Microstructure and charge carrier dynamics in Dy substituted phase stabilized cubic Bi2O3

Article abstract of DOI:10.1039/c5ra10318e

Room temperature phase stabilization of cubic Bi₂O₃ has been achieved by adding Dy₂O₃ as the dopant, using a low temperature citrate-auto-ignition method. The samples were sintered at different temperatures retaining the cubic fluorite structure. Rietveld refinement of the X-ray diffraction profiles has given detailed microstructural information of the prepared samples. The transmission electron micrographs confirmed the presence of atomic planes as obtained from X-ray diffraction. The UV-Vis spectra show a red shift of the absorption peak with the increase in sintering temperature. Impedance spectroscopy studies of the samples exhibited thermally activated non-Debye type relaxation process. In addition, studies of the electrical conductivity have suggested the negative temperature coefficient of resistance (NTCR) behavior of the samples. The comparable values of activation energies, obtained from different parameters, indicated that the ions follow the same type of mechanism for conduction as well as for relaxation. The temperature independence of the mechanisms has been confirmed from scaling of different spectra. The correlation between structural and electrical properties of the samples has been discussed and interpreted accordingly.

Full text of DOI:10.1039/c5ra10318e

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Structural conversion of Bi2O3 from monoclinic to FCC due to doping
29x11mm (600 x 600 DPI)

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Microstructure and Charge Carrier Dynamics in Dy
substituted phase stabilized cubic Bi2O3
Swagata Bandyopadhyay and Abhigyan Dutta*
Department of Physics, The University of Burdwan, Burdwanꢀ713104, India
Abstract
Room temperature phase stabilization of cubic Bi2O3 has been achieved by adding Dy2O3 as
dopant, using low temperature citrateꢀautoꢀignition method. The samples were sintered at
different temperatures retaining the cubic fluorite structure. Rietveld refinement of the Xꢀray
diffraction profiles has given the detailed microstructural information of the prepared samples.
The transmission electron micrographs confirmed the presence of atomic planes as obtained from
Xꢀray diffraction. The UvꢀVis spectra show a red shift of the absorption peak with the increase in
sintering temperature. Impedance spectroscopy studies of the samples exhibited thermally
activated nonꢀDebye type relaxation process. In addition, the studies of electrical conductivity
have suggested the negative temperature coefficient of resistance (NTCR) behavior of the
samples. The comparable values of activation energies, obtained from different parameters,
indicated that the ions follow same type of mechanism for conduction as well as for relaxation.
The temperature independence of the processes has been confirmed from scaling of different
spectra. The correlation between structural and electrical properties of the samples has been
discussed and interpreted accordingly.

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Keywords: cubicꢀBi2O3; Rietveld refinement; Transmission Electron Microscopy; Impedance
Spectroscopy; Relaxation dynamics.
*Author for correspondence: Abhigyan Dutta
Address: Department of Physics, The University of Burdwan, Golapbag, Burdwanꢀ713104,
INDIA email: adutta@phys.buruniv.ac.in ; Telephone: +913422657800; Fax: +91342 2634015
1. Introduction:
In the family of solid oxide full cells (SOFC), Bi2O3 based materials have proven themselves as
one of the most important members because of their superiority in oxide ion conductivity over
conventional Ceria or Zirconia based ionic conductors 1ꢀ4. Out of its different crystallographic
polymorphs, interest has been centered on cubic δꢀBi2O3 because of its ability for highest oxygen
ion conductivity among the family 5. This cubic fluorite structure of bismuth oxide consists of a
disordered oxygen subꢀlattice with a shortꢀrange ordering of oxygen vacancies along the <111>
6
direction . The high ionic conductivity of δꢀBi2O3 is ascribed both to the large number of
oxygen vacancies and high anionic mobility. The high concentration of oxygen vacancies (25%
of the lattice sites) is a result of obtaining the cubic fluorite structure with Bi3+cation. The high
anionic mobility is related to the high polarizability of the Bi3+ cation with its lone pair of
7
electrons . However, this cubic phase is only stable in a narrow temperature range (730°C to
8
melting point), and transforms to monoclinic αꢀphase through a dramatic phase transition . The
cubic phase at high temperature can be stabilized down to room temperature by the additions of
dopants of comparable cation radii such as isovalent rare earth cations (Dy3+ , Ho3+ , Er3+ , Tm3+ ,
Yb3+),Y3+, WO3 etc 1, 9. However, these doped bismuth oxides show lower ionic conductivity and
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undergo an order–disorder transition of the oxygen subꢀlattice below 600°C, which leads to a
time dependent decay in conductivity (aging effect) 6, 9
.
