Facile preparation of uniform barium titanate (BaTiO₃) multipods with high permittivity: impedance and temperature dependent dielectric behavior

Abstract

Perovskite barium titanate (BaTiO₃) multipods were prepared via high temperature solid state reaction. The crystal structure and morphology of BaTiO₃ particles were characterized by X-ray diffraction (XRD), field emission scanning electron microscopy (FESEM), high resolution transmission electron microscopy (HRTEM), and scanning probe microscopy (SPM). The XRD analysis of the crystal structure revealed that a single-phase compound was formed having tetragonal crystal structure. Calorimetric study (DSC) over room to high temperature was used to find the energy involved in different steps of synthesis especially during the initiation and the termination process for the formation of BaTiO₃. These multipods have high average aspect ratio (∼10, where average diameter ∼300 nm and average length ∼3 μm) as seen from FESEM. UV-Vis spectroscopy reveals that the prepared material is UV active. The bulk and surface chemical composition of these BaTiO₃ particles as investigated by Fourier transform infrared (FTIR) and X-ray photoelectron spectroscopy (XPS) spectra reveals that in the prepared BaTiO₃, the titanium ions exist in two different oxidation states, namely Ti³⁺ and Ti⁴⁺. The BaTiO₃ multipod exhibits high permittivity with relatively low dielectric loss. From impedance analysis of the material, the dual resistivity characteristics, one for grain and the other for grain-boundary can be distinguished. An equivalent circuit has been proposed through analysis of the complex impedance plot (Nyquist plot) for BaTiO₃ multipods. This material has perfect capacitative nature as seen from the Bode plot, and can be used for charge storage devices and other electronic applications. From temperature dependent dielectric analysis, the Curie temperature of BaTiO₃ multipods is found to be ∼85 °C.

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1. Introduction

Barium titanate is an important electroactive ceramic material. Over the past few decades, the preparation of barium titanate (BaTiO₃) in different nano forms such as nanoparticles, nanocubes, nanorods, nanowires, and nanotubes has attracted great attention from many researchers particularly because of their unique ferroelectric and piezoelectric properties. These properties are important and essential for the development of different nanoscale devices for transducers, piezoelectric sensors and actuators, energy-harvesting devices, memory devices including ferroelectric random access memories (FRAM), and also for optoelectronic applications.^1–8 Piezoelectric oxides are of interest because of their potential applications in different fields ranging from sensors to radio frequency devices.⁹ Barium titanate is one of the most widely used ceramics in the electronics industry, especially for making multilayer ceramic capacitors (MLCCs).^10,11 Literatures reveal that BaTiO₃ can exist in different crystal structures depending on environmental temperatures, cubic (above Curie temperature), tetragonal (5 °C to Curie temperature), orthorhombic (−90 °C to 5 °C), and rhombohedral (<−90 °C) (Fig. 1).^12–15

Fig. 1 Crystallographic changes of BaTiO₃.^14,15

In the cubic form, all the Ba²⁺ ions occupy eight corners of an elementary cubic cell, whereas single Ti⁴⁺ ion is in the centre of the cube and the O²⁻ ions in the centre of each surface of that cube. However, below the Curie temperature BaTiO₃ exists in the distorted tetragonal structure with a mutual displacement of the centers of positive and negative charges within the sub-lattice. Consequently, a dipole moment arises parallel to one of the cubic areas of the original phase. Such a generated spontaneous polarization in the tetragonal structure is the origin of its ferroelectric and piezoelectric behavior.^16–18 Zhu et al. have prepared barium titanate nanoparticles through hydrothermal technique using titanium hydroxide, titanium dioxide, and barium hydroxide as starting materials where different solvents have used during the product preparation and the purification process.¹⁹ Peng et al. had taken H₂TiO₃ and Ba(NO₃)₂ as the starting materials for the preparation of BaTiO₃ in aqueous medium with other solvents.²⁰ Recently nanocrystalline BaTiO₃ particles have been prepared by wet chemical methods^21–24 such as sol–gel, coprecipitation, and hydrothermal methods where in all the cases solvents are used, so at the end of the process purification is necessary which is time consuming and costly process. Lee et al. have reported the preparation of barium titanate nano powder via hydrothermal and solvothermal synthesis methods and have described their structural characteristics. They have used organic solvents [diethanolamine (DEA) and triethanolamine (TEA)] to control the particle size.²⁵ From the above literature reports, we can conclude BaTiO₃ nanoparticles are usually prepared through wet chemical process. However, high cost and difficulty in process control in these routes forced to find out other ways for the preparations of BaTiO₃ nano particles.^26–28

The present investigation reports the preparation of BaTiO₃ multipods using high temperature solid state reaction followed by sintering, using Ba(OH)₂·8H₂O and TiO₂ as starting materials. The overall reaction for the BaTiO₃ formation through heat treatment of stoichiometric amount of Ba(OH)₂·8H₂O and TiO₂ at temperatures ranging from 700–1200 °C is given below:

The effect of process parameters like temperature on the crystal structure, morphology, optical properties, dielectric, and impedance properties of the formed barium titanate particles are discussed in detail.

