# Low Temperature Dielectric Relaxation inBa1−xBixTi1−xFexO3 System

Authors: Arvind Kumar; R. K. Dwivedi; S. Baboo; Om Parkash
Journal: Journal of Materials
 (2013)

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## Abstract

We report on dielectric properties of polycrystallineBa1−xBixTi1−xFexO3 (BBTF) ceramic system (x=0.02, 0.06, 0.08, 0.10, 0.12, and   0.16). The materials were synthesized by solid state ceramic route. Solid solution formation has been confirmed by powder X-ray diffraction for compositions with x≤0.16. Crystal structure is tetragonal for x≤0.08 and cubic for x≥0.10. Microstructures show that the average grain size is less than one micrometer (1 μ).  Dielectric behavior has been studied as a function of temperature (100 K–400 K) and frequency. Composition with x=0.02 exhibits diffuse phase transition. Compositions with x≥0.10 show ferroelectric relaxor behavior. This shows that diffuse ferroelectric transition behavior changes to relaxor type ferroelectric transition with increasing x.  Plots of dielectric loss (D) versus temperature shows broad maxima which shift to high temperature with increasing  frequency, dispersion in dielectric loss decreases with x below peak maxima and increases above. It may be attributed to Maxwell Wagner type relaxation process for low x (~0.02) and relaxation of nanopolar regions for x=0.16.


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## Body

## 1. Introduction

Compositions based on BaTiO3 (BTO), a well-known ferroelectric material, show significant change in the dielectric behavior near Curie temperature. Its properties are modified by a wide variety of substitutions, possible either at Ba or Ti sites independently or simultaneously. Extensive research work on the effect of isovalent as well as offvalent substitutions on the transition temperature and the dielectric properties of BaTiO3 has been done during the last few decades [1–3]. The substitution of trivalent ions either at A or at B sites causes charge imbalance and requires creation of vacancies in A or B or oxygen sublattice or generation of electrons or holes to maintain the electrical charge neutrality. It has been reported that for small concentration of La3+ substitution, the charge neutrality is maintained by electronic compensation in accordance with the formula Ba1-x2+Lax3+Ti1-x4+Tix3+O3 [1], and for large concentration, excess donor charge on La3+ ions is compensated by Ti vacancies as represented by the formula Ba1-xLaxTi1-5x/4(VTi)////Ox/43 [4].  Substitution of Bi3+ at Ba2+ site in small concentration is reported to exhibit positive temperature coefficient of resistance (PTCR) [5]. Diffuse phase transition has been observed for large concentration Bi3+ [6].Possibility of creation of defects is very much reduced by valence compensated substitutions either on A site or on B site or on both sites simultaneously. For example, solid solutions of BaTiO3-NaNbO3 and Zr-doped BaTiO3 have charge compensation internally. These systems have been found to exhibit diffuse phase transitions (DPTs) [7, 8]. Kityk et al. [9] have reported the spectral dependences of magnetoelectric constant versus the magnetic field frequency for different sizes of the nanoparticles with and without the nanosecond laser pulses illumination on (1-x)BiFeO3-xCuFe2O4 nanocomposites. The performed experiments unambiguously show that the external laser treatment will lead to substantial shift of corresponding dielectric and magnetic parameters in the studied nanocomposites. Similarly, Sn-doped BaTiO3 has shown DPT and relaxor behavior depending on the concentration of Sn [10]. Substitution of La3+ and Co3+ in BaTiO3 simultaneously has also been reported to exhibit DPT behavior, while La3+ and Ni3+ in Ba2+ and Ti4+sites show, fairly sharp transition [11].In view of the above, it was considered worthwhile to study BaTiO3-BiFeO3 solid solutions. BiFeO3 (BFO) crystallizes in a rhombohedral distorted perovskite structure. It is a ferroelectric having high Curie temperature TC=1103 K. A few studies have already been made on the dielectric behavior of the BiFeO3-BaTiO3 solid solutions [12, 13]. These studies show that there are not many reports on BaTiO3 rich side of the BaTiO3-BiFeO3 system [14, 15]. In the present investigations, results of a few compositions on the BaTiO3 rich side have been reported.