A controversy on the stability of δꢀBi2O3 phase at room temperature aroused because
10
Watanabe claimed that, δꢀBi2O3 could not be stabilized by any oxide addition in longꢀterm
aspect. The stabilized bismuth oxides were treated as a quenchꢀin phase or in other words, metaꢀ
9
stabilized phase. A systematic study on the effects of different rare earth dopants on Bi2O3–
Ln2O3 (Ln = Dy, Ho, Er, Tm and Yb) system showed that, the degradation rate of conductivity
depends on the ionic radii and doping concentration. It was also observed that, two different
mechanisms were responsible for degradation. One is phase transformation from fluorite to
rhombohedral, which occurs most rapidly at about 650°C and the other one is the reversible
orderꢀdisorder transformation of the vacancies, which occurs at about 500°C. It was shown that,
the relative decay in conductivity is lowest for Dy2O3 stabilized cubic Bi2O3 9, 11. A recent study
12
on the energetic of doped Bi2O3 has also confirmed that, decrease in the volatility and
susceptibility to reduction of bismuth oxide at high temperatures has been lowest for the Dy
doping. Moreover, the dopant cations affect the nature of the vacancy arrangements in the
oxygen sublattice and the polarizability of the cation affects the stability of the disordered
oxygen sublattice 13, 14. In a recent work 15 on Dy doped cubic bismuth oxide system; it has been
shown that, the oxygen ionic conductivity has been much dependent on crystallite size, prepared
through different synthesis routes.
In the present work, Bi2O3 is successfully stabilized down to room temperature and δꢀ
phase has been found to be stable for long time duration. This has been achieved by singly
doping of Dy2O3, keeping the as prepared sample at lowest possible sintering temperature for the
lowest time duration.
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The main objectives of this work are two folds. Firstly, to prepare the room temperature
phase stabilized Dy doped cubic δꢀBi2O3 and secondly, to investigate the effect of sintering
temperature on various structural, microsructural and ionic transport properties of prepared
samples to enlighten new properties of this interesting solid electrolyte material. To the best of
our knowledge, the analysis of electrical relaxation phenomena of this material has not been
done yet.
2. Materials and methods:
Pure Bi2O3 and doped Bi0.7Dy0.3O1.5ꢀδ were prepared by low temperature citrate auto ignition
method. For pure bismuth oxide, Bi(NO3)3, 5H2O (MERCK, 99%) was used as precursor. First,
the precursor was dissolved in 50 ml conc. HNO3, diluted by 100 ml deꢀionized water and the
solution was stirred for 2 h at temperature 70°C. Citric acid (MERCK, 99.5%) in a 1:3 molar
ratio with the Bi cations, was then dissolved in 200ml deꢀionized water and added to the nitrate
solution under constant stirring. It acts as a chelating agent as well as fuel for the reaction. The
mixture was then stirred for 4 h at temperature 85°C. Due to constant evaporation, amount of
sample became small (~50 ml) and the transparent solution became yellowish. After the
homogeneous yellowish gel was formed, auto ignition process was completed within a minute
and yellowish ash was produced.
For doped Bi0.7Dy0.3O1.5ꢀδ, stoichiometric amounts of Bi(NO3)3, 5H2O and Dy2O3 (ALFA
AESAR, 99.9%) were used as precursors. First Dy2O3 was dissolved in 50 ml conc. HNO3,
diluted by 100 ml deꢀionized water and the solution was stirred at 70°C temperature using
magnetic stirrer for 1 h, until the solution became clear. After that, proper amount of weighted
Bi(NO3)3, 5H2O was mixed in the nitrate solution and again stirred for 2 h . Then citric acid at
1:3 molar ratios with the Bi cations was dissolved in 200 ml deꢀionized water added to the
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solution. The solution was stirred for 4 h at temperature 85°C. Due to constant evaporation the
solution became yellowish and gel/foam was formed and autoꢀignition process was completed
within a minute and produced yellowish powder samples of doped compositions.
The agglomerated yellowish ash was crushed and grinded for 15 min for homogeneous
mixing. The doped samples were divided into three parts and sintered at 600°C, 700°C, 800°C
respectively and pure Bi2O3 was sintered at 600°C, each for 6 h duration with furnace cooling to
room temperature. The samples are abbreviated as DSB1 (600°C), DSB2 (700°C) and DSB3
(800°C) respectively.
Powder XꢀRay diffraction data were obtained at room temperature by Xꢀray
diffractometer (BRUKER, Model D8 AdvanceꢀAXS) using CuKα radiation (λ= 1.5414 Å) in 2θ
range from 20°ꢀ80°, with step size 0.02° and scan rate 0.5 sec/step. The microstructure of the
pure and doped samples were also studied using highꢀresolution transmission electron
microscope (HRꢀTEM) (JEOL; Model: JEMꢀ2010) operated at 200KV. For HRꢀTEM study, a
pinch of powdered sample was dispersed ultrasonically in ethyl alcohol and a drop of colloidal
solution was placed on a 300 mesh carbon coated Cu grid. The grid was dried over night under
high power lamp.
Optical band gap of the pure and doped samples were determined from Ultravioletꢀvisible
(UvꢀVis) absorption spectra, taken at room temperature using Shimadzu spectrophotometer
(Model:1800), in the wavelength range 200ꢀ800 nm. For UvꢀVis study, powdered samples were
dispersed ultrasonically in ethyl alcohol and ethyl alcohol was used as reference during the
absorption measurement.
