a __ b

__ 53 SOLID STATE IONICS

ELXYIER Solid State Ionics 91 (1996) 183-190

Impedance-spectroscopy analysis of Ba,Li,Ti,Nb80,, ferroelectric ceramics

Ming Dong, Jean-Maurice Reau”, Jean Ravez

lnstitut de Chimie de la MatiPre Condenke de Bordeaux, 33608 Pessac Cedex, France

Received 13 June 1996; accepted 3 July 1996

Abstract

Tetragonal-tungsten-bronze-type Ba,Li,Ti,Nb,O,, ceramics were synthesized and sintered under different atmospheres. The dielectric properties of such materials were determined via impedance-spectroscopy measurements. Based on an equivalent circuit, the dielectric relaxation was described. The temperature dependence of various dielectrical parameters was also determined and discussed.

Keywords: Impedance spectroscopy; Ferroelectric ceramic; Ionic conductivity

1. Introduction

Impedance spectroscopy has been widely used for investigating the properties of electric materials and

electrochemistry systems. The goals of impedance measurements are the identification of physical pro-

cesses and the determination of various electrical parameters appropriate for the electrical system studied. This requires the selection of a model in agreement with the measurement data. The most commonly used models are equivalent electrical

circuits consisting of resistors, capacitors, inductors and specialized distributed elements.

In a previous work [l], we studied a Li CMKlTa ,,00403 single crystal using the impedance spectroscopy technique. In this crystal, in addition to

*Corresponding author. Tel.: (33) 56846332; fax: (33) 56842761; e-mail: reau@icmcb.u-bordeauxfr

the ferroelectric properties, a modest level of Li + ion conduction occurs at high temperature. The low-

frequency dielectric dispersion is very significant. Based on the measurement data, an empirical com- plex permittivity E*(w) expression

E*(W) = 6, + Es - Ecz

1 + (h/w,)” + $ [ 1 + (iuIq_)n]

(1)

has been deduced for describing the ac electrical response of the crystal, where both of the following polarization mechanisms were considered:

1. The dielectric relaxation (or lattice response) due to the permanent dipole orientations or other motions which do not involve any long-range displacement of charge carriers, characterized by

0167.2738/96/$15.00 Copyright 01996 Elsevier Science B.V. All rights reserved PII SO167-2738(96)00441-9

184 M. Dong et al. I Solid State tonics 91 (1996) 183-190

the relaxation angular frequency (w,) and the dispersion parameter (m).

3. Results

2. The conductivity relaxation (or carrier response) Data directly measured as complex impedance Z*

resulting from the long-range ionic migration were converted into complex resistivity, electric

identified by the relaxation angular frequency modulus M* and complex permittivity E*, using the (w2) and the dispersion parameter (n). relations:

In this work, Ba,Li,Ti,Nb,O,, ceramics have

been synthesized and sintered under different atmos- pheres in order to determine the influence of thermal

treatment on the dielectric and conduction properties. The above expression (Eq. (1)) is applied to analyze the ac impedance data of Ba,Li,Ti,Nb,O,, ceramics for checking its validity.

2. Experimental

In order to obtain Ba,Li,Ti,Nb,O,, ceramics, an appropriate mixture of fine BaCO,, L&CO,, TiO,

and Nb,O, powders is ground and preheated at 1073 K for 4 h and then heated at 1273 K for 12 h in air, or in 0, flow. XRD analysis shows that each

obtained product is a single phase with a tetragonal tungsten bronze structure (a = 12.478 A, c =3.999 A). Synthesized Ba,Li,Ti,Nb,O,, [BLTN] powders

are ground again, put into disk form and sintered in the same atmospheres for the synthesis at 1423 K for 4 h. Furthermore, a disk sintered in 0, current was

finally annealed at 1123 K under 1000 bars 0, pressure for 48 h. The percentage of theoretical density of each ceramic is 8590%. The ceramics

sintered in air [BLTN-a] and in 0, flow [BLTN-o] are pale yellow, and the ceramic annealed under high 0, pressure [BLTN-ho] is of white color. A new XRD analysis shows that the ceramic is the same phase as the synthesized powder. Gold-paste elec- trodes were deposited on opposite faces of the ceramic disks. The electrical measurements were carried out from 300 to 800 K in air or in O,, in accordance with the synthesis conditions. A pre- liminary heating-cooling cycle was carried out to ensure measurement reproducibility. A frequency sweep from 1 to lo6 Hz with a 100 mV nominal applied voltage was achieved using a Solartron-1260 Impedance/Gain-Phase Analyzer.

p* = Z*k = Z*(Sld), M* = iwC,Z*,

c* = 1 l(iwC,Z*) (2)

where S is the area of the gold electrode, d is the thickness of the ceramic, C, is the vacuum capaci- tance and i=(-1)“,5.