2. Experimental section

2.1 Materials used

Anatase grade titanium dioxide (TiO₂) and Ba(OH)₂·8H₂O were procured from Merck chemical Ltd., India. These two materials were used for the preparation of BaTiO₃ multipods. Commercial grade BaTiO₃ was purchased from Alfa Aesar, Germany and was used for comparing the results of barium titanate multipods with these supplied BaTiO₃. Before the comparison study, the commercial BaTiO₃ was subjected to heat treatment at 500 °C for 6 h in order to remove all the adsorbed moisture (physisorbed/chemisorbed).

2.2 Preparation and purification of BaTiO₃ powder

Barium titanate multipods were prepared via high temperature solid state reaction using stoichiometric amount of Ba(OH)₂·8H₂O (Merck India, %) and anatase grade TiO₂ (Merck India, %). Before taking the weight, both of these oxides were oven dried at 120 °C for 6 h for removing the adsorbed moisture and then these oxides were thoroughly mixed in an agate mortar and loaded in an alumina crucible. The mixture was heated in an electrical muffle furnace at 700 °C for 4 h and 1000 °C for 3 h followed by heating at 1200 °C (twice) for 4 h and 2 h respectively with three intermittent grindings. The resulting powder obtained was ground thoroughly using agate mortar and pestle. The above powder was purified using two solvents (ethanol or 1.0 N HCl solution) before doing the other characterizations. The prepared barium titanate powder was washed with ethanol/1.0 N HCl solution at three different time intervals (24 h, 48 h, and 72 h). The above product was then centrifuged and again washed with respective solvents (ethanol/DI water) for 6–7 times to maintain the neutral pH. The objective of washing the prepared powder with ethanol/1.0 N HCl solution is to remove the impurity present in the final product and to obtain purified barium titanate (BaTiO₃) powder. Finally, the powder was oven dried at 120 °C for 6 h and then taken for XRD analysis. From XRD analysis, it was observed that the powder washed in 1.0 N HCl medium for 72 h (Fig. 2a) gave the best result. Finally, the purified barium titanate powder was compacted into pellets at a pressure of 12 tons for XPS, dielectric, and impedance study etc.

Fig. 2 XRD pattern of (a) prepared BaTiO₃ multipods at different purification conditions, (b) prepared BaTiO₃ (pure) multipods.

2.3 Heat treatment of control samples [TiO₂ and Ba(OH)₂·8H₂O] and commercial BaTiO₃

Heat treatment of titanium dioxide was done at 1200 °C for 6 h in order to compare its characteristics with those of normal titania and BaTiO₃ multipods. Similarly, heat treatment of Ba(OH)₂·8H₂O was also done but it was heat treated up to 700 °C for 6 h instead of 1200 °C as its boiling point is 780 °C.²⁹ After heat treatment process all these samples were washed by ethanol/acid solution followed by water. Moreover, heat treatment of commercial BaTiO₃ was done at 500 °C for 6 h in order to remove all the adsorbed moisture (physisorbed/chemisorbed).

3. Characterization

The crystal structure of different synthesized BaTiO₃ powder samples were characterized by X-ray diffractometer (model PW 3040/60) with CuKα irradiation at λ = 1.5406 Å. The scanned diffractograms spread over the 2θ values from 10° to 90° at a scan rate of 0.13° s⁻¹ using an X'celerator mode. The microstructure and grain size were analyzed through a field emission scanning electron microscope (FESEM, Carl Zeiss SMT AG, Germany), high resolution transmission electron microscope (HRTEM, JEM-2100), and scanning probe microscope (SPM, Multiview-1000™). FTIR spectra of different samples were recorded using IR spectrophotometer (model spectrum RX-I, PerkinElmer, Inc., MA, USA) in the range 400–4400 cm⁻¹. The optical absorption spectra in the UV-visible range were obtained by UV-Vis spectrophotometer (Shimadzu UV-1700). Both dielectric and impedance properties of BaTiO₃ powder were measured using precision LCR meter (Model. Quad Tech 7600) coupled with a homemade parallel plate sample holder. The surface composition of BaTiO₃ multipods was determined through XPS using an Al-Kα excitation, an ESCA-2000 Multilab apparatus, VG microtech. Thermal analyses (TGA and DSC) of different samples were carried out using TGA/DSC 1, STARe System, METTLER TOLEDO at a heating rate of 20°C min⁻¹ under nitrogen atmosphere over the temperature range of 45 °C to 1000 °C. The temperature dependent dielectric properties of BaTiO₃ multipods were measured by Navocontrol, Alpha-A high performance frequency analyzer over the temperature range 40–250 °C at a steady increase of 5 °C up to 180 °C and at three other temperatures (200 °C, 230 °C, and 250 °C).

