Structural, lattice vibrational, optical and microwave dielectric studies on Ca1-xSrxMoO4 ceramics with scheelite structure

Article abstract of DOI:10.1016/j.materresbull.2014.04.064

Structural, optical and microwave dielectric properties of Ca _1-xSr_xMoO₄ (x = 0.0, 0.2, 0.4, 0.6, 0.8 and 1.0) compositions were studied with help of Rietveld refinement and Raman spectroscopy measurements. All these compositions were prepared by solid state reaction method and observed to possess tetragonal scheelite structure with I4₁/a space group. Microwave dielectric properties such as dielectric constant (ε_r), quality factor (Q×f) and temperature coefficient of resonant frequency (τ_f) were measured using Hakki-Coleman method, reflection technique and invar cavity attached to hot plate respectively. ε_r, (Q × ^_f) and τ_f are correlated with molar volume (V_m), MoO bond strength and Raman shift of A_1g mode respectively. All these compounds show good microwave dielectric properties (ε_r = 6.7-9.6, Q × f = 35,000-52,000 GHz and τ_f = -28 to -17 ppm/°C). Band gap of these compositions was observed in the range 3.3-3.5 eV and variation in band gap was fitted with Bowing equation.

Full text of DOI:10.1016/j.materresbull.2014.04.064

Accepted Manuscript
Title: Structural, lattice vibrational, optical and microwave
dielectric studies on Ca1−xSrxMoO4 ceramics with scheelite
structure
Author: S.D. Ramarao S.Roopas Kiran V.R.K. Murthy
PII:
S0025-5408(14)00249-9
DOI:
Reference:
http://dx.doi.org/doi:10.1016/j.materresbull.2014.04.064
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10-3-2014
24-4-2014
Please cite this article as: S.D.Ramarao, S.Roopas Kiran, V.R.K.Murthy,
Structural, lattice vibrational, optical and microwave dielectric studies on
Ca1-xSrxMoO4 ceramics with scheelite structure, Materials Research Bulletin
http://dx.doi.org/10.1016/j.materresbull.2014.04.064
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Structural, lattice vibrational, optical and microwave dielectric studies on
Ca1-xSrxMoO4 ceramics with scheelite structure
S.D. Ramarao1, S. Roopas Kiran2, V.R.K. Murthy1,*
1Microwave laboratory, Department of Physics, Indian Institute of Technology Madras,
Chennai 600 036, India.
2INFN, Sezione di Padova, Via Marzolo 8, 35131 Padova, Italy.
*Corresponding author: Telephone +91-44-22574859; Fax: +91-44-22570545
E-mail: vrkm@iitm.ac.in
Graphical abstract
Highlights
 Microwave dielectric properties of scheelite Ca1-xSrxMoO4 ceramics are studied.
 r correlated with unit cell volume in contrast to polarizability.
 Q×f of these compositions explained with Mo-O bond strength.
 Interesting correlation between f and Raman shift of A1g mode is observed.
 Non monotonic variation in band gap is observed and fitted with bowing equation.
Abstract:
Structural, optical and microwave dielectric properties of Ca1-xSrxMoO4 (x= 0.0, 0.2,
0.4, 0.6, 0.8 and 1.0) compositions were studied with help of Rietveld refinement and Raman
spectroscopy measurements. All these compositions were prepared by solid state reaction
method and observed to possess tetragonal scheelite structure with I41/a space group.
Microwave dielectric properties such as dielectric constant (r), quality factor (Q×f) and
temperature coefficient of resonant frequency (f) were measured using Hakki-Coleman
method, Reflection technique and invar cavity attached to hot plate respectively. r, (Q×f) and
1
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f are correlated with molar volume (Vm), Mo-O bond strength and Raman shift of A1g mode
respectively. All these compounds show good microwave dielectric properties (r = 6.7–9.6,
Qf = 35000–52000 GHz and f = -28 to -17 ppm/oC). Band gap of these compositions was
observed in the range 3.3–3.5 eV and variation in band gap was fitted with Bowing equation.
.
Keywords: Ceramics; X-ray diffraction; Raman spectroscopy; dielectric properties; optical
properties.
1. Introduction
Dielectric ceramics such as Dielectric Resonators (DR) play an important role in the
rapid growth of mobile, satellite and radar communication [1, 2]. These dielectric resonators
should possess high dielectric constant (r>20) for miniaturization of electronic components,
low dielectric loss (high Quality factor) for enhancing the selectivity of particular frequency