For electrical measurement, powdered samples were uniaxially pressed in a 10 mm
diameter stainless steel die into cylindrical shaped pellets of average thickness about 0.17 cm.
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Acetone was used as binder material. The pellets were annealed in air at 200°C for 2 h. The
pellets were then polished to acquire smooth surface and high temperature conductive graphite
pest (MERCK) was applied on both sides of the pellets to make the electrodes. Subsequently, the
coated samples were annealed again at 200°C for 30 min.
Electrical measurements were performed by two probe method using an impedance
analyzer (HIOKI; Model:3532ꢀ50) in the frequency range 42 Hz – 5 MHz and in temperature
range 200°C ꢀ 440°C with 20°C step in air atmosphere inside a tube furnace.
3. Results and discussions:
3.1.
XꢀRay Diffraction and the Rietveld refinement:
Fig. 1(a) shows the XRD pattern of all the doped samples sintered at different temperatures. The
wellꢀindexed diffraction peaks indicate the singleꢀphase cubic fluorite structure for all the
samples. The XRD patterns were compared with standard data JCPDF card No.:71ꢀ2274 for pure
sample and card No.:34ꢀ0376 for doped samples. XRD pattern of pure Bi2O3 confirms pure
single monoclinic phase with space group Pꢀ /ꢂ and that of doped samples confirm the singleꢀ
ꢁ
phase cubic fluorite structure with space group Fmꢀ3m
.
16
For Rietveld analysis, MAUD 2.33
software has been employed. It is designed to
refine simultaneously both the structural (unit cell parameters and atomic positions and
occupancies) and micro structural parameters (crystallite size and r.m.s. strain). Various
structural parameters including lattice parameter (a) and micro structural parameters like particle
17
size (D), r.m.s. microstrain (<ε2>1/2) have been refined by a standard least square method
assuming the peak shapes as a pseudoꢀVoigt function 18, 19. Instrumental broadening has been
corrected by a specially processed standard Si sample. The background of the XRD patterns is
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fitted with a polynomial of degree 5. The Marquardt leastꢀsquares method has been employed to
minimize the difference between experimental and simulated patterns.
This minimization is monitored using two reliability index parameters Rwp (weighted
residual error factor) and Rexp (expected error factor) defined as:
ꢐ/ꢀ
ꢎꢏ
ꢈ
ꢍ
ꢉ ꢋꢉ
ꢊ ꢌ
ꢃꢄꢅ = ꢆ∑
(1)
(2)
ꢄ
ꢇ
ꢇ
ꢎ
∑
ꢈ ꢍ
ꢉ
ꢊ
ꢄ
ꢇ
ꢇ
ꢎꢏꢐ/ꢀ
ꢈ
ꢍ
ꢓꢋꢔ
ꢃꢑꢒꢅ = ꢆ∑
ꢈ
ꢍ
ꢉ
ꢊ
ꢄ
ꢇ
ꢇ
Here, Io and Ic are the experimentally observed and calculated intensities, wi (=1/Io) and N are the
weight and number of experimental observations respectively and P is the number of fitting
parameters. These values again lead to another closely monitored parameter namely goodness of
ꢕwp
fit (GoF) which is defined as: GoF = ꢕ . Refinement cycles are repeated until this GoF reaches a
exp
value near to unity. In the present case, GoF value remains within the range 1.30 to 1.68 which
indicates good fitting quality for all these patterns.
The Rietveld refined patterns for pure Bi2O3 and Dy doped Bi2O3 samples are shown in
Figs. 1(b) and (c) respectively. The monoclinic and cubic phase has been simulated by
considering the COD file no. 9012546 and 9009850 respectively. Pure Bi2O3 contains single
monoclinic phase with lattice parameter a = 5.8479 Å, b = 8.1660 Å, c = 7.5094 Å and α = γ =
900, β = 112.9870 and cell volume = 330.13(Å)3. This monoclinic phase is converted into single
FCC cubic fluorite phase with cell volume ~165(Å)3. This decrease in cell volume with doping is
due to the fact that ionic radius of Dy3+ (1.027Å) is lesser than the ionic radius of Bi3+ (1.17Å).
The Rietveld analysis has exhibited that, no additional phase corresponding to Dy has been
observed in the XRD profiles for the doped samples, which ensures the complete dissolution of
the dopant into the host matrix. The sharp diffraction peaks in intensity as well as the narrow
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spectral width indicate the high quality of crystallinity of the samples. The variation of crystallite
size (D) and r.m.s. microstrain (<ε2>1/2) with sintering temperature of the doped DSB samples
are shown in Fig. 1(d). From this figure, it is clear that, crystallite size (D) increases where as
microstrain decreases with increase in sintering temperature.
