ARTICLE IN PRESS
S.K. Rout et al. / Journal of Physics and Chemistry of Solids 67 (2006) 2257–2262
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the transition temperature (Tm) which is caused by
inhomogeneous distribution of the Zr ion on Ti site and
mechanical stress in the grain [21]. It can be also noticed
from the figures, that higher transition temperatures (Tms)
are observed in the Ca containing composition than the
pure BTZ. When Ca is substituted in 12 coordination sites,
it traps eight near neighbors Oxygen and four more distant
ones. That modification assumes a possible displacement of
Ca2+ out of the oxygen dodecahedron center to induce a
dipolar moment whose occurrence may lead to increase in
transition temperature. The diffuse nature of the transition
in the case of ferroelectric ceramics is usually attributed to
a distribution of grain sizes and/or to a gradient of
quadraticity which leads to a distribution of transition
temperature. This is more pronounced in samples contain-
ing both Ti and Zr may be due to the difference in ionic
radius. Here additional spatial fluctuations in the mixture
of Ti and Zr ions lead to the coexistence of regions of
different Curie temperatures depending up on their
concentration [22] in the solid solution. It is reported
[23], as the grain size decreases, the maximum dielectric
constant and transition temperature decreases. The effect
of grain size originates from the higher surface tension in
smaller grains [24], which acts in the same manner as
hydrostatic pressure thus decreasing the Curie point [25].
In addition, the force experienced by the atoms and ions in
the vicinity of, or far from, the surface of grain are not
similar. These considerations suggest that a quadraticity
gradient may exist between the surface and the bulk of
grains [26]. For smaller grain sizes, however, the superficial
layers of the grains represent a significant fraction and may
dominate the structural and the dielectric measurement
[22].
1 kHz
10kHz
100 kHz
1 MHz
(a)
(b)
100
50
0
140 160 180 200 220 240 260 280 300 320
Temperature (K)
Fig. 3. Temperature dependency of permittivity of Ba0.9Ca0.1Ti0.6Zr0.4O3
at various frequencies: (a) real part; (b) imaginary part.
temperature maximum Tm, depend upon the measurement
frequency for all the compositions. The magnitude of
dielectric constant decreases with increase in frequency and
the maximum shifts to higher temperature. This indicates
that the dielectric polarization is of relaxation type in
nature such as dipolar glasses. In analogy with spin glasses,
such a behavior of the dynamic susceptibility in disordered
ferroelectric is supposed to be concerned with the existence
of the broad spectrum of relaxation times. It is generally
considered that the Debye model is based on the
assumption of a single relaxation time. The model fails
because of the existence of a distribution of relaxation
times. Such a distribution of relaxation time implies that
the local environment seen by individual dipoles differs
from site to site. As shown in the figures, the dielectric loss
values of the ferroelectric phase were reduced substantially
in the paraelectric phase (above Tm). The observed lower
temperature (below Tm) frequency dispersion may also
have some contribution from the space charge effect. The
high value of dielectric loss at 1 kHz is due to the presence
of all types of polarizations including space charge effect. A
gradual decrease of space charge is observed at higher
frequency. An increase in the values of ꢀ00 at lower
temperature region may also be due to the presence of
space charge polarization and those were reduced sub-
stantially at temperatures near paraelectric phase. The
space charge effects are more prominent in the both low
frequency and low temperature regions [18].
A diffuse phase transition is generally characterized by
(a) broadening of dielectric constant versus temperature
curve (b) a relatively large separation (in temperature)
between the maximum of the real (dielectric constant) and
imaginary (dielectric loss) part of the dielectric spectrum (c)
a deviation from Curie–Weiss law in the vicinity of Tm; (d)
frequency dispersion of both e0 and tan d (dielectric loss) in
transition region thereby implying a frequency dependency
of Tm.
It is known that the dielectric permittivity of a normal
ferroelectric above the Curie temperature follows the
Curie–Weiss law described by
ꢀ0 ¼ C=ðT ꢀ T0Þ; ðT4TCÞ,
As a rule [11] this relaxation occurs in disorder ionic
structures, particularly in solid solution. Within the curie
range of temperature, dielectric permittivity achieves very
high value and displays very large dispersion, which is
reminiscent of that found for orientational glasses [19]. The
two cations Ti4+and Zr4+ in the B sites are all
ferroelectrically active, so these cations are off-centered in
the octahedral site and give rise to a local dipolar moment
[20]. Qualitatively, the strongly broadened dielectric peak
indicates that the phase transition is of a diffuse type near
where T0 is the Curie–Weiss temperature and C is the
Curie–Weiss constant. Fig. 4 shows the plot of inverse
dielectric constant versus temperature at different frequen-
cies of two different single phase compositions in the
system Ba1ꢀxCaxTi0.6Zr0.4O3 ; (a) x ¼ 0.0, (b) x ¼ 0.1. A
clear deviation from Curie–Weiss law can be seen in all
representative frequency. The parameters obtained at
1 kHz and 1 MHz are listed in Table 1. The parameter
DTm, which describes the degree of the deviation from the