4. Results and discussion

4.1 X-ray diffraction analysis

X-ray diffraction analysis (XRD) was done on the prepared sample (BaTiO₃) which revealed the presence of some unknown peaks along with the BaTiO₃ peaks as shown in Fig. 2a. The obtained BaTiO₃ powder was purified as described earlier in the Experimental section. The XRD results of both purified/impure BaTiO₃ powders are given in Fig. 2a and b respectively. In Fig. 2a, “24 E” stands for washing of BaTiO₃ powder for 24 h in ethanol (E) medium whereas “24 H” stands for washing of BaTiO₃ powder for 24 h in HCl (H) medium. There are distinct differences in plots (Fig. 2a and b) of purified and unpurified samples of BaTiO₃. Some extra peaks due to traces amount of impurity in unpurified samples (Fig. 2a) vanishes in plot of purified sample (Fig. 2b). In fact, the purified sample exhibits all well defined peaks reported for neat BaTiO₃. Diffraction peaks for prepared BaTiO₃ nanoparticles are observed at 2θ = 22.29°, 31.53°, 38.92°, 45.06/45.31°, 50.87°, 56.34°, 65.93°, 70.48°, 75.03°, and 79.44° and these peaks represent the Bragg reflections from the (100), (110), (111), (002)/(200), (102), (211), (220), (212), (310), and (311) planes respectively.³⁰ The observed diffraction peaks (Fig. 2b) reveal the tetragonal crystal structure for BaTiO₃ particles and the obtained XRD patterns are matching well with the standard XRD pattern of BaTiO₃ particle (JCPDS card no. 79-2264). The tetragonal nature of the prepared BaTiO₃ multipods is also evident from the XRD peak splitting [(002) and (200)] at 2θ ∼ 45,³⁰ where the ratio of I₀₀₂/I₂₀₀ is ∼0.54 as reported by Zhu et al.^30–34

Fig. 3 describes the comparison of XRD pattern of BaTiO₃ multipods with normal titania, heat treated control samples [TiO₂ and Ba(OH)₂·8H₂O], and commercial BaTiO₃. It is observed that all the peaks of BaTiO₃ multipods are fully matching with those of commercial BaTiO₃ supplied by Alfa Aesar, Germany. Diffraction peaks for normal TiO₂ particles are observed at 2θ = 25.45°, 36.90°, 37.86°, 38.64°, 48.06°, 53.85°, 54.95°, 62.27°, 62.81°, 68.96°, 70.34, 75.07, and 76.10°. But after heat treatment at 1200 °C, new peaks are observed which is due to the anatase to rutile phase transition in TiO₂ at temperature above 900 °C.³⁵ There are number of peaks observed for heat treated Ba(OH)₂·8H₂O, which are not present in the final product (BaTiO₃ multipods).

Fig. 3 Comparison of XRD pattern of BaTiO₃ multipods with normal titania, heat treated control samples [TiO₂ and *Ba(OH)₂·8H₂O], and commercial BaTiO₃. [*Ba(OH)₂·8H₂O = BH].

