Phase diagram, crystal chemistry and lithium ion conductivity in the perovskite-type system Pr0.5+xLi0.5−3xTiO3

SOLID STATE IONICS

Solid State Ionics 91 (1996) 33-43

ELSEWIER

Phase diagram, crystal chemistry and lithium ion conductivity in the perovskite-type system Pro.5+,Li,., _ J30, M. Morales’,

A.R. West*

University of Aberdeen, Department of Chemistry, Meson Walk, Aberdeen AB9 2lJE. UK Received

13 September

1995; revised 22 May 1996; accepted

31 May 1996

Abstract The stoichiometry, polymorphism and electrical behaviour of solid solutions Li,5_3xPr,,+,Ti0, with perovskite-type structure have been studied. Data are shown in the form of a phase diagram, XRD patterns for the three polymorphs, A, C,

and p, temperature- and composition-dependence of their lattice parameters and Arrhenius conductivity plots. Microstructure and composition were studied by electron probe microanalysis. Maximum conductivity is 4 X 10e6 S cm-’ at 25°C for x = 0.08. An insulating surface layer, seen in samples coated with Au electrodes, disappears in contact with molten LiClO,. Keywords: Perovskite-type

systems;

Phase diagram;

Crystal chemistry;

1. Introduction Research on solid ionic conductors is important to develop solid state lithium batteries. Several studies have focused on the doping of compounds such as Li,XO, and Li,YO, (X = Si, Ge, Ti; Y = P, As, V) [l-6] to give non-stoichiometric materials with structures related to y,r-L&PO4 and y-Li,ZnGeO,. Among such materials, Li,,,V,,,Ge,.,O, [7] has the highest Li+ ion conductivity at room temperature, 4 X lop5 S cm-‘. Recently, fast ion conductors with perovskite-like conductivity structure and higher than Li,,,V,,,Ge,,,O, have been reported [&lo]. These have a general formula Li,,,_,,RB,,,+,TiO,, where RE is a rare earth such as La, Pr, Nd, and Sm

Lithium

ion conductivity;

Stoichiometry

[ 11,121. The maximum conductivity is found in the lanthanum system, with a value 1.1 X 10m3 S cm-’ at 25°C for composition x = 0.07 [9]; more recently, the phase diagram and crystal chemistry of the systems: Li,,_jxREo,5+l TiO, with RE = La, Nd have been reported [ 131. The aim of the present work has been to investigate the stoichiometry range, thermal stability, crystal chemistry and electrical behaviour of corresponding materials with RE = Pr. One particular problem observed with all these materials which could limit their potential use is the presence of large resistances in series with the low resistance of the bulk material; a method to eliminate this resistance is also investigated here.

2. Experimental *Corresponding author. ‘Permanent address: Universitat de Barcelona, Dept. Quimica Inorganica, Barcelona, Spain. 0167-2738/96/$15.00 Copyright PII SO167-2738(96)00420-l

01996

Pr,O, , (99.9% Janssen Chimica), 99 + %) and Li,CO, (BDH 99%)

