Research Letters in Materials Science

VolumeΒ 2008Β (2008), Article IDΒ 746256, 5 pages

http://dx.doi.org/10.1155/2008/746256

## Complex Impedance Spectroscopic Properties of Ceramics

Department of Physics and Meteorology, Indian Institute of Technology (IIT) Kharagpur, Kharagpur 721302, India

Received 27 November 2007; Accepted 18 February 2008

Academic Editor: StephenΒ Danforth

Copyright Β© 2008 Praveen Khatri et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The polycrystalline sample of was prepared by a high-temperature solid-state reaction technique. The effect of temperature on impedance parameters was studied using an impedance analyzer in a wide frequency range (βHz). The real and imaginary parts of complex impedance trace semicircles in the complex plane. The temperature-dependent plots reveal the presence of both bulk and grain boundary effects above C. The bulk resistance of the material decreases with rise in temperature. This exhibits a typical negative temperature coefficient of resistance (NTCR) behavior of the material. The modulus analysis suggests a possible hopping mechanism for electrical transport processes of the material. The nature of variation of dc conductivity suggests the Arrhenius type of electrical conductivity.

#### 1. Introduction

Dielectric oxide ceramics with high permittivity, low dielectric loss, and near zero
temperature of dielectric constant are critical elements in components such as
resonators, oscillators, and filters for wireless communications [1β3]. Relatively
few ceramic systems are currently available with the properties needed for
practical applications at various operating frequencies [4]. Recently the materials
having the coupling between the ferroelectric and ferromagnetic ordering
parameters received considerable
attention of the researchers to study their both fundamental physics and device
engineering [5]. A new perovskite-related phase with composition 3CaO:Nb_{2}O_{5} in the system of CaOβNb_{2}O_{5} was reported long ago by Ibrahim et al. [6]. Recent studies of phase
equilibria study [7] of the CaOβNb_{2}O_{5} system undertaken in air atmosphere in the higher CaO composition (70β90βmol %) showed
that the 3β:β1 molar composition of system can have a small amount of Ca_{2}Nb_{2}O_{7} as impurity phase. Three equilibrium phases, Ca_{3}Nb_{2}O_{8},
Ca_{2}Nb_{2}O_{7}, and CaNb_{2}O_{6},
of CaO:Nb_{2}O_{5} systems were shown in the earliest
published work [6]. Substitution of Ba (group IIA element) at the Ca sites and
vanadium at the Nb of the above system can provide many solid
solutions with many interesting properties for wide industrial
applications. Detailed literature survey of the system exhibits that not much
has been reported on the importance of the material for applications, therefore,
we have extensively studied the various properties
of Ba_{3}V_{2}O_{8} compound. The work done on
structural and dielectric properties of the compound have been reported
elsewhere [8]. In this paper, the electrical (complex impedance) properties of
Ba_{3}V_{2}O_{8} are reported.

#### 2. Experimental Details

The polycrystalline sample of Ba_{3}V_{2}O_{8} was prepared by a high-temperature solid-state reaction technique using
high-purity (99.9%) ingredients BaCO_{3} and V_{2}O_{5}:
in a suitable stoichiometry. These ingredients were mixed thoroughly; first in
an air atmosphere for 1 hour, and then in alcohol (i.e., methanol) for 1 hour. The
homogeneous mixture of the compound was calcined in an alumina crucible at 925^{Β°}C
for 5 hours. The process of grinding and calcinations was repeated several times
until the formation of the desired compound was confirmed (using X-ray
diffraction pattern). The calcined fine powder was cold pressed into
cylindrical pellets of 10βmm diameter and 1-2βmm of thickness
at a pressure of βNm^{2} using a hydraulic press.
Polyvinyl alcohol (PVA) was used as binder to reduce the brittleness of the
pellets. The binder is burnt out during high-temperature sintering. The pellets
were sintered at an optimized temperature (975^{Β°}C) and time (10 hours)
in air atmosphere using an alumina crucible. In order to study the electrical/impedance properties of the compound, both the flat and parallel
surfaces of the samples were polished and electroded with air-drying conducting
silver paint. After electroding, the pellets were dried at 150^{Β°}C for
4 hours to remove moisture (if any) and then cooled them to room temperature
before taking electrical measurements. The impedance parameters were obtained
using a computer-controlled impedance analyzer (HIOKI 3532 LCR HiTESTER) in a
wide frequency range (10^{2}β10^{6}βHz) at different temperatures (23β500^{Β°}C).

#### 3. Results and Discussion

##### 3.1. Impedance Studies

The grain, grain boundary, and interface properties of ceramics are studied using the complex impedance formalisms, which include the determination of capacitance (bulk and grain boundary), relaxation frequency, and electronic conductivity. A polycrystalline material usually gives grain and grain boundary properties with different time constants leading to two successive semicircles. The electrical properties of a material are often represented in terms of some complex electrical parameters like complex permittivity , complex impedance , electric modulus , and loss tangent tan . They are related to each other as follows: where is the series resistance, ( resonance frequency), the capacitance in series, the imaginary factor, and is the vacuum capacitance of the circuit elements. Above four expressions give a wide scope for graphical representation. The complex impedance of the electrode/ceramic/electrode structures can be demonstrated as the sum of the single RC circuit with parallel combination.

