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Journal of Sol-Gel Science andTechnology ISSN 0928-0707 J Sol-Gel Sci TechnolDOI 10.1007/s10971-014-3296-6
Analysis of structural and electricalproperties of Ni2+:Zn2SiO4 ceramicpowders by sol–gel method
B. Chandra Babu & S. Buddhudu
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ORIGINAL PAPER
Analysis of structural and electrical properties of Ni2+:Zn2SiO4
ceramic powders by sol–gel method
B. Chandra Babu • S. Buddhudu
Received: 6 February 2013 / Accepted: 5 February 2014
� Springer Science+Business Media New York 2014
Abstract Present paper reports on the synthesis and
electrical properties of Ni2?:Zn2SiO4 (Zn2-xSiO4 =
xNi2?, x = 0.0, 0.25, 0.50 and 0.75 mol%) ceramic pow-
ders by a conventional sol–gel method. The structural
details of Ni2?:Zn2SiO4 ceramic powders have been
investigated from the measurement of XRD, FT-IR, Raman
spectral profiles and SEM images. The results reveal that
these ceramic powders are all in nanometer sized-grains of
spherical forms with willemite structures. The XRD and
EDAX results have thus corroborated the successful doping
of Ni2? ions into the Zn2SiO4 matrix. The dielectric real
(e0), imaginary (e00) parts, loss tangent (tan d) and AC
conductivity (rac) properties as the function of frequency
have been carried out and those are strongly dependent on
Ni concentration and this behaviours have been explained
on the basis of Maxwell–Wagner type of interfacial space
charge polarization. Complex impedance analysis data
shows only one semicircle corresponding to the grain
boundary volume and thus suggesting that the conduction
occurrence through grain boundary volume in Ni2? doped
samples and it has been explained using the Cole–Cole
expression.
Keywords Sol–gel method � Ceramic powders �Electrical properties
1 Introduction
There has been a great deal of interest in understanding the
properties of nanosized dielectric materials like transition
metal ions containing composites. These composites have
good potential uses in different fields because of their
having hardness, high melting point, low density, low
coefficient of thermal expansion, high thermal conductiv-
ity, good chemical stability and improved mechanical
properties such as higher specific strength, better wear
resistance and specific modulus [1–4]. Zinc silicate (wil-
lemite, Zn2SiO4) has long been identified as a good host
matrix for dopant rare earth and transition metal ions in the
display of encouraging luminescent properties [5, 6].
Willemite has a wide range of applications like phosphor
hosts, electrical insulators, glazes and pigments and also an
important component in glass ceramics. Higher values of
electrical resistivity could be achieved by doping suitable
host matrices with proper divalent cations or by controlling
their microstructures. The ultrafine particles are predomi-
nantly controlled by grain boundaries as barriers for elec-
trons flow and as results of that, there is a reduction in eddy
current losses [7].
Among the transition metal ions Ti, Cr, Mn, V, Mo and
Ni etc., the chromium ions exist in multi valent states, viz.,
Cr3?, Cr4?, Cr5? and Cr6?. The same is true in the case of
other transition metal ions Ti, Mn and V. Hence, it has
become difficult to have the control over the required or
suitable valence state of these ions in the host matrices to
get the desired properties like luminescence. Unlike these
ions, the Ni2? ions mostly exist in divalent state only and
that are more stable and there is no need of any special
experimentation in retaining nickel ions in divalent state
[8]. These types of composite materials have potential
applications in diverse areas such as electronic applications
B. Chandra Babu (&) � S. Buddhudu
Department of Physics, Sri Venkateswara University,
Tiruapti 517502, AP, India
e-mail: chandrababuphd@gmail.com
S. Buddhudu
e-mail: drsb99@hotmail.com
123
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DOI 10.1007/s10971-014-3296-6
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(opto-electronic device, optical-fibers, optical fibers
amplifiers, chemical and thermal properties), electro-
chemical and catalytic properties, laser diodes and light
emitting diodes, industrial applications in aircraft and at a
wide range of frequencies [9, 10]. It is well known that the
conductivity and the dielectric properties of ceramics are
strongly dependent on frequencies and temperatures.
Hence, study on such properties at different frequencies,
temperatures and chemical compositions could provide
vital information about the kind of additives required to
obtain high quality materials for practical applications [11,
12]. Moreover, dielectric properties of ceramics depend
upon several factors including the method of preparation,
heat treatment, sintering conditions chemical composition,
cation distribution and crystallite structure or size [13].
