Low Temperature Dielectric Relaxation in Ba_1−𝑥Bi_𝑥Ti_1−𝑥Fe_𝑥O₃ System

Abstract

We report on dielectric properties of polycrystalline Ba_1−𝑥Bi_𝑥Ti_1−𝑥Fe_𝑥O₃ (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.

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 Ba_1−𝑥²⁺La_𝑥³⁺Ti_1−𝑥⁴⁺Ti_𝑥³⁺O₃ [1], and for large concentration, excess donor charge on La³⁺ ions is compensated by Ti vacancies as represented by the formula Ba_1−𝑥La_𝑥Ti_1−5𝑥/4(V_Ti)^////_𝑥/4O₃ [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 𝑇_𝐶=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 with 𝑥=0.02,0.06,0.08,0.10,0.12,0.16, and 0.20 in the Ba_1−xBi_xTi_1−xFe_xO₃ (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 CuK_α 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 with 𝑥≤0.16 were recorded by Rigaku, Japan, using CuK_α 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, ratio 𝑐/𝑎, and volume of the unit cell and grain size recorded from microstructures in the Ba_1−𝑥Bi_𝑥Ti_1−𝑥Fe_𝑥O₃ system.

Figure 1 

X-ray diffraction patterns for the compositions with 𝑥=0.02,0.06,0.08, and 0.10 in the system Ba1−𝑥Bi𝑥Ti1−𝑥Fe𝑥O3.

The unit cell volume decreases gradually with 𝑥. The tolerance factor ‘‘𝑡’’ determined by taking average ionic radius of A site cations “⟨𝑟_A⟩,” average ionic radius of B site cations “⟨𝑟_B⟩,” and ionic radius of O anion “⟨𝑟_O⟩” 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 ⟨𝑟_A⟩and ⟨𝑟_B⟩ with 𝑥.

Microstructures of all these compositions at the same magnification (50,000x) are shown in Figure 2. 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 (𝜀^′_𝑟) 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.

(a)

(b)

(c)

(d)

(e)

(f)

Figure 2 

Microstructures for the compositions Ba1−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.

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(b)

Figure 3 

Variation of (a) dielectric loss and (b) dielectric constant with temperature for composition Ba0.98Bi0.02Ti0.98Fe0.02O3.

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Figure 4 

Variation of (a) dielectric loss and (b) dielectric constant with temperature for composition Ba0.94Bi0.06Ti0.94Fe0.06O3.

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Figure 5 

Variation of (a) dielectric loss and (b) dielectric constant with temperature for composition Ba0.92Bi0.08Ti0.92Fe0.08O3.

(a)  

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Figure 6 

Variation of (a) dielectric loss and (b) dielectric constant with temperature for composition Ba0.90Bi0.10Ti0.90Fe0.10O3.

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Figure 7 

Variation of (a) dielectric loss and (b) dielectric constant with temperature for composition Ba0.88Bi0.12Ti0.88Fe0.12O3.

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Figure 8 

Variation of (a) dielectric loss and (b) dielectric constant with temperature for composition Ba0.84Bi0.16Ti0.84Fe0.16O3.

Figures 4 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 𝜀^′_𝑟 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 for 𝑥∼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 log 𝜏 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=𝜏_𝑜𝑒^{𝐸𝑎/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 log𝑅_𝑔 versus 1000/𝑇 plots, where 𝑅_𝑔 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 (from 𝐷 versus 𝑇 plots) for compositions 𝑥 in the Ba_1−𝑥Bi_𝑥Ti_1−𝑥Fe_𝑥O₃ system.

(a)

(b)

Figure 9 

Variation of (a) log 𝜏 with 1000/𝑇 and (b) log𝑅𝑔 versus 1000/𝑇 for a typical composition Ba0.90 Bi0.10Ti0.90Fe0.10O3.

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 1𝜀_𝑟=1𝜀_rm+𝐶⁻¹𝑇−𝑇_𝑐^𝛾, (1) where 𝐶=2𝜀_rm𝛿², 𝜀_rm=dielectricconstant at 𝑇_𝐶, 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/𝜀_𝑟−1/𝜀_rm] versus log(𝑇−𝑇_𝐶)^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 of ln(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 compositions 𝑥≤0.16 in polycrystalline Ba_1−xBi_xT_i1−xF_xO₃ 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.

Acknowledgments

Financial assistance from the Department of Science and Technology, Government of India (Project No. SR/S-3/ME/0048/2009-SERC), is gratefully acknowledged. The authors are thankful to Dr. Ravi Kumar, a scientist Inter University Accelerator Centre (IUAC), for extending dielectric measurement facility at low temperature. They are also thankful to IIT Roorkee for doing XRD and Scanning Electron Microscopy (SEM).