and near-zero temperature coefficient of resonant frequency (f). Perovskites (ABO3) and
complex perovskites (ABB'O3) were extensively studied for microwave dielectric resonator
applications with substitution of different cations at A- and B-sites [3-5].
Recently researchers focused on the microwave dielectric properties of A2+B6+O4
compositions with scheelite and wolframite structures. Depending on the ionic radius of A-
site cation, the A2+B6+O4 (A: Ca, Sr, Ba; B: Mo, W) compounds exhibit scheelite structure
with I41/a space group and wolframite structure with P2/c space group [6, 7]. In scheelite
structure A- and B-site cations possess coordination number eight and four respectively
whereas in wolframite structure both cations possess six coordination numbers. Numerous
investigations were reported on scheelite compounds for cathode material in solid oxide fuel
cells [8], photo catalytic [9] and photoluminescent materials [10, 11]. Vibrational spectra
were also reported by many researchers with complete assignment of Raman and IR modes
[12-14]. Recently these A2+B6+O4 compounds gained much attention in LTCC technology
2
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o
because of their lower sintering temperatures (≤ 1200 C) and flexibility for the substitution
of different elements at A- and B-site to obtain optimum microwave dielectric properties. The
compounds with lower sintering temperature and good microwave dielectric properties was
reported by Zhou et al. in xBi(Fe1/3Mo2/3)O4–(1ꢀx)BiVO4 system in which the Raman and
Infrared spectroscopy were implied to understand the phase transition mechanism. With
increasing the x value from 0 to 0.1 the phase transition temperature observed to decrease
o
o
from 255 C to -9 C and obtained good microwave dielectric properties even at lower
sintering temperatures [15]. Zhou et al. reported the ultralow sintering temperature (around
o
620 C) compound with higher dielectric constant and lower f values by substituting Li1+
and Bi3+ at A-site of A(W,Mo)O4 compounds [16].
Yoon et al. reported the structure and microwave dielectric properties of AWO4
compounds based on the ionic radius of A-site cation and observed that the compounds with
lower ionic radius of cations at A-site possessed higher quality factor [17]. Puller et al.
explained the microwave dielectric properties of AWO4 (A= Mg, Zn, Ni and Co) compounds
with extrinsic parameter such as density [18]. Kim et al. studied the microwave dielectric
characteristics of (1-x)CaWO4 – xLaNbO4 compounds and observed an interesting correlation
between the quality factor and atomic packing fraction [19]. Choi et al. calculated the
polarizability of Mo in AMoO4 (A= Ca, Sr, Ba, Mg, Zn, and Mg) compounds using least
square refinement in conjunction with the Clausius–Mosotti relation and correlated f with the
unit cell volume of [7]. Kim et al. correlated the quality factor, f of scheelite A2+B6+O4
compounds with the packing fraction and oxygen bond valence (VO) respectively [20]. A
similar correlation was also observed by Liao et al. in ZnTiNbTaO8 compound [21].
However, a slight contradictory result was observed by Kim et al. in the case of NiWO4
compound and correlated the lower quality factor of NiWO4 with presence of unpaired 3d
electrons in Ni2+ even though NiWO4 has higher packing fraction [22]. Zhou et al. reported
3
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that the dielectric constant of scheelites got enhanced with substitution of Bi+3 and alkali
earth elements at A-site of A2+B6+O4 compounds [23, 24]. Hence the microwave dielectric
properties of A2+B6+O4 compounds would depend on the structural parameters such as
packing fraction [20] and bonding characteristics [25].
In the present paper we report the structural, lattice vibrational, microwave dielectric
and optical properties of Ca1-xSrxMoO4 (x = 0.0, 0.2, 0.4, 0.6, 0.8 and 1.0) compounds.
Rietveld refinement was performed on all these compositions to study phase purity of these
compositions. Lattice vibrational characteristics such as Raman shift of A1g mode of these
compositions were analyzed from the Raman spectra. Microwave dielectric properties of
these compounds are correlated with lattice vibrational characteristics in conjunction with
structural parameters. The variation in the band gap of these compositions is fitted with
