Dielectric behaviour of (Ba0.77Ca0.23)(Ti0.98Dy0.02)O3 ceramics

In this study, BaTiO3 is modified with Ca 2+ and in addition doped with Dy at the B site lattice. The main idea is to search for new lead-free ferroelectric material and improve their properties. For this purpose, the barium calcium titanate (BCT) as a host and the rare earth element Dy as an activator were used to fabricate a multifunctional material. The obtained ceramics was found to be homogeneous, dense and a single phase material with no evidence of secondary phases. The dielectric study showed that TC increases with the addition of dopants and the obtained ceramics behaves like a relaxor ferroelectric. Some important structural parameters and dielectric properties of dysprosium modified barium (calcium) titanate ceramics are presented.


I. Introduction
Barium titanate (BaTiO 3 ) is an important ceramic material for electronic and memory devices.The ability of the material to form solid solutions with different dopant ions makes the material versatile for various applications [1].The solid solubility of the material depends on the site of substitution, charge compensation mechanism involved and solid solubility limit of a dopant.Dopant in the BaTiO 3 ceramics can occupy either octahedrally coordinated Ti 4+ site or dodecahedrally coordinated Ba 2+ site.There are several reports on the different A site and B site dopants modifying the electrical properties of BaTiO 3 ceramics [2][3][4][5][6].In recent years, a considerable amount of work has been done on the ferroelectric properties of BaTiO 3 .In addition to BaTiO 3 , there are other different perovskites which have been reported as ferroelectrics [7].On heating, BaTiO 3 undergoes a ferroelectric/paraelectric phase transition to the cubic polymorphism at the Curie temperature (T C ) of 120 °C.The substitution of iso-valent cations, such as Ca 2+ alter its lattice constant and thereby its dielectric properties.Iso-valent substituted BaTiO 3 is the potential candidate for various electronic applications and has been actively studied.Among them Ca doped BaTiO 3 is considered to be one of the important candidate for lead free electro optic modulators and memory devices [8].Solid solutions of Ba 1-x Ca x TiO 3 (for x = 0.05 to 0.9) have been widely studied as well as their relaxor nature.The material shows single phase up to x = 0.3 in different study and thereafter it becomes diphasic [9].Ca 2+ has a smaller ionic radius than Ba 2+ .However, it has been pointed out that the Ca ion in Ba 1-x Ca x TiO 3 might have greater atomic polarisability, thereby intensifying the interactions between the Ti ions and, thus, compensate the decrease of T C .
Substitution of aliovalent cations in BaTiO 3 resulted in significant change in electrical properties because of their acceptor/donor behaviour [10].Trivalent rare earth cations have moderate atomic radii between Ba 2+ and Ti 4+ ions and ability to substitute both A and B site and so they are widely used to modify BaTiO 3 [11][12][13][14][15][16].
Ferroelectric materials may be divided into two different classes depending on whether they are normal (classical) or diffuse (relaxor) ferroelectrics [17].The typical characteristic of the later is that at least two different cations have to be localised in the same crystallographic site.Actually, the ABO 3 oxide perovskites show fully ordered transitions, mesoscopic disorder leading to the relaxor behaviour and dipolar glass states [18][19][20][21][22][23].In addition, to the usual application of the ferroelectric materials, relaxors are of great interest for dielectrics in capacitors and actuators [24].Relaxor ferroelectrics have been widely studied in recent years due to their remarkable properties and wide prospects of practical applications [25,26].The relaxor ferroelectric generally belongs to the family with mixed cations ferroelectric and pervoskite structure with general chemical formula AA ′ BB ′ O 3 .Maximum dispersion in relaxor ferroelectric is believed to originate from polar nano regions (PNR) inside which apparent ferroelectric-like order exists.
The most intensively studied relaxor materials are usually lead based ceramics and their derived compounds such as lead magnesium niobate (PMN), lead magnesium niobate-lead titanate (PMN-PT), lead scandium titanate (PST), lead lanthanum zirconate titanate (PLZT) etc. [27,28].But, because of their volatility and toxicity these materials are becoming undesirable.These days with the recent growing demand of global environmental protection research much attention has been attracted to lead-free environmentally friendly and heavy metal free materials.Researchers have shown their interest in the solid solution system of perovskite BaTiO 3 like, barium zirconium titanate (BZT), barium calcium titanate (BCT), barium magnesium titanate (BMT), barium strontium titanate (BST) etc., with different concentrations of dopants and their combinations i.e. double perovskite system.In the present study an attempt is made to study the relaxor behaviour and the effect of dysprosium at the solid solubility limit of Ba 0.77 Ca 0.23 TiO 3 ceramics.

