Structure and electrical properties of lead-free Bi_0.5Na_0.5TiO₃-based ceramics for energy-storage applications

Abstract

A new energy-storage ceramic system based on (1 − x)(Bi_0.5Na_0.5TiO₃–BaTiO₃)–xNaTaO₃ ((1 − x)(BNT–BT)–xNT) is reported in this study. XRD refinement indicated a composition induced rhombohedral to tetragonal phase transition. All the samples exhibited a dense microstructure with an average grain size of 1.2–1.9 μm. The introduction of NT greatly improved the temperature stability of the dielectric properties for the BNT–BT system. For compositions x = 0.03–0.15, the working temperature range spanned over 260 °C satisfying TCC_{150 °C} ≤ ±15%. The electric conductivity as a function of frequency followed the double power law. In the temperature region of 325–500 °C, the activation energy of DC conduction ranged from 1.47 eV to 1.71 eV, indicating intrinsic band-type electronic conduction. The optimum energy-storage properties were obtained in 0.90(BNT–BT)–0.10NT with an energy-storage density of 1.2 J cm⁻³ and energy-storage efficiency of 74.8% at 10 kV mm⁻¹. The results demonstrate that (1 − x)(BNT–BT)–xNT ceramics are promising candidates for high-temperature energy-storage applications.

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1. Introduction

Capacitors play an important role in energy-storage systems. Compared to batteries, capacitors possess faster charge–discharge times and higher power density.^1,2 However, the energy that capacitor dielectrics can store is much less than fuel cells or lithium ion batteries.³ Thus, the development of new capacitor materials with a high energy-storage capacity is a challenge for researchers. Additionally, since electronic equipment is often exposed to extreme temperatures in industrial applications, such as space exploration and deep oil/gas well drilling,^4,5 the temperature reliability of capacitor materials is also very important.

Bi_0.5Na_0.5TiO₃ (BNT) based ceramics have been actively studied for energy-storage application in recent years.^6–10 Among the reported systems, (1 − x)Bi_0.5Na_0.5TiO₃–xBaTiO₃ (BNT–BT) binary solid solution at the morphotropic phase boundary (MPB, 0.06 ≤ x ≤ 0.10)¹¹ is a promising candidate for high-temperature energy-storage capacitors. On the one hand, the existence of double dielectric anomalies over the studied temperature range can help to improve the temperature stability of the dielectric properties. On the other hand, BNT–BT shows large maximum polarization, which is favorable for obtaining high energy-storage density. Modifications of BNT-based high-temperature energy-storage ceramics focus on expanding the temperature range with stable permittivity, as well as improving their energy-storage density and efficiency.

Niobates are the most widely reported members to modify the dielectric and ferroelectric properties of BNT-based ceramics, such as NaNbO₃,^12,13 KNbO₃,^14,15 (Li, Ag)NbO₃,¹⁶ Na_0.5K_0.5NbO₃,^17–20 and (Na, Bi)NbO₃.²¹ Tantalum and niobium belong to same family in the periodic table of elements. According to J. König²² and M. Spreitzer,²³ tantalate addition can significantly broaden the dielectric anomaly of BNT ceramics. However, the exact dielectric temperature stability has not been reported, neither has the effect of tantalate on the ferroelectric properties.

To explore the potential use of tantalate modified BNT-based ceramics for temperature-stable energy-storage application, a new system based on (1 − x)(0.92Bi_0.5Na_0.5TiO₃–0.08BaTiO₃)–xNaTaO₃ ((1 − x)(BNT–BT)–xNT) ternary solid solution was prepared in this work. The effects of NT on the structure, dielectric stability, electrical properties, and energy-storage properties of the system were comprehensively investigated.

