Impedance Study of Temperature-Stable Relaxor Dielectrics in the System of BCT-BMT Ceramics

Abstract

Preparation of a lead-free system (Ba_0.8Ca_0.2)TiO_3-xBi(Mg_0.5Ti_0.5)O₃ (BCT-BMT) with x = 0, 0.1, 0.2, 0.3, 0.4, and 0.5 was carried out using a solid-state reaction technique. X-ray (XRD) diffraction analysis confirmed a tetragonal structure for x = 0, which shifted to cubic (pseudocubic) at x ≥ 0.1. From Rietveld refinement, a single phase with a tetragonal symmetry model (P4mm) was observed for x = 0, and however, for sample x = 0.1 and sample x = 0.5, the data are modeled to cubic (Pm3m). Composition x = 0 showed a prominent Curie peak, typical of ordinary ferroelectrics with a Curie temperature (T_c) ∼130 °C, modified to a typical relaxor dielectric at x ≥ 0.1. However, samples at x = 0.2–0.5 displayed a single semicircle attributed to the bulk response of the material, whereas a slightly depressed second arc appeared for x = 0.5 at 600 °C, indicating a slight contribution to the electrical properties, ascribed to the grain boundary of the material. Finally, the dc resistivity increased with the increase of the BMT content and the solid solution increased the activation energy from 0.58 eV at x = 0 to 0.99 eV for x = 0.5. Adding the BMT content eliminated the ferroelectric behavior at compositions x ≥ 0.1 and led to a linear dielectric response and electrostrictive behavior with a maximum strain of 0.12% for x = 0.2.

Introduction

Lead-free piezoelectric and dielectric materials are being investigated. Relaxor perovskite ceramics with temperature-stable relative permittivity have been of particular interest in advanced capacitor technologies.^1,2 Among these, Bi-based perovskites with another stable perovskite like BaTiO₃ have shown excellent piezoelectric and dielectric properties for high-temperature applications.^3,4 At high temperatures, the majority of these materials are relaxors with nearly uniform relative permittivity, such as Bi_1/2Na_1/2TiO₃-BaTiO₃-K_0.5Na_0.5NbO₃, Bi_1/2Na_1/2TiO₃-BaTiO₃-K_0.5Na_0.5NbO₃-CaZrO₃, BaTiO₃-BiScO₃,⁵ and BaTiO₃-Bi(Zn_1/2Ti_1/2)O₃-BiScO₃. In our previous study, the (Ba_0.8Ca_0.2)TiO₃-xBi(Mg_0.5Ti_0.5)O₃ system (BCT-BMT) is a relaxor at x ≥ 0.1, offering temperature stability in relative permittivity within ±15% variation to a maximum temperature of ∼550 °C and with a minor limit of ∼45 °C with tan δ ≤ 0.025 from 100 to 430 °C.⁶

In such temperature-stable dielectric ceramics, under the applied electric field, the electrical conductivity is usually considered the result of the thermally activated process depending on the nature of the charge carriers. AC impedance analysis is an important technique to characterize ceramic materials specifically to give an insight into its electrical conductivity, their types, and Arrhenius activation energy.⁷ The frequency-dependent impedance data have both real (resistive) and imaginary (reactive) parts Z* = Z′ – Z″, Y* = Y′ + Y″, and ε* = ε′ – jε″. Data in the complex plane are often analyzed through the display of semicircular arcs or the continuity of these semicircular arcs, whose behavior varies with temperature. The numbers of these arcs tell us how many electrical phenomena take place, and the contribution to the electrical properties is either due to the grain, grain boundary, and/or electroding effect.⁸ Furthermore, these complex quantities were mainly analyzed by four complex formulas, where impedance Z*, electric modulus M*, dielectric constant ε*, and admittance Y* are linked as follows

1

2

3

4

where is the free space capacitance of the measuring cell and ω = 2πf corresponds to the angular measurement frequency while .

This research aims to examine the dielectric relaxation behavior and electrical properties of the temperature-stable dielectric BCT-BMT ceramic system; impedance spectroscopy has been employed in detail.

