Full text of DOI:10.1051/epjap:2001171

Eur. Phys. J. AP 15, 97–104 (2001)
THE EUROPEAN
PHYSICAL JOURNAL
APPLIED PHYSICS
ꢀ
c EDP Sciences 2001
Microwave dielectric relaxation of ferroelectric
PLZT ceramics in the range of 300–900 K
1
,2,a
2
3
4
A. Mouhsen
, M.E. Achour , J.L. Miane , and J. Ravez
1
er
D ´e partement de Physique, Facult ´e des Sciences et Techniques, Universit ´e Hassan 1 , Settat, Morocco
D ´e partement de Physique, Facult ´e des Sciences, Universit ´e Moulay Isma ¨ı l, Meknes, Morocco
PIOM, ENSCPB, avenue Pey-Berland, BP 108, 33402 Talence, France
2
3
4
ICMCB, avenue du Dr. A. Schweitzer, 33608 Pessac, France
Received: 8 June 2000 / Revised: 26 December 2000 / Accepted: 15 March 2001
Abstract. Dielectric response of PLZT(x/65/35) ceramics (with x = 0, 2, 4, 5 ) was studied using radio
frequency and microwave techniques in the temperature range 300–900 K and with a frequency range of
2
9
9
1
0 Hz–3 × 10 Hz. Dielectric relaxation appears around 1 × 10 Hz at room temperature. The relaxation
frequency softens at T and the dielectric relaxation exists in both paraelectric and ferroelectric phases and
c
depends on x the lanthanum concentration. A model of correlation chains gives some keys for understanding
the frequency behaviour of such materials.
PACS. 77.84.Dy Niobates, titanates, tantalates, PZT ceramics, etc. – 77.22.Gm Dielectric loss and relax-
ation – 41.20.Jb Electromagnetic wave propagation; radiowave propagation
◦
1
Introduction
TiO2 and ZrO2 at 900 C for 12 hours. The powder was
then pressed isostatiscally in a latex container under
It has been shown recently that ceramics derived from
4
000 bars for 10 min. The resulting cylindral sample
BaTiO3, Pb(Mg1/3Nb2/3)O3 [PMN] and PZT present a
measuring about 3 cm in diameter and 5 cm in height
dielectric relaxation within the microwave range of around
◦
9
was sintered at 1200–1250 C for 2 hours. Due to partial
1
×10 Hz [1–3]. The methods used (cavity using an on-line
evaporation of volatile PbO mainly at the sample periph-
ery, the latter was eliminated mechanically, leading to a
cylinder of about 1 cm in diameter and 3 cm in height.
A diamond wire saw was used to prepare disks of about
transmission or wave guide methods) are suitable to de-
termine the dielectric permittivities of homogeneous ma-
terials. A review of these methods is given in the liter-
ature [4–11]. The study of such relaxations requires the
ability to work over both large frequency and tempera-
ture ranges: measurements using coaxial cells and network
analysers at the moment can be used to cover a band of
1
(
cm diameter and 1 mm thickness. The compactness
ratio of experimental density to theoretical density) was
close to 0.97 for all samples [12].
7
10
1
0 Hz–2 × 10 Hz. Up to now these measurements were
limited to temperatures below 420 K due to experimen-
tal difficulties. It was the case for the study of BaTiO3 3 Experimental technique
and PMN type ceramics well suited because their Curie
temperatures are relatively low (393 K and 266 K respec- Heating of a sample could be achieved either by a con-
tively).
ventional oven or by optical means using laser or im-
It is possible to extend the range of dielectric mea- age oven [13]. Within the frequency range used in this
surements to 850 K thanks to development of a new de- study, the sample was placed in a measuring cell connected
vice. This device has allowed us the study of ceramics at through a coaxial line to a network analyser (HP8510B).
higher Curie temperatures. The present work deals with A conventional oven has the disadvantage that the mea-
dielectric properties of lead lanthanum zirconate titanate suring cell and the connection between the cell and the
[
PLZT] ceramics whose Curie temperature varies from 500 coaxial line that provides the wave propagation are at high
to about 650 K.