A chemical synthesis of organic–inorganic composites
can be provided by the sol–gel process. The sol–gel process
is broadly defined as one in which a useful product is pre-
pared from a solution or suspension of precursor materials
via hydrolysis and polycondensation. Sol–gel technique has
been considered as a versatile procedure, in the production
of a wide variety of optical and dielectric materials and it
offers a clear advantage over the other methods in the
achieving the dopant ions distribution uniformly in the host
matrices at lower temperatures [14]. Since there exists no
report in literature so far on the electrical properties of
Ni2?:Zn2SiO4 sol–gel ceramic powders as function of fre-
quency, we have undertaken this work, in understanding
their composition-properties at room temperature using
XRD, FTIR, Raman, SEM, EDAX, dielectric spectroscopy
and impedance spectroscopy techniques.
2 Experimental study
2.1 Materials
All the chemicals used in the present work, were of ana-
lytical and high pure grade from M/s Merck and Sigma-
Aldrich. The precursors were TEOS (SiOC2H5)4 (99 %
Aldrich) as SiO2 Source, Zinc nitrate (Zn(NO3)2 as ZnO
source, and nickel chloride (NiCl2�6H2O) as dopant source
Ni2? ions, high pure ethanol (EtOH) has been used as the
solvent with a 0.2 ml of HCl as the catalyst.
2.2 Preparation of Zn2-xSiO4:xNi2? ceramic powders
Zn2SiO4 and Zn2-xSiO4 doped xNi2? different (x = 0.0,
0.25, 0.50 and 0.75 mol%) concentrations sol–gel ceramic
powders were prepared by a sol–gel method as shown in
Fig. 1. Tetraethylorthosilicate (TEOS) and (Zn(NO3)2�6H2O) were weighed by maintaining a 2:1 molar ratio and
those were separately dissolved in appropriate amounts of
ethyl alcohol (EtOH) and after that each of these solutions
was stirred for 15 min. Weighting of (0.25, 0.50, 0.75 and
0.0 mol%) of nickel chloride was used to dissolve those
separately in double ionized water and then stirred for
about 10 min. To the resultant zinc sol and Ni2? ions were
added and such a mixed solution was added to the SiO2
solution. After, a required amount of 0.2 ml HCl was added
as the catalyst for the hydrolysis of TEOS, after a few
minutes of stirring, a clear and transparent nature solution
was obtained, again each of which was continuously stirred
for about 12 h at *75–80 �C and was found to be stable
enough for a long time. Transparent xero-gels were
obtained by allowing the precursor to evaporate in air for 2
or 3 months. With and without Ni2? ions containing Zn2
SiO4 solutions were prepared and thus obtained as- syn-
thesized dry sol–gels upon baking them at 120 �C for 12 h
in order to remove the moisture content with in the sample.
Ni2?:Zn2SiO4 sol–gel ceramic powders were obtained after
calcinations at 1,000 �C for 2 h in air electrical furnace.
To carry out electrical measurements part of the powder
sample materials was pressed into circular disk shaped
pellets using a small amount of PVA as a binder to reduce
the brittleness of the pellet with an applied pressure of
Fig. 1 Block diagram on synthesis of Ni2?:Zn2SiO4 ceramic pow-
ders by a sol–gel method
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10 ton, which was burnt out during high-temperature sin-
tering. Then the pellets were sintered at 1,000 �C for 2 h in
an air atmosphere. The samples were cooled by a slow
cooling of those to room temperature. Sintered pellets were
polished by fine emery paper to make both the surfaces
smooth and parallel and silver paste coating was applied on
the opposite surface of pellets to make it as a the pellets
were electrode with air-drying conducting silver paste and
also, thereby forming a parallel plate capacitor geometry.
2.3 XRD profile measurements
The prepared sol–gel powder ceramics were characterized
on a 3003 TT SEIFERT X-ray diffraction system with
CuKa line (k = 1.5418 A) of radiation, XRD patterns were
recorded in the 2h range of 108–808 with a scanning rate of
0.028/s and the peaks were analyzed by using the standard
JCPDS card. The crystallite size of the samples was cal-
culated using full width at half maxima (FWHM) by using
Debye–Scherrer’s formula [15].