Results and Discussion

Phase and Grain Structure Analysis

Figure 1a–c illustrates the X-ray diffraction patterns of the (1-x)BCT-xBMT ceramic system, where x ranges from 0 to 0.5, for powders of sintered ground pellets with 2θ ranges of 20–80°, 20–24°, and 42–48°, respectively. The samples have a perovskite structure (ABO₃) with no traces of secondary phases, showing that the BMT amount was completely mixed into the matrix and formed a uniform solid solution of the samples. The sharp peaks suggested high crystallinity. The end member Ba_0.8Ca_0.2TiO₃ (x = 0) have the tetragonal structure changed to cubic (pseudocubic) at x ≥ 0.1. As observed in the magnified Figure 1a,b, the main diffraction peaks shifted when the BMT amount was increased to a lower 2θ degree that suggested an increase in the crystal volume size. It might be due to the replacement of Mg²⁺ (ionic radius 0.072 nm) with Ti⁴⁺ (ionic radius 0.0605 nm) in the ABO₃ structure.⁹

Figure 1.

(a–c) X-ray diffraction patterns of BCT-BMT bulk ceramics.

As the ionic radius of Mg is larger than the ionic radius of Ti, the crystal volume is increased. The XRD of samples x = 0, 0.1, and 0.5 was further confirmed with full pattern refinement exhibited in Figure 2a–c. It was observed that a single phase with a tetragonal symmetry model (P4mm) matched well with the experimental data. However, for sample x = 0.1 and the last sample x = 0.5, the data could be modeled to the cubic (Pm3m). The increasing BMT content induces residual stress (by chemical modifications), producing local structural heterogeneity that disturbs the long-range ferroelectric pattern as described elsewhere.¹⁰⁻¹³ Samples displayed the best fitting with an excellent goodness-of-fit factor (χ² ≤ 1.42). Also, the lattice parameters and crystal volume size are estimated and are displayed in Table 1. Rietveld refinement structural parameters of BCT-BMT dielectrics are summarized via the FullProof suite (where Pm4m and Pm3̅m space groups stand for tetragonal and pseudocubic symmetry, respectively).¹⁴⁻¹⁷

Figure 2.

(a–c): Rietveld refinement structural analysis of BCT-BMT dielectrics via the Full Prof suite.

Table 1. Summarized Rietveld Refinement Structural Parameters of BCT-BMT Dielectrics.

refined parameters/compositions (x)	x = 0.0	x = 0.1	x = 0.5
space group	Pm4m	Pm3̅m	Pm3̅m
lattice parameters (Å)	a = b = 3.969790 & c = 4.015350	a = b = c = 3.981990	a = b = c = 3.998100
lattice volume (Å3)	63.63863457	63.13940648	63.90884331
goodness of fit (χ2)	1.42	1.23	1.40

The microstructural analysis of the ceramic system with compositions x = 0, 0.1, 0.2, and 0.3 revealed a relatively dense structure. The average grain size was estimated by a linear intercept method. For composition x = 0, the estimated average grain size was ∼8 μm, which decreased to ∼3 μm for x = 0.5, Figure 3. The dopant Mg inhibits the grain growth in the sintering process as reported in the research. The appearance of grains with well-separated grain boundaries suggests that during the sintering process, the grain growth process is almost complete.

Figure 3.

(a–d) SEM micrographs of chemically etched surfaces for x = 0, 0.1, 0.2, and 0.3.

As a preliminary study, SEM-EDS was performed for selected samples x = 0.1 and 0.5 to examine any compositional variation inside the grains. Figure 4 shows the SEM micrograph and EDS elemental mapping for x = 0.1. A domain structure in several grains was evident from the SEM micrograph. Examination of composition x = 0.1 revealed a compositional contrast in the grains. EDS mapping showed a segregation of Bi³⁺ and Ca²⁺ in several grains. However, there was little or no evidence of Mg²⁺ nonuniformity in the grains of the examined sample. Other elements, Ba²⁺ and Ti⁴⁺, were uniformly distributed throughout the grains.¹⁷

Figure 4.

SEM-EDS elemental mapping indicating Bi³⁺ and Ca²⁺ segregation in the grains for composition x = 0.1.

Figure 5 shows the SEM micrograph and EDS elemental mapping for x = 0.5. A domain structure in several grains was evident from the SEM micrograph. A careful analysis by SEM-EDS mapping showed that there was no detectable chemical nonuniformity in the grains for composition x = 0.5.

Figure 5.

Illustration of SEM-EDS elemental mapping for composition x = 0.5.