Elsevier Science B.V. All rights reserved

TiO, (Aldrich were used as

34

M. Morales,

A.R. West I Solid State Ionics 91 (1996) 33-43

starting materials. Pr,O,, and TiO, were dried overnight at 900°C prior to weighing. It was assumed that during reaction, Pr,O, , lost oxygen to effectively be considered as Pr,O,. These chemicals were weighed, mixed in an agate mortar with acetone, dried and heated at 700°C for 2 h to drive off CO,. After grinding, samples were pressed into pellets and covered with powder of the same composition to avoid losing lithium during thermal treatment. The pellets were fired at 1150°C for 12 h giving green products which were reground, repelleted and fired at 1250°C for 12 h. A further treatment was carried out on samples with 0.10 I x < 0.12 at 1300°C and x = 0.13, 0.14 at 1400°C for 4 h. For phase diagram studies, small pelleted samples were wrapped in platinum foil envelopes, placed in a furnace and annealed isothermally for 30 min in order to reach equilibrium. Finally, they were removed from the furnace and quenched to room temperature on a brass plate. Crystalline phase identification was carried out by powder X-ray diffraction, XRD, with a PhilipsHagg-Guinier camera, CuKo 1 radiation. Lattice parameters were obtained using a Stoe Stadi diffractometer in transmission mode with a small linear position sensitive detector (psd), Ge monochromator and CuKo, radiation. Data were collected over the range 10” I 28 I 120”, with Si as external standard. Stoichiometry and homogeneity of selected samples was checked by electron probe microanalysis using a Cameca SX51 EPMA instrument. Electrical measurements were carried out using a Hewlett-Packard 4192A impedance analyzer and Solar&on 1250/ 1286 frequency response analyser over the range 3 X lop2 Hz
3. Results and discussion 3.1. Phase diagram The join Li,,,Pr,,,TiO,-Pr,,,TiO, in the system Pr,O,,-Li,O-TiO, was chosen for a detailed study since Li+ ion conducting perovskites were reported to have compositions that lay on this join [9-l 11. All attempts to synthesise single phase perovskite-like

materials outside this join yielded multiphase materials. This join was studied by synthesising compositions of general formula Li,,S_3xPr0.5+xTi03 and annealing at different temperatures. The appropriate heating conditions to yield equilibrium products were found by trial and error. The results were used to construct the phase diagram shown in Fig. 1. A large range of perovskite-like solid solutions forms along this join. Single phase materials form over the range 0.02 0.14 a mixture of p, Ti,Pr,O, and TiO, was observed. The polymorph A forms only at high temperatures for x I 0.11; the minimum temperature at which it is stable on the phase diagram is 1050°C for composition x = 0.05; to either side it forms only at higher temperature. Although phase A is stable only at high temperatures, it can, nevertheless, be readily preserved to room temperature by quenching. The polymorph C forms over a short region, x < 0.05, from about 1000°C to 14OO”C, but it is also readily quenched to room temperature. The transition between C and A, Fig. 1, shows continuous character. Some powder XRD lines of the C polymorph show splitting (Fig. 2, Fig. 3) which increases on moving away from the C-A phase boundary. The low temperature polymorph p extends along the whole range of compositions, 0.025 < x < 0.145; its upper temperature of stability increases with x and it appears to be the only phase present for 0.12<1<0.145. Narrow regions of transitional character separate the phase fields of A and p, and of C and p. These are characterised by XRD patterns, in which either the reflections of A remain unsplit and lines of p appear broadened or in which both split reflections of C and broadened lines of p are observed. These regions became narrower as the phase transition temperature increases, Fig. 1. 3.2. Crystal chemistry The three polymorphs, A, C, and p have perovkite-related structures as judged by similarity in their XRD patterns, Fig. 4. Differences between the

M. Morales,

A.R. West I Solid State Ionics 91 (1996)

35

33-43

0 c1

A

c

-_---A

0

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

X

Fig.

~

1. Phase diagram of the system Pr, ,+ILi, ,_,,TiO,.

(2 4 0)/o/(04 2) pz;>\,C\23)

a

/

\

,’

(2 4 OY(O 4 2) (1 2 3) \

(321)~’

:

c

(3 2 (2 .4 0) (0 4 2b ?, /_

* 3)

I

/

i’

/’ \

~------!~,~~I~~~~~~,’ 58.25

ss.50

_L- ._. ,,/

58.15

2@

59.00

~~. --

59.25

59.50

Fig. 2. Evolution of reflections (3 2 1). (2 4 0), (0 4 2) and (1 2 3) vs. composition of polymorph C for samples heated at 1100°C then quenched to room temperature: (a) x = 0.05; (b) x = 0.04; (c) x = 0.03.