II. Materials and Methods
Dy modified (Ba,Ca)TiO 3 ceramics were prepared just above its solid solubility limit, i.e.Ba 0.77 Ca 0.23 TiO 3 , by conventional solid state reaction (SSR) technique.Stoichiometric proportion high purity powders of BaCO 3 (99.9%pure Merck), CaCO 3 (99.9%pure Merck), TiO 2 (99.9% pure Merck) and Dy 2 O 3 (99.9%pure Merck) were grounded for more than 6 h with acetone medium in an agate mortar for homogeneous mixing of powders.The composite powders were conventionally calcined at 1280 °C for 4 h in an electrical fur-nace.Then the calcined powders were once again thoroughly mixed and ground for 2 h, mixed with 2 wt.% of polyvinyl alcohol (PVA) as binder and pressed into disk-shaped pellets of 10 mm diameter and finally the green ceramics were sintered at 1320 °C for 6 h.
The ceramics were structurally characterized by an X-ray diffractometer.The X-ray powder diffraction profiles of the samples were recorded using graphite filtered CuKα radiation from a highly stabilized and automated X-ray generator operated at 30 kV and 20 mA.The data were recorded within the angular range 10-90°.Scanning electron microscopy (SEM) JEOL JSM 6480LV was used for the observation of the microstructure of the ceramics.An electron beam of 10 kV and 57 µA was used for the SEM study.For dielectric measurement, both sides of the samples were polished for smooth surfaces to a thickness of 0.7 mm.Electrodes were made by applying silver paste on both sides of the specimen and annealed at 350 °C for 5 min.Dielectric measurement was carried out over the frequency range 1 kHz to 1 MHz using an LCR meter connected to PC.The dielectric data was collected at an interval of 5 °C while heating at a rate of 0.5 °C per min.