Dcrystallite ¼kk
b 2hð Þ cos hð1Þ
where D was the crystallite size, k was Scherrer’s con-
stant = 0.9, k = 1.5406 A (X-ray wavelength), and b was
FWHM at diffraction angle 2h. D is the average diameter of
the crystallite size. All the peaks were indexed and lattice
constants (a and c) and cell volume of unit cell for each con-
centration were calculated by the following relations respec-
tively [16, 17]:
sin2 h ¼ k2
3a2þhkþ k2� �
þ k2
4c2
� �l2 ð2Þ
Here k is the X-ray wavelength, a and c are the lattice
constants and (h k l) are the corresponding Miller indices.
V ¼ a2c sin 120o ð3Þ
2.4 Physical properties
The porosity (P) of all the samples has been determined
from the formula [18]
P ¼ 1� dm
dx
ð4Þ
where dm and dx are the measured (bulk) density and X-ray
(theoretical) density, respectively. The measured density
has been calculated using the relation
dm ¼m
V¼ m
mr2hð5Þ
where h is the height, r is the radius and m is the mass of a
cylindrical pellet of the sample. The X-ray density was
calculated by using the formula
dx ¼ZM
NVð6Þ
where Z is the number of atoms per unit cell, M is the molecular
weight of one formula unit and N is Avogadro’s number and
V is the volume of the unit cell of the sample respectively.
2.5 FT-IR spectral analysis
To obtain information about the coordination of the
ligands, the FTIR spectrum of powder sample was recorded
on a Thermo Nicotet Avator 360 FT-IR spectrophotometer
in the range 400–4,000 cm-1 using KBr pellet.
2.6 Raman spectral analysis
Raman spectra were measured using a confocal Raman
microscope (Lab RAM HR 800, Horiba Jobin–Yvon SAS,
France) equipped with a 532 nm Nd:YAG laser (Torus Laser,
Laser Quantum, France) with laser power 50 mW, 2 scans and
a 50X LWD air-dry visible objective (NA = 0.50
WD = 10.6 mm lieu Microsystems of Model BX 41) and
attached with a Filetiyar multichannel CCD detector. Each
Raman spectrum were measured in the range 100 and
1,200 cm-1, with a spectral resolution of 0.35 cm-1/pixel with
a 1,800 g/mm grating at the confocal pinhole was a set to
400 nm. Lab Sepc software under Windows was used to con-
trol the Raman system, for data acquisition and saving the data.
2.7 SEM and EDAX measurements
Scanning electron microscopy images and energy disper-
sive X-ray spectrometry (EDAS) profiles were used to
investigate sample morphology and thus carried out the
elemental analysis of the samples studied. EDAS was
carried out on an Oxford instruments detector on the SEM
over the range 0–20 keV.
2.8 Electrical measurement
The electrical parameters (impedance and capacitance) of
the sample were measured in the frequency range from
100 Hz to 1 MHz using a phase sensitive millimeter (PSM
1700) LCR meter. The dielectric constant has been calcu-
lated using the relation [19].
�0 ¼ Csd
A�0
ð7Þ
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where Cs is the capacitance, d the thickness of pellet, A the
area of the cross section, e0 is the permittivity of free space
(8.85 9 10-14 F/cm). The complex dielectric constant e00
of the samples was calculated using the relation:
�00 ¼ �0 tan d ð8Þ
where tan d is the dielectric loss tangent which is propor-
tional to the loss of energy from the applied field into the
sample (this energy is dissipated as heat) and therefore
denoted as dielectric loss. The loss tangent (tan d) has been
calculated from the relation:
tan d ¼ �00
�0ð9Þ
AC conductivity of the samples was determined using
the relation [20]:
rac ¼d
A
Z0
Z02 þ Z002
� �ð10Þ
where d is the thickness of sample, A is effective area; Z0 is
the real part of the complex impedance and Z00 is the
imaginary part of the impedance.
3 Results and discussion
3.1 X-ray diffraction and physical properties
The room temperature XRD pattern of all the samples of
Zn2-xSiO4:xNi2? (x = 0.0, 0.25, 0.50 and 0.75 mol%)
sol–gel ceramic powders sintered at a temperature of
1,000 �C is depicted in Fig. 2. The diffraction pattern show
sharp and well defined single diffraction peaks and it can
be seen that all the compositions remained the pure wil-
lemite (a-Zn2SiO4) phase. The peak positions agree well
with those of the standard pattern reported by the Joint
Committee on Powder Diffraction Standards (JCPDS, 79-
2005) for Zn2SiO4 in Willemite structure. Further, no other
impurity peak was observed in the XRD pattern showing
the single phase sample formation. All the samples
exhibited main diffraction peaks corresponding to (1 1 0),
(3 0 0), (2 2 0), (1 1 3), (1 3 2), (1 4 0), (0 4 2), (0 3 3), (2 2
3), (5 1 1), (1 2 4), (3 3 3), (4 4 0) and (7 1 3) planes
indicated that doped samples exhibit the rhombohedral
a = b and c with space group Rð3Þ (148) structure and the
highly doped samples show some additional peaks [20, 21].