4.2 High temperature TGA/DSC analysis

DSC analysis from room temperature to high temperature was carried out in order to find out the energy involved during barium titanate particle formation through reaction of barium hydroxide with titanium dioxide especially during the initiation and the termination process. Fig. 4A and B represent the TGA/DSC curves over the temperature range 45–1000 °C for stoichiometric mixture of Ba(OH)₂·8H₂O and TiO₂, where Fig. 4A shows the TGA/DSC plot of the mixture during the first heating (1st run) and Fig. 4B represents the TGA/DSC plot of the mixture during the second heating (2nd run). During the first heating the weight and enthalpy changes are due to chemical reactions taking place in the system for formation of BaTiO₃ whereas the changes during 2nd heating are mainly due to further modification of formed BaTiO₃ during heating process. Fig. 4C shows the TGA/DSC result of impure BaTiO₃ whereas Fig. 4D represents the TGA/DSC result of the purified BaTiO₃. Fig. 4A shows three endothermic peaks at 81.15 °C, 135.5 °C, and 377.8 °C which are due to the three corresponding weight losses from the mixture. In case of Fig. 4B, there is only marginal weight loss but endothermic peaks at 71.6 °C, 396.6 °C, 650.2 °C, 761 °C, and 796 °C are observed which are due to the inter-diffusion (phase change) of BaTiO₃ crystals and unreacted Ba(OH)₂·8H₂O and TiO₂ crystals. Fig. 4C and D represent TGA and DSC plots for purified BaTiO₃ multipods produced by solid state reaction and same BaTiO₃ after chemical purification. The area under the endothermic peak (at 759.28 °C, Fig. 4D) is smaller than the area under the peak at 822.15 °C (Fig. 4C), which is due the presence of very minor quantities of impurity in case of purified BaTiO₃ (Fig. 4D). In Fig. 4A–D beyond 800–850 °C, the DSC curve undergoes an exothermic phase transition (moves towards the exothermic end) which belong to the crystalline phase changes.³⁶

Fig. 4 TGA/DSC curve for Ba(OH)₂·8H₂O and TiO₂ mixture (A) 1st run, (B) 2nd run; TGA/DSC curve of (C) impure BaTiO₃ and (D) purified BaTiO₃.

4.3 Morphological analysis via FESEM, HRTEM, and SPM

The FESEM images of neat titania (TiO₂), mixture of Ba(OH)₂·8H₂O and TiO₂ at room temperature, and BaTiO₃ prepared at different reaction conditions (temperature) are presented in Fig. 5. It is observed at ambient temperature that neat titania particles are spherical in nature where as Ba(OH)₂·8H₂O particles are rice grain shaped crystals (Fig. 5a and b). But solid state reaction between Ba(OH)₂·8H₂O and TiO₂ at different temperatures lead to the formation of different types of BaTiO₃ particles. In the initial stages of calcination process the inter-diffusion of Ba²⁺ ions to TiO₂ phase and Ti⁴⁺ ions to Ba(OH)₂·8H₂O phase took place prior to formation of BaTiO₃. When this was calcined at 700 °C (Fig. 5c), clustered mass was found to form due to inter-diffusion of counter ions. In this sample of barium titanate only one or two rod likes shape particles are observed, which may be due to the initiation of BaTiO₃ particle formation. In fact, with the increase in reaction (calcinations) temperature, the extent of inter-diffusion of Ti⁴⁺ ions and Ba²⁺ ions increases leading to increase in concentration of BaTiO₃ nanoparticles along with decrease in concentration of unreacted masses (TiO₂ and Ba(OH)₂·8H₂O). However, the increase in calcination temperature also modifies the shape of the BaTiO₃ particles. High temperature (≥1000 °C) treatment favors the anisotropic growth of barium titanate crystal in one direction. This unidirectional growth of BaTiO₃ particles at 1000 °C leads to formation of grain shaped particles. This process further continues to form final star shaped BaTiO₃ multipods when subjected to 1200 °C. The anisotropic growth of barium titanate crystals can be controlled by manipulating the temperature and time of reaction.³⁷ From Fig. 5d, it is clear that some BaTiO₃ particles formation is almost complete at calcination temperature 1000 °C. However, still there is small amount of unreacted clusters. When the calcination temperature is further increased to 1200 °C, BaTiO₃ multipod formation becomes complete as seen from Fig. 5e and f (low and high magnification images of BaTiO₃ particles). These BaTiO₃ multipods are crystalline in nature as apparent from XRD analysis. Each BaTiO₃ multipod consists of triangular-shaped blade like particles having higher width in the middle portion of particles with sharp ends with average particle length of ∼3 μm and average particle diameter of ∼300 nm (Fig. 5f). It is seen that each particle with high diameter in the middle with sharp ends are attached with each other at the centre and star like particle cluster is formed. These pictures reveal that as the calcinations temperature increases the formation of grain like particles increases. This is mainly because of increase in rate of diffusion process with rise in temperature. However, from XRD analysis of different BaTiO₃ samples reveals that some impurities are associated with BaTiO₃ particles (Fig. 2a) and this impurity can be removed by chemical purification process.

Fig. 5 FESEM images of (a) neat titania powder, (b) mixture of Ba(OH)₂·8H₂O and TiO₂ at room temperature, (c) BaTiO₃ at 700 °C, (d) BaTiO₃ at 1000 °C, (e) BaTiO₃ multipods at 1200 °C (low magnification), and (f) star shaped BaTiO₃ multipods at 1200 °C (high magnification).