## 2. Experimental

An effort has been made to synthesize the compositions withx=0.02,0.06,0.08,0.10,0.12,0.16, and 0.20 in the Ba1−xBixTi1−xFexO3 (BBTF) by a solid state ceramic method. Stoichiometric amounts of BaCO3, Bi2O3, TiO2, and Fe2O3 (Sigma-Aldrich Chemicals, having purity ≥99.0) powders were mixed thoroughly in a mortar pestle for 6 hrs using acetone as a mixing medium followed by drying in air. The dried powders were calcined at 800°C in air for 10 hrs in an alumina crucible and then furnace cooled. Calcined powders were ground for an hour using mortar and pestle. 2 wt% of PVA solution was added as a binder and mixed thoroughly. These powders were compacted under an optimum load in the form of cylindrical disc (dia ~13 mm) and thickness 1-2 mm using 2 wt% solution of PVA as binder. Two pellets for each composition in this system were placed in transparent alumina crucible and kept in the furnace at room temperature. Initially, the samples were heated slowly up to 400°C and held at this temperature for 2 hr to burn off the binder. Thereafter, the temperature was raised rapidly up to 1100°C at a heating rate of 5°C per minute. The pellets were sintered in air at this temperature for 2 hrs. The density of sintered samples was measured using Archimedes principle.Sintered pellets were ground, and powder X-ray diffraction (XRD) patterns were recorded using a Rigaku X-ray Diffractometer employing CuKα radiations with Ni filter. For microstructural studies, one of the sintered pellets was polished using emery paper of grades 1/0, 2/0, 3/0, 4/0, and 5/0 successively followed by polishing on a velvet cloth with diamond paste of the orders of 1 and 1/4 μm. These pellets were washed using distilled water followed by methanol. Then, these were etched chemically. The etchant used was 10 ml of 10% HCl containing 2-3 drops of HF. Chemically etched pellets were washed with distilled water and coated with gold by sputtering. The microstructures were recorded using SEM (JEOL PSM 800) at room temperature. The average grain size of samples was obtained by line intercept method.Dielectric measurements at a few selected frequencies were carried out using an Agilent 4285A precision LCR meter in the temperature range 100 K to 400 K. Shielded test leads were used for all electrical connections. Before starting the measurements, the samples were heated at 100°C for 1 hr to remove any adsorbed moisture. The surfaces of the discs were polished and coated with silver paste to make electrodes for measuring dielectric properties.