The increase in lattice parameter and crystallite size with increase in sintering temperature
indicates the grain growth of the samples with sintering temperature. This is because of the fact
that, the thermal energy generates a force that reduces the total area of grain boundary. Due to
the reduction of total area of grain boundary, the actual number of grains per unit volume
decreases and grain size increases. This grain growth can further be explained by the following
equation 20,
ꢖꢗ − ꢖꢘꢗ = ꢙꢚ
(3)
Where, D is the average grain size at time t, D0 is the average initial grain size, n is the grainꢀ
growth exponent depending on the growth mechanism and K is a constant that could be
expressed by the following relationship:
ꢟ
ꢙ = ꢙꢘꢛꢜꢝ ꢞ− ꢕꢠꢡ
(4)
Where, Q is the activation energy required for growth, K0 is a constant, R is the gas constant and
T is the absolute temperature.
Structural models of the pure and doped Bi2O3 samples have been generated using the atomic
coordinates obtained from Reitveld analysis and the models are presented in Figs. 2(a) and (b)
respectively. In the crystal structure of pure Bi2O3, as shown in Fig. 2(a), all the Bismuth atoms
(Bi) are situated at the 4e site with the atomic coꢀordinate Bi1 (0.524, 0.1831, 0.3613), Bi2
(0.0409, 0.0425, 0.7762) and all oxygen atoms are situated at the 4e sites with the atomic coꢀ
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ordinate O1 (0.78, 0.30, 0.71), O2 (0.242, 0.044, 0.134), O3 (0.271, 0.024, 0.513). All the atomic
positions were fixed during the whole refinement process. When this pure Bi2O3 is doped with
Dy atom, the monoclinic structure is converted into FCC cubic structure, which is shown in Fig.
2(b). Here all Bi and Dy atoms are situated at the 4a site and oxygen atoms (O1 and O2) are
situated at the 8c and 32f sites respectively. The Wyckoff position and fractional occupancy of
the atoms for the sample DSB3 are listed in Table 1. Values of different structural and
microstructural parameters like lattice parameter (a), cell volume (V), crystallite size (D), r.m.s
microstrain (<ε2>1/2), Rwp, Rexp, GoF are listed in Table 2. The Rietveld refinement also shows
that r.m.s. microstrain decreases with increase of sintering temperature which indicates the better
stability of the samples with rise in sintering temperature.
3.2 Transmission electron microscopy analysis:
Further proof of crystallinity of the prepared samples has been given using room temperature
high resolution transmission electron microscopy (HRꢀTEM) study. In Fig. 3(a), the nanoꢀ
architecture of the sample DSB3 is shown with several hundred nanometers in the planar
dimensions. All other samples also follow similar type of structural information. It can be
inferred that, the process of sample preparation is sufficient to construct such type of flake nanoꢀ
structures.
The orientation of the lattice plane is confirmed by using the simulated lattice pattern in Fig. 3
(b) with orientation along (200) direction. In the inset of Fig. 3 (b), the exact lattice spacing
(dTEM) ~ 0.296 nm is confirmed by the difference of the peak heights. This lattice spacing (dTEM
)
value is comparable with that obtained from Rietveld analysis (dXRD) for (200) plane of the same
sample. The proof of crystal symmetry is given by using the selected area electron diffraction
pattern as shown in Fig. 3 (c). In this figure, the bright and intense dots can be indexed in a cubic
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cell and absence of intermediate small dots also confirms the phase purity even in the nano scale
region. From this reciprocal lattice reconstruction of DSB3, it can be concluded that, the
structure is not associated with any superstructure. The pattern in Fig. 3(c) has been found to be
tilted at 2.6o with positive xꢀaxis. So the arrow heads are found to be tilted. Another high
resolution TEM image of the sample is also shown in Fig. 3(d). To confirm the contributing
lattice planes, we have also shown the fast Fourier transform (FFT) pattern in the left upper panel
of Fig. 3(e) which is taken from the selected part of Fig. 3(d) as indicated by the red box. It can
be confirmed from the distinct circular rings in the FFT image that, the contributing lattice planes
are (200) and (220). The simulated lattice pattern signifies the different orientations of these two
planes in the right upper and lower panel of Fig. 3(e). Further confirmation of cationic position is
given by using the atomic model as shown in Fig. 3(f). Comparing with Figs. 3(d) and 3(f), it can
be concluded that, Bi/Dy is localized at the same Wyckoff site and no distinction is possible due
to their common site sharing.
3.3. UltravioletꢀVisible (UvꢀVis) spectroscopy:
The UvꢀVis absorption spectra for all the samples are shown in Fig. 4(a). The samples exhibited
a distinct absorption band in UVꢀregion (<400 nm). The optical band gap ꢢꢣ can be determined
by the classical tauc equation 21,
(ꢤ. ꢢꢔꢍ = A. (ꢢꢔ − ꢢꢣ)q
(5)
Where, the symbols have their usual meaning. Fig. 4(b) shows the (αhν)2 vs hν plot of the sample
DSB3 and band gap is determined by extrapolating the linear portion of this plot to (αhν)2 equal
to zero. The obtained values of optical band gap (ꢢꢣ) for prepared samples are listed in Table 3.