2. Experimental procedure

(1 − x)(BNT–BT)–xNT (x = 0.01, 0.03, 0.05, 0.10, 0.15) ceramic samples were prepared by traditional solid-state reaction method.^8,24–26 First, the raw powders Bi₂O₃ (purity 99.0%), Na₂CO₃ (purity 99.8%), TiO₂ (purity 98.5%), BaCO₃ (purity 99.0%) and Ta₂O₅ (purity 99.99%) were mixed according to the stoichiometric formula and ball milled with zirconium media in ethanol for 24 h. After drying at 100 °C, the powder mixture was calcined at 800 °C for 2 h and subsequently ball-milled again for 24 h. Then, the powders were pressed into pellets of 12 mm in diameter and 1 mm in thickness under a uniaxial pressure of 200 MPa. The pellets were sintered at 1150 °C for 2 h. To minimize the evaporation of volatile elements, the pellets were embedded in self-source powder during sintering.

Phase structure was determined using X-ray powder diffraction (Cu Kα radiation, PANalytical X'Pert PRO, Eindhoven, the Netherlands) operated at 40 kV and 40 mA. Microstructure was studied by scanning electron microscope (Quanta 450 FEG, FEI, Hillsboro, USA). Electrodes were fabricated with fire-on silver paste at 500 °C for 15 min. Electrical properties measurements were carried out with a precision LCR meter (E4980A, Agilent, Santa Clara, USA) using a customer designed furnace and computer-controlled data collection system. To determine the ferroelectric properties, the sintered samples were polished to a thickness of 0.3 (±0.02) mm and then the test was performed using a ferroelectric material test system (HVI0403-239, Radiant Technology, USA) in a silicone oil bath at 10 Hz.

3. Results and discussion

3.1 Structure characterization

The room temperature XRD patterns of (1 − x)(BNT–BT)–xNT ceramics with 2θ = 20–80° (Fig. 1) show pure perovskite structure for all the samples. The Rietveld refinement was conducted to clarify the phase constitution. In agreement with recent work from G. Viola,²⁷ optimal fits to the XRD patterns were achieved using a combination of the space groups R3c and P4bm. The lattice parameters, atomic positions of the Bi, Na, Ba, Ti, Ta, O atoms, and occupancy have been refined using X'Pert HighScore Plus software. The reliability factor R_wp (the subscript “wp” means “weighted profile”) value in each composition was below 10%, indicating a high credibility of the refinement. The lattice parameters obtained from the Rietveld refinement were listed in Table 1. It is obvious from the refinement results that rhombohedral R3c phase and tetragonal P4bm phase almost equally accounted for fifty percent in the sample x = 0.01. With the increase of NT content, P4bm gradually transformed into a dominating phase. When x = 0.15, P4bm phase fraction reached 79.4%. It is known that rhombohedral R3c is polar phase, tetragonal P4bm is weakly polar phase.^28,29 The introduction of NT into BNT–BT system caused polar → weakly polar phase transition. The composition change induced phase constitution transition is also reported in alkalis-substituted BNT-based system²⁷ and in rare earth modified BiFeO₃ multiferroics.³⁰

Fig. 1 Rietveld refinement patterns of (1 − x)(BNT–BT)–xNT ceramics. The black circles and the red lines represent the observed and refinement data, respectively. The blue lines are the difference between the observed and calculated diffraction patterns, the pink and green bars are Bragg reflections for R3c and P4bm.

Table 1 Calculated lattice parameters of (1 − x)(BNT–BT)–xNT ceramic samples by refinement of room-temperature XRD data

Composition	Phase fraction (%)	Lattice parameters		Rwp
		a (Å)	c (Å)
x = 0.01	R3c 49.5	5.561	13.619	6.2%
	P4bm 50.5	5.522	3.901
x = 0.03	R3c 41.1	5.548	13.623	6.4%
	P4bm 58.9	5.519	3.900
x = 0.05	R3c 30.5	5.546	13.626	9.1%
	P4bm 69.5	5.519	3.907
x = 0.10	R3c 24.8	5.536	13.642	4.7%
	P4bm 75.2	5.524	3.901
x = 0.15	R3c 20.6	5.534	13.624	4.6%
	P4bm 79.4	5.521	3.908