phases are confined to various line splittings and the presence of additional lines in the C and p phases. Polymorph A appears to be a simple cubic perovkite, Table 1. Its cell volume increases in a significantly non-linear way with decreasing lithium content, Fig. 5. The polymorph C (Table 2) is an orthorhombic distortion of A, with an approximately 4 times larger unit cell. The cells of A and C are related by: a = d2a, + 6, b, = 2a,, and c, = d2a, - S, where aI is the cell parameter of the cubic A phase and 6 is the degree of orthorhombicity. The orthorhombicity 6 is both compositionand temperature-dependent. Figs. 2 and 3 show directly the splitting of the 321,123 and 240,042 reflections associated with the orthorhombicity parameter, 8. Studies by neutron diffraction have shown that the C polymorph in the Pr and Nd systems is an orthorhombic phase, space group: Pbnm [14] with a structure related to compounds such as GdFeO,, La,_,TiO, [15] and (CaZr),-.(LiTa),O, 1161. The polymorph p is a tetragonal perovskite with unit cell: a, = a, - 8, c, = 2a, + A (Table 3), where the tetragonal distortions S and A decrease as temperature increases, becoming zero close to the stability region of polymorph A, Fig. 6.

36

M. Morales,

L-

58.25

A.R. West f Solid State Ionics 91 (1996) 33-43

-I 58.50

58.75

28

59.00

59.25

59.50

Fig. 3. XRD pattern in the region of overlapping reflections (3 2 I), (2 4 O), (0 4 2) and (1 2 3) of Pr, 53Li0 4, TiO, polymorph from 1100°C: (a) experimental and fitted data; (b) fitted profile and individual peaks.

C quenched

a

__ I__ b

LL--

_Ll-

!

AL 25.0

soil

75:o

100:0

20

Fig. 4. XRD patterns of: (a) Pr,,,,Li, 26Ti03 quenched from 1250°C (polymorph C); (cc) Pr,,,Li,,,TiO, quenched from 1100°C (polymorph @).

A); (b) Pr, ,,Li,,,

TiO, quenched

from 1100°C (polymorph

M. Morales, Table 1 X-ray powder diffraction 1200°C (phase A) k

h 1 1

1 2 2 2 2 3 3 3 2 3 4 4

0 1 1 0 1 1 2 0 1 1 2 2 0 1

data for Pr, ,,Li,,,,TiO,

1

d “hr

0 0 1 0 0 1 0 0 0 1 2 1 0 1

quenched

d,,,,

3.8405 2.7171 2.2189 1.9214 1.7187 1.5690 1.3588 1.2812 1.2153 1.1587 1.1095 1.0273 0.9608 0.9060

3.8434 2,1177 2.2190 1.9217 1.7188 1.5691 1.3589 1.2811 1.2154 1.1588 1.1095 1.0272 0.9609 0.9059

from

57OI---

0.06

0.09

0.10

1

d “h%

d,.,,,.

III,

5 100 19 35 3 38 15 2 11 2 4 12 2 5

0

0

3.8390 3.8329 2.7191 2.7119 2.7052 2.3065 2.2182 2.2099 1.9173 1.7180 1.7146 1.7106 1.5687 1.5668 1.5642 1.5622 1.3599 1.3557 1.35 14 1.2143 1.2127 1.2123 1.2102 1.1581 1.1558 1.1093 1.1047 1.0273 1.0264 1.0257 1.0236 0.9592 0.9584 0.905 1 0.9039 0.9027

3.8359 3.8342 2.7193 2.7118 2.703 1 2.3084 2.2 184 2.2096 1.9180 1.7188 1.7148 1.7106 1.5685 1.5673 1.5642 1.5623 1.3596 1.3559 1.3516 1.2146 1.2130 1.2125 1.2103 1.1580 1.1559 1.1092 1.1048 1.0274 1.0262 1.0259 1.0236 0.9590 0.9585 0.9049 0.9039 0.9025

2 4 20 100 25 2 12 12 53 2 1 2 15 10 13 17 3 13 2 5 5 5 2 1 1 2 2 2 2 2 2 1 2
0.11

Pr 05+xLi 053XTiO,

Fig. 5. Cell volume vs. composition from 1350°C.

3.3.