III. Results and discussion
X-ray diffractograms of the prepared BaTiO 3 and Ba 0.77 Ca 0.23 TiO 3 ceramics are presented in Figure 1a, whereas XRD pattern of Ba 0.77 Ca 0.23 Dy 0.02 Ti 0.98 O 3 is shown in Fig. 1b.X-ray analysis, the fingerprint of a material, shows that the investigated ceramics are single phase materials without evidence of any secondary phases.The X-ray parameters are given in Table 1.Detailed X-ray parameters of Ba 0.77 Ca 0.23 Dy 0.02 Ti 0.98 O 3 ceramic are given in Table 2 including hkl indices of different planes.For precise structural characterization of a material, it is necessary to understand its flawless crystallographic parameters.Based on these parameters, crystallite size, strain, different peak profile parameters like, peak position, integral breadth, unit cell  Figure 2 shows the scanning electron microscope (SEM) images of BaTiO 3 , Ba 0.77 Ca 0.23 TiO 3 and Ba 0.77 Ca 0.23 Dy 0.02 Ti 0.98 O 3 ceramics.The microstructure is found to be dense and the grains are uniformly distributed.The sample I (BaTiO 3 ), has a little bit larger grain sizes than the sample II Ba 0.77 Ca 0.23 TiO 3 .This may be attributed to the fact that Ca 2+ acts as grain growth inhibitor and Ca 2+ enters into the sub-lattice of Ba 2+ atoms.But, in the sample III (Ba 0.77 Ca 0.23 Dy 0.02 Ti 0.98 O 3 ) the grain size further increases in the studied range.The ceramo-graphs shows very clear grains and grain boundary.This may be attributed to the reason that, Dy 3+ may be replacing Ti 4+ ions in spite of going into the A-site.The lattice parameter is found to decrease relative to the undoped sample, due to the shrinkage of the unit cell.The unit cell volume is lower (64.47Å 3 ) compared to the parent sample.Aliovalent substitutions cause a distortion of the lattice.The interactions between B-site ions and O 2-become stronger resulting in an increase in T C and Dy 3+ tends to occupy B sites rather than A-sites.The rare-earth elements, having its 4 f orbital totally screened by 5s and 5p orbital, play an important role in deciding the electrical and magnetic properties.
Because of the larger radius, the substitution of Dy 3+ for Ti 4+ in B-sites may depress the oriented displacement of B-site ions in the oxygen octahedrons, which are responsible for the spontaneous polarization.Aliovalent substitutions cause a distortion of the lattice.The interactions between B-site ions and O 2-become stronger resulting in an increase in T C and Dy 3+ tends to occupy B sites rather than A-sites.Because of the larger radius, the substitution of Dy 3+ for Ti 4+ in B-sites may depress the oriented displacement of B-site ions in the oxygen octahedrons, which are responsible for the spontaneous polarization.This is attributed to distortion produced Dy 3+ ions on B-sites, which locally produces deformation in the lattice due to a crystal field potential.This may also be due to atomic mass and volume of the dopant, which affect Dy−O distances on octahedral sites, suggesting that Dy 3+ ions occupied octahedral lattice sites.
Figure 3 shows the temperature dependent dielectric constant (ε) of the bulk Ba 0.77 Ca 0.23 Dy 0.02 Ti 0.98 O 3 ceramics at different frequencies (from 1 kHz to 1 MHz).The value of temperature dependent permittivity increases gradually to maximum value (ε m ) with temperature up to the transition temperature and then decreases smoothly indicating a phase transition.The maximum of dielectric permittivity, ε m , and the corresponding maximum temperature T m , depend upon the measurement frequency.The magnitude of dielectric constant decreases with increase in frequency and the maxima are shifting towards higher temperature.A fre-quency dispersion takes place for T ≪ T m and the value of ε m decreases when frequency increases.This indicates that the dielectric polarization is of relaxation type in nature.At 1 kHz, the dielectric maximum (ε m ) of Ba 0.77 Ca 0.23 Dy 0.02 Ti 0.98 O 3 ceramic and the observed high value of T m is due to the higher grain size.The dielectric constant appreciably increases with temperature within the range of 300-400 °C, from which it can be deduced that Dy-doping has caused the existence of a new phase transformation temperature, thereby, changing the polarization and dielectric properties of the ceramics.The high value of the dielectric constant at low frequencies is due to the accumulation of charges at the interfaces between the sample and the electrodes, i.e., Maxwell-Wagner polarization and interfacial polarization.As the frequency increases, the dipoles in the samples reorient themselves fast enough to respond to the applied electric field resulting in the increase in dielectric constant at higher frequencies, which is attributed to the increase in the grain size.The SEM micrographs show more aggregated grains within its microstructure.
The increase in dielectric constant as a function of concentration is because of the grain aggregates which induce the internal stress within the grains.When a finegrained ceramics are subjected to field, the grain is subjected to an internal stress which depends on the orientation of all the surrounding grains.Thus, the in- crease in dielectric constant is observed.The stress system would tend to suppress the spontaneous deformation and force the grain back toward the cubic state.As Dy is doped in ceramics, the Curie temperature of ceramics has been shifted toward higher temperature due to the internal stresses developed within the ceramics.Meanwhile, temperature dependant dielectric constant exhibited broad peak indicating the diffuse phase transition.It is reported that as the grain size decreases, the maximum dielectric constant and transition temperature decrease [25].The temperature and frequency variation of the imaginary part (Fig. 4) of dielectric permittivity shows that, the maximum dielectric temperature shifted to higher values on increasing frequencies.Here the evolution of frequency dispersion is characterized by an increase in dielectric loss when frequency increases.Additionally, there is a deviation from Curie-Weiss law.
It is known that the dielectric permittivity of a normal ferroelectric above the Curie temperature follows the Curie-Weiss law described by: where T 0 is the Curie-Weiss temperature and C is the Curie-Weiss constant.The value of the Curie-Weiss temperature T 0 is greater than that of T m and also there is an appreciable difference between the T dev (401.7 °C) and T m .Thus, a strong dielectric dispersion is evidenced leading to Vogel-Fulcher behaviour.
Figure 5 shows the plot of inverse dielectric constant versus temperature at different frequencies.The differ-  3. The parameter ∆T m , which describes the degree of the deviation from the Curie-Weiss law, is defined as: where T CW denotes the temperature from which the permittivity starts to deviate from the Curie-Weiss law and T m represents the temperature of the dielectric maximum.The Curie temperature is determined from the graph by extrapolation of the reciprocal of dielectric constant of the paraelectric region and the values obtained are given in Table 3.
The diffuse characteristics of ferroelectricparaelectric phase transition are known to deviate from the typical Curie-Weiss behaviour and can be described by a modified Curie-Weiss relationship [29,30]: where γ and C are assumed to be constant.The parameter γ gives information on the character of the phase transition: For γ = 1, a normal Curie-Weiss law is obtained, and γ = 2 describes a complete diffuse phase transition [31].
Figure 6 shows the plot of ln(1/ε − 1/ε m ) vs. ln(T − T m ).The value of γ was found to be 1.9 at frequency 10 kHz (Table 3).Thus, it is clear that, there is a clear diffuse phase transition.The diffuse phase transition and deviation from Curie-Weiss type behaviour may be assumed due to disordering.The diffusiveness occurs  mainly due to the compositional fluctuation and structural disordering in the arrangement of cations in one or more crystallographic sites of the structures.The randomly distributed electrical field in a mixed oxide system is reported to be the main reason leading to the relaxor behaviour.Aliovalent cations incorporated in a perovskite lattice have been reported to serve as donors or acceptors, which could affect the electrical characteristics greatly, even though the solubility remained at the trace level.
The broadening of the phase transition is better illustrated by plotting the reduced dielectric constant ε/ε m as a function of reduced temperature (τ) at different frequencies (Fig. 7).The full width of the plot has very little dispersion over a wide frequency range similar to the observation made in other relaxor materials [32].Ba 2+ ions are replaced by Ca 2+ ions in the first stage, which have a smaller ionic radius.Moreover, aliovalent substitutions cause a distortion of the lattice.The interactions between B-site ions and O 2-become stronger resulting in an increase in T C and Dy 3+ tends to occupy B site rather than A-sites.Because of the larger radius, the substitution of Dy 3+ for Ti 4+ in B-sites may depress the oriented displacement of B-site ions in the oxygen octahedrons, which are responsible for the spontaneous polarization.Yet another parameter, which is used to characterize the degree of relaxation behaviour in the frequency range of 100 Hz to 10 kHz, is described by [33]: The value of ∆T relax was determined to be zero K for the present sample.The above characterization done on the basis of Curie-Weiss law and the value of empirical parameters like ∆T m , γ, and ∆T relax suggest that the permittivity of Ba 0.77 Ca 0.23 Dy 0.02 Ti 0.98 O 3 ceramic follows Curie-Weiss law only at temperatures much higher than T m .Thus, the large deviation from the Curie-Weiss type behaviour, large relaxation temperature ∆T relax , and γ = 1.9, suggest also that Ba 0.77 Ca 0.23 Dy 0.02 Ti 0.98 O 3 is a relaxor ferroelectric.
The frequency dependency of T m is shown in Fig. 8 as ln f vs. 1000/T m .The observed frequency dependence of T m was empirically evaluated using Vogel-Fulcher's relation and computed using the following equation: where f 0 is the high temperature extrapolation of the attempt frequency, E a is the measurement of average activation energy, k B the Boltzman constant, T ν f the static freezing temperature of polarization fluctuation and f is the pre exponential factor.All these dielectric characteristics are typical for relaxor behaviour.The fitting parameters for the compositions are found to be, E a = 0.1105 eV, T f = 102.6K, f 0 = 101.9× 10 Hz.The fitting parameters having close agreement with the data of Vogel-Fulcher's relation suggests that the relaxor behaviour in the system is analogous to that of a dipolar glass with polarization fluctuations above a static freezing temperature.