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Fig. 2 illustrates the SEM images of (1 − x)(BNT–BT)–xNT ceramics thermal etched at 1000 °C for 30 min. All the samples exhibited dense microstructure with no pores. Promoted grain growth can be observed with the addition of NT. The average grain sizes were determined by the linear intercept method to be 1.2, 1.3, 1.3, 1.4, 1.9 μm for x = 0.01, 0.03, 0.05, 0.10, 0.15 respectively. Similar trends have been reported in oxide added and niobate modified BNT–BT ceramics.^12,31 As is generally recognized, A-site elements such as bismuth and sodium in BNT-based systems volatilize inevitably due to their low melting points,^12,32 leading to the presence of oxygen vacancies, which is beneficial to mass transportation during sintering.³¹ This is assumed to be responsible for the grain growth in (1 − x)(BNT–BT)–xNT system with the increase of NT content.

Fig. 2 SEM images of (1 − x)(BNT–BT)–xNT ceramic samples: (a) x = 0.01, (b) x = 0.03, (c) x = 0.05, (d) x = 0.10, (e) x = 0.15.

3.2 Dielectric properties

The permittivity and dielectric loss as a function of temperature at different frequencies (1 kHz, 10 kHz, 100 kHz) for (1 − x)(BNT–BT)–xNT (x = 0.01–0.15) ceramics were presented in Fig. 3(a)–(e). The dielectric properties of pure BNT–BT without NT addition were reported in ref .12.

Fig. 3 (a–e) Dielectric constant and dielectric loss as a function of temperature measured at different frequencies, (f) permittivity gap |ε_s − ε_m|, T_s, and T_m at 1 kHz of (1 − x)(BNT–BT)–xNT ceramics.

The temperature dependence of permittivity curves were characterized by double dielectric anomalies. As shown in Fig. 3(a), the first dielectric anomaly was located at the temperature of T_s (about 105 °C at 1 kHz), accompanied with obvious frequency dispersion, which is caused by thermal evolution of R3c and P4bm polar nano-regions mixture.²⁸ The second dielectric anomaly was located at the temperature of T_m (around 250 °C at 1 kHz), which is also regarded as the Curie temperature (T_C).^33,34 It is the temperature at which the permittivity (ε_m) reaches a maximum value. T_m was identified as the antiferroelectric–paraelectric phase transition point.^19,35 However, it has been demonstrated by in situ Transmission Electron Microscopy recently that no structural change can be observed across T_m.²⁹ Instead, the anomaly at T_m is believed to originate from a mixed contribution of R3c → P4bm transition and thermal evolution of P4bm polar nano-regions.²⁸ Compared to pure BNT (T_C = 320 °C),³⁶ the Curie point of this system was largely reduced by the introduction of BT and NT.

In the temperature-dependent loss tangent curves, a peak in 0–90 °C temperature range can be observed for all compositions, which is often defined as the depolarization temperature (T_d) of the system.²⁵ In the range of 150–350 °C, the loss tangent was lower than 0.04. At higher temperature (≥400 °C), the dielectric loss underwent a sharp rise. This is related to the increased conductivity, which will be discussed in the following part.

With the increase of NT addition, T_s continuously decreased while T_m remained unchanged, as shown in Fig. 3(f). The permittivity gap |ε_s − ε_m| largely reduced from ∼1660 in x = 0.01 to ∼185 in x = 0.10 (Fig. 3(f)), leading to an improvement in the temperature stability of permittivity. We adopted temperature coefficient of capacitance (TCC) to evaluate the temperature stability of dielectric properties for (1 − x)(BNT–BT)–xNT ceramics in this paper, as shown in eqn (1).

where C_T represents the capacitance at any temperature within the measuring range, C_{base temp.} is the capacitance at base temperature.