Bowing equation.
2. Experimental Procedure
Ca1-xSrxMoO4 (x= 0.0, 0.2, 0.4, 0.6, 0.8 and 1.0) compounds were synthesized by
conventional solid state reaction method. Proportionate amounts of starting reagents CaCO3
(99.95%), SrCO3 (99.9%) and MoO3 (99.95%) (Alfa Aesar, USA) were mixed and hand
ground in an agate mortar with distilled water medium for 2 h. All these compounds were
o
calcined at 900 C for 3 h. Cylindrical pellets of about 8 mm diameter and 7 mm thickness
were prepared using uniaxial hydraulic press by adding 3 wt% PVA to the calcined powders.
All these compacted pellets were sintered in temperature range 1100 – 1300 oC for 3 h.
Phase identification was done by obtaining powder diffraction data of all the sintered
samples using Philips PANAlytical X'pert Pro X-ray diffractometer with X’Celerator detector
and Cu K radiation at acceleration conditions of 40 kV and 30 mA. The incident and
receiving soller slits of 0.02 rad and the divergent slit of 1o were used and data was collected
in the range of 10–120o with a scan step of 0.017o. Rietveld refinement was performed using
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GSAS suite with EXPGUI to obtain the cation–oxygen bond lengths in Ca1-xSrxMoO4 (x= 0.0,
0.2, 0.4, 0.6, 0.8 and 1.0) compounds [26, 27]. Raman spectra of polished and thermally
etched samples were collected using Horiba Jobin Yvon HR800 UV Raman spectrometer
equipped with Peltier-cooled charge-coupled device detector. He-Ne laser source (=632.8
nm) was used for the measurement and the laser output power measured at the sample was
about 3 mW. The optical band gap of these compounds was calculated from the optical
absorption spectra using UV-Vis dual beam spectrophotometer (Jasco V-570) at room
temperature.
The bulk densities of all these samples were measured using the Archimedes
technique. Microstructures of polished and thermally etched samples were observed by FEI
Quanta 400 high resolution Scanning Electron Microscopy. Microwave dielectric
characterization was done using Vector Network Analyzer (Agilent PNA-L N5230C).
Dielectric constant was obtained by Hakki-Coleman method [28]. Quality factor was measured
by reflection technique with gold coated copper cavity. Temperature coefficient of resonant
o
frequency (TCF) measured in the temperature range of 25-85 C using an invar cavity. The
TCF was calculated by the following formula
f85  f25
f25 (85 25)
 f 
ppm/oC
(1)
where f85 and f25 are the resonant frequencies at 85oC and 25oC respectively.
3. Results and Discussion
3.1 Structure and Lattice Vibrational Analysis
The room temperature XRD patterns of Ca1-xSrxMoO4 (x= 0.0, 0.2, 0.4, 0.6, 0.8 and
1.0) are shown in the Fig. 1. It is clearly understood from this figure that, all these
compositions form a solid solution with tetragonal scheelite structure and I41/a (No: 88, Z=4)
space group. All these patterns were indexed with JCPDS file number 29-351 and 30-1287. As
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the ionic radius of Sr2+ (1.26 Å) is greater than Ca2+ (1.12 Å) [29], with substitution of Sr2+ in
place of Ca2+ the lattice parameters get increased which inturn increases the unit cell volume.
Correspondingly all the XRD reflections are observed to shift to lower angle side as shown in
Fig. 1.
Rietveld refinement was performed on all these compositions to examine the variation
in bond length of cation–oxygen bonds and nature of bonding. The initial parameters for the
refinement of CaMoO4 system was taken from Daturi et al. [6]. The refined plot for
Ca0.6Sr0.4MoO4 composition is shown in Fig. 2 as a representative. All the refinement
parameters such as fractional atomic coordinates, occupancies and thermal parameters of
Ca0.6Sr0.4MoO4 composition are given in Table 1. The Rietveld discrepancy indices Rwp, Rp
are around 8% and 5% respectively. Goodness of fit (2) values are in the range of 1.2–2.0
which indicate that the patterns are well fitted with I41/a space group and conforming the
formation of tetragonal scheelite structure.
The unit cell representation of scheelite Ca0.6Sr0.4MoO4 compound is shown in Fig. 3.
The green, wine and blue colored spheres represent Mo, (Ca/Sr) and oxygen atoms
respectively. It is seen from the Fig. 3 that the unit cell comprises of four formula units. This
