Modulus spectroscopy study on Ferroelectric Lithium and Titanium modified Lead Potassium Neobate Ceramics

IOSR Journal of Applied Physics (IOSR-JAP)
e-ISSN: 2278-4861.Volume 7, Issue 2 Ver. II (Mar. - Apr. 2015), PP 16-21
www.iosrjournals.org
DOI: 10.9790/4861-07221621 www.iosrjournals.org 16 | Page
Modulus spectroscopy study on Ferroelectric Lithium and
Titanium modified Lead Potassium Neobate Ceramics
P. Easwaraji1
, Dr.M.P.Srinivasarao2
, M. Srikanth3
(Physics Department, G.M.R.I.T,Rajam, Srikakulam District, Andhrapradesh, India)
Abstract:Ferroelectric lithium and titanium modified Lead Potassium Neobate Ceramics were prepared by
solid state reaction method. The modulus represents the real dielectric relaxation process. The usefulness of the
modulus representation in the analysis of relaxation properties was demonstrated both for ionic conductors and
polycrystalline ceramics. The complex electrical modulus is a parameter that can be expressed as Fourier
transform function )(t gives the time evolution of electric field with in the dielectric. Variation of real part
(𝑀
′
)of electrical modulus with frequencyand temperatures was measured on the prepared modified and
unmodified materials.The high frequency side of 𝑀′′
peak represents the range of frequency in which the ions
are strictly confined to their potential well and ions can make only localized motions with in the wells. The
activation energy of D.C conduction can be obtained from Arrhenius plot of 𝑀′′
peak frequencies.
Keywords: Ferroelectrics, electrical modulus, D.C.conduction, Arrhenius plot
I. Introduction
The biggest use of ferroelectric ceramics have been in the areas such as dielectric ceramics for
capacitor applications, ferroelectric thin films for nonvolatile memories, piezoelectric materials for medical
ultrasound imaging and actuators, and electro- optic materials for data storage and displays. In the past few
decades, many books and reviews have been written explaining the concepts of ferroelectricity in materials [1-
12].From the physical point of view, the electrical modulus corresponds to the relaxation of the electric field in
the material when the electric displacement remains constant. Therefore, the modulus represents the real
dielectric relaxation process [13]. The usefulness of the modulus representation in the analysis of relaxation
properties was demonstrated both for ionic conductors [14] and polycrystalline ceramics [15]. In practice,
regions of low capacitance, such as grain interiors, are characterized using M′′
data, whereas more resistive
regions, such as grain boundaries and pellet surface layers, which often have higher associated capacitances, are
characterized using M′′
spectra [16].
II. Preparation
In the present work the ceramic compositions of modified and unmodified Lead Potassium Niobate,
have been prepared by using a high temperature sintering technique. Analar grade chemicals of PbO, K2CO3,
Li2CO2, Nb2O5 and TiO2 have been taken to prepare the compositions like (i).Pb0.77K0.46Nb2O6:0.23:PKN, (ii).
Pb0.77K0.26Li0.20Nb2O6 : 0.23Li:PKN (iii). Pb0.77K0.26Li0.20Ti0.25Nb1.8O6 : 0.23LiTi:PKN. For each composition
the weighed raw materials have been grinded in an agate mortar and pestle for more than 8 hours. Calcination
of the mixture was done at 9000
C for 4 hours in a platinum crucible covered with a lid. The calcined powder
again grinded by adding a binder 5% Polyvinyl Alcohol to bring the particles closer. The powder obtained after
grinding with PVA has been pellatized, using a steel die by applying a pressure of (3-5) Tons/cm2
. The sintered
pellets were polished to make the two surfaces parallel and dried over a hot plate. The samples which were
electroded having dimensions around 10 mm diameter and 2.3 mm thickness have been used to study the
modulus spectroscopy properties.
III. Experimental
The real and imaginary part of electrical modulus at various temperatures and frequencies have been
calculated using series resistance Rs and dielectric loss D values obtained from HIOKI 3532-50 LCR
HiTESTER.
IV. Results And Discussions
The complex electrical modulus is a parameter that can be expressed as Fourier transform function
)(t gives the time evolution of electric field with in the dielectric,
"'
*  i