Typical complex resistivity p* plots are shown in Fig. 1. At each temperature, only one depressed arc

could be observed; the arcs pass through the origin. The dc resistivity p. and the dc conductivity gddc

(crddc = 1 lpo) could be approximately estimated. One could find that, at each temperature, gddc(aLTN_)=

Odc(BLTN-o) > vddc(BLTN-ho) (Fig’ 2)’

While the complex resistivity plots give emphasis

to elements with the largest resistance, the electric modulus plots highlight those with the smallest capacitance. We present the typical complex electric

modulus plots in Fig. 3. The presence of overlapping arcs in the spectra suggests the existence of several relaxations with different mean time constants in such materials. As M* = 1 /E*, the smallest semicir-

cle in the complex electric modulus plot corresponds to the biggest capacitance. One could see that the biggest capacitance occurs about 643 K, which

implies that a dielectric anomaly may appear about 643 K.

The temperature dependencies of the real permit- tivity (dielectric constant) E’ are plotted in Fig. 4. For each ceramic, one dielectric anomaly was found, which corresponds to the ferroelectric-paraelectric phase transition temperature T,. In the paraelectric phase, the frequency dispersions of E’ are strong. They are decreasing as the ceramics are sintered (or annealed) under higher oxygen pressure. This is consistent with the evolution of the color of the ceramics (from pale yellow to white) and the de- crease of the dc conductivity ~~~~~~~~~~~~~

vddc( BLTN-o) ’ cddc( BLTN-ho) ). Such phenomena might be explained by the partial reduction of Ti4+ and Nb5+ ions into Ti3+ and Nb4+ ions, and the simultaneous

M. Dong et al. I Solid State Ionics 91 (1996) 183-190 185

Z.OE+OS

(4

WE+00 l.OEtOS Z.OEiJJS 3.OE+OS

O.OE+oo 1 .OE+os Z.OEiOS LOEMS

Z.OE+os

03

F c l.OEHS _? a

O.OE+oo

p’(nm)

jBLTN-ha/

O.OE+oo l.OE+OS LOEMS 3.OEW5

p'GW

Fig. 1. Complex resistivity plots for the ceramics.

creation of oxygen vacancies, under a less oxidizing atmosphere. Such results imply that the BLTN ceramics may have a mixed conduction: the anionic conduction due to the oxygen vacancies and the electronic conduction resulting from the partial re- duction of the Ti4+ and Nb’+ ions.

On the other hand, Ba,Ti,Nb,O,, ceramics [BTN] were prepared under the same conditions [2].

-4 00

-5 50

-6 SO

I20 I40 I60 I 80 200

1000/T(K')

Fig. 2. Arrhenius plot of estimated dc conductivity

ceramics.

for the

The dc conductivity is plotted in Fig. 2 for com-

parison. One could find that ~~~~~~~~~~~~ > ~,,~(~r~_~). Such a result suggests that the cationic conduction

(Li + ionic conduction) is the main contribution to

the electrical conduction in BLTN ceramics.

4. Discussion

From the above measurement results one could see that electronic-, anionic- as well as cationic-type conductions can exist in BLTN ceramics. In the

following part, we shall analyze the ac impedance data of the simplest ceramic, BLTN-ho. In such a

case, as a matter of fact, both electronic and anion conductions are negligible.

4.1. Equivalent circuit modelling

The electrode effect in this ceramic can be neg-

lected (Fig. lc). The equivalent circuits for this ceramic might consist of two elements in series: the first represents the bulk (or intragranular) properties and takes into account the dielectric and conductivity relaxation, and the second corresponds to the grain

M. Dong et al. I Solid State Ionics 91 (1996) 183-190 186

2.m-0,

(4

O.OE+OO l.OE-03 LOEd 3.OE-03

M’

2.0~~03

(b)

$ l.OE-03

O.OE+oa

O.OEtOO l.OE-03 Z.OE-03 3.OE-03

t.OE-03 , I

g l.OE-03

O.OE+OO

O.OE+OO l.OE-03 2.oFA3 3.0~~03

M'

Fig. 3. Complex electric modulus plots for the ceramics.

boundary properties (Rgb and C,, associated in parallel). The characteristic complex impedance equation of this model is as follows:

z*(o) = ZZ”,, + zg*

where

ZZ”lk = ioc:* 0 bulk

and

R ZZb =

gb 1 + iwC,,R,,

W)

(3c)

in Eq. (3b), &k is given by Eq. (1). A fitting

approach in the temperature region 500-800 K is

followed by using complex nonlinear least-squares fitting [3] of both the real and the imaginary parts of Z*(w) (Eqs. (3a), (3b), (3~)). Typical fitting results

are shown in Fig. 5, where the relative residuals are defined by [4]:

A,e = z’ -z;,, “7 and Ai, =

zms - z%, Zk .

