Dielectric, modulus and impedance analysis of LaF3 nanoparticles

Article abstract of DOI:10.1016/j.physb.2010.06.004

Lanthanum fluoride nanoparticles have been synthesized by the simple method of direct precipitation from an aqueous solution. TG/DTA analysis confirms the sample formation at low temperature (300 °C). Structure of LaF₃ nanoparticles has been an

Full text of DOI:10.1016/j.physb.2010.06.004

Physica B 405 (2010) 3803–3807
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Physica B
journal homepage: www.elsevier.com/locate/physb
Dielectric, modulus and impedance analysis of LaF3 nanoparticles
D. Arun Kumar a,b, S. Selvasekarapandian a,c,n, H. Nithya b, A. Sakunthala b, M. Hema b
a Department of Physics, Bharathiar University, Coimbatore 641 046, India
b DRDO-BU Center for Life Sciences, Bharathiar University, Coimbatore 641 046, India
c Kalasalingam University, Krishnankoil, Srivilliputhur 626 190, India
a r t i c l e i n f o
a b s t r a c t
Article history:
Lanthanum fluoride nanoparticles have been synthesized by the simple method of direct precipitation
from an aqueous solution. TG/DTA analysis confirms the sample formation at low temperature (300 1C).
Structure of LaF3 nanoparticles has been analyzed by XRD and LaF3 is found to be in tysonite structure.
From the XRD spectra the average particle size is found to be 15 nm using the Scherrer formula. The
impedance, modulus and dielectric spectra analysis of the prepared LaF3 nanoparticles has been studied
using AC impedance spectroscopy. The ionic conductivity of LaF3 nanoparticles is significantly increased
by an order from 10ꢀ6 to 10ꢀ5 S cmꢀ1. The modulus and dielectric spectra analysis confirms the non-
Debye type behavior in the material.
Received 24 November 2009
Received in revised form
27 March 2010
Accepted 2 June 2010
Keywords:
LaF3
Chemical synthesis
Electrical properties
Dielectric properties
& 2010 Elsevier B.V. All rights reserved.
1. Introduction
range of 300–530 1C, the ionic conductivity of nanoscale CaF2 was
1–2 orders of magnitude higher than that of coarse grain
polycrystalline CaF2 and CaF2 single crystal. Subsequently, Wu
and his group synthesized nanophase PdF2 in the same way and
the ionic conductivity was found to increase by an order of
magnitude higher than that of crystalline PdF2 [12]. Recently, LaF3
thin films with particle size ranging from 50 to 90 nm were
prepared by vacuum evaporation and conductivity was studied
[13]. LaF3 superfine powder with particle size ranging from 100 to
200 nm was also synthesized with the microwave heating method
and the results indicated that grain refining of LaF3 could increase
its ionic conductivity [14]. Other methods such as micro emulsion
[15] and hydrothermal means [16] were applied to synthesize
nano-crystalline LaF3 powder. In the present work nano-crystal-
line lanthanum fluoride has been synthesized by the simple
method of direct precipitation from aqueous solution as reported
by Da xiong et al. [17]. The prepared lanthanum fluoride
nanoparticles have been subjected to AC impedance spectroscopic
analysis with LaF3 as the electrolyte and aluminium as the
blocking electrodes within the frequency range 42 Hz–4 MHz. To
our knowledge the modulus and dielectric studies have not been
carried out on LaF3 and hence an attempt has been made to study
the electrical properties of LaF3 nanoparticles.