scheelite structure is composed with (Ca/Sr)O8 bisdisphenoid and MoO4 tetrahedra in which
the (Ca/Sr)O8 polyhedra arranged in zigzag manner along c-axis [30]. Each (Ca/Sr)O8
polyhedra is surrounded by four (Ca/Sr)O8 polyhedra and are connected by edge sharing. The
MoO4 tetrahedra are connected to the (Ca/Sr)O8 polyhedra by sharing its corner with
(Ca/Sr)O8 polyhedra. The local environment of (Ca/Sr)O8 bisdisphenoid and MoO4 tetrahedra
are shown in Fig. 4(a) and Fig. 4 (b) respectively.
In order to study the influence of Sr2+ substitution at A-site of CaMoO4 compound on
lattice vibrations of this compound, we have performed room temperature Raman
spectroscopy measurements on Ca1-xSrxMoO4 (x= 0.0, 0.2, 0.4, 0.6, 0.8 and 1.0) compounds.
6
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Fig. 5a shows the room temperature Raman spectra of Ca1-xSrxMoO4 (0, 0.2, 0.4, 0.6, 0.8, and
1.0) compositions in the frequency range 50–1000 cm-1. It is clearly understood from these
Raman spectra that, all these compositions form in scheelite structure with I41/a space group
[31]. The lattice vibrations in the scheelites structured compounds are categorized into internal
modes which correspond to vibrations inside the [MoO4]2- molecular units and external mode
that are assigned to lattice vibrations of motion of M2+ metal ions and rigid [MoO4]2-
molecular units. The Td symmetry of [MoO4]2- tetrahedrons in free space is reduced to S4
symmetry in crystal lattice due to crystal field effect. In scheelite structure the primitive cell
possesses two [MoO4]2- units consequently, the S4 symmetry of [MoO4]2- tetrahedron changes
to C4h that results to Davydov Splitting [13, 32]. As a result of crystal field effect and
Davydov splitting, the degeneracy of [MoO4]2- vibrations corresponding to Td symmetry in
free space is resolved. The group theoretical analysis predicts that 26 modes are possible in the
case of tetragonal scheelite structured compounds with I41/a space group which are distributed
as irreducible representations.
 = 3Ag + 5Bg+ 5Eg+ 5Au+ 3Bu+ 5Eu
(2)
Out of which the Ag, Bg and Eg vibrations are Raman active whereas Au, Bu and Eu
vibrations are IR active. In the present study 12 vibrational modes are observed for
Ca1-xSrxMoO4 (0, 0.2, 0.4, 0.6, 0.8, and 1.0) compositions and are shown in Fig. 5a. In the
Raman spectra, a dominant intense mode is observed at 881.7 cm-1 for x= 0.0 composition
which is assigned to s(Mo–O) (symmetric vibrations of Mo–O stretching mode, A1g) and an
antisymmetric stretching mode, as(Mo–O) at 850.5 cm-1. The modes below 350 cm-1
correspond to external modes, while internal modes are observed at higher wave number side.
The assignment of all Ag, Bg and Eg modes are shown in Fig. 5a. With addition of higher ionic
radius Sr2+ in the place of lower ionic Ca2+, the unit cell volume increases which in turn affect
the interatomic distances in the MoO4 tetrahedra and causing the decrease in the covalence of
7
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bond between cation and MoO4. Out of these effects, the A1g mode of CaMoO4 shifts to lower
wave number side with increase of Sr2+ substitution. However, we observed an anomaly in our
present study. The increase in the internal symmetric stretching mode frequency (A1g, Fig 5a)
and decrease of maximum external mode frequency (Eg, Fig. 5b) result to the decrease of
interaction between internal and external modes in Ca1-xSrxMoO4 (0, 0.2, 0.4, 0.6, 0.8, and
1.0) compounds. This combined affect shows impact on the shift and FWHM of A1g mode in
the case of end members (x=0.0 and 1.0). The A1g mode becomes broader in the composition
range 0.2  x ≤ 0.8 that can be attributed to the presence of complex environment (presence of
Ca2+ and Sr2+ ions in A-site) around the MoO4 tetrahedron and influences the rigidity of
tetrahedron in the scheelite structure.
3.2 Density and Microstructure
Densities of Ca1-xSrxMoO4 (x= 0.0, 0.2, 0.4, 0.6, 0.8 and 1.0) ceramic compositions
were measured using Archimedes principle with an accuracy of 0.005 whereas the theoretical
densities of these ceramic compounds were calculated using the following equation [21].
nM
th 
g.cm-3
(3)
NV
Where n, M and V represent the number of formula units per unit cell, molecular weight and