Schematic model for different steps of formation of nano barium titanate particles through solid state reaction is proposed and shown as Scheme 1. The formation of BaTiO₃ nanoparticles from Ba(OH)₂·8H₂O and TiO₂ through solid state reaction is mainly due to inter-diffusion of Ti⁴⁺ and Ba²⁺ ions. As mentioned earlier the rate and extent of inter-diffusion process increase with increase in calcination temperature resulting in the formation of shell of BaTiO₃ accompanied with release of water vapors during reaction process. As the process goes, there is continuous thickening of BaTiO₃ shell formation. This formation of BaTiO₃ particles continues till the reactants (Ba(OH)₂·8H₂O and TiO₂) exhausts. However, taken in equimolar amount, traces of unreacted barium hydroxide and titania remain as impurity in the final BaTiO₃ particles produced at highest temperature. Increase in temperature not only increase the extent of reaction but also modifies the shape of the BaTiO₃ particles as mentioned earlier. At the highest temperature of calcination, the best triangular blade shaped (multipods) barium titanate particles are formed which are clustered in the form of star (Fig. 5e and f). The aspect ratio of such particles is high having average width ∼300 nm and length ∼3 μm. To understand the elemental composition of BaTiO₃ multipods formed, a selected area of particle cluster is targeted for analysis (Fig. 6) and the composition of various elements present at that spot are furnished in Table 1.

Scheme 1 Proposed reaction model for the preparation of BaTiO₃ multipods.

Fig. 6 FESEM + EDS image of prepared BaTiO₃ multipods.

Table 1 EDS value of BaTiO₃ multipods

Element	Weight%	Atomic%
O K	49.05	63.01
Ti K	12.45	18.21
Ba L	38.50	18.77
Total	100

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The HRTEM image of these BaTiO₃ particles is presented in Fig. 7a. From this image, it is observed that all nano particles are cylindrical grain like structure and have regular shape with high aspect ratio. The SAED pattern (Fig. 7b) exhibits distinct sharp diffraction patterns in consistent with XRD measurements. This confirms that the BaTiO₃ particles are single crystalline in nature. The first four points/dots are assigned to reflection from the planes (100), (110), (111), and (200) respectively. These planes of tetragonal structure as revealed here and in good agreement with the XRD result discussed earlier.

Fig. 7 (a) HRTEM image and (b) SAED pattern of prepared BaTiO₃ multipods.

SPM image and height profile of BaTiO₃ particles are presented in Fig. 8a and b respectively. From the height profile (Fig. 8b), the formation of nanoparticles are confirmed through three distinct peaks (1, 2 and 3). Individual single particles of BaTiO₃ can be detected in Fig. 8a at three different positions (1, 2 and 3) which was also seen from FESEM and HRTEM images. So from all these morphological analyses (FESEM, HRTEM, and SPM), the shape of BaTiO₃ nanoparticles are like star shaped multipods with single/double/multi triangular blades.

Fig. 8 (a) SPM image and (b) height profiling of BaTiO₃ multipods.

4.4 Fourier transform infrared (FTIR) spectroscopy

Fig. 9A(a)–(d) represents the FTIR spectra of neat TiO₂ (dried), Ba(OH)₂·8H₂O (dried), and BaTiO₃ (sintered at 1000 °C and 1200 °C). IR bands at 1442, 1058 and 857 cm⁻¹ are characteristic peaks of CO₂, which may be due to the areal CO₂.^38,39 The broad IR band centered at ∼592 cm⁻¹ is typical of the Ti–O stretching vibrations in BaTiO₃ (in TiO₆ octahedra),⁴⁰ and the peak at 452 cm⁻¹ corresponds to the Ti–O bending vibrations (which is found to be at 449 cm⁻¹ for BaTiO₃ sintered at 1000 °C).^40–42 The broad band observed at 3368 cm⁻¹ corresponds to the –OH stretching vibration and the band at 1632 cm⁻¹ is due to –OH bending vibration.⁴¹ The adsorption region spreading over ν ≈ 800–450 cm⁻¹ is also characteristic of oscillation of M–O bonds, where M = Ba and Ti. The band at 431 cm⁻¹ (Fig. 9B) as observed in the case of BaTiO₃ sintered at 1200 °C may be attributed to the oscillation of Ba–O bonds.⁴³ However, similar peak could not be precisely detected for TiO₂ and BaTiO₃ sintered at 1000 °C.