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It may be found that, ꢢꢣ decreases significantly with the sintering temperature from 2.46 eV to
2.07 eV for the doped samples in comparison with the pure one (2.71 eV).
In addition, the wavelength, at which the strong absorption occurs, decreases for the samples
from Bi2O3 to DSB3. It exhibits the red shift of the spectra with the increasing sintering
temperature. This red shift can be partially explained by the shrinkage of energy band gap with
22
an increase in particle size . The increased particle size due to grain growth at higher sintering
temperature results in larger number of atoms in the particle causing the greater splitting of
energy level resulting in the shrinkage of optical band gap. This is also consistent with the XRD
results.
3.4 Electrical properties:
The ionic transport properties of the samples have been examined using impedance
spectroscopy. The frequency dependent electrical properties of the materials can be expressed in
terms of complex dielectric constant (ε*), complex impedance (Z*), complex electric modulus
(M*) and tangent loss (tanδ). These quantities are related to each other by the following relations;
Z*(ω) = Z′ (ω) – j Z′′ (ω)
ε*(ω) = ε′ (ω) – j ε′′ (ω)
M*(ω) = M′ (ω) + j M′′ (ω)
(6)
(7)
(8)
ɛ
′′
ꢥ
′′
tanδ =
=
′′ = ꢀ ꢦ
(9)
ɛ
′
ꢥ
′
ꢦ′
Where, ꢧꢨ, M′, ε′ and ꢧꢨꢨ, M′′, ε′′ are the real and imaginary parts of impedance, modulus and
permittivity respectively.
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3.4.1 Impedance spectra analysis:
In general, the complex impedance spectra consist of two or three semicircular arcs as
shown in the schematic representation in Fig. 5(a). The pictorial representation of the equivalent
circuit required for explaining the various charge migrations and polarization phenomenon
occurring in the sample is shown in the inset of Fig. 5(a). Here Rb, Rgb, Re and ꢩb, ꢩgb, ꢩe are the
resistance and phase elements of bulk, grain boundary and electrode contribution respectively.
‘ꢩ’ represents the modified capacitive phase element, deviated from the ideal behavior. The true
value of capacitance (C) is calculated from the expression –
ꢁ
ꢬ
ꢪ = ꢃꢁꢫꢬ
ꢩ
(10)
ꢬ
Where, a lies between 0 and 1. The fit using the equivalent circuit is done using ECꢀLab
software. In our experiment, most of the specimens exhibit a single semicircular arc (total
impedance Rtotal = Rb + Rgb) at high frequency range with an extension (electrode contribution Re)
at low frequency range. Fig. 5(b) shows the complex impedance plot of DSB3 sample at
different temperatures. The depressed and broad semicircular arcs indicate the presence of nonꢀ
Debye type relaxation process. The same behavior has also been observed for all the other
samples. The radius of the semi circular arc decreases with increase in temperature indicating
increase in conductivity. This conductivity increment with the rising temperature may be due to
the lowering of barrier for which mobility of charge carrier increases 23. It also indicates that, the
oxygen ion conduction in bulk and grain boundary region is a thermally activated process similar
to that of semiconducting materials. This increase of conductivity with temperature is due to the
increase of free oxygen vacancies i.e. most of the oxygen vacancies are free to migrate when
measuring temperature increases. The variation of bulk conductivity (σb) and grain boundary
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conductivity (σgb) with measuring temperature for the sample DSB3 is shown in the inset of Fig.
5(b).
Fig. 5(c) shows the complex impedance plots for all the samples at a fixed measuring
temperature. This figure shows that, both bulk and gain boundary resistance decreases and total
conductivity increases with increase of sintering temperature. The reciprocal temperature
dependence of the total conductivity for all the samples are shown in Fig. 5(d) which obeys the
Arrhenius equation given by,
ꢮ
σ = ꢭꢠꢊ expꢞ− ꢯ ꢠ
ꢡ
(11)
ꢬ
ꢰ
Where, ꢱꢲ is preꢀexponential factor, ꢢꢳ is the activation energy for electrical conduction, kB is
the Boltzman’s constant and T is the absolute temperature. The values of activation energy
(ꢢꢳꢭꢍ, obtained from the slope of the curve in Fig. 5(d), are listed in Table 3.
It has been found that, the values of bulk and grain boundary resistance is much higher
for the pure sample in comparison with the doped samples because, stabilization of the
monoclinic Bi2O3 structure into cubic fluorite δꢀBi2O3 structure increases the number of oxygen
vacancies to a great extent. In case of doped samples, total conductivity increases with increase
in sintering temperature because, crystallite size increases which results in the decrease in grain
boundary and consequently its contribution to the total conductivity. The increase of
conductivity with sintering temperature can also be understood by measuring a term, called grain
boundary blocking factor (α) which is expressed as, 24
α = ꢕ
(12)
ꢴꢵ
ꢕ
ꢶ
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Where, Rgb is grain boundary resistance and Rt is total resistance. For each of the doped samples,
α is calculated using the parameters obtained from the fitting of impedance spectra at a fixed
measuring temperature and is found to decrease from 0.7937 to 0.6577 with rise in sintering
temperature from 6000C to 8000C. Due to this decrease in blocking factor (α), grain boundary
conductivity increases with increase of sintering temperature.