(4) mea\

One could see that an optimum fit has been obtained as the relative residuals are spread random- ly around the log f axis; the relative errors are less

than 3% in the measurement frequency range, in

agreement with the experimental error. Therefore, an excellent agreement between experimental and theo-

retical calculation data has been obtained in a wide frequency range, confirming the validity of the electrical model proposed. The parameters a,,, m, n,

qr q, L ‘s* R,b and C,, were gained from a best

fit to the Z*(w).

4.2. Temperature dependence of the various

parameters

4.2.1. The dc conductivity rddc

Fig. 6 exhibits the variation of log a,, versus the reciprocal temperature for the BLTN-ho ceramic. A slope change appears at T,, two different activation energies AE, could be estimated, 1.11 and 0.75 eV, for the ferroelectric and the paraelectric phases, respectively.

From the ferroelectric state to the paraelectric one, the activation energy decreases significantly; this means that the barrier of the motion of Li+ ion

decreases clearly. As the spontaneous polarization disappears in the paraelectric state, one may consider that Li+ ion displacements are correlated closely with the spontaneous polarization. Such a hypothesis is supported by a significant increase of the Curie

M. Dong et al. / Solid State lonics 91 (1996) 183-190 187

1iKlO

aoa

E’ ~

400

2oc

+ 0.5 kHz - 1.0 kllz -5 kllz -10 kllz -20 kHz - lOOkHE

(BLTN-o)

-0.5kHz - 1.0 kHz -5 kHz

(BLTN-ho)

-0.5 kHz - 1.0 kIiz -5 kHz -1Okliz -2Okliz -1OOkHz

300400xlo600700800300400soo600700 .500300 400 ml 600 700 so0 T(K) T(K) TO<)

Fig. 4. Variations of 6’ with temperature at different frequencies.

temperature 7’, with the introduction of Li+ ions in

the ferroelectric ceramics derived from BTN [21.

4.2.2. The exponents m and n

The fitting leads to a fixed value of m, independent of the temperature, equal to unity. This result means that the lattice polarization mechanism is not disper- sive, and that it is associated with neither the charge

carriers nor the defects. The values of the exponent n relative to the ionic conduction mechanism are about 0.61-0.63 and are independent of the temperature.

There is no apparent drop of n at the transition region. This behaviour is different from that of

LiTaO, or Pb*KNb,O,, [1,5], suggesting that the charge carriers in the BLTN-ho ceramic are probably

not coupled with the ‘soft mode’ mechanism [61.

4.2.3. The characteristic frequencies f, and f,

The temperature dependence of each of the characteristic frequencies (f, = w,/2n) is plotted in Fig. 7. No minimum is observed for both frequencies at the transition point. At T,, f, shows only a slope change. These results suggest also that the ferroelec- tric-paraelectric transition in BLTN-ho seems to be not related to the ‘soft mode’ mechanism. In the 500-800 K temperature range, if f, is in the fre- quency measurement range, f, is lower.

4.2.4. The ‘injinitely ’ high frequency permittivity

l , and the static permittivity E,

The temperature dependence of l , and l , is shown in Fig. 8. A sharp e, peak appears at T,. The 6, data obey a Curie-Weiss law: e,=C/(T-TO) for the paraelectric phase. The value of the Curie-Weiss constant C is 1.25 X lo5 K. It is characteristic of a

displacive ferroelectric. The extrapolated temperature

TO is 478 K. Since TO is lower than T, (643 K), the ferroelectric-paraelectric transition seems to be of the first order [6]. A e, maximum is also shown, but at a temperature a little higher than T,.

4.2.5. Dielectric constant e’

The dielectric constant E’ of the ‘bulk’ could be derived from Eqs. (3b):

E, = E m

+ 15, - e, X [l + (o/w,)~ cos(m7r/2)]

1 + 2(0/w, )” cos(m7r/2) + (w/w, )2m

+ %(w/w,)” sin(nn/2). 0

(5)

The first two terms represent l llattj and the third

terms &,). The temperature dependencies of E&_) and E{,,,,)

are shown in Fig. 9, at three frequencies, i.e. lo*, lo3 and lo4 Hz. One could see that a ellattj maximum

appears at T,; eliat,) is nearly independent of the

M. Dong et al. I Solid State lonics 91 (1996) 183-190 188

LIE+,

(4

z* 6.OE+6

0% A*

Z* IS+6

-3

- 0 1% A*

3%

Fig. 5. Typical fitting results for BLTN-ho ceramic: (0) are

measured 2’ data; (0) are measured Z” data; the lines are

calculated results.

frequency in a large frequency range around T,. A maximum of E:,,,,) is shown at a temperature T,,,,, higher than T, and the difference (T,,,,, - T,) in- creases when the frequency decreases. It results that

1.2 1.4 1.6 1.8

1~0

Fig. 6. Arrhenius plot of calculated gdd, conductivity for BLTN-ho

ceramic.