Fig. 9 FTIR spectra of (A) neat titania, Ba(OH)₂·8H₂O, and BaTiO₃ sintered at 1000 °C and 1200 °C, (B) selected portion of BaTiO₃ sintered at 1000 °C and 1200 °C.

4.5 UV-visible spectra

The room temperature UV-visible absorption spectra of neat titania, Ba(OH)₂·8H₂O, and different BaTiO₃ particles (prepared at three different sintering conditions) are presented in Fig. 10. The distinct UV absorption peak of BaTiO₃ sintered at 1200 °C is observed at λ = 264 nm whereas for BaTiO₃ sintered at 1000 °C and BaTiO₃ sintered at 700 °C such distinct peaks could not be detected. For neat titania a low intensity absorption peak at λ = 229 nm is observed but Ba(OH)₂·8H₂O does not show any typical UV absorption peak. The observed UV absorption peak of the prepared BaTiO₃ multipods can be assigned to the electronic transition in these multipods due to the presence of some Ti³⁺ along with Ti⁴⁺ mainly because of structural defects present in barium titanate.⁴⁴ So it may be concluded that the BaTiO₃ multipod as prepared in the present investigation is expected to be an useful candidate for optoelectronic applications and UV laser.¹⁶

Fig. 10 UV-Vis absorption spectrum of neat titania, Ba(OH)₂·8H₂O, and BaTiO₃ multipods (at three different temperatures).

4.6 X-ray photoelectron spectroscopy (XPS) analysis

The XPS survey spectra of compacted BaTiO₃ multipods and high resolution spectra of individual elements, Ba_3d, Ti_2p, and O_1s are presented in Fig. 11(a)–(d). The survey spectra observed here are very similar to the reported literature.⁴⁵ From the survey spectra, it is observed that the intensity of Ti_2p peak is quite small as compared to Ba_3d and O_1s peaks, the fact was also apparent from EDS data presented in Table 1. O_1s is splitted into two peaks present at around 529.73 eV and 530.71 eV which corresponds to oxygen atoms in the form of Ba–O–Ti and Ti–O–Ti respectively.⁴⁶ The Ba_3d peak can be resolved into two components (Ba_3d5/2 and Ba_3d3/2), where these peaks (Ba_3d5/2 at 778.81 eV and Ba_3d3/2 at 794.19 eV) correspond to barium in BaTiO₃.⁴⁷

Fig. 11 XPS spectra of BaTiO₃ compacted powder: (a) survey spectra of BaTiO₃ multipods; high resolution signals of (b) Ba_3d (c) Ti_2p, and (d) O_1s elements.

The Ba_4d signal is observed at 87.88 eV,⁴⁷ whereas Ba_4p signal is observed at 175.9 eV, which are due to different barium orbitals in BaTiO₃ (as observed in survey spectrum). The Ti_2p peak can be resolved into two components (Ti_2p3/2 and Ti_2p1/2), which can be deconvoluted into 4 peaks using Gaussian functions, two of which are located at around 457.36 eV and 463.66 eV, consistent with the Ti_2p3/2 and Ti_2p1/2 peaks of Ti⁴⁺ in BaTiO₃ whereas other two peaks are located at around 456.42 eV and 462.21 eV, consistent with the Ti_2p3/2 and Ti_2p1/2 peaks of Ti³⁺ in BaTiO₃.⁴⁸ The observed binding energy (BE) of Ti_2p3/2 (Ti³⁺) is around at 456.42 eV, which is somewhat smaller than the reported value of Ti_2p3/2 (Ti⁴⁺). This downshift of the BE of Ti_2p3/2 indicates that the oxidation state of Ti in BaTiO₃ multipods shifts from Ti⁴⁺ to Ti³⁺. Some of the Ti⁴⁺ oxidation state in BaTiO₃ transformed to Ti³⁺ state in order to balance the oxygen vacancies present in the system.⁴⁹ From XPS analysis, it is apparent that there are some structural defects in the sample and these are due to local oxygen vacancies in synthesized material. The XPS analysis is a useful technique to detect the surface chemical composition and material structure.⁴⁹ The C_1s peak as observed in survey spectra may be due to the carbon of CO₂ in the air.