The different fitting parameters (ai, Ri) obtained from complex impedance spectra and calculated
values of capacitance (Ci) and conductivity for the bulk (σb) and grain boundary (σgb)
contribution at 3000C for the samples are listed in Table 4. For all the samples, the value of
frequency exponent (ai) for both bulk and grain contribution is less than unity (ai<1), indicating
the presence of nonꢀDebye type relaxation for all the compositions.
Fig. 6(a) shows the frequency variation of the imaginary part of the complex impedance
(Z′′) at different temperatures for a particular sample (DSB3). Z′′ value shows a peak maxima
(Z′′max) at a particular frequency (relaxation frequency ωmax) and this peak shifts towards higher
25
frequencies with increasing temperature indicating the presence of relaxation in the system .
The peak frequency ωmax is characterized by composition and structural arrangements of atoms in
the sample.
Fig. 6(b) shows the scaling behavior of Z′′ spectra. Here the frequency axis is scaled by
relaxation frequency ωmax and Z′′ is scaled by Z′′max. The spectra for all the compositions obey the
timeꢀtemperature superposition principle (TTSP) i.e. all the Z′′ spectra at different temperatures
superimposed on a single master curve. This behavior simply indicates that, the change in
temperature only changes the number of charge carriers without changing the conduction
mechanism 26.
Using the value of ωmax, the relaxation time has been calculated using the equation,
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ꢷꢸꢳꢒꢹ = 1
Where, τ = CR, is the relaxation time.
(14)
Fig. 7 shows the variation of τ with reciprocal of absolute temperature. It has been observed that,
the value of τ decreases with increase of measuring temperature for all the samples and its
temperature dependence nature follows the Arrhenius relation given by,
ꢮ
τ = ꢺꢠꢊ expꢞ− ꢯ ꢠ
ꢡ
(15)
ꢬ
ꢰ
Where, ꢹꢲ is preꢀexponential factor, ꢢꢳ is the activation energy of electrical relaxation, kB is the
Boltzman’s constant and T is the absolute temperature. The values of activation energy (ꢢꢳꢺꢍ
calculated from this plot are listed in Table 3 and shows a small but gradual decrease with
increase in sintering temperature. These values are comparable with the previously reported
values 14.
3.4.2. Modulus spectroscopy analysis:
Fig. 8(a) shows the frequency dependence of imaginary part of modulus M′′(ꢷ). An
asymmetric maximum can be observed for M ′′ ( ꢷ ) at frequency ωmax. The asymmetric
broadening of the peak indicates a spread of relaxation with different time constants, and hence
the relaxation in the material is a nonꢀDebye type. The region where the peak occurs is an
indication of the transition from longꢀrange to shortꢀrange mobility with increase in frequency.
The most probable relaxation time τm can be calculated from the peak frequency ωmax
using the relation ωmax.τm = 1. The inset of Fig. 8(a) shows the reciprocal temperature
dependence of ωmax for all the compositions which also obeys the Arrhenius relation.
The values of the activation energy for the most probable relaxation time (ꢢꢺ ) obtained
ꢻ
from the slope of the curves are given in Table 3 which again show the same type of variation
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with the increase in sintering temperature. All the three types of activation energies (ꢢꢳꢭ,
ꢢꢳꢺ, ꢢꢺ ) are found to be comparable with each other which indicates that the ions have to
ꢻ
overcome the same barrier while conducting as well as when relaxing.
The scaling of the modulus isotherms is shown in Fig. 8(b) where the frequency axis is
scaled by ωmax and M′′(ꢷ) is scaled by M′′max. The perfect overlap of all the curves on a single
master curve at all temperatures indicates that the dynamical processes are temperature
independent.
4. Conclusions:
Bismuth Oxide has been successfully stabilized into its cubic fluorite δꢀphase at room
temperature by doping of Dy2O3 using low temperature citrate autoꢀignition method. Xꢀray
diffraction analysis confirmed the cubic fluorite structure of the doped samples at room
temperature. Various structural and microstructural parameters were estimated using Rietveld
refinement of the Xꢀray diffraction profiles. It was found that crystallite size and microstrain
exhibit opposite behaviour with increase in sintering temperature. The presence of different
lattice planes and the proof of crystallinity was confirmed from HRꢀTEM study. The UvꢀVis
spectra exhibited the red shift with sintering temperature because of grain growth of the samples.
The complex impedance plots revealed that, both grain and grain boundary resistance decreased
with rise in measuring temperature indicating the NTCR behaviour of the samples. The electrical
relaxation processes occurring in the material have been found to be temperature independent.
Comparable values of three types of activation energy indicate the single conduction mechanism.
The conductivity, activation energy and other electrical properties were found to be strongly
influenced by the sintering temperature of the materials.