In the study of temperature stable dielectrics, such as XnR (X represents the minimum temperature of −55 °C; n means the maximum temperature, n = 7 for 125 °C and n = 8 for 150 °C; R symbolizes percentage of the capacitance variation limit ±15% in the whole temperature range) multi-layer ceramic capacitor (MLCC) dielectrics and high-temperature capacitor materials, researchers employ different benchmark working temperatures to calculate TCC.^37,38 Among them, 25 °C and 150 °C are the most commonly used ones. Therefore, we evaluated the temperature stability of dielectric properties for (1 − x)(BNT–BT)–xNT ceramics in the benchmark of both 25 °C and 150 °C.

Fig. 4 shows the variation of TCC in the range of −55 °C to 400 °C at 1 kHz, the dashed lines indicate the working temperature ranges with TCC ≤ ±15%. It should be noted that the working temperature range of x = 0.01–0.10 was too narrow on the baseline of 25 °C, so the data was omitted in Fig. 4(a). For the composition x = 0.15, the operational temperature range expanded to −6 to 312 °C with moderate permittivity (ε_r, 25 °C = 1472) and low dielectric loss (tan δ, 25 °C = 0.031), demonstrating a potential in wide-temperature stable capacitor material. Whereas the dielectric stability at the low temperature end (lower than 0 °C) need to be further improved. On the baseline of 150 °C (Fig. 4(b)), compositions with x = 0.03–0.15 all displayed favorable dielectric temperature stability. The working temperature range spanned over 260 °C (Table 2), which is superior to previously reported high-temperature dielectrics.³⁷

Fig. 4 TCC of (1 − x)(BNT–BT)–xNT ceramics at 1 kHz: (a) base temperature 25 °C; (b) base temperature 150 °C.

Table 2 Dielectric properties of (1 − x)(BNT–BT)–xNT ceramics at 1 kHz

x	εr (25 °C)	tan δ (25 °C)	Temperature range satisfying |ΔC/C25 °C| ≤ 15%	εr (150 °C)	tan δ (150 °C)	Temperature range satisfying |ΔC/C150 °C| ≤ 15%
0.01	1981	0.062	—	4758	0.007	94–200 °C
0.03	1767	0.067	—	3533	0.005	77–356 °C
0.05	1785	0.062	—	3130	0.004	66–336 °C
0.10	1722	0.048	—	2226	0.004	36–295 °C
0.15	1472	0.031	−6 to 312 °C	1554	0.004	3–284 °C

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3.3 AC conductivity

Fig. 5 shows the frequency dependence of AC conductivity for (1 − x)(BNT–BT)–xNT ceramics at several temperature points between 200 °C and 500 °C. In the lower temperature range (200–375 °C), AC conductivity underwent an exponential growth with frequency in the whole range from 10 Hz to 1 MHz. At higher temperature (400–500 °C), AC conductivity behaved differently. At low frequency, conductivity almost kept constant, while in high frequency region, conductivity increased with frequency. The boundary frequency of these two regions is known as hopping frequency.^39,40 With temperature increasing, the hopping frequency shifted towards higher value in all the compositions.

Fig. 5 Frequency dependence of AC conductivity for (1 − x)(BNT–BT)–xNT ceramics at several temperature points between 200 °C and 500 °C.

AC conductivity in solid materials can be expressed as:⁴¹

σ_ac = σ(0) + σ(ω) (2)

where ω is angular frequency; σ(0) is frequency independent DC conductivity part, sometimes it is written as σ_dc;⁴² σ(ω) is frequency dependent part. σ(ω) obeys universal dynamic response:^43–45 σ(ω) = Aω^s, which is also called Jonscher's power law,^40,46 0 < s < 1.