4.7 Dielectric and impedance behavior of BaTiO₃ multipods

The dielectric spectra in terms of semi-log plots of log f vs. dielectric constant (ε′) and dielectric loss (ε′′) against frequency are given in Fig. 12a. From this plot, it is observed that both dielectric constant and loss factor increase with the decrease in frequency but the increase is very small over the frequency range 10⁶ to 10² Hz, there after sudden increase in both dielectric constant (ε′) and loss (ε′′) with further decrease in frequency can be detected. It is noteworthy that the prepared BaTiO₃ multipods exhibits almost frequency independent dielectric constant (ε′) and loss (ε′′) over a wide frequency range, 10³ to 10⁶ Hz. It is also observed from Fig. 12a (inset) that the magnitude of dielectric loss is less than the dielectric constant over entire frequency range of measurement, this indicates that the prepared material is a good candidate for charge storage device and can serve the purpose of useful component in electronic devices. Fig. 12b shows the AC impedance (|Z|) and phase angle of BaTiO₃ multipods as a function of frequency which is also known as Bode plot. It was apparent from this figure that the impedance (|Z|) is frequency dependent and decreases with the increase in frequency. The increase in impedance (|Z|) with the decrease in frequency is an indication of the existence of space charge polarization in the material.⁵⁰ The plot of real impedance (Z′) against imaginary impedance (Z′′) (Fig. 12c) is well known as Nyquist plot where, Z′ represents the bulk resistance (RB) and Z′′ represents the maximum value of angular frequency (ω_max), i.e., the top part of the semicircle, and is given by:where, R_B = bulk resistance and C_B = bulk capacitance.

Fig. 12 (a) Plot of log f vs. ε′ and ε′′, (b) Bode plot for BaTiO₃ multipods, and (c) Nyquist plot for BaTiO₃ multipods, (d) simplified equivalent circuit, and (e) schematic representation of BaTiO₃ grain boundary and grain interior.

The impedance spectroscopy in terms of Nyquist plot is characterized by the appearance of the semicircular arcs. This semicircular arc for the present systems indicates the occurrence of dielectric relaxation spectra with a relatively narrow range of relaxation time. The impedance value at very high frequency is R_g whereas at very low frequency is R_g + R_gb as depicted in Fig. 12c. At both very high and very low frequencies, the phase angle is nearly zero (Fig. 12b). However, at intermediate frequencies the phase angle started to approach −90°, the phase angle of an ideal capacitor. In this region, the slope was often (but not always) close to −1 (ideal capacitor).⁵¹ Any practical dielectric having loss characteristics cannot be represented only by a loss free capacitor, rather it is a combination of capacitor and resistor, the later gives the path for loss current. Various types of combination of capacitors and resistors are possible to represent different dielectric materials effectively. For the present system also similar combination as described in Fig. 12d is proposed. From Fig. 12b, it was observed that the slope of impedance curve is −0.844 which is very close to −1, so the prepared BaTiO₃ particles can act as an ideal capacitor. The obtained impedance data can be correlated with proposed equivalent circuits using electrochemical impedance spectroscopy (EIS) data analysis software (ZSimpWin) to design an equivalent circuit (Randles cell) to represent prepared BaTiO₃. The equivalent circuit for semiconducting lossy BaTiO₃ based material was first proposed by Heywang,⁵² as a common example for a simplified equivalent circuit.⁵³ The impedance of the RC-parallel combination is given as

where, R_g is the grain resistance, R_gb is the grain-boundary (Fig. 12e) resistance and C_gb is the grain-boundary capacitance. The dc impedance equals to (R_g + R_gb), while the intercept of the impedance curve at high frequencies with the real axis equals to R_g. So the BaTiO₃ may be considered as an electrically different two phase system, i.e., one inter-grain and other inside bulk.

The dielectric constant of barium titanate multipods is compared with the control samples [heat treated TiO₂ and Ba(OH)₂·8H₂O] and is presented in Fig. 13a. The significant increase in dielectric constant for BaTiO₃ multipods at low frequency region is due to interfacial and space charge polarization. Though the difference in the dielectric constant at high frequency region is small, the value of dielectric constant of BaTiO₃ multipods is more than the control samples (heat treated titania and barium hydroxide). Fig. 13b represents the comparison of permittivity (ε′) of BaTiO₃ multipods with commercial BaTiO₃ particles. It observed that the prepared BaTiO₃ multipods have higher dielectric constant than the commercial BaTiO₃ particles over the entire frequency range of measurement (10 Hz to 1 MHz). There is a significant increase in dielectric constant especially at low frequency region for the prepared sample. Fig. 13c illustrates the AC impedance (|Z|) and phase angle of BaTiO₃ multipods and commercial BaTiO₃ as a function of frequency which is also known as Bode plot. As we have discussed earlier the slope of impedance curve for BaTiO₃ multipods is −0.844 (Fig. 13c) which is very close to −1, so the prepared BaTiO₃ multipods can act as an ideal capacitor.⁵¹ Moreover, from Fig. 13c it is observed that as the impedance vs. frequency curve is not a straight line in case of commercial BaTiO₃ particles, it has two slopes. At high frequency region (1 kHz to 1 MHz) its value (−0.831) is close to −1 whereas it is −0.27 at low frequency region (10 Hz to 1 kHz). This dual nature of commercial sample makes it unsuitable as capacitative material especially at low frequency range (10 Hz to 1 kHz).