Modulus spectroscopy study on Ferroelectric Lithium and Titanium modified Lead …
M*
( )()(/1) "'*
 iMM 
= M }]/)(){exp(1[ dttdti  
=  ])()/[( 2''2'"'
 i
Variation of real part (M′
)of electrical modulus with frequency (45Hz – 5MHz) at various
temperatures (30 – 5950
C) has been shown in fig.1 (a,b,c). At a constant temperature, M′
increases with increase
in frequency and takes nearly a constant value. At low frequency and high temperature region, M
'
approaches
zero conforming an appreciable electrode and /or ionic polarization [17].
10
2
10
3
10
4
10
5
10
6
0.0
6.0x10
-5
1.2x10
-4
1.8x10
-4
2.4x10
-4
3.0x10
-4
Pb0.77
K0.46
Nb2
O6
M
l
log f Hz
300
O
C
340
O
C
380
O
C
400
O
C
420
O
C
440
O
C
460
O
C
480
O
C
500
O
C
520
O
C
540
O
C
560
O
C
580
O
C
595
O
C
(a)
1x10
0
2x10
0
3x10
0
4x10
0
5x10
0
6x10
0
7x10
0
0.0
5.0x10
-5
1.0x10
-4
1.5x10
-4
2.0x10
-4
2.5x10
-4 495
O
C
500
O
C
505
O
C
510
O
C
515
O
C
520
O
C
525
O
C
530
O
C
540
O
C
550
O
C
Pb0.77
K0.26
Li0.2
Nb2
O6
M'
log f Hz
(b)
1x10
0
2x10
0
3x10
0
4x10
0
5x10
0
6x10
0
7x10
0
0.0
2.0x10
-3
4.0x10
-3
6.0x10
-3
8.0x10
-3
1.0x10
-2
1.2x10
-2
1.4x10
-2
400
O
C
410
O
C
425
O
C
440
O
C
460
O
C
490
O
C
540
O
C
Pb0.77
K0.26
Li0.2
Ti0.25
Nb1.8
O6
M
1
logf(Hz)
(c)
Fig.1: Variation of real part of electrical modulus with frequency at different temperatures
Variation of imaginary part of modulus M′′
with frequency at various temperatures (300-5950
C) has
been shown in fig.2(a,b,c). As the temperature increases peak frequency of M′′
shifts to higher frequency side.
The low frequency side of peak represents the range of frequency in which the ions can move over long
distances, i.e., ions can perform successful hopping from one site to the neighboring site. The high frequency
side of M′′
peak represents the range of frequency in which the ions are strictly confined to their potential well
and ions can make only localized motions with in the wells[18-21].

10
2
10
3
10
4
10
5
10
6
0.0
2.0x10
-5
4.0x10
-5
6.0x10
-5
8.0x10
-5
1.0x10
-4
Pb0.77
K0.46
Nb2
O6
M
ll
log f HZ
300
O
C
340
O
C
380
O
C
400
O
C
420
O
C
440
O
C
460
O
C
480
O
C
500
O
C
520
O
C
540
O
C
560
O
C
580
O
C
595
O
C
(a)
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5
-2.0x10
-4
0.0
2.0x10
-4
4.0x10
-4
6.0x10
-4
8.0x10
-4
1.0x10
-3
1.2x10
-3
1.4x10
-3
1.6x10
-3 Pb0.77
K0.26
Li0.2
Nb2
O6
M
ll
log f HZ
495
O
C
500
O
C
505
O
C
510
O
C
515
O
C
520
O
C
525
O
C
530
O
C
540
O
C
550
O
C
(b)
1x10
0
2x10
0
3x10
0
4x10
0
5x10
0
6x10
0
7x10
0
0.0
1.0x10
-3
2.0x10
-3
3.0x10
-3
4.0x10
-3
5.0x10
-3
6.0x10
-3
380
O
C
400
O
C
410
O
C
425
O
C
440
O
C
460
O
C
490
O
C
540
O
C
Pb0.77
K0.26
Li0.2
Ti0.25
Nb1.8
O6
M
11
logf(Hz)
(c)
Fig.2: Variation of Imaginary part of electrical modulus a with frequency
The shift in the frequency of M′′
peak corresponds to the so called conductivity relation. Since the
change in the dielectric constant of the grain boundary phase is relatively small (almost constant) with
temperature, the change in the value of M′′
indicates the grain contribution. The activation energy of D.C
conduction can be obtained from Arrhenius plot of M
"
peak frequencies. The reciprocal of frequency of
M′′
peak represent the time p .
Fig.3(a,b,c) shows the normalized imaginary part of the electric modulus M′′
Mmax
′′
as a function of
logarithmic frequency at several temperatures in corresponding compositions of PBKNN. The
M′′
Mmax
′′
parameter exhibits a peak or maximum value with a slightly asymmetric degree at each temperature.
The region of the left of the peak is one where the carriers are confined to potential wells being mobile over
short distance. The frequency range at around the peak indicates the transition from short range to long –range
mobility, considering the decrease in frequency. In the peak, the relaxation is defined by the condition ωτ = 1.
Where, τis the most probable relaxation time. The reciprocal of frequency of M″ peak frequency (fmax) represent
the time scale of transition from long range mobility and is defined as the characteristic relaxation time , τ =
(2πf)-1
.