Dielectric Study

Figure 6 depicts the temperature-dependent dielectric constant ε_r as well as dielectric loss tangent, tan δ, with respect to frequency ranging from 1 kHz to 1 MHz. The composition with x = 0 displays a prominent Curie peak, indicating that it is a typical ferroelectric material with a Curie temperature (T_c) of approximately 130 °C.¹⁸ For x equal to 0.1, the dielectric properties transformed into those characteristics of a relaxor ferroelectric material, with relative permittivity exhibiting the notable frequency-dependent characteristic of relaxor systems.¹⁹ Incorporation of BMT decreased the maximum relative permittivity, ε_r max ∼2000 at x = 0.1 to 875 for x = 0.5. With an increase in the value of x, there is a reduction in the temperature sensitivity of the relative permittivity at temperatures above T_m of all the values of x tested; the smallest temperature dependence was observed for x = 0.5. The loss tangent, tan δ, at temperature sharply rose for x = 0–0.1 and shifted to higher temperatures with an increase of x.

Figure 6.

Relative permittivity measurements were taken for a range of frequencies x = 0.0–0.5.

According to Figure 3, the high-temperature permittivity for x = 0.5 had a very low frequency dependence, where tan δ stayed ≤0.025 up to 430 °C.

Impedance Study

The impedance spectra for the BCT-BMT system were analyzed at various frequencies from 0.1 Hz to 1 MHz throughout a wide range of temperature. Figure 7 and its inset display the logarithmic variation of the imaginary portion of impedance (Z″) with the log of frequency at various temperatures. The values of Z″ peaks decreased with the increase of temperature and shifted toward the higher frequency for all compositions. For x = 0, the dielectric relaxation starts at ≥250 °C and no relaxation peak was observed below 250 °C. For compositions x = 0.1 and 0.2, the relaxation occurred at ≥300 °C and merges for all temperatures at higher frequencies, whereas for compositions at x ≥ 0.3, relaxation peaks started at temperatures of ≥350 °C, Figure 7. The relaxation frequency (ω_m) was found to be shifted to a larger frequency with enhancing temperature. The discrete peaks start to merge into each other at f ≥ 100 Hz. At higher frequency, the merging of distinct peaks shows a possible release of space charges that lowers the material’s barrier properties. The relaxation process normally seems to be due to the presence of immobile species at lower temperatures and defects such as inhomogeneities and space charges at higher temperatures. Consequently, with increasing temperature, the decreasing impedance at low frequencies suggests that the compound showed a negative temperature coefficient of resistance (NTCR)-type behavior similar to that of semiconductors.^7,8

Figure 7.

(a–f) Variation of Z″ spectra in the temperature range of 400–600 °C, inset from 25 (RT) to 350 °C for x = 0–0.5.

Figure 8 depicts the complex impedance diagrams at a temperature of 500 and 600 °C for the BCT-xBMT system. Compositions x = 0 and 0.1 showed electrical heterogeneity, and data can be fitted into two semicircles, indicating two relaxation processes, e.g., comprising the effect of the grain and grain boundary of the material. For composition x = 0, the grain radii were smaller than the grain boundary and became further smaller as the temperature increased. However, samples at x = 0.2–0.5 displayed a single semicircle attributed to the bulk response of the material, whereas a slightly depressed second arc appeared for x = 0.5 at 600 °C, indicating a slight contribution to the electrical properties ascribed to the grain boundary of the material. Each semicircular pattern was fitted based on the RC parallel circuit. The intercepts of these semicircles on the real part axis give the resistance of the component (grain and grain boundary effect).

Figure 8.

(a–d) Plots of complex impedance for x = 0–0.5 at 500 and 600 °C.

Measurements of DC resistivity were taken directly from the intercepts of semicircles on the Z′-axis of complex impedance plots (Figure 8). The rise of temperature reduced the radii of complex impedance plot semicircles, indicating the decrease in dc resistivity for all compositions. Values of bulk and grain boundary resistivity were deduced from the impedance spectra. It was also observed that the dc resistivity improved with the increase of the BMT content. For x = 0, the value of dc resistivity was ∼1.7 × 10³ Ω·m at 450 °C, while compositions x = 0.4 and 0.5 have a resistivity of ∼3.5 × 10⁶ and ∼1.7 × 10⁷ Ω·m at 450 °C, respectively, Table 2. The capacitance values were calculated using the formula²⁰

5

where 2πf_max is the angular frequency of the complex impedance plot at maxima of the semicircular pattern and RC is the capacitive time constant. The value of capacitance deduced for x = 0 at the maximum frequency is 2.9 nF at 500 °C and 94 nF for x = 0.5 at 500 °C, Table 2.