Based on literature, some of the unknown peaks may cor-
respond to on live structure of non-willemite Ni2SiO4.
The calculated crystallite size (D) and the lattice param-
eters (a = b and c) and cell volume (V (A3)) also been studied
for different doping concentrations of each sample are
depicted in Table 1. It can be observed from Table 1 that the
crystallite size, lattice parameter and cell volume of Zn2SiO4
do not significantly change with nickel doping. And also it
could be indicated that Zn2? ions could be substituted by
Ni2? ions in regular lattice sites, due to smaller difference in
their ionic radii for Ni2? (69 pm) and for Zn2? (74 pm).
During the sintering process, a force is generated making the
material dense. When the driving force of the grain boundary
for each grain is not homogeneous, the sintering by attains a
non-uniform grain size distribution. XRD pattern of the
Ni2?-doped sample is almost the same as that of the un-
doped sample. No characteristic diffraction peaks of dopant
have been observed because the mole ratio of Ni2? in the
doped sample was low and the solid state solution of
Ni2?:Zn2SiO4 was formed.
The calculated grain size and the percentage of porosity
(P) for the present sol–gel ceramic powder are given in
Table 1. It is clear from the Table 1, that X-ray density is
Fig. 2 X-rd profiles of Zn2-xSiO4:xNi2? (x = 0, 0.25, 0.5,
0.75 mol%) sol–gel ceramic powders
Table 1 Values of different parameters for rhombohedral crystal
system of Ni2? ions doped willemite a-Zn2SiO4 with space group
Rð3Þ (148) ceramic powders by sol–gel method
Parameters X = 0.0 X = 0.25 X = 0.50 X = 0.75
Crystallite size (nm) 54.99 55.17 59.12 55.09
Lattice constant
a = b (A)
13.890 13.930 13.970 13.926
Lattice constant c (A) 9.31 9.34 9.34 9.33
Cell volume (V/A3) 1,555 1,569 1,578 1,567
X-ray density dx
(g/cm3)
4.26 4.21 4.17 4.15
Bulk density db
(g/cm3)
2.18 2.68 2.10 3.31
Porosity (fraction) 0.48 0.36 0.49 0.20
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higher than that of apparent (bulk) density. It may be due to
the existence of pores in the materials, which depends on
sintering conditions. This behaviour is attributed to the fact
that the substitution of Ni2? ions in these samples may
affect the grain size development during the sintering
process. This leads to a decrease in oxygen vacancy con-
centration and increase in porosity [22].
3.2 Vibrational analysis: FTIR and Raman spectra
Figure 3 presents FT-IR spectra of samples containing dif-
ferent nickel ions doping concentration sintered at 1,000 �C.
The characteristic strong vibrational modes of these mate-
rials are observed at the locations of 870 cm-1 (t1 SiO4);
911, 935 and 977 cm-1 (t3 SiO4), 460 (t4 SiO4), 577 (t1
ZnO4) and 616 cm-1 (t3 ZnO4); where t1 stands for totally
symmetric stretching, t3 is for asymmetric stretching and t4
asymmetric deformation [23]. The appearance of the
vibrations of SiO4 and ZnO4 groups clearly suggest the
formation of the Zn2SiO4 phase. The FT-IR spectral profiles
are almost identical and exhibit strong bands between 400
and 800 cm-1, which are typical metal–oxygen vibrations
for the willemite structure. In addition, all spectra show a
broad band around 3,645–3,265 cm-1 and from 1,620 to
1,640 cm-1 assigned to the stretching vibrations and bend-
ing vibrations modes of O–H of adsorbed molecular water
hydrogen bond to molecular water respectively [24]. All the
characteristic absorption bands are summarized in Table 2.