The plot of versus
(Nyquists diagram) at different temperatures (275β450^{Β°}C)
is shown in Figure 1. The inspection of the semicircle showed that there is a
depression angle instead of a semicircle centered on the real axis. The
behavior of the electrical response follows Cole-Cole formalism
[9]. It is observed that
at lower temperatures (shown in inset), a single semicircular arc appears. This
single semicircular arc suggests the presence of grain interior (bulk) property
of the material [10]. However, at higher temperatures, another arc appears, and
the spectrum comprises of two semicircular arcs with their centers lying below
the real axis. The high-frequency semicircle (first arc) can be attributed to
the bulk (grain) properties of the material arising due to a parallel
combination of bulk resistance () and bulk capacitance ().
The value of bulk resistance () and grain boundary resistance ()
above 400^{Β°}C has been obtained from the intercept of the semicircular
arc on real axis (). The electrical process taking place within the material
can be modeled on the basis of brick-layer model [11]. However, with subsequent
rise in temperatures, both the grain and grain-boundary phenomena appear to
merge into a single arc (pattern) suggesting a substantial modification in the
overall electrical behavior of the material.

Figure 2(a) shows the variations of
real part of impedance with frequency at different temperatures. This plot
is suitable for evaluation of the relaxation frequency of most resistive
component. The peak occurs above 300^{Β°}C, and shifts to higher frequencies
on increasing temperature. This exhibits the occurrence of relaxation in the
system. The relaxation frequency is obtained either from the plot of *Z* versus
frequency or semicircles (from the Nyquist plot). The peak broadening (due to
increase in temperature) suggests the presence of temperature-dependent
relaxation processes in the compound [12]. The relaxation process is due to the
presence of immobile species at low temperature and defects at higher
temperature. Figure 2(b) shows the variation of with frequency at
different temperatures. The imaginary part of impedance decreases with rise in
frequency. This plot exhibits that conduction is increasing with rise in
temperature and frequency. The coincidence of the impedance *Z* values at higher
frequencies at all the temperatures indicates a possible release of space
charge [13].

##### 3.2. Modulus Studies

The complex electric modulus was
calculated using the relations; , where , and , geometrical capacitance = ( permittivity of free space, *A* = area of the electrode surface,
and *t* = thickness). In order to confirm the ambiguity arising in connection with
the presence of grain boundary effect at elevated temperatures, the impedance
data has been replotted in the modulus formalism at the same temperatures (Figure 3). It shows two semicircular arcs in the complex modulus plots with a small
semicircle at low frequency and very large semicircular arc in the high-frequency
region at all the temperatures. A relative comparison of the complex impedance spectrum and
modulus spectrum of Ba_{3}V_{2}O_{8} shows two arcs in
the modulus pattern with different radius, whereas only one arc in the
impedance spectrum.

Figure 4(a) shows the variation of
and as a function of frequency at selected temperatures. It shows a very low
value (approximately zero) of *M* in the low-frequency region. A continuous
dispersion on increasing frequency may be due to the short-range mobility of
charge carriers. Figure 4(b) exhibits that the maxima of the imaginary
components of modulus () shift towards higher relaxation
frequencies with rise in temperature. This behavior suggests that the
dielectric relaxation is thermally activated in which hopping
mechanism of charge a carrier dominates intrinsically. The asymmetric broadening
of the peak indicates the spread of relaxation with different time constant,
and hence, relaxation in the material is of non-Debye type .The magnitude of
the peak increases on increasing temperature.

The electrical conductivity(s) is a
thermally activated process, and obeys the Arrhenius law where the symbols have their
usual meanings. Figure 5(a) shows the variation of (bulk conductivity ) against . The activation energy (Ea) of Ba_{3}V_{2}O_{8} can be calculated from the slope of a straight line (Figure 5(a)), and the corresponding
value of Ea is found to be 1.28βeV. The bulk conductivity of the sample was
evaluated from the complex impedance plots at different temperatures. The value
of grain-boundary resistance (R) at different temperatures is also estimated
from the complex impedance spectrum. In this case, dc conductivity increases
with rise in temperature showing a typical characteristic of a semiconductor
(i.e., negative temperature coefficient of resistance).

The peak frequency helps to evaluate relaxation time () using a relation . The
variation of as a function of temperature (275β475^{Β°}C)
is shown in Figure 5(b) (inset). The variation of as a function of inverse of
absolute temperature appears to be linear which follows the relation , where the symbols have their usual meaning. The value of
activation energy is found to be 1.29βeV.

#### 4. Conclusions

The polycrystalline sample Ba_{3}V_{2}O_{8} of prepared by a high-temperature solid-state reaction technique. Complex
impedance spectroscopy was used to characterize the electrical properties of
the material. The electrical conduction in compound is due to bulk and grain-boundary
effect. Both the bulk and grain boundary resistance decrease with rise in
temperature indicating a typical NTCR behavior of the compound. This compound
also exhibits the temperature-dependent relaxation phenomena. Electrical
modulus analysis has confirmed the presence of hopping mechanism in the
material. The ac conductivity shows a typical
Arrhenius type of electrical conductivity. The activation energy of the
compound was found to be 1.28βeV (due to grain).

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