However, the AC conductivity data in Fig. 5 did not obey the simple Jonscher's power law, but double power law:^47–49

σ_ac = σ(0) + A₁ω^s₁ + A₂ω^s₂ (3)

which describes three different contributions to conductivity. (i) σ(0) corresponds to the long range transport of mobile charge carriers, i.e., DC conductivity;⁵⁰ (ii) A₁ω^s₁ (0 < s₁ < 1) characterizes the translational hopping motion (or short range hopping) at low frequency;⁵¹ (iii) A₂ω^s₂ (0 < s₂ < 2) is associated with localized or reorientational hopping motion.^51,52 In ceramic systems with distinct electrical micro-structures, A₁ω^s₁ and A₂ω^s₂ are supposed to be related to grain boundary and grain, respectively.⁵³

Fig. 6 shows the variation of power exponents s₁ and s₂ with temperature fitted by the double power law. s₁ represented the power exponent in 20 Hz to 10 kHz, ranging in 0.4–1.0. s₂ characterized the power exponent above 10 kHz, ranging from 0.6 to 1.7. It should be noted that the AC conductivity above 400 °C kept constant in a wide frequency range for all the compositions, so the data above 400 °C was fitted by simple power law instead. Thus only s₂ can be observed in Fig. 6 in 400–500 °C. With the increase of temperature, both s₁ and s₂ gradually reduced. It is known that the power exponents represent the degree of interaction between the mobile ions and the lattice, dependent on intrinsic material characteristics and temperature.^54,55 The increased interaction at high temperature was supposed to be responsible for the decrease of s₁ and s₂.⁵⁴ Additionally, the exponent s₂ in all the samples reached a minimum at ∼400 °C, which was the onset of the sharp rise in temperature-dependent dielectric loss curves (Fig. 3).

Fig. 6 (a–e) Temperature dependence of the exponents s₁ and s₂, (f) comparison of the exponents at 325 °C for (1 − x)(BNT–BT)–xNT ceramics.

Fig. 7(a)–(e) represents the variation of conductivity with inverse of absolute temperature (i.e. ln σ_ac versus 1000/T) at different indicated frequencies for (1 − x)(BNT–BT)–xNT ceramics, in which the DC conductivity values were obtained by the above power law fitting. The conductivities gradually increased with increasing temperature, indicating a thermally activated conduction process.^56–58 The activation energy of conduction can be calculated by Arrhenius relationship:^41,59–61

where σ₀ is the pre-exponential factor, E_a is the activation energy of conduction, k_B is the Boltzmann constant, k_B = 1.38 × 10⁻²³ J K⁻¹. The obtained E_a values were listed in Fig. 7(f) and (g). Within the measuring temperature range, the activation energy of conduction (i.e. the slope in Fig. 7(a)–(e)) exhibited different values in the low temperature region (150–300 °C) and the high temperature region (325–500 °C). Within the same temperature region, E_a reduced with frequency, which is also observed in other systems.^48,62 As mentioned above, at low frequency, the conductivity is related to the long range transport of mobile charge carriers, corresponding to large E_a. At high frequency, the reorientational hopping motion of the charge carriers is restricted to the neighbouring lattice sites,⁴⁹ thus corresponding to small E_a value. At a certain frequency for each composition, E_a in the high temperature region was much larger than that in the low temperature region. In 325–500 °C, the activation energy of DC conduction ranged in 1.47–1.71 eV, which is close to the reported data in BNT-based ceramics.^36,56,63 Since the band gap of BNT–BT ceramics is around 3.2–3.4 eV,^64–66 there could be electronic states near the Fermi-level.⁶¹ So, it is supposed that (1 − x)(BNT–BT)–xNT system exhibits intrinsic band-type electronic conduction, which is analogous to that in BNT–BT–CZ,⁶³ BNT–BT–KNN⁵⁶ and BNT–BT–NBN²¹ materials.

Fig. 7 (a–e) Temperature-dependent variation of conductivity at different indicated frequencies and (f and g) the activation energy of conduction at different temperature range for (1 − x)(BNT–BT)–xNT ceramics.