Figure 4 shows an important influence of the doping of
nickel ions on the vibrational state of the pure Zn2SiO4 ceramic
powder Raman spectra recorded at room temperature. The
spectrum of crystalline Zn2SiO4 possess vibrational features
strong Raman scattering centered at 868, 903 and 947 cm-1
which are originated from the surface of siloxane group and a
sharp intense peak at 472 cm-1 originate from siloxane link-
age; besides some weak signal bands appeared in lower fre-
quency side 107, 221, 290 and 405 cm-1 have been assigned to
the 5-, 6-, 10-membered rings present in this structure [24]. The
Raman bands, from 0 to 300 cm-1 which corresponding to the
lattice vibrations, the region between 800–1,100 and
300–700 cm-1 region was assigned to the stretching and
bending vibrations of the SiO4 group respectively [24, 25]. To
make it more clear, Raman bands are reported in Table 2.
3.3 SEM and EDAX analysis
Figure 5 shows a typical morphology and composition of
pure (Fig. 5a) and 0.5 % Ni-doped (Fig. 5b) Zn2SiO4 cera-
mic powders. Samples were in the powder form for SEM
analysis. Powder was stick on the sample holder using
double sided tape and gold coated with sputter coater. SEM
micrographs show the presence of larger spherical aggre-
gates of smaller individual nano size particles and the pre-
sence of Ni is confirmed the results of XRD and EDAX that
the Ni is successfully doped in the Zn2SiO4 host matrix. The
grain size of Zn2SiO4 phase isn’t restrained to grow exactly
with introducing Ni2? ions into ceramic system.
Fig. 3 FT-IR profiles of Zn2-xSiO4:xNi2? (x = 0, 0.25, 0.5,
0.75 mol%) sol–gel ceramic powders
Fig. 4 Raman spectra of Zn2-xSiO4:xNi2? (x = 0, 0.25, 0.5,
0.75 mol%) sol–gel ceramic powdersTable 2 Comparison of SiO4 vibrational bands of Ni2? ions doped
willemite a-Zn2SiO4 with space group Rð3Þ (148) ceramic powders
by sol–gel method
Composition
(x)
(mol%)
FT-IR bands (SiO4) Raman bands (SiO4)
t1
(cm-1)
t3
(cm-1)
t4
(cm-1)
Stretching
(cm-1)
Bending
(cm-1)
X = 0 868 920 466 866, 904, 943 391, 472
X = 0.25 870 922 463 869, 906, 946 406, 474
X = 0.50 868 922 464 869, 906, 944 405, 474
X = 0.75 869 926 462 869, 906, 946 397, 474
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3.4 Dielectric constant
The dielectric constant is represented by e = e0 - ie00,where e0 is real part of dielectric constant and describes the
stored energy while e00 is imaginary part of dielectric
constant, which describes the dissipated energy.
Figure 6a, b show the variation of real (e0) and imagi-
nary (e00) parts of the dielectric constant for Zn2-xSiO4:
xNi2? (x = 0.0, 0.25, 0.50 and 0.75 mol%) sol–gel cera-
mic powders has a function of frequencies (100 Hz–
1 MHz) at room temperature. It is clear from these Fig. 6a,
b that it has strong frequency dependence in the lower
frequency region. The decrease in dielectric constant value
exponentially with increasing frequency is a normal
behaviour observed in high frequency limit in most of the
ceramics materials. The dielectric constant decreases with
the increase in frequency and become constant at high
frequencies for all compositions and this type of dispersion
behaviour can be explained on the basis of Maxwell–
Wagner model type interfacial polarization [26, 27].
According to this model, a dielectric medium is assumed to
be made up of well conducting grains which are separated
by poorly conducting (or resistive) grain boundaries. Under
the application of external electric field, the charge carriers
can easily migrate the grains but are accumulated at the
grain boundaries. This process can produce large polari-
zation and high dielectric constant. The dielectric constant
decreases with frequency as various polarization processes
Fig. 5 SEM images and EDAX profiles of a Zn2SiO4 and b 0.5Ni2?:Zn2SiSO4 sol–gel ceramic powders
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ceases at higher frequencies. The small conductivity of
grain boundary contributes to the high value of dielectric
constant at low frequency [28].