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5. Acknowledgements:
One of the authors (SB) thankfully acknowledges The University of Burdwan for granting stateꢀ
funded fellowship. AD thankfully acknowledges the financial assistance from Department of
Science and Technology (Govt. of India) (Grant no: SR/FTP/PSꢀ141ꢀ2010). The authors (SB and
AD) also acknowledge the instrumental support from DST (Govt. of India) under departmental
FIST programme (Grant no: SR/FST/PSꢀIIꢀ001/2011) and University Grants Commission (UGC)
for departmental CAS scheme.
6. Reference:
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R. Punn, A.M. Feteira, D.C. Sinclair, C. Greaves, J. Am. Chem. Soc. , 2006, 128, 15386ꢀ
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E.D. Wachsman, K.T. Lee, Science, 2011, 334, 935ꢀ939.
D.W. Jung, K.L. Duncan, E.D. Wachsman, Acta Mater., 2010, 58, 355–363.
K.T. Lee, H.S. Yoon, E.D. Wachsman, J. Mater. Res., 2012, 27, 2063–2078.
M. Drache, P. Roussel, J.P. Wignacourt, Chem. Rev., 2007, 107, 80ꢀ96.
E.D. Wachsman, S. Boyapati, M.J. Kaufman, N.X. Jiang, J. Am. Ceram. Soc., 2000, 83,
1964ꢀ1968.
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E.D. Wachsman, J. Eur. Ceram. Soc., 2004, 24, 1281ꢀ1285.
M.J. Verkerk, K. Keizer, A.J. Burggraaf, J. Appl. Electrochem., 1980, 10, 81ꢀ90.
N. Jiang, E.D. Wachsman, J. Am. Ceram. Soc., 1999, 82, 3057ꢀ3064.
A. Watanabe, Solid State Ionics, 1990, 40, 889ꢀ892.
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S. Boyapati, E.D. Wachsman, B.C. Chakoumakos, Solid State Ionics, 2001, 138, 293ꢀ
304.
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T.B. Tran, A. Navrotsky, Chem. Mater., 2012, 24, 4185ꢀ4191.
S. Boyapati, E.D. Wachsman, N. Jiang, Solid State Ionics, 2001, 140, 149ꢀ160.
R. Li, Q. Zhen, M. Drache , A. Rubbens , C. Estournes , R.N. Vannier, Solid State Ionics,
2011, 198, 6ꢀ15.
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L.Lutterotti, MAUDWEB,Version2.33,http://www.ing.unitn.it/~maud/news.html.
B. Ghosh, S.K. Pradhan, J. Alloys Compd., 2009, 477, 127ꢀ132.
R.A. Young, in, Introduction to the Rietveld method, ed, R.A. Young, The Rietveld
method, Oxford University Press; Oxford, 1993, pp. 1ꢀ38.
R.A. Young, D.B. Wiles, J. Appl. Cryst., 1982, 15, 430ꢀ438.
S. Suwanboon, P. Amornpitoksuk, P. Bangrak, Ceram. Int., 2011, 37, 333–340.
Sk. Anirban, A. Dutta, J.Phys. Chem. Solids, 2015, 76, 178–183.
M. Elahi , D. Souri, Ind. J. Pure & Appl. Phys., 2006, 44, 468ꢀ472.
T. Badapanda, V. Senthil, S.K. Rout, S. Panigrahi, T.P. Sinha, Mater. Chem. Phys., 2012,
133, 863ꢀ870.
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A. Rouahi, A. Kahouli, A. Sylvestre, E. Defay, B. Yangui, J. Alloys Compd.2012, 529,
84ꢀ88.
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R.M. Batista, E.N.S. Muccillo, Ceram. Int.2011, 37, 1929–1934.
B. Behera, P. Nayak, R.N.P. Choudhary, J. Alloys Compd., 2007, 436, 226ꢀ232.
S. Saha, T.P. Sinha, Phys. Rev. B., 2002, 65, 134103.1ꢀ7.
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Figure captions:
Figure 1: (a) XRD patterns of different doped samples with Bragg peak positions; Typical
Rietveld refined output of the XRD patterns of (b) Pure Bi2O3 and (c) Dy doped cubic Bi2O3
samples [Experimental (Io) data are shown as (o), simulated patterns (Ic) are shown by solid red
lines, (Io–Ic) (lower blue line) represents the corresponding difference for each of the pattern.].
(d) Variation of particle size and r.m.s. microstrain of doped cubic Bi2O3 samples with sintering
temperature.
Figure 2: (a) Crystal structure of pure Bi2O3 sample possessing monoclinic structure. (b) Crystal
structure of Dy doped stabilized δꢀBi2O3 sample possessing face centred cubic structure.