Electron

probe

of phase A; samples quenched

microanalysis

from

k

>

0.07

quenched

2 0 0 2 0 1 2 2 4 0 2 0 2 4 4 2 0 4 0 0 6 2 0 2 6 4 4 2 4 6 4 8 0 2 6 2

%

0.06

data for R, ,,Li, ,,TiO,

h

1

005

Table 2 X-ray powder diffraction 1100°C (phase C)

III,,

Cubic system: a, = 0.38434( 1) nm, V= 0.05677( 1) nm3, Z = 1. Silicon was used as external standard.

004

31

A.R. West I Solid State Ionics 91 (1996) 33-43

(EPMA)

Some samples along the join Li,,,Pr,,,TiO,Pr,,,TiO, were studied by EPMA to obtain both element analyses and elemental maps. Elemental analyses were carried out with a fixed beam of 15 kV and 20 nA over 10 different points on the sample surface, with SrTiO, as the standard for Ti, 0 and PrF, for Pr. Lithium content could not be obtained directly but could be calculated assuming an oxygen content of 3 and valencies 3 + and 4 + for Pr and Ti, respectively. The elemental maps of Ti, Pr and 0

1 2 1 0 1 2 0 0 3 2 1 3 2 0 1 4 2 0 4 1 3 2 4 0 4 0 5 4 3 2 0 4 5 3 3

1 0 1 2 2 0 2 0 1 2 3 1 0 2 3 0 2 4 2 1 3 4 2 2 0 4 1 2 1 4 0 4 3 3 5

Orthorhombic system (S.G.: Pnma), a0 = 0.54384(5) nm, b, = 0.76716(7) nm, c, = 0.54064(5) nm, V= 0.22556(2) nm3, Z = 8.

were produced with an electron beam of 15 kV and 20 nA. Elemental maps were obtained for three samples on the join: two outside the single phase region, Fig. 1, x = 0.02 and x = 0.15, and one inside, x = 0.08. Back-scattered electron, BSE, images of x = 0.02 and x = 0.15, Fig. 7a and c, showed the presence of at least two phases. In (a), a greyish area for the majority_ phase corresponds to a perovskite compound; the darker area for x = 0.02 was richer in Ti,

38

M. h4orales, A.R. West / Solid State Ionics 91 (1996) 33-43

Table 3 X-ray powder diffraction 800°C (phase p)

0

0

0

0

1 0

0

1

0

1 0

1 0 1

I 1 0 0 0 1 0 1 2 1 1 1 0 0 1 0 2 2

1 3

1 1 2 1 1 1 2 1 0

1 Tetragonal 0.11347(2)

1

1 1 0 2

1 2 0 0 2 1 2 2 1 2 2 2 2 0 0 3 2 2 3 2 3 3 1 3 4

1 2 0 1 2 0 3 1 2 3 4 0 3 1 4 2 1 4 2 3 5 3 4 0 1 6 2 1 5 4 3 6 4 2 8 6 2

a

data for Pr, s,Li, ,,TiO,

7.7279 3.8623 3.8319 3.4333 2.7200 2.7103 2.5743 2.5573 2.2184 2.1369 1.9306 1.9165 I .8665 1.8599

1.7239 1.7161 1.6735 1.5725 1.5667 1.5373 1.4326 1.4266 1.3601 1.3551 1.3350 1.2202 1.2126 1.1980 1.1474 1.1092 1.0966 1.0292 1.0267 1.025 1 0.9094 0.9067 0.9038

quenched

7.7226 3.8613 3.8332 3.4335 2.7203 2.7105 2.5742 2.5575 2.2185 2.1370 1.9306 1.9166 1.8665 1.8602 1.7243 1.7167 1.6735 1.5725 1.5667 1.5375 1.4326 1.4268 1.3602 1.3552 1.3348 1.2201 1.2130 1.1975 1.1475 1.1092 1.0967 1.0293 1.0266 1.0250 0.9094 0.9068 0.9038

system: a, = 0.38332( 1) nm, c, = 0.77226(4) nm3, Z = 2.