Fig. 13 Comparison of permittivity (ε′) of BaTiO₃ multipods (a) with control samples [heat treated TiO₂ and Ba(OH)₂·8H₂O], (b) with commercial BaTiO₃; (c) Bode plot comparison between BaTiO₃ multipods and commercial BaTiO₃.

4.8 Effect of temperature on dielectric constant/permittivity and impedance of BaTiO₃ multipods

Fig. 14(a)–(c) represents the temperature dependent behavior of dielectric constant (permittivity) at three different frequencies (10, 10³ and 10⁶ Hz) for barium titanate powder prepared through high temperature solid state reaction. The value of dielectric constant is the highest at the lowest measurement frequency (10 Hz) and least at the highest frequency (1 MHz). As mentioned earlier the increased dielectric constant at low frequency is mainly due to increased contribution of space charge polarization along with dipolar polarization. It is also interesting to note that dielectric constant changes marginally with increase in temperature but suddenly shoots up to high value at the temperature 85 °C which represent its Curie point. This is found to be true for all measurement frequencies. Above ∼85 °C, the prepared sample attains the cubic structure where in the unit cell of BaTiO₃ “Ti” atom exists in the equilibrium position in the center of the octahedra. However, when electric field is applied the position shifting of “Ti” with respect to oxygen atom occurs causing some induced dipoles. In fact, this crystal structure changes can be assumed to be due to distortion of edges of unit cubic cell and this distortion results in spontaneous polarization.⁵⁴ In fact, this polarization arises due to movement of “Ti” atoms with respect to adjacent oxygen atoms and this gives rise to spontaneous polarization below Curie temperature where it exists in forms other than cubic structure (symmetrical structure with no bond distortion). The high dielectric constant of barium titanate is due to the permanent dipole in the structure below the Curie temperature. Due to the less stable lattice structure in vicinity of phase transitions, the Ti⁴⁺ ions have an increased mobility giving a higher dielectric constant at these transitions.

Fig. 14 (a–c) Dielectric constant values of BaTiO₃ multipods as a function of temperature and frequency.

The variation of impedance (|Z|) with frequency (log f) at different temperatures is presented in Fig. 15. Impedance (|Z|) increases with the decrease in frequency, however at any particular frequency |Z| decreases with increase in temperature. In fact, the semilog plots of |Z| vs. frequency at three temperatures (80 °C, 85 °C, and 90 °C) are very close to each other when variations at lower temperatures (40 °C and 70 °C) and at 100 °C are shown in the same plot. However, it has been observed that the lowest impedance value at any particular frequency is observed for the measurement temperature 85 °C.

Fig. 15 Variation of impedance with frequency at different temperatures.

This decrease in impedance indicates that the AC conductivity (σ_ac) of BaTiO₃ multipods increases with the increase in temperature and attains the highest value at ∼85 °C, which is the Curie point of the developed material. This result further corroborates the variation of permittivity against temperature as given in Fig. 14(a)–(c), where sudden increase in dielectric constant at Curie point (∼85 °C) was also observed. The reason for sudden increase in AC conductivity (σ_ac) or permittivity (ε′) at ∼85 °C is described under the section “temperature dependent dielectric constant/permittivity”.

5. Conclusions

Solid state reaction and sintering at different temperatures forms BaTiO₃ with different shapes. Star shaped BaTiO₃ multipods consisting of protruding cones (average base diameter ∼300 nm and length ∼3 μm) from the centre of stars have been prepared by solid state reaction and sintering at 1200 °C. The Curie temperature of this material is found to be ∼85 °C. SAED and X-ray diffraction analyses reveal that these multipods have tetragonal structure. A dielectric study reveals that dielectric loss is less than the dielectric constant over a wide frequency range (10² to 10⁶ Hz). The Bode plot confirms the capacitative nature of this material indicating its application as charge storage device. UV sensitivity of this material is also an interesting feature which implies that this material may be exploited for optoelectronic devices.

Acknowledgements

The authors would like to thank Indian Institute of Technology Kharagpur, India for its research facility and for providing fellowship. The authors are also thankful to Department of Physics & Meteorology, Indian Institute of Technology Kharagpur, India for XPS study.

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