volume of these compounds whereas N represents the Avogadro’s number (6.0221023 mol-1).
All the measured (m) and theoretical densities (th) are given in Table. 2. From these we have
calculated the percentage of theoretical density ( = (m/th)100) of all these compounds and
observed to possess more than 95% theoretical density. SEM micrographs of polished and
thermally etched samples were collected by FEI quanta 400 high resolution Scanning Electron
Microscope and are shown in Fig. 6(a)–(f). These micrographs reveal that all the samples are
well densified and possess uniform grain size with less porosity. The densities of Ca1-
xSrxMoO4 (x= 0.0, 0.2, 0.4, 0.6, 0.8 and 1.0) ceramics are given in Table 2.
8
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3.3 Microwave Dielectric Properties
3.3.1 Dielectric constant (r)
The dielectric constant of Ca1-xSrxMoO4 (x= 0.0, 0.2, 0.4, 0.6, 0.8 and 1.0) was
measured by Hakki-Coleman method [28] at respective resonant frequency which vary in
between 10 to 12 GHz. With increase in the Sr2+ the dielectric constant decreases from 9.6 to
7.4. According to Shannon additive rule with substitution of high polarizable Sr2+ (4.24 Å3)
ion in place of low polarizable Ca2+ (3.16 Å3) ion [33], the dielectric constant should increase
which is not observed in our present study. The dielectric constant mainly depends on the
density, secondary phases [20, 34], ionic polarizability [25] and molar volume [35] of the
compounds. From XRD patterns and microstructural analysis, it is observed that these
compositions possess no secondary phases and possess more than 95% theoretical density.
According to Clausius-Mosotti equation, dielectric constant depends on polarizability and
molar volume of the compounds. In order to explain the contradiction in the dielectric constant
variation and on which parameter it will depend, we calculated the rate of increase of molar
volume (dVm/dx) and ionic polarizability (dD/dx) with Sr2+ substitution. It is noticed that the
molar volume increases more rapidly than ionic polarizability and is shown in Fig. 7. Hence,
molar volume plays predominant role in the variation of dielectric constant of Ca1-xSrxMoO4
(x= 0.0, 0.2, 0.4, 0.6, 0.8 and 1.0) system.
As the dielectric constant depends on the density and porosity of the samples, the
measured values of dielectric constant are corrected to the porosity using the following
formula [17].
r  exp. (11.5P)
(4)
where r, exp are the porosity corrected and experimentally observed dielectric constants
m
th.
and P 1
m: measured density, th: Theoretical density.
9
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The porosity corrected dielectric constants of these compositions are given in Table 2.
The variation in r of Ca1-xSrxMoO4 (x= 0.0, 0.2, 0.4, 0.6, 0.8 and 1.0) compositions is
correlated with the molar volume (Vm) of these compositions and is shown in Fig. 8.
3.3.2 Quality factor
Quality factor (Q×f) of all the Ca1-xSrxMoO4 (0, 0.2, 0.4, 0.6, 0.8 and 1.0) ceramics
were measured using reflection cavity technique with gold coated copper cavity at the
respective resonant frequencies which are in the frequency range 10 to 12 GHz and are shown
in Fig. 9. The quality factor decreases from 51500 GHz at x = 0.0 to a minimum value 35500
GHz at x=0.4 compound and again increased to 48500 GHz at x=1.0. It is well known that the
quality factor of microwave dielectric ceramics depends on extrinsic losses which arises from
the presence of defects, secondary phases, grain size and porosity where as the intrinsic losses
are related to crystal structure and bonding character of ions of the materials [36-40]. The
effect of extrinsic losses are minimal as the Rietveld refinement reveals that there are no
secondary phases present in Ca1-xSrxMoO4 (0, 0.2, 0.4, 0.6, 0.8 and 1.0) and microstructural
analysis indicate that all the compounds possess uniform grain size with less porosity.
Quality factor predominantly depends on the bond parameters such as bond strength
[41, 42]. Weakly bounded cations with oxygen will give additional dielectric loss, because
the ions rattle more freely in the MoO4 tetrahedron and interact strongly with the anharmonic
phonons. The Mo-O bond strength in Ca1-xSrxMoO4 (0, 0.2, 0.4, 0.6, 0.8, and 1.0) compounds
were calculated using the following equations
V 
v
(5)