temperature. The standard materials that were used (es-
pecially the dielectrics presently used for the connections)
did not allow temperatures above about 450 K. For this
2
Preparation of ceramics
reason an optical method was chosen, a CO laser emit-
2
ting in the infrared at 10.6 µm. The beam of this laser
The compositions Pb(
were prepared by a solid state reaction from PbO, La2O3,
Lax(Zr0.65Ti0.35)(1
)O3
−x/4
1−x)
had a diameter of 1 cm and a divergence of 0.1 mrd. Its
power was controlled by computer and variable from 20
to 200 W in steps of 0.1 W.
a
e-mail: mouhsen@ibnsina.uh1.ac.ma

98
The European Physical Journal Applied Physics
The measuring cell was a open ended coaxial temperature for PbZr0.65Ti0.35O3 (PZT(0/65/35)) and
probe [14,15] fixed to the switchboard APC7 and made Pb0.95La0.05Zr0.65Ti0.35O3 (PLZT(5/65/35)) ceramics. A
0
from Invar to limit dilatations. The central conductor of maximum of ε occurs at the Curie temperature Tc
the coaxial line came into contact with the sample at (Tc(0/65/35) = 630 K and Tc(5/65/35) = 505 K).
0
one end, while the other end is connected to the network Figure 4 shows the variations of ε for compositions cor-
analysor. The sample was fixed against the coaxial con- responding to the following values of x: 0, 2, 4 and 5.
0
00
stituting the cell by a system of springs. In the part that
The frequency variations of ε and ε show the char-
keeps the sample in place, a hole was made through which acteristic behavior of a dielectric relaxation, a decrease in
0
00
the laser beam passed to heat the sample. The laser beam ε and a maximum in ε at the relaxation frequency near
9
was widened so that the heating of the sample on the rear to 10 Hz (Figs. 5 and 6). The dielectric relaxation can
face (the face in contact with the central conductor) was also be characterised by a Cole-Cole response function of
as uniform as possible (∆T < 10 K at T = 900 K). To get dipolar elements [21,22]:
a homogeneous distribution of the laser power on the sam-
h
i
−
1
∗
(1−α)
ple, the beam was spread over all of the rear face thanks to
an infrared mirror system. In these conditions, the sample
ε (ω) = ε∞ + ∆ε 1 + (iωτ)
.
could be bring to high temperatures during a time long ω is the angular frequency (ω = 2πf), τ is a relaxation
enough to avoid fractures, but short by comparison to the time, the relaxation frequency is defined by f = 1/2πτ
r
heating period in a conventional oven. Moreover the cell and is experimentally given by the frequency at the max-
0
0
was heated only by the thermal transfer due to its con- imum of ε . α is a positive constant (0 ≤ a < 1) and is
tact with the sample and it remained at relatively low a characteristic parameter of the Cole-Cole diagram that
00
0
temperatures, which allowed the use of coaxial lines and can be determined from the function ε (ε ), ε is the per-
∞
APC7 connections in contact with the measuring cell. The mittivity at frequencies greater than the relaxation fre-
sample temperature was measured using thermocouples quency f , ∆ε is the amplitude of the variations of ε from
r
or an optic pyrometer for temperature below 800 K and low to high values of the ratio f/f . For all the compo-
r
a sapphire fibre (ACCUFIBER) thermometer for higher sitions (x = 0, 2, 4 and 5%), the study of the thermal
temperatures.
evolution indicates that the relaxation frequency f goes
through a minimum close to the phase transition temper-
r
ature Tc and that the dielectric dispersion ∆ε presents a
maximum (Figs. 7 and 8). Figures 9 and 10 show Cole and
Cole diagrams of the PZT ceramic (x = 0) and Figure 11
the variations of the α parameter as a function of the tem-
perature and lanthanum concentration x.
