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30.1 Introduction
So-called ferroelectric materials may be divided into two classes: ferroelectrics
and relaxors (Table 30.1) [1]. Typically, relaxors have at least one
crystallographic site that is occupied by two or more ions. Unlike ferroelectrics,
relaxors exhibit what is known as a diffuse transition: the real part of the
permittivity
′
ε
r
is high but the maximum of
′
ε
r
= ( )fT
is wide. In relaxors,
there is a strong influence of the frequency f of the electric field on the
′
ε
r
= ( )fT
curves; when f increases,
′
ε
r
decreases and the
′
ε
r
maximum
temperature increases [1]. The latter refers to T
m
(not T
C
) owing to its large
variation with f. Concerning the
′′
ε
r
= ( )fT
curve, when f increases, the
imaginary part of the permittivity
′′
ε
r
increases and the
′′
ε
r
maximum
temperature increases. The dielectric curve of a Pb(Mg
1/3
Nb
2/3
)O
3
(PMN)
ceramic is a good example [2]. In many relaxors, the relationship between f
and T
m
can be described using the Vogel–Fulcher (VF) relationship [3, 4]:
Log = log –
( – )
0
a
mVF
ff
E
kT T
30.1
where f
0
is the Debye frequency, T
m
the temperature of
′
ε
r
max
at the given
frequency f, T
VF
the static freezing temperature, E
a
the activation energy and
k the Boltzmann constant [5, 6]. In addition, there is a deviation from the
Curie–Weiss law (
′
ε
r
= C/(T–T
0
)). The value of the Curie–Weiss temperature
T
0
is greater than that of T
m
. To date, various physical models have been
proposed to explain the properties of relaxors [7]: compositional fluctuations
and diffuse phase transition [8, 9], the superparaelectric model [10], the
nanostructure-octahedral model [11–17], the dipole-glass or the more recently
derived model [18, 19], the random-field model [20, 21], the domain-wall
model [22] and the random-layer model [23, 24]. Solid-state chemistry aspects
of lead-free relaxor ferroelectrics have also been developed [25, 26].
In addition to the usual applications for ferroelectrics, relaxors are of
great interest as dielectrics in capacitors and actuators [27]. Most relaxors
30
Lead-free relaxors
A SIMON and J RAVEZ, University Bordeaux1, France