Figure 3:(a) A typical bright field TEM image of single nanoꢀflack for the sample DSB3; (b)
The simulated lattice plane with spacing 0.296 nm corresponds to (200) plane for the sample
DSB3. In the inset the peak height and the difference between peaks corresponds to intensity of
the lattice and the lattice spacing respectively; (c) The selected area electron diffraction pattern
of DSB3 is shown along three perpendicular directions. The main diffraction dots of the cubic
lattice lie at the intersections of the horizontal and vertical arrows directions. The zone axis is
found to be tilted along 2.6o (d) The lattice plane is shown for DSB3. The upper left in (e)
corresponds to the fast Fourier transform (FFT) of the selected zone from (d) The circular rings
in the FFT correspond to diffraction from two different lattice planes. The simulated planes are
also found to be oriented along (200) and (220) directions. (f) The atomic model corresponds to
the orientation of the cations in (d) with viewing direction along [100]. The blue and gray
spheres correspond to Bi/Dy and O respectively.
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Figure 4: (a) UvꢀVis absorption spectra of all the doped samples at room temperature.
[Absorption spectrum of pure sample at room temperature is shown in inset] (b) Tauc plot for the
sample DSB3; the calculated optical band gap for the sample is also shown.
Figure 5: (a) A model of impedance spectra for calculating different parameters. The equivalent
circuit is also shown in the inset of the figure. (b) The complex impedance spectra for the sample
DSB3 at different measuring temperatures. The variation of bulk (σb) and grain boundary
conductivity (σgb) with measuring temperature is shown in the inset. (c) The complex impedance
plot for all the compositions at a specific temperature. (d) Arrhenius plots of conductivity for all
the samples.
Figure 6: (a) Frequency variation of imaginary part of impedance (Z'') at different temperatures
for the sample DSB3 [The solid lines indicate the theoretical fit]. (b) Master plot or scaled curve
of Z'' at different temperatures for the sample DSB3.
Figure 7: The variation of relaxation time with reciprocal of absolute temperature for all the
doped Bi2O3 samples.
Figure 8: (a) The frequency dependence of M'' for the sample DSB3 at various temperatures [the
solid lines indicate theoretical fit]. Inset shows the Arrhenius plot of the most probable relaxation
frequency (ωmax) obtained from modulus formalism for all the samples [the solid lines denote the
straightꢀline fit] (b) Master curve for M'' at various temperatures for the sample DSB3.
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Table 1 : Refined Structural Data for the sample DSB3:
Atom
Wyckoff Position Atomic coordinate
(x,x,x)
Fractional Occupancy
Bi / Dy
O1
4a
8c
0
0.6932 / 0.2968891
0.18615
0.25
O2
32f
0.3617
0.29373
Table 2 : Composition wise values of lattice parameter (a), Cell Volume (V), crystallite size (D),
r.m.s. micro strain (<ε2>1/2) and Rietveld refinement parameters Rexp (%), Rwp (%) and GoF. :
Sample
Lattice
Cell
Crystallite
Size D
r.m.s.
Rwp
Rexp
Name parameter volume
microstrain
(%)
(%)
GoF
a (Å)
V (Å)3
(nm)
<ε2>1/2
(× 10ꢀ4)
17.10
6.28
DSB1
DSB2
DSB3
5.4837
5.4852
5.4868
164.8988
165.0327
165.1833
40.53
88.44
16.5 12.64
1.30
25.7 15.23 1.68
20.4 15.25 1.33
121.40
2.73
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Table 3: The values of total activation energy for dc conductivity (ꢼꢽꢾ), activation energy for
relaxation (ꢼꢽꢿ), activation energy for most probable relaxation time τm (ꢼꢿ ) and optical band
ꣀ
gap (ꢼꣁ) for all the samples:
Sample
Name
Activation energy Activation energy
Activation energy
for most probable
relaxation time τm
Optical
band
for dc conductivity
for relaxation
(ꢼꢽꢾ)(eV)
(ꢼꢽꢿ) (eV)
gap(ꢼꣁ)
(ꢼꢿ )(eV)
(eV)
2.71
2.46
2.21
2.07
ꣀ
Bi2O3
DSB1
DSB2
DSB3
1.16
1.17
1.16
1.15
ꢀ
1.10
1.17
1.15
1.13
1.16
1.14
1.11
Table 4: Values of frequency exponent (ai), resistance (Ri), capacitance (Ci) and conductivity
(σi) for the bulk and grain boundary contribution of all the samples at 3000C:
Grain
Rb(ꢁ)
Grain boundary
Rgb(ꢁ)
σb
σgb
Sample
Name
(ꢁꢀ1.cmꢀ1)
(x 10ꢀ5)
(ꢁꢀ1.cmꢀ1)
(x 10ꢀ6)
(x 104)
(x 104)
ab
Cb(pF)
agb
Cgb(nF)
35.36
156.13
158.95
172
0.11
1.10
1.16
1.36
0.15
2.14
0.87
2.86
3.43
7.08
Bi2O3
DSB1
DSB2
DSB3
0.98
0.99
0.98
0.99
20.49
1.96
1.86
1.59
0.97
0.99
0.82
0.98
24.64
7.54
6.29
3.04
31.50
82.50
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Figure: 1
Figure: 2
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Figure: 3
Figure: 4
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4
Figure: 5
Figure: 6
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Figure: 7
Figure: 8
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