i
ij
j
R -d




ij 

ij
(6)
v  exp
ij
b
where Rij is the bond valence parameter, dij is the bond length between i and j atoms
and b is commonly taken as universal constant equal to 0.37 Å. The Mo-O bond lengths are
10
Page 10 of 37

obtained by Rietveld refinement. The obtained bond valence sum is used to calculate the bond
strength (S) which is defined as the ratio of bond valence sum of cation and its coordination
number. The variation of Mo-O bond strength in all these Ca1-xSrxMoO4 (0, 0.2, 0.4, 0.6, 0.8,
and 1.0) compositions is shown in Fig. 9. It can be observed that the variations in both quality
factor and Mo-O bond strength with Sr substitution are analogous to each other and are given
in Table 3.
3.3.3 Temperature coefficient of resonant frequency (f)
The temperature coefficient of resonant frequency (f) is related to temperature
coefficient of dielectric constant () as
1
 f  -1 - 
(7)
2
In the above equation ‘1’ is the coefficient of thermal expansion and is in the range of
10 ppm/oC for all the ceramics. So f mainly depends on temperature coefficient of dielectric
constant ( ). Form Clausius-Mosotti equation,  can be derived from following expression.
 -1   2




1 
 T



 

A B  C
(8)






V

T
1
V
1
V
T
1








P



P
m
m
Where A  
B 
C 

 



3V T
3
3

m 
T
m 
V
Where ‘m’ and ‘V’ represents the polarizability and volume of macroscopic, small
sphere respectively.
The term A gives the dependence of polarizability on the temperature and is always negative
because of anharmonic effect of potential well where the ions will vibrate. With increase in
temperature, the polarizability of constant number of dipoles will increase because of volume
expansion and is given by term B. According to Bosman and Havinga [43], the first two
terms A and B are related with the volume expansion which are nearly of equal magnitude but
opposite in sign, therefore the effect of A and B on  is negligible. The third term C gives the
restoring force acting on the ions and this restoring force depends on the shape of the
11
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potential well, hence the term C is explained with the structural parameters of the constituent
elements in the compounds.
In general, temperature coefficient of capacitance (TCC) is directly proportional to
temperature of coefficient of dielectric constant () [44]. Diao et al. observed that the
temperature coefficient of capacitance (TCC) decreases with increase Raman shift [35]. From
this, it is clearly understood that the f depends on Raman shift. In our present work, from
Raman spectra (fig. 5a), it is clearly seen that with Sr2+ substitution A1g mode is shifting
towards the higher wavenumber side (from 881.7 cm-1 of x = 0.0 compound to 889.8 cm-1 of
x = 1.0) whereas highest external mode Eg (fig. 5b) is moving towards the lower wavenumber
side (from 270.6 cm-1 for x = 0.0 compound to 235.4 cm-1 for x = 1.0) which inturn influences
the rigidity of cation and oxygen environment and decrease the restoring force required to
recover the degree of distortion of oxygen polyhedra. The temperature coefficient of resonant
frequency of ABO4 ceramic compounds is observed to be influenced by the complex
environment around the oxygen polyhedra [20]. In Ca1-xSrxMoO4 (x=0.0, 0.2, 0.4, 0.6, 0.8
and 1.0) compositions, with increase in Sr2+ content the f values varied from -28 to -17
ppm/oC. This variation in f could be attributed to bonding characteristics of cation oxygen
polyhedra which influences the Raman shift of A1g mode. The Raman shift and f values are
given in Table 3 and the variation both these parameters with Sr2+ substitution is shown in
Fig. 10.
3.4 Optical Properties
The optical properties of Ca1-xSrxMoO4 (x=0.0, 0.2, 0.4, 0.6, 0.8 and 1.0) compositions
were studied by collecting the optical absorption (OA) of these compositions. The optical
absorption spectra of these compositions in 340–550 nm range are shown in Fig. 11 and is
observed that the absorption edge shifts from 394 nm for x = 0.0 to 369 nm for x = 1.0. The
relation between optical band gap, absorbance and photon energy is given as [45].
12
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n/2
h  h  Eopt
(9)