4
Permittivity measurements
Modes matching methods allowed the calculation of the
reflection coefficient (or the admittance) of the interface
between the coaxial line and the cylindrical structure con-
taining the material to be studied [16–18]. The numerical
methods used for modes matching showed that this type
of interface was associated with an admittance Y = G+jB
and that it could therefore be represented by an equiva-
lent circuit RC [14,15,19]. In the method used here, the
elements R and C of the equivalent circuit were deter-
mined from measurements on reference samples of known
permittivities. The complex permittivity of a sample was
measured using numerical inversion of the measured re-
flection coefficient S11 at the interface coaxial-sample.
6
Discussion
The lead zirconate titanate (PZT 65/35) and lanthanum-
modified lead zirconate titanate (PLZT x/65/35) ceramics
are characterised by a dielectric response that is strongly
dependent on temperature and frequency.
They present similarities with the BaTiO3 type ceram-
ics with respect to the following features:
2
6
For low frequencies (10 Hz–13 × 10 Hz) and at room
temperature, measurements were made using a general ra-
dio frequency cell connected to an impedance analyzer
• existence of dielectric relaxation of Cole-Cole type at
microwave frequencies for both ferroelectric and para-
electric phases;
HP4192A (or HP4291A). For frequencies greater than
• existence of a minimum of relaxation frequency at the
8
1
0 Hz, the cell used was an open-ended coaxial probe con-
phase transition.
nected to a network analyzer HP8510B. In this frequency
range the equivalent circuit reduces to a capacity C, since
the conductance G is very small, and consequently has no
effect in the calculation of the reflection coefficient [20].
Figure 1 shows the results obtained for a PLZT (5/65/35)
ceramic and the good agreement between the results com-
ing from the three different apparatus.
However it is different by three main points:
•
•
•
whatever the temperature, the values of the relaxation
frequency fr are significantly higher in the case of the
PZT;
0
values of the permittivity ε of the PZT ceramics are
lower than those obtained for the BaTiO3 type ceram-
ics with similar compactnesses;
the parameter α increases for T > Tc and in particular
when x = 0. This behaviour was also observed in the
PMN ceramics. It is related to local fluctuations in
x [2] and to the existence of domains with composition
different from the mean composition (x/35/65).
5
Experimental results
Figures 2 and 3 show the thermal evolution of the
0
real permittivity ε as a function of frequency and

A. Mouhsen et al.: Microwave dielectric relaxation of ferroelectric PLZT ceramics
99
3/=7ꢀꢁꢂꢃꢁꢂꢄꢁꢅ
H ꢀ
H ꢁ
+
3ꢆꢇꢈꢉ$
+
3ꢆꢉꢈꢇ$
+
3ꢊꢁꢇꢋ%
H
H
Iꢌꢀ+]ꢅ
0
00
Fig. 1. Frequency dependence of permittivity ε and dielectric losses ε of the (5/65/35) PLZT ceramic, at room temperature.
0
0
,1GHz
,5GHz
1GHz
1
1
1
200
100
000
2GHz
3GHz
4GHz
[ꢀ ꢀꢁ
9
8
7
6
5
00
00
00
00
00
Hꢀc
2
00
300
400
500
600
700
800
900
T(K)
0
Fig. 2. Temperature dependence of permittivity ε at various frequencies of the (0/65/35) PZT ceramic.
Many theories, including some related to intrinsic and
extrinsic mechanisms, have been put forward to explain
the origin of the high frequency dielectric relaxation in
the case of the ferroelectric perovskites of BaTiO3 type:
• the dielectric dispersion is related to the jump of the
4+
Ti ions, in octahedron site, between different wells
of potential [27].
