Low Temperature Dielectric Relaxation in System
We report on dielectric properties of polycrystalline (BBTF) ceramic system (, 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 . Crystal structure is tetragonal for and cubic for . 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 exhibits diffuse phase transition. Compositions with show ferroelectric relaxor behavior. This shows that diffuse ferroelectric transition behavior changes to relaxor type ferroelectric transition with increasing . Plots of dielectric loss (D) versus temperature shows broad maxima which shift to high temperature with increasing frequency, dispersion in dielectric loss decreases with below peak maxima and increases above. It may be attributed to Maxwell Wagner type relaxation process for low (~0.02) and relaxation of nanopolar regions for .
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 , and for large concentration, excess donor charge on La3+ ions is compensated by Ti vacancies as represented by the formula . Substitution of Bi3+ at Ba2+ site in small concentration is reported to exhibit positive temperature coefficient of resistance (PTCR) . Diffuse phase transition has been observed for large concentration Bi3+ .
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.  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 BiFeO3-CuFe2O4 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 . 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 .
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 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.
An effort has been made to synthesize the compositions with , 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 with were recorded by Rigaku, Japan, using CuKα radiation at a scanning rate 2° per minutes. XRD patterns of compositions with are shown in Figure 1. XRD patterns of the samples with and 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 having tetragonal structure and compositions with are found to have cubic structure. The tetragonality (ratio) decreases with increasing up to . 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.
The unit cell volume decreases gradually with . The tolerance factor ‘‘’’ determined by taking average ionic radius of A site cations “,” average ionic radius of B site cations “,” and ionic radius of O anion “” for different compositions is given in Table 1. The tolerance factor also decreases with which varies from 1.058 for for . It is due to continuous decrease in and with .
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 and dielectric loss () 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 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.
Figures 4 and 5 show that compositions with and 0.08 plots show an anomaly at 375 K and a broad hump at 175 K in the versus 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 . Its position slightly changes with increasing frequency for the sample with . This shows the onset of signature of relaxor behavior. Frequency dependence of ferroelectric to paraelectric transition increases with increasing .
Plots of dielectric loss with temperature for , 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 exhibit loss maxima in versus plots. Temperature of the peak maxima shifts towards higher temperature with increasing frequency. Frequency dependence before peak maxima decreases with increasing . Frequency dependence before peak maxima is more than after the peak maxima. These compositions exhibit ferroelectric relaxor behavior .
Peak temperature determined at all frequencies and plot of log versus 1000/ are shown. Here, is the relaxation time which is given by , where f is frequency of measurements. Plot of log versus 1000/ for a typical composition with 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 , are given in Table 2. This data for activation energy has been found to be in agreement with the activation energy data determined from versus 1000/ plots, where is the grain resistance and has been determined from versus plane plots .
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].
is plotted with temperature according to the relation proposed by Uchino and Namura  for those compositions which show ferroelectricity at room temperature where , at , and indicates deviation from Curie Weiss temperature. The power exponent is 1 for normal ferroelectric behavior, and its value is 2 for ferroelectric relaxor behavior. Plots of versus are shown in Figure 10 for compositions with . Power exponent varies from 1.43 for for . This clearly indicates that for , the diffuse phase transition is seen. System with exhibits ferroelectric relaxor behavior. The material can be used as a capacitor application.
All the samples with compositions in polycrystalline Ba1−xBixTi1−xFxO3 ceramics system have shown single phase formation. The microstructure analysis showed that the grain size increased with increasing of content in BBTF system. Compositions up to have tetragonal structure, whereas compositions with have cubic structure. Dielectric behavior has exhibited ferroelectric diffuse phase transition for and ferroelectric relaxor behavior for . Dispersion in dielectric loss with 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 (~0.02) and relaxation of nanopolar regions for .
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).
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