Table 2. Maximum Frequency Corresponds to the Capacitances as a Function of Temperature.

sample	temperature (°C)	fmax (Hz)	C(nF)	RC (μs)
x = 0	(a)
	400	1.3 × 105	0.4 (g)
	500	2.5 × 105	2.9 (g)	0.4 × 10–5
x = 0.1	(b)
	500	5011	67.3
	600	1.26 × 105	38.9	0.79 × 10–5
x = 0.2	(c)
	500	398	33.4
	600	1.26 × 104	54.4	0.77 × 10–4
x = 0.3	(d)
	500	79	1.55
	600	3.98 × 103	89.1	0.25 × 10–3
x = 0.4	(e)
	500	31.6	1.56
	600	1.58 × 103	1.34	0.63 × 10–3
x = 0.5	(f)
	500	13	94.8
	600	0.63 × 103	1.05	1.58 × 10–3

dc Conductivity from Impedance Data

Figure 9 exhibits that the temperature-dependent bulk electrical conductivity (dc) measured from the complex impedance data obeys the Arrhenius relationship²¹

6

where E_a represents the electrical conductivity activation energy, T is the absolute temperature, and k_B is the Boltzmann constant (8.6173 × 10^–5 eV). Activation energy values for all compositions were computed from the slope of the logarithmic plots of σ_dc versus T^–1 by least squares fitting of data at the high-temperature region (450–600 °C), Figure 6. Adding BMT content to the solid solution increases the activation energy from 0.58 eV at x = 0 to 0.99 eV at x = 0.5, Table 3. These values of activation energies are close to the conduction mechanism due to oxygen vacancies (∼1 eV) in the perovskite systems, which suggests the electrical conductivity caused by thermally activated oxygen vacancies.²² Values of dc resistivity deduced from the impedance data were consistent with the values by the direct dc method, ∼10⁶ Ω·m at 500 °C.

Figure 9.

Logarithmic plots of conductivities versus T^–1 for x = 0–0.5.

Table 3. Activation Energy (E_a) and Electrical Resistivity (ρ) at 500 °C.

sample (x)	activation energy (Ea) eV	resistivity (Ω·m) at 500 °C
0	0.58	0.43 × 103
0.1	0.67	9.9 × 103
0.2	0.77	8.8 × 104
0.3	0.93	3.0 × 105
0.4	0.94	3.9 × 105
0.5	0.99	1.6 × 106

Ferroelectric and Strain Analysis

Room-temperature polarization–electric field, Figure 10a, displays the results of the (P–E) response measurement at 1 Hz. For x = 0, a typical ferroelectric behavior was observed with remnant polarization, P_r ∼12 μC/cm² and coercive field of E_c ∼ 8 kV/cm. Adding the BMT content eliminated the ferroelectric behavior at compositions x ≥ 0.1 and directed to the linear dielectric response.

Figure 10.

(a, b): Room-temperature polarization and strain field behavior for (a) 0–0.5 and (b) 0, 0.1, 0.2, and 0.5 at 1 Hz.

Figure 10b shows the induced strain at a field of 50 kV/cm for x = 0, 0.1, 0.2, and 0.5. For x = 0, a standard butterfly loop was seen with a maximum strain of less than 0.17% at a field of 50 kV/cm. Including BMT into the solid solution led to the electrostrictive behavior with an extreme strain of 0.12% for x = 0.2.²³⁻²⁵

The crystallite size and lattice strain effect in the prepared ceramic were estimated by adopting the Williamson–Hall (W–H) method.¹⁴⁻¹⁶

7

where k = 1.5405, λ = 0.89 Å, β = full width at half maxima (FWHM), θ = half of the diffraction angle, and t = crystallite size of the sample. The relation shows a straight line, in which η is the gradient (slope) of the line and is the y-intercept. The instrumental broadening factor is subtracted to calculate the crystallite size, by the relation β = β_o – βi, where β_o = observed X-ray peak FWHM, βi = FWHM due to instrumental effects, and β = remaining FWHM. To calculate the crystallite size, we have plotted the W–H plot between β cos θ and 4sin θ. A linear fit to the experimental data gives a slope that represents the strain and a y-intercept that gives information regarding the crystallite size. The average crystallite size of ceramics decreases (i.e., 65.31–45.16 nm) and strain increases from 5.96 × 10^–3 to 6.9 × 10^–3 as the Mg²⁺ content increases in the BMT-BCT ceramics [Figure 11], attributed to the replacement of Mg²⁺ (ionic radius 0.072 nm) with Ti⁴⁺ (ionic radius 0.0605 nm) in the ABO₃ structure. Thus, the increase in the Mg²⁺ content results in an increase in the lattice strain, which further results in the reduction of crystallite size of these ceramics.