But these models are not able to explain the dielec-
•
•
the dielectric relaxation is caused by the piezoelectric tric relaxation at high frequencies [1]. A microscopic re-
resonance of grains in the ceramics [23,24];
laxation mechanism was proposed [28,29]. This model of-
the dielectric dispersion is correlated with the piezo- fers a microscopic description of the dielectric relaxation
electric resonance of ferroelectric domains in both crys- mechanism in the BaTiO3 based on the fact that a Ti
tals and ceramics [25,26]; ion which is displaced out of the centre of an oxygen
4+

100
The European Physical Journal Applied Physics
0
0
,1GHz
,5GHz
1GHz
2GHz
2
1
1
1
1
1
000
800
600
400
200
000
[ꢀ ꢀꢁꢂꢁꢃ
3
GHz
4GHz
Hꢀc
2
00
300
400
500
600
700
800
900
T (K)
0
Fig. 3. Temperature dependence of permittivity ε at various frequencies of the (5/65/35) PLZT ceramic.
x=0%
x=2%
x=4%
1
1
1
1
600
400
200
000
x=5%
Iꢀ ꢀꢄꢀ*+]
Hꢀc
8
00
2
00
300
400
500
600
700
800
900
T (K)
0
Fig. 4. Temperature dependence of permittivity ε of the (x/65/35) PLZT ceramic (with x = 0, 2 4 and 5) at 1 GHz.
octahedron can occupy different potential wells. The re-
When considering the model of correlation chains, the
laxation process is associated with the cooperative jumps first point to emphasize is that the cooperative motion
4+
4+
4+
of Ti between these different wells and the formation of between the Zr and Ti ions in the PZT ceramic is co-
4+
correlation chains. The shift of the Ti ion would be co- herent for a length lc shorter than that corresponding to
4
+
herent at a length lc corresponding to a correlation chain. Ti ions in the BaTiO3 and so fr (PZT) > fr (BaTiO3)
4+
4+
The increase of lc when T tends to Tc leads to an increase at Tc. Firstly the substitution Zr -Ti in lead-free ce-
in ∆ε and a decrease in fr: indeed the elementary dipo- ramics causes a small decrease in the fr value at Tc
8
7
lar moment is not that of a crystallographic unit cell, but (fr(BaTiO3) ∼ 10 Hz; fr(BaTi0.8Zr0.2O3) ∼ 7×10 Hz):
4+
4+
that of the correlation chain and in a simplified model the Zr ions fulfill the role of relaying the Ti ion in
2
p
the BaTi1−xZrxO3 solid solution. On the contrary, the
neglecting dipole interactions: ∆ε = n3
, where n is
ε0kT
2+
2+
Pb -Ba substitution leads to an increase of fr at Tc
the number of correlation chains per unit volume and p is
the dipolar moment of the correlation chains. This model
explains the very high values of the measured permittivity.
8
2+
(
fr (Ba0.95Pb0.05TiO3) ∼ 3 × 10 Hz) [30,31]. The Pb
2
ion and its 6(sp) lone pair cause a stronger distortion
of the crystalline system compared to the Ba ion. The
2+

A. Mouhsen et al.: Microwave dielectric relaxation of ferroelectric PLZT ceramics
000
300
101
1
Hꢀc
x = 0
Hꢀs
2
2
1
1
5
0
50
00
50
00
0
9
8
7
6
5
00
00
00
00
00
Hꢀc
Hꢀs
7
,5
8
8,5
9
9,5
10
log f (Hz)
0
00
Fig. 5. Frequency dependence of permittivity ε and dielectric losses ε of the (0/65/35) PLZT ceramic, at room temperature.
2
1
1
1
1
1
000
800
600
400
200
000
400
Hꢀc
x = 0,05
Hꢀs
3
2
1
0
00
00
00
Hꢀc
Hꢀs
7
,5
8
8,5
9
9,5
10
log f (Hz)
0
00
Fig. 6. Frequency dependence of permittivity ε and dielectric losses ε of the (5/65/35) PLZT ceramic, at room temperature.
x=0%
logFr
9
9
,02
,01
9
600
5
5
4
4
3
50
00
50
00
50
8
8
8
,99
,98
,97
300
2
00
300
400
500
600
700
800
900
T (°K)
Fig. 7. Temperature dependence of relaxation frequency and dielectric dispersion ∆ε of the (0/65/35) PZT ceramic.