0.0

-1.0

Fig. 7. Variation of characteristic frequencies f, and f, with

temperature.

the maximum of E’ (E’ = l llattj + E&J increases and its temperature moves off T, towards high tempera- tures when the frequency decreases (Fig. 4). The bulk capacitance, C, can be calculated from E’; at a temperature near T,, its value (about lo-” Fcm-‘) is typical of those values expected for the ferroelec- tric materials [7].

M. Dong et al. I Solid State tonics 91 (1996) 183-190 189

600

14ooo

0 D

so0 600 700 ooo

T(k)

Fig. 8. Temperature dependence of 5 and E,.

j----_

Fig. 9. Temperature dependence of l j,,,,, and E;,,,,) at lo2 and IO4

HZ.

4.2.6. The grain boundary resistance and

capacitance

As the microscopic structure of the grain boundary is unknown, the variation of log( l/R,,) versus the reciprocal temperature is presented in Fig. 10. On both sides of T,, the temperature dependence of the grain boundary resistance follows an Arrhenius law.

1.2 1.4 1.6 1.0

log<)

Fig. 10. Arrhenius plot of lIRp, for BLTN-ho ceramic.

One noticeable slope change occurs at the transition point. It suggests that the microstructure of the grain boundary may change during the ferroelectric- paraelectric transition. The grain boundary capaci-

tance C,, does not depend on the temperature. Its value (3.3 X 1O-ro-4.7X lo-” F cm-‘) is typical of

those expected for the grain boundary capacitances [7]. The characteristic relaxation frequency fgb of the grain boundary could be estimated from the relation 2n&R,,C,,= 1. The fgb varies in the 103-lo5 Hz

range, that is in the same frequency domain as f, (the frequency range of the ‘bulk response’). Conse-

quently, only one depressed semicircle is observed in the complex impedance plots (l-lo6 Hz) (Fig. lc).

5. Conclusions

The low-frequency dielectric dispersion phenom-

ena in Ba,Li,Ti,Nb,O,, ferroelectric ceramics have been analyzed via ac impedance spectroscopy mea- surements.

Ceramics treated under different atmospheres may have electronic, anionic and cationic conductions. When oxidizing the ceramics under high oxygen pressure, the low-frequency dielectric dispersion could be significantly decreased as the electronic and anionic contributions are smaller and smaller.

190 M. Dong et al. I Solid State Ionics 91 (1996) 183-190

The general dielectric response expression, which

was proposed for the LiTaO,-type single crystal, was once again applied successfully to the high oxygen pressure annealed Ba,Li,Ti,Nb,O,, ferroelectric

ceramics. The various dielectric parameters associ- ated with both ‘lattice’ and ‘carrier’ polarization

mechanisms and their variation with temperature have been determined. The charge carrier contribu-

tion influences strongly the ‘bulk’ properties of these materials.

The temperature dependence of the grain-bound- ary resistance follows an Arrhenius law. The grain- boundary capacitance is not sensitive to the tempera-

ture. A modification of the microstructure of the grain boundary appears probably at the ferroelectric-

paraelectric transition point.

References

[I] M. Dong, J.-M. Reau, J. Ravez, G. Joo and P. Hagenmuller,

J. Solid State Chem. 116 (1995) 185.

[2] M. Dong, J.-M. Reau and J. Ravez, in: Proc. of

Electroceramics V, Aveiro, Portugal (Sept. 1996).

[3] J. Ross Macdonald, J. Electroanal. Chem. 378 (1994) 17.

[4] Bernard A. Boukamp, J. Electrochem. Sot. 142 (1995) 1885.

[5] Lu Zhigao, J.P. Bonnet, J. Ravez, J.-M. Reau and P.

Hagenmuller, J. Phys. Chem. Solids 53 (1992) 1. [6] M.E. Lines and A.M. Glass, in: Principles and Applications

of Ferroelectrics and Related Materials, Chapter 5 (Claren-

don Press, Oxford, 1977).

[7] J.T.S. Irvine, DC. Sinclair and A.R. West, Adv. Mater. 2

(1990) 132.