3.4 Energy-storage properties

Energy-storage parameters were calculated based on the P–E loop of the samples. As shown in Fig. 8, the discharge (or recoverable) energy-storage density W was evaluated by integrating the area between the polarization axis and the discharge curve. The area of the P–E loop represented the energy loss density W_Loss. Due to the existence of W_Loss, the energy that can be recovered is smaller than the energy delivered to the capacitor.³ Thus, the energy-storage efficiency η is also an important parameter for energy-storage capacitor dielectrics.

Fig. 8 Schematic diagram of energy-storage parameters calculation.

Recoverable energy-storage density:⁶⁷

Charge energy-storage density:

W′ = W + W_Loss (6)

Energy-storage efficiency:

The P–E hysteresis loops of (1 − x)(BNT–BT)–xNT ceramics measured at 10 Hz and room temperature under different electric field were shown in Fig. 9. In all the compositions, the polarization did not saturate within the measured field range. For x = 0.01, the maximum polarization (P_m) increased from 9.3 to 44.8 μC cm⁻² with electric field increasing from 2 to 8 kV mm⁻¹. Under 10 kV mm⁻¹, the P–E loop of x = 0.01 exhibited typical relaxor ferroelectric characteristics with large P_m (∼50.9 μC cm⁻²) and medium remnant polarization (P_r ∼ 24.9 μC cm⁻²). With increase in NT content, the P–E loop became more and more slim. When x = 0.15, P_m and P_r reduced to 25.1 μC cm⁻² and 2.1 μC cm⁻² at 10 kV mm⁻¹, respectively. The variation of polarization as a function of composition was shown in Fig. 10(a). The change of P–E loops indicated that the long-range ferroelectric order was disturbed with the introduction of NT. This is caused by the decrease of polar rhombohedral phase proportion and increase of weakly polar tetragonal phase proportion, as certified by XRD analysis.

Fig. 9 P–E loops and energy-storage densities of (1 − x)(BNT–BT)–xNT ceramics under different electric field.

Fig. 10 (a) P_m, P_r, P_m − P_r (b) energy-storage density and energy-storage efficiency of (1 − x)(BNT–BT)–xNT ceramics under 10 kV mm⁻¹.

The insets of Fig. 9 shows the energy-storage densities as a function of electric field. The W–E curves underwent a gradual increment in the slope under lower electric field and then maintained linearity to the maximum applied electric field. Fig. 10(b) summarizes the calculated energy-storage density and energy-storage efficiency of all the samples at 10 kV mm⁻¹. For x = 0.01, the energy-storage density was no higher than 0.7 J cm⁻³ due to the large remnant polarization. With the increase of NT content, W exhibited a great increase, reaching 1.1–1.2 J cm⁻³ for x = 0.03–0.10. However, further addition of NT reduced the energy-storage density since the maximum polarization sharply dropped. For the energy-storage efficiency, it kept increasing from 28.4% in x = 0.01–80.6% in x = 0.15. By an overall consideration of W and η, the optimum energy-storage properties at 10 kV mm⁻¹ was obtained in 0.90(BNT–BT)–0.10NT with W = 1.2 J cm⁻³ and η = 74.8%, which is comparable to other reported BNT-based energy-storage ceramics.^6,20,68

4. Conclusion

Dense (1 − x)(BNT–BT)–xNT (0.01 ≤ x ≤ 0.15) ceramics were fabricated via high-temperature solid-state reaction method. All the samples exhibited single perovskite structure with no secondary impurity. XRD refinement indicated a composition induced polar rhombohedral phase (space group R3c) → weakly polar tetragonal phase (space group P4bm) transition. With the increase of NT addition, the permittivity gap at the anomaly temperatures |ε_s − ε_m| largely reduced, leading to favorable dielectric temperature stability. In the compositions of x = 0.03–0.15, the working temperature range spanned over 260 °C satisfying TCC_{150 °C} ≤ ±15%. In the high temperature region (325–500 °C), the activation energy of DC conduction E_a = 1.47–1.71 eV, which was approximately half the band gap of BNT–BT ceramics, indicating intrinsic band-type electronic conduction. The optimum energy-storage properties was obtained in x = 0.10 with W = 1.2 J cm⁻³ and η = 74.8% at 10 kV mm⁻¹.