g
Where ‘’ is the absorbance, ‘h’ is plank’s constant, ‘’ is the frequency and ‘ Egopt ’ is
optical bang gap. The value of ‘n’ depends on the characteristics of transition in a material i.e.
n = 1 for direct band gap materials and n = 4 for indirect bang gap material. The bang gap of
Ca1-xSrxMoO4 (x=0.0, 0.2, 0.4, 0.6, 0.8 and 1.0) compositions were estimated by extrapolating
the linear region on the higher photon energy region of (h)2 versus photon energy (h) plots
that are not shown here. The observed band gap of CaMoO4 and SrMoO4 samples are 3.30 eV
and 3.51 eV and slightly deviated from the reported values which may be attributed to the
large grain size and intrinsic defects in the samples [31, 46]. With Sr2+ substitution the band
gap increases from 3.30 eV to 3.51 eV. We also observed a non linear variation in the band
gap with Sr2+ substitution and is shown in Fig. 12. Osamura et al. explained the non linear
behavior of band gap in Ga1-xInxN thin films with help of Bowing effect [47]. So in order to
explain the non linear behavior in band gap of Ca1-xSrxMoO4 (x=0.0, 0.2, 0.4, 0.6, 0.8 and 1.0)
compounds with help of Bowing effect, the observed band gap values were fitted with the
following equation yielding a smaller ‘c’ value 0.17 eV [48].
E  1 x Eg,A  xEg,B  cx 1 x
(10)




g
where Eg,A, Eg,B are band gap of CaMoO4 and SrMoO4 respectively. ‘c’ is the Bowing
parameter which is effected by atomic size difference and chemical ionicity mismatch and ‘x’
is the concentration of Sr2+. It is clear from the Fig. 12 that, the observed values are well fitted
with the Bowing equation.
Conclusions
The Ca1-xSrxMoO4 (x = 0.0, 0.2, 0.4, 0.6, 0.8 and 1.0) ceramic compositions were
successfully prepared via conventional solid state reaction method and all the compositions
were observed to possesses tetragonal scheelite structure with I41/a space group. All these
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compounds possess more than 95% theoretical density. The effect of Sr2+ substitution on the
bonding characteristics and microwave dielectric properties was studied with help of Rietveld
refinement and Raman spectra of these compositions. The microwave dielectric properties
such as dielectric constant (r) and quality factor (Q×f) were correlated with the molar volume
(Vm) and Mo-O bond strength of these compositions respectively. Temperature coefficient of
resonant frequency (f) was explained with Raman shift of A1g mode in these compositions.
Well dense samples possess good microwave dielectric properties (r= 6.5 – 9.7, Q×f = 35000
–52000 GHz, f = -28 to -17 ppm/oC). The non linear variation in the band gap of these
compositions and was fitted the bowing equation.
Acknowledgements
The authors are thankful to University Grant Commission, New Delhi, India for
providing financial assessment in the form of Senior Research Fellowship.
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Fig. 1. Room temperature XRD patterns of Ca1-xSrxMoO4 compounds.
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Fig. 2. Rietveld refinement plot of Ca0.6Sr0.4MoO4 compound.
Fig. 3. Unit cell representation of Ca0.6Sr0.4MoO4 (along b-axis view).
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Fig. 4a. Local environment of (Ca/Sr)O8 bisdisphenoid (c-axis view) in scheelite structure.
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Fig. 4b. Local environment of MoO4 (along c-axis view) tetrahedra in scheelite structure.
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Fig. 5a. Room temperature Raman spectra of Ca1-xSrxMoO4 compounds.
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Fig. 5b. Raman spectra of Ca1-xSrxMoO4 compounds (150–350 cm-1).
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Fig. 6(a-f). SEM micrographs of Ca1-xSrxMoO4 compounds.
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Fig. 7. Rate of change of molar volume and ionic polarizability of Ca1-xSrxMoO4 compounds.
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