The higher value of dielectric constant can also be
explained on the basis of interfacial/space charge polariza-
tion due to inhomogeneous dielectric structure. The inho-
mogeneities present in the system may be due to the porosity
and grain boundaries. The polarization decreases with the
increase in frequency and then reaches a constant value due
to the fact that beyond a certain frequency of external field
the hopping between different metal ions (Zn2?, Ni2?)
cannot follow the alternating field. It is also been observed
that the value of dielectric constant decreases with the
increase in Ni2? dopant. Hence, as the dopant concentration
increase more zinc ions will be substituted by nickel ions and
thereby decreasing the dielectric polarization, which in turn
decreases dielectric constant. As it can be seen from Fig. 6a,
b, Ni2? ions (x = 0.0, 0.25, 0.50, 0.75 mol%) samples,
Ni2? = 0.5 mol% has higher dielectric constant in the fre-
quency range selected, whereas the e0 of the samples with
x = 0.0, 0.25, 0.50, 0.75 mol% remain almost unchanged,
implying a good frequency stability.
3.5 Dielectric loss
Loss tangent or loss factor tan d represents the energy
dissipation in the dielectric system. Figure 7 shows the
variation of dielectric loss factor with frequency at room
temperature. It has been observed that tan d decrease with
the increase in frequency for all the compositions, which
may be due to the space charge polarization. The decrease
of tan d with the increasing frequency is attributed to the
fact the hopping frequency of charge carriers cannot follow
the changes of the externally applied electric field beyond a
certain frequency limit. The dielectric losses of the samples
increase with increase in Ni2? ions up to 0.5 mol% in
lower frequency (\50 Hz) and decrease for higher doping
concentration (0.75 mol%) and beyond. Therefore,
dielectric losses decrease at higher frequency. These types
of variations in the dielectric losses are characteristic of the
dipole orientation and electrical conduction and space
charges, thus, more dielectric relaxation can be observed
giving rise to more dielectric losses [29].
3.6 AC conductivity
Figure 8 shows the variation of AC conductivity with
frequency (100 Hz–1 MHz) for different compositions at
room temperature. It has been observed that AC conduc-
tivity starts to increase with increasing in frequency for all
Fig. 6 Variation of a real (e0) and b imaginary (e’’) parts with
frequency for different compositions of Zn2-xSiO4:xNi2? (x = 0,
0.25, 0.5, 0.75 mol%) sol–gel ceramic powders
Fig. 7 Variation of dielectric loss (tan d) with frequency for different
compositions of Zn2-xSiO4: xNi2? (x = 0, 0.25, 0.5, 0.75 mol%) sol–
gel ceramic powders
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compositions, which is a common feature of ceramic
materials. Total conductivity of the system is given by [30]
r ¼ ro Tð Þ þ r x;Tð Þ ð11Þ
Here, first term on R.H.S is DC conductivity which is
independent of frequency. The second term is pure AC
conductivity due to the electron hoping between the metal
ions. It has been observed that AC conductivity gradually
increases with increases in frequency of applied AC filled
because of the increase in frequency enhances the electron
hopping of charge carriers among localized states [31]. It
can also be seen from Fig. 8 that AC conductivity increases
with increase in dopant concentration up to 0.5 mol% and
then decreases at 0.75 mol% and above. It may be attrib-
uted that the dopant of Ni2? ions are acceptors for Zn2SiO4
and however, the substitution of Zn2? with Ni2? can take
place up to a certain limit [32].
Figure 9 shows the variation of log rac versus log (x)
with frequency (100 Hz–1 MHz) for different composi-
tions at room temperature. The AC conductivity obeys the
empirical formula of the frequency dependence given by
the AC power law:
rac ¼ Axn ð12Þ
where A and ‘n’ are constant, n is a dimensionless parameter
and A has the conductivity unites. The exponent ‘n’ has been
calculated as a function of compositions for each sample by
plotting log rac versus log (x) according Eq. 12, which
represents straight lines with slope equal to the exponent ‘n’
and intercept part equal to log A on vertical axis at log x = 0
[33]. Inset in Fig. 9 shows the variation of ‘n’ as a function of
Ni2? doping. It can be seen that the exponent ‘n’ is found to
be composition dependent. It is reported that ‘n’ has values
between 0 and 1 [34]. When n = 0, the electrical conduction
is frequency independent of DC conduction and for n [ 0,
the conduction is frequency dependent or AC conduction
[35]. In the present study, the values of the exponent ‘n’ lie
between 0.324 and 0.600, which suggests that the conduction
mechanism in studied samples is AC conduction and is due to
hopping of charge.