102
The European Physical Journal Applied Physics
x=5%
'H
log(Fr)
9
,01
9
740
7
7
6
6
6
6
6
20
00
80
60
40
20
00
8
8
8
8
,99
,98
,97
,96
580
2
00
300
400
500
T (°K)
600
700
800
900
Fig. 8. Temperature dependence of relaxation frequency and dielectric dispersion ∆ε of the (0/65/35) PZT ceramic.
ꢀꢀ7ꢀꢀꢁꢀ7F
T = 594 K
5
4
3
2
36 K
63 K
52 K
95 K
H'
Fig. 9. Cole-Cole diagram of the PZT ceramic (x = 0) below the ferro-paraelectric transition temperature.
strong distortion in the PZT goes with an important transparent ceramics to be obtained (compactness = 1),
4+
4+
tetragonality (c/a > 1) which allows the Ti and Zr
which is important in view of electrooptic applications.
ions to have displacements from the octahedron center
that are clearly different owing to a steric effect due to
the different sizes of these two cations. The role of the
Zr ion as a relay in the correlation chain will be made
more difficult, the correlation chains will be more short
and the value of fr higher.
The parameter α, a phenomenological parameter that
describes the dielectric relaxation, varies also with the
temperature (Fig. 11). In fact, this parameter is linked
to the dynamic motions of polar elements. In the fer-
roelectric phase, α ≈ 0, demonstrating thus the exis-
tence of only a simple dipolar reorientation mechanism
4+
(
Debye relaxation). The response function is exponential
2
+
−t/τ
Concerning the progressive replacement of Pb
by ϕ(t) ∝ e
. This implies a simple mechanism, inter-
3+
La , the weak quantities that are introduced seem to nal to the correlation chains and not dependent on their
play no noticeable role on the variation of fr at Tc that re- size (α is independent of the temperature in this region).
mains close to 1 GHz for all the lanthanum concentrations In contrast, when T > Tc, α depends on the tempera-
0
(
Figs. 7 and 8). On the contrary, the value of ε (Tc) in- ture. Therefore the dipolar reorientation mechanism be-
creases with the amount of lanthanum (Fig. 4); in this case comes more complex (Cole-Cole relaxation). The pres-
it is the quality of the compactness of the ceramics that ence of couplings inside short correlation chains becomes
is responsible. Indeed the addition of lanthanum allows highly likely together with the interaction with long range

A. Mouhsen et al.: Microwave dielectric relaxation of ferroelectric PLZT ceramics
103
7ꢀ!ꢀ7F
T = 850 K
7
6
24 K
93 K
6
36 K
H'
Fig. 10. Cole-Cole diagram of the PZT ceramic (x = 0) below the ferro-paraelectric transition temperature.
0
0
0
,16
,14
,12
x=0
x=0,02
x=0,04
x=0,05
0
,1
D
0
0
0
0
,08
,06
,04
,02
0
2
00
300
400
500
600
700
800
900
T (K)
Fig. 11. Temperature dependence of Cole-Cole parameter α of the (x/65/35) PLZT ceramic (with x = 0, 2, 4 and 5).
polarisation of the environment of these chains. That is long range in the paraelectric phases. It is remarkable
to say that interactions over long distances are going to that the small amount of lanthanum (a few percent) does
appear (between correlation chains and/or between dif- not modify the relaxation frequency but introduces a new
ferent composition zones). In the time domain, this be- mechanism of interaction in the ferroelectric phase since
haviour can be described by means of the Kohlrausch- PZT presents a Debye relaxation, and PLZT (with x = 2
Williams-Watts stretched exponential function [32] which to 5%) a Cole-Cole relaxation.