(1 12)

from

52 3 5 41 100 63 6 14 23 6 16 35 12 4 2 2 10 20 37 5 5 3 15 8 1 7 11 3 4 6 4 7 7 7 2 2 4 nm, V =

as shown by the light regions in the Ti elemental map, Fig. 7b and is attributed to Li,TiO,. In (c) the grey background is, again, the majority perovskite phase, the black areas are pores and the lighter specks are richer in Pr, as shown by the light regions in the Pr elemental map, Fig. 7d, attributable to Pr,Ti,O,. In the sample x = 0.08, only one phase, having a homogeneous elemental distribution (Fig. 7e-h) was found; dark areas represent porosity.

,’

b (I

I 4Y(l

, 58.25

S8.So

2 2)

-

~--~---~.

58.75

59.00

_~-_ 59.25

59.50

28 Fig. 6. Evolution of reflections (1 1 4) and (1 2 2) vs. annealing temperature: (a) 1200°C [phase A-reflection (1 1 2)]; (b) 1150°C [phase PI; (c) 800°C [phase PI. Data recorded at room temperature, for composition x = 0.08.

The results of in Table 4. These expected values contents showed Table 4.

elemental analyses are summarised values are in good agreement with of starting compositions. Oxygen larger deviations as indicated in

3.4. AC measurements These measurements were carried out from 25°C to 200°C for compositions 0.03 5 x % 0.09. Two semicircles and a spike were observed in the impedance complex plane plots. The centres of the semicircles were clearly depressed below the baseline, indicating a non-Debye response for these materials [17]. This kind of response has been detected in other ionic conductors [ 18-201. An equivalent circuit, Fig. 8, with two RC and two constant phase elements, CPE [21], has been used to fit the high frequency data; these elements are assigned to bulk and grain boundary responses. An additional CPE element was used to model the low frequency spike; all fitting used the Zview [22]

M. Morales,

A.R. West I Solid State Ionics

91 (19%)

33-43

39

Fig. 7. BSE images and elemental maps for Pr, ,+,Li, ,_,,TiO,: (a) BSE, x = 0.02; (b) elemental map of Ti, x = 0.02; (c) BSE, x = 0.15; (d) map of Pr, x = 0.15; and (e) BSE, (f) map of Ti, (g) map of Pr, (h) map of 0 for x = 9.08. In the elemental maps, elemental concentration is proportional to brightness.

M. Morales, A.R. West I Solid State Ionics 91 (1996) 33-43

40

Table 4 Elemental

analyses

by EPMA of Pr,,+,Li,,_,,TiO,

samples

Pr,,,+J4,,,-,~TiO,

Starting

X

Pr

Ti

Li

Pr

Ti

0”

0.04 0.06 0.07 0.08 0.09 0.10

0.54 0.56 0.57 0.58 0.59 0.60

1.OO 1.00 1.00 1.oo 1.00 1.00

0.38 0.32 0.29 0.26 0.23 0.20

0.54(2) 0.564(8) 0.57( 1) 0.579(8) 0.59( 1) 0.596(5)

1.00(3) l.OO( 1) 1.00(2) 1.00(l) 1.00(2) 1.00(l)

2.83( 10) 2.84(6) 3.10(6) 2.94(4) 2.93(7) 2.91(4)

compositions

Experimental

values (EPMA)

d Experimental values of oxygen contents have larger uncertainty than values for Pr and Ti due to the difficulty in separating the OKa signal from that emitted by the carbon coating and partial absorption of the OKo signal by the carbon. Expected oxygen contents are 3.00; experimental values are within 2-3 esds of the expected value.