Electrochemical sensors have been widely used in applications
such as critical care, safety, industrial hygiene, process controls,
emissions monitoring, etc. Solid electrolyte sensors are good
electrolytes and offer excellent potential for use in electrochemi-
cal sensors [1]. Fluorides have been widely applied in many fields
such as sensors, batteries and actuators, and additive and wear
resistant materials. Fluoride ion is one of the smallest anion with
high mobility. Lanthanum fluoride exhibits high ionic conductiv-
ity at ambient temperatures among other rare earth fluorides
[2,3]. Lanthanum fluoride based chemical sensors have been
applied for sensing fluoride, oxygen and carbon monoxide
because of its high chemical stability and high ionic conductivity
[4–7]. The ability of lanthanum fluoride to sense dissolved oxygen
has been utilized to construct biosensors with an enzyme as
auxiliary electrode [8]. Miura et al. [3] and Matayoshi et al. [9]
reported the use of lanthanum fluoride as the electrolyte material
in glucose and oxygen sensor based on its high fluoride ion
conductivity. As the world approaches towards nanotechnology,
an effective method to increase the ionic conductivity of fluorides
is by having them in nano-size. As the particle size approaches the
nano-scale the ionic conductivity increases by an order of
magnitude. In 1993, Wu et a1 [10] and Puin et al. [11] synthesized
CaF2 nano-crystals of average grain size 16 nm. In the temperature
2. Experimental method
Lanthanum nitrate (La(NO3)3 ꢁ 6H2O) and ammonium fluoride
(NH4F) were purchased from Merck and Hi-Media, respectively,
and used without further purification. Lanthanum fluoride
n Corresponding author at: Kalasalingam University, Krishnankoil, Srivilliputhur
626 190, Tamil Nadu, India. Tel.: +91 4563 289042.
E-mail address: sekarapandian@yahoo.com (S. Selvasekarapandian).
0921-4526/$ - see front matter & 2010 Elsevier B.V. All rights reserved.
doi:10.1016/j.physb.2010.06.004

3804
D. Arun Kumar et al. / Physica B 405 (2010) 3803–3807
nanoparticles were prepared by first dissolving 0.3 mol/L lantha-
num nitrate in double distilled water and then mixing with 1 mol/L
ammonium fluoride dissolved in double distilled water. The
lanthanum fluoride nanoparticles are formed instantly while
adding the fluoride solution with the nitrate solution following
the equation
LaðNO3Þ3 þ3NH4F-LaF3 þ3NH4NO3
ð1Þ
The nanoparticles were washed with double distilled water
several times and then calcined at 350 1C for 24 h. The resultant
powder was then pressed into pellets of diameter 1 cm and
thickness of 1 mm using a hydraulic press for 10 min.
TG/DTA analysis has been carried out using Perkin Elmer STA
6000 to confirm the formation temperature of the sample. X-ray
diffraction analysis has been done using a PANalytical Xpert Pro
X-ray diffractometer with CuKa1 radiation as the source material.
AC impedance spectroscopic analysis was performed using a
computer controlled Hioki 3532 LCZ meter within the frequency
range 42 Hz–4 MHz at different temperatures using aluminium as
the blocking electrodes.
20
30
40
50
60
70
80
2θ (degree)
Fig. 2. X-ray diffractogram of lanthanum fluoride powders.
3. Results and discussion
powders to be in the hexagonal phase. The average particle size
has been calculated using the Scherrer formula given by
3.1. TG/DTA analysis
Fig. 1 shows TG/DTA traces of the as prepared LaF3 precursor. A
slight endothermic peak around 100 1C accompanied by a small
weight loss in the TG curve ascribed to the removal of water from
the precursor is observed. The broad endothermic peak at around
300 1C accompanied with a drastic weight loss in the TG curve is
ascribed to the removal of nitrates from the precursor. The TG
curve confirms the formation temperature of the sample to be
around 300 1C.