Figure 11.

Williamson–Hall plots for BCT-BMT at x = 0, 0.2, and 0.5 ceramics.

Conclusions

In this study, the solid-state reaction method was employed to prepare the (Ba_0.8Ca_0.2)TiO₃-xBi(Mg_0.5Ti_0.5)O₃ system, which is also referred to as BCT-BMT. The system was synthesized with a range of x values, including x = 0, 0.1, 0.2, 0.3, 0.4, and 0.5. For (x = 0), a tetragonal structure was discovered, which transformed to cubic (pseudocubic) when x was greater than or equal to 0.1. The composition x = 0 exhibits a strong Curie peak, characteristic of common ferroelectrics with a Curie temperature of (T_c) 130 °C, which changed to a typical relaxor dielectric at x ≥ 0.1. For composition x = 0, the grain radii were smaller than the grain boundary and became further smaller as the temperature increased. However, samples at x = 0.2–0.5 displayed a single semicircle attributed to the bulk response of the material, whereas a slightly depressed second arc appeared for x = 0.5 at 600 °C, indicating a slight contribution to the electrical properties ascribed to the grain boundary of the material.

It was also observed that the dc resistivity improved with the increase of the BMT content. Moreover, it was observed that the inclusion of the BMT content into the solid solution resulted in a significant increase in the activation energy from 0.58 eV for x = 0 to 0.99 eV for x = 0.5. These values of activation energies are close to the conduction mechanism due to oxygen vacancies (∼1 eV) in the perovskite systems. Adding the BMT content eliminated the ferroelectric behavior at compositions x ≥ 0.1 and led to a linear dielectric response and electrostrictive behavior with a maximum strain of 0.12% for x = 0.2.

Experimental Methods

The following ceramic compositions were formed using conventional solid-state processes by utilizing initial powders: CaCO₃ (99% purity, Sigma-Aldrich, St. Louis, MO), TiO₂ (99.9% purity, Sigma-Aldrich), BaCO₃ (99%, α Aesar, Ward Hill, MA), MgO (99%, α Aesar), and Bi₂O₃ (99%, Alpha Aesar). Mixtures were weighed according to stoichiometric ratios after drying at 250 °C overnight and stored in a desiccator before cooling to room temperature. The particles were then ball-milled in isopropanol for 24 h using stabilized zirconia grinding medium. The dry powder is sieved through a 300 μm shade and then calcined at 800 to 1100 °C for 3 h. The calcined powders were sieved and treated with 24 h of ball milling, and 1% weight binder was applied (Ciba Glascol HA4: Ciba speciality Chemicals, Bradford, U.K.). The fine particles were formed into discs by 65 MPa uniaxial pressing in a 10 mm steel die, followed by 300 MPa cold isostatic pressing. To prevent the loss of volatile bismuth oxide, the pellets were covered with a powder of the same composition and sintered for 3 h at 1050–1400 °C in an alumina crucible. For phase analysis, the sintered pellet was then crushed to a powder, which was characterized by X-ray powder diffraction (XRD, Bruker D8, Cu, Kα∼5406; scan speed, 1°/min). A scanning electron microscope (Hitachi SU 8230 cold FESEM, Japan) was used to carry out microstructural investigation on chemically etched polished pellets. For electrical characterization, sintered particles were ground to about 1 mm thickness. Electrodes were formed by firing silver paste on opposite parallel surfaces in a furnace at 550 °C for 10 min. The dielectric relative permittivity and loss tangent were determined by utilizing an impedance analyzer (HP Agilent, 4192A Hewlett Packard, Santa Clara, CA) over a temperature range of 20–600 °C. The complex impedance analysis was carried out as a function of temperatures from 25 to 600 °C at a constant dc voltage of 0.1 V and frequencies between 0.1 Hz and 1 MHz, using a Salatron (Salatron analytical, TN). The polarization was measured at 1 Hz, and the strain field measurement was carried out at frequency 1 Hz using a LC precision analyzer (Radiant Technologies Inc., Albuquerque, New Mexico).

The authors declare no competing financial interest.