Fig. 8. Equivalent circuit for fitting AC data; parameters for Pr,) sIILiO26Ti03 at 50°C.

listed are

0

software package, with a typical set of fitted results shown in Fig. 9. Capacitances for each component were 3 pF, 6 nF and 0.1-0.05 ~_LF,respectively. The first and second values indicate a bulk and grain boundary response [23]; the third capacitance is probably too small for it to be related to an electrode-sample double layer and is probably linked to a low conductivity layer on the pellet surface. The impedance response of this layer depended somewhat on sample history: a well-resolved, almost vertical spike in the complex impedance plane was observed only after the pellet with electrodes attached, had been heated to > 100°C. At lower temperatures, but only for pellets that had been exposed to the atmosphere for a few days, the nearly vertical spike had, instead, a much lower slope and took the form of either a poorly-defined Warburg impedance, or a distorted semicircle(s). For samples

2.5x10’

5.0x10J Z’ i Qcm

Fig. 9. Plots of {Z” vs. Z’} and as inset, {Y’. Y” vs. log f} for Pr, s,LiO 26TiO, at 50°C: 0 experimental and n fitted.

that had been recently heated to > 100°C the vertical spike was retained to lower temperatures in the impedance plots, with an essentially unchanged capacitance value. These initial results, with Au electrodes, were reminiscent of similar phenomena seen with palumina single crystals [24]: in dried samples, a vertical spike was seen with capacitance 0.01-0.1 p,F and on exposure to moisture, the spike collapsed into a poorly defined semicircle. Those results were attributed to the presence of a Na’free layer on the crystal surface, which, in the absence of moisture was insulating but which became conducting, presumably due to protons, on exposure to moist air. It

M. Morales,

In order to investigate further the origins of the low frequency spike, measurements were carried out with electrodes of carbon felt soaked in a solution of anhydrous 0.5 M LiClO, in polypropylenecarbonate (PC). The impedance data showed bulk and grain boundary responses as before and a spike, as before but inclined at -40” to the Z’ axis and with a capacitance value several orders of magnitude larger, -0.1 mF, Fig. 10. Taking into account the large surface area of the carbon electrodes and the fact that the LiCIO,/PC liquid provides an intimate contact with both the pellet surfaces and the carbon, these high capacitance values are attributed to double layer phenomena rather than to electrochemical decomposition reactions, consistent with conduction by Li+ ions. The disappearance of the low capacitance vertical spike is attributed to wetting of the resistive, Lit-free surface layer on the pellet, primarily by in-diffusion of Li’ ions; the detailed mechanism is, however, notknown. Bulk conductivity data extracted from the impedance complex plane plots are shown in Arrhenius format in Fig. 11. Plots are linear and the conductivity is highest and activation energy lowest for x = 0.08, with conductivity value at 25°C of 3.8 X

therefore seemed that in the present materials, a Li+-deficient or Lie-free surface layer may be present whose electrical properties depended greatly on the presence or absence of moisture. -2000

- 1500

-1000 E c: .I

”

N -500 -

. . Frequency (Hz)

0 0

f ..

..

.I 2.

0

5001 0

’

’

500

’

’

I

1000

’

1500

1

’

’

2000

1

2500

Z/C&m

Fig.

10. Plots of {Z” Pr,.,,Li, 29TiO, at 250°C graphite electrodes. High when data fall below the

vs. Z’} and {E’, E” vs. log f} for using: 0 Au electrodes and n LiCIO,/ frequency data show inductive effects Z” = 0 axis.

-4 L 2.0

41

A.R. West / Solid State Ionics 91 (1996) 33-43

-_ 2.4

2.8 1000/l

Fig. 11. Arrhenius

conductivity

(l/K)

plots of Pr, ,+,Li, ,_,xTiO,.

3.2

M. Morales, A.R. West I Solid StateIonics91 (1996) 33-43

42

L

$02

0.03

_--

0.04

0.05

0.06

-------A47 0.07

0.08

0.09

0.10

X

Fig. 12. Activation

energy (e,) and conductivity

lop6 S cm-‘. The variation in conductivity with composition, Fig. 12, is quite small compared with the analogous lanthanum system in which a large variation has been observed [9].

4. Conclusions Single phase solid solutions have been synthesised in the Pr0.5+XLi0.5-3XTiO, system over the composition range, 0.02
at 25°C vs. composition

in Pr,,,+xLi,, ,_,xTiO,.

surface layer was replaced by a much larger, - lop4 F, electrode spike. The large value of this capacitance is attributable to the high surface area of the porous graphite electrode. The maximum conductivity in this system was 3 X lop6 S cm-r at 25°C for the composition TiO,. The nature of the electrode rePr0.,,Li,.,6 sponse indicates that the level of electronic conduction is negligibly small, and therefore, conduction is by means of Li+ ions.