0:94
l
y
D ¼
ð2Þ
b2y cos
where is the wavelength of the X-ray source, b2 the full width
l
y
at half maximum, and
size calculated using the Scherrer formula is found to be 15 nm.
y the diffraction angle. The average particle
3.3. Impedance spectra analysis
3.2. Structural analysis
Electrical properties of electro-ceramics at fixed frequency do
not give a whole set of properties towards the evaluation of the
electric parameters as a function of temperature. Hence in order
to understand the frequency dependent phenomena associated
with grain boundaries region and intrinsic properties of material,
electrical properties of the material were studied over a wide
range of frequencies with respect to temperature. Argand
diagrams, imaginary part of complex impedance Zn versus its real
part, allow one to determine the bulk ohmic resistance of the
material as a function of temperature and thereby temperature
dependence of conductivity. Fig. 3(a)–(c) shows the Cole–Cole
plot of impedance at different temperatures. The complex
X-ray diffractogram of the prepared lanthanum fluoride
powder is shown in Fig. 2. All the peaks match with JCPDS Card
no. 32-0483, which shows the system to be in tysonite structure
and in hexagonal phase with space group p3c1. In this structure
the fluorine ions are located on three distinct sub lattices F1, F2
and F3 in the ratio 12:4:2 per unit cell as reported earlier [18]. The
¯
peaks observed at 2
y values, 24.731, 27.661, 43.641 and 50.521
correspond to the (1 1 0), (1 1 1), (3 0 0) and (3 0 2) plane
reflections, respectively, which confirms the lanthanum fluoride
350
impedance diagram shows two well-defined regions,
a
100
semicircle in the high frequency region, which is related to the
grain interior resistance in the bulk of the electrolytes, and a spike
in the low frequency region, which is attributed to the effect of
blocking electrodes. At low frequencies the complex impedance
plot shows a straight line parallel to the imaginary axis, but the
double layer at the electrode–electrolyte interface causes
the curvature. The bulk capacitance values are calculated using
the relation
300
90
250
80
200
70
150
o
maxRbCb ¼ 1
ð3Þ
60
100
The bulk capacitance (Cb) values are found to be in the order of
pico farad (pF), which indicates the nature of grain interior
resistance. The bulk capacitance values indicate ionic transport
through grain interior and the values have been tabulated in
Table 1. The grain interior resistance is contributed by the motion
of Fꢀ ions along the grains and is known as the bulk resistance of
the material [19]. The centre of the semicircle falls below the real
axis, indicating the non-Debye nature of the material.
50
40
50
0
100
200
300
400
500
Temperature oC
Fig. 1. TG/DTA traces for the LaF3 precursor.

D. Arun Kumar et al. / Physica B 405 (2010) 3803–3807
3805
0.018
633K
80
70
60
50
40
30
20
10
0
0.016
0.014
0.012
0.010
0.008
0.006
0.004
0.002
0.000
-0.002
643K
653K
663K
673K
683K
693K
703K
713K
723K
(a)
633K
643K
653K
663K
673K
2
3
4
5
6
7
8
9
0
10
20
30
40
50
60
70
80
log ω
Z' (kOhm)
Fig. 4. Logarithm of
o versus real part of modulus of LaF3 at different
Fig. 3. Cole–Cole plot for LaF3 at (a) 633–673 K, (b) 683–723 K and (c) 308 K.
temperatures.
Table 1
0.008
633K
Transport parameters of lanthanum fluoride at different temperatures.
