen, ti. R. I~Iarrison and It. Sato, Solid State Ionics, 9-10, 225 (1983).
F tO I---
b
!
10
I
I 2.0
t
I
3.~
3.
1000/T (K-h
4. FIGURE 5. Conductivity plot of Co'°+-doped ¢~-alumina sample, from skull melt growth. 5. the activation energy values was found, the quality of the fits showed a marked improvement, especially at high frequencies ( > l Mllz), with the additional parallel capacitor. This may indicate that the often overlooked spinel blocks may influence, albeit slightly, the AC measurenlents of the fl-aluminas. (Note: the test cell calibration assumes a stray parallel capacitance due to the cell configuration and therefore is accounted for in the final conductivity analysis and is not related to the conductivity model described).
6.
7.
Courtesy of J. B. Bates.
8.
D. R. White, Ph.D. Thesis, Purdue University {19851. It. Engstrom and a. C. Wang, Solid State lonics, 1, 4:tl {1980).
9.
1O. II. Engstrom, J. B. Bates, W. E. Brundage, and J. C.. Wang, Solid State Ionics, 2, 265 (1981). ll.
A. K. Jonscher, J. Mat. Sei. ~ Phys. Stat. Sol. (a) ~ 665 (1975).
12.
J. P. Bates, Oak Ridge National Laboratory, private communication (January 1985).
13.
J . P . Boilot, G. Collin, P. tt. Collomban, and R. Comes, Phys. Rev., 1322, 5912 (1980).
14.
J. B. Bates, H. Engstrom, J. C. Wang, B. C. Lauson, N. J. Dudney, and W. E. Brundage, Solid State Ionies, 5, 159 (1981). J. C. Wang, J. B. Bates, N. J. Dudney, and H. Engstrom, Solid State lonics, 5, 35 (1981). H. Sato and R. Kikuchi, J. Physique, C7, 159 (1977).
ACKNOWLEDGEMENTS
We wish to thank Dr. Harold Harrison for his help in the preparation of materials. We would also like to thank Dr. J. B. Bates of Oak Ridge National Laboratories and Dr. Herbert Engstrom of Magnetic Peripherils, Inc. for their help in the development of the phase synchronous detection systems as well as many useful discussions and suggestions during the course of this work. The work was supported by NSF, MRL Grant DMR 80-20249.
15. 16.
553 (1978);
17.
A. Imai and M. Harata, Japan J. Appl. Phys., 11, [2] 180 (1972).
18.
M. S. Whittingham and R. A. Huggins, J. Electrochem. Sot., 118, 1 (1971).
19.
S. J. Allen, A. S. Cooper, F. DeRosa, J. P. Remeika, and S. K. Ulasi, Phys. Rev., B17, 10, 4031 (1978).
DEDICATION
This paper is dedicated to the memory of Dr. Haroid tlarrison who passed away unexpectedly on June 22, 1985. Dr. Harrison was a prime contributor in the area of crystal growth and was a key member
S. Chen, D. R. White, H. Sato, C. J. Sandburg, and H. R. Harrison, Proceedings of the Conference on High Temperature Solid Oxide Electrolytes, Brookhaven National Laboratory, Department of Applied Science, Vol. 2, 121 (1983). S. (-:hen, D. R. White, H. Sato, J. B. Lewis, and W. R. Robinson, J. Solid State Chem., in press. D . B . McWhan, P. D. Dernier, C. Vettier, A. S. Cooper, and J. P. Remeika, Phys. Rev., t317, 4043 (1978).