Acknowledgments The authors thank Dr. A. Pappin for supplying LiClO,/carbon electrode, Dr. A. Coats for her advice on the EPMA, and EPSRC for financial support of the Electron Probe. This work was sponsored by the Ministerio de Education y Ciencia (Spain) through a fellowship to Manuel Morales.

References [l] H.Y.P. Hong, Mater. Res. Bull. 13 (1978) 117. [2] M.A.K.L. Dissanayake and A.R. West, .I. Mater. Chem. 1 (1991) 1023. [3] A.D. Robertson and A.R. West, Solid State Ionics 58 (1992) 351. [4] J.T.S. Irvine and A.R. West, in: High Conductivity Solid Ionic Conductors: Recent Trends and Applications, ed. T. Takahashi (World Scientific, Singapore, 1989).

M. Morales,

A.R. West I Solid State Ionics 91 (1996) 33-43

[5] M.A.K.L. Dissanayake, R.P. Gunawardane, H.H. Sumathipala, G.K.R. Senadeera, PW.S.K. Bandaranayake, M.A. Careem and A.R. West, in: Solid State Ionic Material, ed. B.V.R. Chowdari et al. (World Scientific Press, Singapore, 1994) pp. 199-203. [6] C.K. Lee and A.R. West, J. Mater. Chem. 1 (1991) 149. [7] J. Kuwano and A.R. West, Mater. Res. Bull. 15 (1980) 1661. [8] Y. Inaguma, Chen Liquan, M. Itoh, T. Nakamura, T. Uchida, H. Ikuta and M. Watihara, Solid State Commun. 86( 10) ( 1993) 689. [9] H. Kawai and J. Kuwano, J. Electrochem. Sot. 141(7) (1994) L78. [lo] Y. Inaguma, Chen Liquan, M. Itoh and T. Nakamura, Solid State Ionics 70-71 (1994) 196. [I I] M. Itoh, Y. Inaguma, Woo-Hwan Jung, Liquan Chen and T. Nakamura, Solid State Ionics 70-71 (1994) 203. [12] L.L. Kuchergin, N.B. Bhakhum, N.V. Porotnikov and K.I. Petrov, Russian J. Inorg. Chem. 29(4) (1984) 506. [13] S. Garcia, A.D. Robertson, A. Coats and A.R. West, J. Mater. Chem. 5 (1995) 1405. [14] J.M.S. Skakle, G.C. Mather, M. Morales, RI. Smith and A.R. West, J. Mater. Chem. 5 (1995) 1807.

43

[15] M.J. MacEachem, H. Dabkowska, J.D. Garrett, G. Amow, W. Gong, Guo Liu and J.E. Greedan, Chem. Mater. 6 (1994) 2094. [16] RI. Smith and A.R. West, J. Solid State Chem. 108 (1994) 29. [17] A.K. Jonscher, in: Dielectric Relaxation in Solids (Chelsea Dielectrics Press, London, 1983) Chap. 5. [ 181 D.P. Almond, G.K. Duncan and A.R. West, Solid State Ionics 8 (1983) 159. [19] A.K. Jonscher and J.M. Reau, J. Mater. Sci. 13 (1978) 563. [20] D.P. Almond, C.C. Hunter and A.R. West, J. Mater. Sci. 19 (1984) 3236. [21] J.R. MacDonald, in: Impedance Spectroscopy. Emphasizing Solid Materials and Systems (Wiley-Interscience, New York, 1987) Chap. 2. [22] Zview (ver. 1.2), Graphics and Analysis Software, Scribner Associates, 1994. [23] J.T.S. Irvine, D.C. Sinclair and A.R. West, Adv. Mater. 2 (1990) 138. [24] P.G. Bruce, A.R. West and D.P. Almond, Solid State Ionics 7 (1982) 57.