643K
653K
663K
673K
683K
693K
703K
713K
723K
0.007
0.006
0.005
0.004
0.003
0.002
0.001
0.000
-0.001
Temperature (K) Conductivity (S cmꢀ1
)
Cb (pF) Relaxation time (s)
b
633
643
653
663
673
683
693
703
713
723
5.4 ꢂ 10ꢀ6
9.0 ꢂ 10ꢀ6
1.2 ꢂ 10ꢀ5
1.4 ꢂ 10ꢀ5
1.7 ꢂ 10ꢀ5
2.1 ꢂ 10ꢀ5
2.8 ꢂ 10ꢀ5
3.4 ꢂ 10ꢀ5
4.6 ꢂ 10ꢀ5
5.6 ꢂ 10ꢀ5
0.24
0.33
0.35
0.32
0.32
0.39
0.37
0.41
0.47
0.52
7.83 ꢂ 10ꢀ7
4.54 ꢂ 10ꢀ7
3.56 ꢂ 10ꢀ7
1.85 ꢂ 10ꢀ7
1.53 ꢂ 10ꢀ7
1.27 ꢂ 10ꢀ7
9.72 ꢂ 10ꢀ8
7.65 ꢂ 10ꢀ8
6.13 ꢂ 10ꢀ8
4.75 ꢂ 10ꢀ8
0.83
0.81
0.84
0.83
0.85
0.87
0.89
0.89
0.89
0.88
According to Hoff et al. [20] the mobility of fluoride ions varies
with the positions they occupy. At low temperature most of the
fluoride ions present in the lattices F2 and F3 find it difficult to
move; the conductivity is contributed from the small amount of
highly free F1 site fluoride ions and hence conductivity is low. As
the temperature increases more and more fluoride ions turn to
occupy the high mobility sub-lattice positions, resulting in high
conductivity and this takes place around 623–723 K in the present
study. The ionic conductivity is calculated using the relation
2
3
4
5
6
7
8
9
logω
Fig. 5. Logarithm of
o versus imaginary part of modulus of LaF3 at different
temperatures.
been shown in Figs. 4 and 5, respectively. It is evident from Fig. 4
that for all temperatures, M0 reaches a constant value at higher
frequencies. Also at lower frequencies M0 approaches nearly zero,
confirming the presence of an appreciable electrode and/or ionic
polarization in the temperature range studied. The value of M0
increases from the low frequency value towards the high
frequency value as temperature increases [21,22].
l
s
¼
ð4Þ
RA
where R is the resistance of the material, l the thickness of the
pellet (cm) and A the area of the pellet (cm2). The conductivity at
308 K is found to be 2.7 ꢂ 10ꢀ6 S cmꢀ1 and at 723 K it is found to
be 5.6 ꢂ 10ꢀ5 S cmꢀ1
.
Fig. 5 shows a single asymmetric peak in the temperature
range studied, indicating the non-exponential decay of the
electric field. The broad nature of the peaks can be interpreted
as being the consequence of distribution of relaxation time.
Moreover, such peaks are broader than the Debye peak, which
is usually attributed to an ideal ionic conductor [23]. The
capacitance values are calculated at the maximum frequency
using the relation M00 ¼Co/2Cb. The capacitance value is found to
be in the range of pF, which implies that the peak observed is
due to the relaxation in bulk type components [24]. The
peak frequency of M00 shifts towards the high frequency
region as temperature increases, which implies conductivity
relaxation suggesting that the dielectric relaxation, is activated
3.4. Modulus spectra analysis
The modulus spectra mainly reflect the bulk properties of the
sample. Electric modulus relaxation studies have been carried out
between 633 and 723 K in the complex modulus Mn formalism.
The complex modulus is given by the inverse of complex
dielectric permittivity
1
M* ¼
¼ MuþjM00
ð5Þ
e*
Variations of real (M0) and imaginary (M00) parts of the electric
modulus as functions of frequency at various temperatures have

3806
D. Arun Kumar et al. / Physica B 405 (2010) 3803–3807
thermally, in which a hopping process of charge carriers is
predominant [25].
is commonly known as o(nꢀ1) variation or non-debye nature of
behavior, where the space charge regions with respect to
frequency are explained in terms of ion diffusion [27]. At high
frequencies due to the large periodic reversal of the field at the
electrode interface, the contribution of charge carriers, especially
ions, towards the dielectric constant decreases with increase in
temperature.
3.5. Stretching parameter
The frequency dependence of modulus has been described by
the Kohlraush–Williams–Watts (KWW) function
F
(t), which
Fig. 7 shows the plot of log
o
versus log e00 at different
describes the electric field decay [26]:
temperatures. The plot has been fitted linearly and the slope of
the straight line has been found to be in the range ꢀ0.8 to ꢀ0.9.