β
can be derived ϕ(t) ∝ exp[−(t/τ) ] from different the-
oretical models and where β is a shape parameter that
lies between 0 and 1. In the frequency domain, the most
general form that has been proposed to describe the non-
Debye behaviour is the Havriliak-Negami relaxation func-
7
Conclusion
The development of a microwave dielectric measur-
ing device, able to operate at high temperatures,
has allowed the study of ceramics with composition
(1−α) γ
tion Φ(ω) = [1+(iωτ)
shape parameters that lie in the range 0 < α, |γ| < 1 (γ =
= 0: Cole-Cole
] [33], where α and γ are both
−
1, α = 0: Debye relaxation, γ = −1, −α 6
Pb(
Lax(Zr0.65Ti0.35)(1−x/4)O3 (PLZT) around their
1−x)
relaxation, 0 > γ > −1, 0 < α < 1: Cole-Davidson re-
laxation [34]), and τ is a relaxation time. These functions
characterize different interaction mechanisms at short and
Curie temperature (505 ≤ Tc ≤ 630 K). The value of Tc
decreases with x most notably due to of the reduction
2+
in the amount of Pb , this latter generally resulting in

104
The European Physical Journal Applied Physics
ferroelectric distortions caused by the existence of the
9. G. Maz ´e -Merceur, J.L. Bonnefoy, J. Garat, R. Mittra,
IEEE URSI/AP-S Proc., Chicago, 1992.
2
6
(sp) lone pair. Studies of frequency variations showed
a dispersion of permittivity that comes from a Debye 10. J. Grigas, J. Microwave Dielectric Spectroscopy of Di-
9
electrics and Related Materials, Gordon and Breach Sci.
type relaxation close to 10 Hz. This relaxation exists
Publi., 1994.
in both the paraelectric and ferroelectric regions and the
1
1
1. Y.M. Chen, J.Q. Liu, J. Comput. Phys. 53, 429 (1984).
2. The authors thank M. Decamp for preparation of ceramic
samples.
frequency of relaxation shows a minimum at the Curie
temperature Tc. As for BaTiO3, this relaxation can be
clarified by a potential model of double potential wells.
8
13. B. Chevalier, M. Chatard-Moulin, J.P. Astieret, P. Guillon,
J.C.M.M., Limoges, 1991.
The value of fr at Tc (∼ 9 × 10 Hz) for PLZT ceram-
ics is greater than that earlier obtained from ceramics of
1
1
1
1
1
4. M. Rzepecka, S. Stuchly, IEEE Trans. Instrum. Meas. IM-
8
BaTiO3 (fr ∼ 10 Hz). This result implies that the co-
24, 27 (1975).
4+
4+
operative motion between Ti and Zr ions in PLZT
ceramics is coherent within a shorter length of correla-
5. M. Stuchly, T. Athey, G. Samaras, G.E. Taylor, IEEE
Trans. Microwave Theory Tech. MTT-30, 87 (1982).
6. N.E. Belhaj, A. Fourier, IEEE Trans. Microwave Theory
Tech. MTT-34, 346 (1986).
7. S. Breton, P. Gelin, Y. Baziard, A. Gourdenne, Rev. Phys.
Appl. 23, 1249 (1988).
8. D.L. Gershon, J.P. Calame, Y. Carmel, T.M. Antonsen, M.
Hutcheon, IEEE. Trans. Microwave Theory Tech. MTT-
47, 1640 (1999).
4+
tion chains lc than that for only the Ti ions in BaTiO3
ceramics. Thanks to its particular configuration it is the
2+
Pb ion that plays an indirect but fundamental role. The
2+
3+
replacement of Pb by La has no effect on the relax-
ation frequency, but modifies the long range interactions
as well in the ferroelectric phase as in the paraelectric
phase.
19. G.P. Grant, R.N. Clarke, G.T. Symm, N.M. Spyrou, J.
Phys. E Sci. Instrum. 22, 757 (1989).
20. J.L. Miane, M. Ech-chaoui, Revue des composites et
mat ´e riaux avanc ´e s 2, 115 (1992).
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