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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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