(a) (b)
1 2 3 4 5 6 7
0.0
0.2
0.4
0.6
0.8
1.0
Pb0.77
K0.26
Li0.2
Ti0.25
Nb1.8
O6
M
11
/M
11
max
logf(Hz)
425
0
C
440
0
C
460
0
C
490
0
C
540
0
C
(c)
Fig.3: The normalized imaginary part of M11
/M11
max of impedance as a function of frequency at several
temperatures.
The relaxation time exhibits a thermally activated dependence. The dc conductivity relaxation can be
obtained from the peak position, i.e., fmax. Fig.4 (1000/T Vsωp, )shows the Arrhenius plot, relaxation angular
frequency , ]/exp[0 KTEp   as a function of inverse of temperature, where 0 is the pre exponential
factor of angular frequency, 0 be the relaxation time and T is the absolute temperature.

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8
10
2
10
3
10
4
10
5
Pb0.77
K0.46
Nb2
O6
relaxationalangularfreqency,p
1000/T (1/K)
(a)
1.20 1.22 1.24 1.26 1.28 1.30
3.1x10
3
3.1x10
3
3.2x10
3
3.3x10
3
3.3x10
3
3.4x10
3
3.4x10
3
3.5x10
3
3.5x10
3
Pb0.77
K0.26
Li0.2
Nb2
o6
1000/T (1/K)
(b)
1.20 1.25 1.30 1.35 1.40 1.45
10
3
10
4
Pb0.77
K0.26
Li0.2
Ti0.25
Nb1.8
O6
1000/T (1/K)
(c)
Fig.4: The Arhenius plot of relaxation frequency as a function of 1000/T
The activation energies obtained from fig.4(a,b,c) are tabulated in table I
TableI: Activation energies of relaxation energies frequencies from M′′
peaks as a function of 1/T
Composition Temperature range (O
C) Dc conduction activation energy (ev)
0.23PKN 390-520 0.29
0.23Li:PKN 580-520 0.54
0.23LiTi:PKN 530-590 0.49
V. Conclusions
d.c conduction activation energies are calculated using the M′′
peak frequencies in all the three compositions.
The value liesbetween 0.29ev – 0.54 ev.
The d.c and a.c conduction activation energies are calculated from Arrhenius plots and the values of activation
energies reveals the ionic conduction mechanisms in the compositions under investigation.
References
[1]. H. D. Megaw, Ferroelectricity in Crystals (Methuen, London, 1957)
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[6]. T. Mitsui, I. Tatsuzaki, and E. Nakamura, An Introduction to the Physics of Ferroelectrics (Gordon and Breach, London, 1976)
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[15]. J.liu, Ch-g Dun , W..G.Yin, Q, NMeiR.W.Smith and J.R. Hardy J.Chem.Phys. 119,2812(203).
[16]. N. Horse, and A.R.West, J. Am.Ceram.Soc.Japan 79, 1633 (1996).
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cryst.Solids, 275, 116 (2000).
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Modulus spectroscopy study on Ferroelectric Lithium and Titanium modified Lead Potassium Neobate Ceramics

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Modulus spectroscopy study on Ferroelectric Lithium and Titanium modified Lead Potassium Neobate Ceramics