## 3. Results and Discussion

XRD patterns of all these samples withx≤0.16 were recorded by Rigaku, Japan, using CuKα radiation at a scanning rate 2° per minutes. XRD patterns of compositions with x≤0.08 are shown in Figure 1. XRD patterns of the samples with x=0.12 and x=0.16 are similar. The X-ray patterns of polycrystalline BBTF ceramics confirm the formation of single phase. XRD patterns were indexed, and lattice parameters and unit cell volume have been determined using a software ‘‘CELL’’ and are given in Table 1. Compositions with x≤0.08 having tetragonal structure and compositions with 0.10≤x≤0.16 are found to have cubic structure. The tetragonality (c/aratio) decreases with increasing x up to x~0.08. Theoretical densities have been calculated from the molecular weight and unit cell volume of each composition. Bulk density has been calculated from the mass and dimensions for each sample.Table 1
The structure, lattice parameters, ratioc/a, and volume of the unit cell and grain size recorded from microstructures in the Ba1-xBixTi1-xFexO3 system.
Compositions (x)
Structure
Lattice parameters (Å´)
Ratioc/a
Volume (Å´)3
a
b
c
0.02
Tetragonal
3.98
3.98
4.05
1.01
64.38
0.06
Tetragonal
3.99
3.99
4.02
1.00
64.22
0.08
Tetragonal
4.00
4.00
4.00
1.00
64.01
0.10
Cubic
4.00
4.00
4.00
1.00
64.01
0.12
Cubic
4.00
4.00
4.00
1.00
64.00
0.16
Cubic
3.99
3.99
3.99
1.00
63.98Figure 1
X-ray diffraction patterns for the compositions withx=0.02,0.06,0.08, and 0.10 in the system Ba1-xBixTi1-xFexO3.The unit cell volume decreases gradually withx. The tolerance factor ‘‘t’’ determined by taking average ionic radius of A site cations “〈rA〉,” average ionic radius of B site cations “〈rB〉,” and ionic radius of O anion “〈rO〉” for different compositions is given in Table 1. The tolerance factor also decreases with x which varies from 1.058 for x=0.02to1.033 for x=0.16. It is due to continuous decrease in 〈rA〉and 〈rB〉 with x.Microstructures of all these compositions at the same magnification (50,000x) are shown in Figure2. It has been observed that grain size for all these samples is less than 1 micrometer. The grain size has been found to increase with increasing concentration of dopants. Plots of the dielectric constant (εr′) and dielectric loss (D) with temperature at several frequencies for all these samples in the temperature range 100–400 K, are shown in Figures 3, 4, 5, 6, 7, and 8. Composition with x~0.02 shows a broad anomaly at around 392 K, and its position is frequency independent (Figure 3). Low temperature anomalies, observed in BatiO3, are not seen clearly in this sample. The broad anomaly is due to ferroelectric to paraelectric transition as in the case of BaTiO3, and transition is of diffuse nature.Microstructures for the compositionsBa1-xBixTi1-xFexO3 with (a) x=0.02, (b) x=0.06, (c) x=0.08, (d) x=0.10, (e) x=0.12, and (f) x=0.16.
(a)
(b)
(c)
(d)
(e)
(f)Variation of (a) dielectric loss and (b) dielectric constant with temperature for composition Ba0.98Bi0.02Ti0.98Fe0.02O3.
(a)
(b)Variation of (a) dielectric loss and (b) dielectric constant with temperature for composition Ba0.94Bi0.06Ti0.94Fe0.06O3.
(a)
(b)Variation of (a) dielectric loss and (b) dielectric constant with temperature for composition Ba0.92Bi0.08Ti0.92Fe0.08O3.
(a)
(b)Variation of (a) dielectric loss and (b) dielectric constant with temperature for composition Ba0.90Bi0.10Ti0.90Fe0.10O3.
(a)
(b)Variation of (a) dielectric loss and (b) dielectric constant with temperature for composition Ba0.88Bi0.12Ti0.88Fe0.12O3.
(a)
(b)Variation of (a) dielectric loss and (b) dielectric constant with temperature for composition Ba0.84Bi0.16Ti0.84Fe0.16O3.
(a)
(b)Figures4 and 5 show that compositions with x=0.06 and 0.08 plots show an anomaly at 375 K and a broad hump at 175 K in the εr′ versus T plots. The low temperature structural phase transition may  be orthorhombic to tetragonal, and the former is ascribed to tetragonal to cubic phase. The later transition is independent of frequency for composition x~0.06. Its position slightly changes with increasing frequency for the sample with x=0.08. This shows the onset of signature of relaxor behavior. Frequency dependence of ferroelectric to paraelectric transition increases with increasing x.Plots of dielectric loss with temperature forx~0.02, shown in Figure 3(a), show two anomalies one in temperature range  around 100–150 K and other one in the temperature range 300–350 K. Temperature of these anomalies shifts to higher temperature with increasing frequency. Compositions with x≥0.06 exhibit loss maxima in D versus T plots. Temperature of the peak maxima shifts towards higher temperature with increasing frequency. Frequency dependence before peak maxima decreases with increasing x. Frequency dependence before peak maxima is more than after the peak maxima. These compositions exhibit ferroelectric relaxor behavior [16].Peak temperature determined at all frequencies and plot of logτ versus 1000/T are shown. Here, τ is the relaxation time which is given by τ=1/2πf, where f is frequency of measurements. Plot of log τ versus 1000/T for a typical composition with x=0.10 is shown in Figure 9. Values of activation energy for dielectric relaxation, determined by least square fitting of the data for all the compositions to the Arrhenius relation τ=τoeEa/kT, are given in Table 2. This data for activation energy has been found to be in agreement with the activation energy data determined from logRg versus 1000/T plots, where Rg is the grain resistance and has been determined from Z′′ versus z′ plane plots [17].Table 2
The composition, temperature range, and activation energy calculated (fromD versus T plots) for compositions x in the Ba1-xBixTi1-xFexO3 system.
Composition (x)
Structure
Temp. range (K)
E
A (eV)
0.02
Tetragonal
235–246
1.5
246–253 K
1.2
0.06
Tetragonal
172–215
0.50
215–221
1.1
0.08
Tetragonal
235–261
1.2
261–282
0.92
0.10
Pseudo cubic
242–261
1.3
261–282
0.4
0.12
Pseudo cubic
250–275
1.2
275–295
0.52
0.16
Pseudo cubic
235–246
1.5
246–253 K
1.2Variation of (a) logτ with 1000/T and (b) logRg versus 1000/T for a typical composition Ba0.90Bi0.10Ti0.90Fe0.10O3.
(a)
(b)Diffuse phase transition may be explained on the basis of presence of microheterogeneities in these materials. Microheterogeneities arise due to random occupation of A and B sites by different ions. Such a heterogeneous distribution of cations leads to different state of polarization and, hence, different relaxation times in different regions. This causes dielectric maxima to get diffuse [16, 18, 19].ε
r
-
1 is plotted with temperature according to the relation proposed by Uchino and Namura [20] for those compositions which show ferroelectricity at room temperature
(1)1εr=1εrm+C-1(T-Tc)γ,
where C=2εrmδ2, εrm=dielectricconstant at TC, and δ indicates deviation from Curie Weiss temperature. The power exponent γ is 1 for normal ferroelectric behavior, and its value is 2 for ferroelectric relaxor behavior. Plots of log[1/εr-1/εrm] versus log(T-TC)γ] are shown in Figure 10 for compositions with x≤0.08. Power exponent γ varies from 1.43 for x=0.02to2.0 for x=0.08. This clearly indicates that for x≤0.08, the diffuse phase transition is seen. System with x≥0.08exhibits ferroelectric relaxor behavior. The material can be used as a capacitor application.Figure 10
Variation ofln(1/ε-1/εm) with ln(T-Tm) for compositions x=0.02,0.06,and0.08  in system Ba1-xBixTi1-xFexO3.


## 4. Conclusions

All the samples with compositionsx≤0.16 in polycrystalline Ba1−xBixTi1−xFxO3 ceramics system have shown single phase formation. The microstructure analysis showed that the grain size increased with increasing of x content in BBTF system. Compositions up to x≤0.08 have tetragonal structure, whereas compositions with x≥0.10 have cubic structure. Dielectric behavior has exhibited ferroelectric diffuse phase transition for x=0.02 and ferroelectric relaxor behavior for x≥0.10. Dispersion in dielectric loss with x over the frequency range 100 kHz to 2.6 MHz below and above peak maxima reveals the switching of dielectric relaxation from  Maxwell Wagner type relaxation process for low x(~0.02) and relaxation of nanopolar regions for x=0.16.



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