The slope value close to ꢀ1 indicates that DC conduction is
predominant in the present sample. The deviation in the slope
value from unity may be attributed to space charge effects at low
frequencies [28].
ꢀ
ꢁ
Z
1
1
tÞ df
dt
o
M*ð
o
Þ ¼
1ꢀ
dteðꢀj
ð6Þ
e1
0
The Kohlraush–Williams–Watts (KWW) function is given by
t0Þb
F
ðtÞ ¼ eðꢀt=
where
describes the breadth of the distribution in the limits of
parameters of the stretched exponential
ð7Þ
The dissipation (loss) factor tan
Tan
Fig. 8 shows the plot between log
d is given by the equation
t
o is the time at which ^(t) decays to 1/e and the exponent
b
d
¼
e00
=eu
ð9Þ
and tan d. Elissalde and
0obo1. The t0 and b
o
function are, respectively, the conductivity relaxation time and
the Kohlraush exponential function. The non-exponential char-
acter of the electric field decay is a result of microscopic
Ravez [29] have reported two types of relaxations, one in the low
frequency region and the other in the high frequency region. The
peak in the low frequency region is attributed to the real dielectric
heterogeneity of the system. The stretching parameter
calculated by extracting FWHM of the modulus peak using
¼1.14/FWHM and is given in Table 1, which implies non-Debye
type relaxation for all temperatures. The smaller the value of
b has been
b
633K
663K
6
b
,
693K
723K
the greater the deviation with respect to Debye type relaxation.
From Table 1 it is found that the relaxation time calculated from
the M00 plot at the maximum of the peak decreases with increase
in temperature.
5
4
3
2
1
3.6. Dielectric analysis
The dielectric properties of a system can be characterized
using frequency dependent parameters, which may define
complex permittivity. The real and imaginary parts of dielectric
e0 and e00, respectively, are calculated using the formula
1
e* ¼
ð8Þ
joCZ*
where Zn is the complex impedance, C¼
e
oA=d, A is the effective
area of the electrodes, d the thickness of the pellet, eo the
pffiffiffiffiffiffiffi
o
versus e00 at different temperatures for LaF3 is
2
3
4
5
6
7
8
permittivity,
o is 2pn and j ¼ ꢀ1.
log ω
A plot of log
Fig. 7. Logarithm of
o
versus log e00 for LaF3 at different temperatures.
shown in Fig. 6. The dispersion of dielectric constant is high at low
frequency for all temperatures and this may be attributed to the
formation of space charge region at the electrode interface, which
6
5
4
3
2
1
0
633K
1000000
653K
673K
693K
713K
633K
643K
653K
663K
673K
683K
693K
700K
713K
723K
900000
800000
700000
600000
500000
400000
300000
200000
100000
0
-100000
2
3
4
5
6
7
8
2
3
4
5
6
7
8
9
log
ω
log ω
Fig. 6. Logarithm of
o
versus dielectric loss e00 at different temperatures.
Fig. 8. Logarithm of
o
versus tan d at different temperatures for LaF3.

D. Arun Kumar et al. / Physica B 405 (2010) 3803–3807
3807
constant of the material due to Maxwell–Wagner polarization and
the peak observed around the high frequency may be attributed
to dielectric relaxation. From the figure a relaxation is observed in
the high frequency region. This may be attributed to interface
charge relaxation at the grain boundaries.
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4. Conclusion
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LaF3 nanoparticles of average grain size 15 nm were prepared
at room temperature by direct precipitation from an aqueous
solution. TG/DTA analysis presents the formation of LaF3 at
300 1C. The ionic conductivity value calculated from impedance
plot is found to be 7.2 ꢂ 10ꢀ5 S cmꢀ1 at 723 K. The modulus
spectra analysis shows the non-Debye nature behavior of the
material. The higher value of dielectric represents the increase in
polarizability in the material.
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