IV. Conclusions
The perovskite Ba 0.77 Ca 0.23 Dy 0.02 Ti 0.98 O 3 ceramics was prepared through a solid state reaction route.The room temperature XRD study suggests that the composition has a single phase in teragonal symmetry.The dielectric study of the compositions shows a typical relaxor like behaviour.The relaxor behaviour observed in this ceramics can be induced by many reasons, such as microscopic compositions fluctuation, the merging of micro-polar regions into macro-polar regions, or a coupling of the order parameter and the local disorder mode through the local strain.In perovskite-type compounds the relaxor behaviour appears when at least two cations occupy the same crystallographic sites A or B. Both Ti and Dy are ferroelectrically active and these cations are off-centred in the octahedral site giving rise to a local dipolar moment.A quantitative characterization of the relaxor behaviour based on the empirical parameters (∆T m , ∆T res , and ∆T CW ) confirms the relaxor behaviour of Ba 0.77 Ca 0.23 Dy 0.02 Ti 0.98 O 3 composition.In addition, there is a strong deviation from Curie-Weiss law.A deviation for T < T dev is the characteristic of dipole interactions responsible for some type of short range order.The large curvature of 1/ε around T m is in good agreement with a strongly diffuse phase transition.

Figure 5 .
Figure 5. Inverse dielectric constant (1/ε) vs. temperature of Ba 0.77 Ca 0.23 Dy 0.02 Ti 0.98 O 3 ceramics at different frequencies ent parameters obtained are listed in Table3.The parameter ∆T m , which describes the degree of the deviation from the Curie-Weiss law, is defined as:

Figure 7 .Figure 8 .
Figure 7. Reduced dielectric constant ε/ε m as a function of reduced temperature (τ) at different frequencies

Table 1 .
Compositions of TiN samples obtained by RBS analyses

Table 2 .
The XRD pattern matches with tetragonal barium titanate (ref.ID 980034393) and the following parameters for the studied Ba 0.77 Ca 0.23 Dy 0.02 Ti 0.98 O 3 ceramics were obtained: crystal system -tetragonal; Bravais type -body centred; space group -I41/acd; a = b = 3.9963(4) Å and c = 4.0370 Å, with cell volume of 74.47 Å 3 .The calculated (d cal ) and observed (d obs ) values of inter-planner distances were found to be in good agreement with each other.

Table 3 .
Temperature dependency dielectric parameters of the composition Ba 0.77 Ca 0.23 Dy 0.02 Ti 0.98 O 3 ceramics at different frequencies