3.7 Impedance analysis
Impedance spectroscopy has been a frequency response
technique used to unravel the complexities involved in
electro ceramic materials. The influence of doping con-
centration, impurities and second phase precipitation are
also usually investigated by this technique. The measure-
ments of impedance give us information about the resistive
(real part) and reactive (imaginary part) components of
electrical parameters and hence provide a clear picture of
material properties. A widely used frequency dependent
complex dielectric function is represented by.
�� ¼ �0ðxÞ � i�00ðxÞ ð13Þ
It is well know that the behaviour of the impedance
spectra for various materials is explained using Cole–Cole
or Nyquist plot, in which Z00 is plotted on the vertical axis
the Z0. The Cole–Cole plot is particularly useful for
materials, which possess one or better separated relaxation
processes with comparable in magnitudes and obeying the
Debye or Cole–Cole functional forms. The plot can be
drawn for any five complex parameters such as impedance
(Z*), the permittivity (e*), the admittance (Y*), the elec-
trical modulus (M) and dielectric loss (tan d). The
parameters are related to each others as follows:
Fig. 8 Variation of ac conductivity with frequency for different
compositions of Zn2-xSiO4: xNi2? (x = 0, 0.25, 0.5, 0.75 mol%) sol–
gel ceramic powders
Fig. 9 Variation of log rac with respect to log x for Zn2-xSiO4:
xNi2? (x = 0, 0.25, 0.5, 0.75 mol%) sol–gel ceramic powder with
inset showing variation of exponent ‘n’ with composition
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tan d ¼ �00
�0¼ M00
M0¼ Z0
Z0ð14Þ
The electrical characteristic of materials is exhibited by
the appearance of semicircular arcs in Nyquist plots. The
plot can give two semicircles, depending upon the elec-
trical properties of the materials. The first semicircle at low
frequency represents the resistance of grain boundary and
second one obtained at high frequency corresponds to the
resistance of grain or bulk properties [36]. The complex
impedance has been calculated from the relation:
Z� xð Þ ¼ Z0 xð Þ � iZ00ðxÞ; ð15Þ
where Z0 and Z00 are real and imaginary impedance and can
be written as.
Z 0 ¼ Rg
ð1þ xgCgRgÞ2þ Rgb
ð1þ xgbCgbRgbÞ2
ð16Þ
Z 00 ¼�R2
gxgCg
ð1þ RgCgxgÞ2þ
�R2gbCgxg
ð1þ RgbCgbxgbÞ2ð17Þ
where Rg and Cg represent the resistance and the capaci-
tance of the grains, respectively. While, Rgb and Cgb rep-
resent the corresponding terms for the grain boundary
volume. A schematic electrical model/circuit diagram
depicting has been shown in Fig. 10, this circuit which
pertains to the Eqs. 16 and 17 in the present work. From
this figure, it is clearly indicated that a typical electro-
chemical cell and its equivalent circuits, showing the
responses in and complex impedance plots with: (1) non-
blocking electrodes and (2) blocking electrodes. The
resistance values for the grain and grain boundary have
been calculated from the intercepts on the real part of Z
(Z0) axis, whereas the capacitance values are obtained from
the highest frequency of the semi- circular arcs [37]. The
relaxation times can be calculated by the expressions:
sg ¼1
xg
¼ CgRg ð18Þ
sgb ¼1
xgb
¼ CgbRgb ð19Þ
Values of impedance parameters thus calculated are
presented in Table 3.
Figure 11a shows the variation of real part of impedance
(Z0) as a function of applied frequency for different com-
positions at room temperature. It is observed that Z0 has
higher values at lower frequency and decreases with
increase in frequency and attains a constant value in the
higher frequency domain for all the compositions. A dec-
rement trend in the real part of impedance (Z0) with an
increase in frequency could be due to an increase in AC
conductivity with frequency from all the compositions of
samples, which are corroborated by AC conductivity
measurement. Since, impedance is inversely proportional
to the conductivity; it decreases with an increase in doping
ion content. Figure 10b shows the variation of imaginary
part of impedance (Z00) as a function of applied frequency
for different commotions at room temperature. It is clear
from the Fig. 11b, Z00 shows the peaking behaviour and
reaches a maximum Z00max and then decrease with further
increase in frequency and goes to very small values at
higher frequencies. It has also been observed that both the
values of Z0 and Z00 are found to decrease up to 0.5 mol%
and then start increasing with a further increase in the
compositions. The decreasing value of both Z0 and Z00
means increasing loss in resistive property of the samples.
Fig. 10 Typical electrochemical cell and their equivalent circuits
along with the responses in and complex impedance plots with:
(i) non-blocking electrodes and (ii) blocking electrodes
Table 3 Complex impedance properties, AC conductivity and power
law of exponents ‘n’ of Ni2?:Zn2SiO4 ceramic powders by sol–gel
method
Composition
(x)
(mol%)
rac
(S/cm)
n Rgb
(MX)
Cgb (F) sgb (S)
X = 0 3.354E-4 0.600 4.58 5.91E-4 2.70E-4
X = 0.25 4.162E-4 0.356 2.83 3.30E-11 9.36E-5
X = 0.50 8.203E-4 0.324 1.79 2.56E-11 4.60E-5
X = 0.75 2.893E-4 0.428 3.29 2.84E-11 9.36E-5
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Such behaviour is expected due to the presence of space
charge polarization in a material. The existence of Debye
relaxation peaks in the imaginary part of complex imped-
ance at low frequencies may be due to the existence of
space-charge relaxation at low frequencies, which is related
to the charge carriers in association with oxygen vacancies
[38]. The change in the relaxation peak may be due to the
change in hopping frequency with doping. It can be seen
that the values of Z00 max decrease with the increase in
hopping indicating decrease in loss in the system.
The resistive part Z0 is plotted against the reactive part
(Z00) to distinguish between the grain and grain boundary
contributions for the various compositions of Ni2? doped
Zn2SiO4 sol–gel ceramic powders as shown in Fig. 12 The
size of semicircle changes with the increase in doping
concentration of Ni2? doped Zn2SiO4. As the compositions
increases, the diameter of the semicircle decreases indi-
cating the reduction of grain interior resistance as shown in
Table 3. The resistances are calculated from the circular
arc intercepts on the Z0 axis, while the capacitance values
are abstained from the maximum of the circular arcs [39].
The maximum height in each semicircle is Z0 = -Z00,therefore by using this condition we can calculated the
capacitance for grain boundary and relaxation times by
using the relations (Eqs. 18 and 19). It is observed that the
Nyquist/Cole–Cole plot shows only one semicircle for all
compositions. The results suggest that the grain boundary
volume in Ni2? doped Zn2SiO4 sol–gel ceramic powder is
high because of the small crystallite sizes and hence con-
duction takes place predominantly through grain boundary,
its well match with the Fig. 5b. For the composition
x = 0.5 %, even though the grain boundary volume frac-
tion is small, the presence of single semi-circle in the
impedance plot suggests that the grain and grain boundary
have equal resistances.
4 Conclusions
It could be concluded that the Ni2?:Zn2SiO4 ceramic
powders have successfully been synthesized using sol–gel
method. The XRD, FT-IR, Raman and SEM images could
reveal a pure phase crystalline (willemite structure). The
crystalline, particle size and lattice parameters are found to
be decreasing with an increase in Ni2? concentration. Thus
results have demonstrated that the dielectric constants and
tan d exhibiting normal dielectric behaviour and a
decreasing trend has been observed with an increase in the
frequency and dopant ion concentration change, which are
explained in terms of Maxwell–Wagner model. The AC
conductivities are increasing with an increase in frequency
and dopant concentrations, showing that small polaron are
responsible for conductions in these sol–gel ceramics. The
Fig. 11 Variation of a real (e0) and b imaginary (e’’) part of
impedance with frequency for different compositions of Zn2-xSiO4:
xNi2? (x = 0,0.25,0.5,0.75 mol%) sol–gel ceramic powders
Fig. 12 Nyquist plots for different compositions of Zn2-xSiO4:xNi2?
(x = 0, 0.25, 0.5, 0.75 mol%) sol–gel ceramic powders
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dielectric properties (e0, e00, tan d) and AC conductivity
show that there is a maximum value for 0.5 mol% of Ni
doping in Zn2SiO4. The complex impedance spectra show
only one semi-circle corresponding to the grain boundary
resistance up to 0.5 mol% of Ni doping, suggesting a
dominance of grain boundary resistance in the present
study. The obtained dielectric constant and dielectric loss
tangent of the samples at higher frequency region with low
conductivities are found to be useful for potential
applications.
Acknowledgments One of us (B.C.B) would like to thank the UGC,
New Delhi for the award of a Rajiv Gandhi National Fellowship
(RGNF) to him to carry out the present study.
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