Acknowledgements

This work was supported by National Natural Science Foundation of China (No. 51372191), National Key Basic Research Program of China (973 Program) (No. 2015CB654601), International Science and Technology Cooperation Program of China (2011DFA52680), the Fundamental Research Funds for the Central Universities (WUT: 152401002 and 152410002).

References

1. S. Kwon, W. Hackenberger, E. Alberta, E. Furman and M. Lanagan, IEEE Electr. Insul. Mag., 2011, 27(2), 43–55.
2. K. Yao, S. Chen, M. Rahimabady, M. S. Mirshekarloo, S. Yu and F. E. H. Tay, et al., IEEE Trans. Ultrason. Ferroelectrics Freq. Contr., 2011, 58(9), 1968–1974.
3. T. M. Correia, M. McMillen, M. K. Rokosz, P. M. Weaver, J. M. Gregg and G. Viola, et al., J. Am. Ceram. Soc., 2013, 96(9), 2699–2702.
4. P. Hagler, P. Henson and R. W. Johnson, IEEE Trans. Ind. Electron., 2011, 58(7), 2673–2682.
5. R. Dittmer, E.-M. Anton, W. Jo, H. Simons, J. E. Daniels and M. Hoffman, et al., J. Am. Ceram. Soc., 2012, 95(11), 3519–3524.
6. J. Ye, Y. Liu, Y. Lu, J. Ding, C. Ma and H. Qian, et al., J. Mater. Sci.: Mater. Electron., 2014, 25(10), 4632–4637.
7. G. Viola, H. Ning, M. J. Reece, R. Wilson, T. Correia and P. Weaver, et al., J. Phys. D: Appl. Phys., 2012, 45(35), 355302.
8. R. A. Malik, A. Hussain, A. Zaman, A. Maqbool, J. U. Rahman and T. K. Song, et al., RSC Adv., 2015, 5(117), 96953–96964.
9. X. Lu, J. Xu, L. Yang, C. Zhou, Y. Zhao and C. Yuan, et al., Journal of Materiomics, 2016, 2(1), 87–93.
10. Y. Pu, M. Yao, H. Liu and T. Frömling, J. Eur. Ceram. Soc., 2016, 36(10), 2461–2468.
11. M. Chen, Q. Xu, B. H. Kim, B. K. Ahn, J. H. Ko and W. J. Kang, et al., J. Eur. Ceram. Soc., 2008, 28(4), 843–849.
12. Q. Xu, T. Li, H. Hao, S. Zhang, Z. Wang and M. Cao, et al., J. Eur. Ceram. Soc., 2015, 35(2), 545–553.
13. Q. Xu, Z. Song, W. Tang, H. Hao, L. Zhang and M. Appiah, et al., J. Am. Ceram. Soc., 2015, 98(10), 3119–3126.
14. X. Jiang, B. Wang, L. Luo, W. Li, J. Zhou and H. Chen, J. Solid State Chem., 2014, 213, 72–78.
15. H. Ni, L. Luo, W. Li, Y. Zhu and H. Luo, J. Alloys Compd., 2011, 509(9), 3958–3962.
16. L. Wu, N. Liu, F. Zhou, W. Wu, Y. Teng and Y. Li, J. Alloys Compd., 2010, 507(2), 479–483.
17. J. Ding, Y. Liu, Y. Lu, H. Qian, H. Gao and H. Chen, et al., Mater. Lett., 2014, 114, 107–110.
18. F. Gao, X. Dong, C. Mao, F. Cao, G. Wang and S. T. Zhang, J. Am. Ceram. Soc., 2011, 94(12), 4162–4164.
19. F. Gao, X. Dong, C. Mao, W. Liu, H. Zhang and L. Yang, et al., J. Am. Ceram. Soc., 2011, 94(12), 4382–4386.
20. J. Hao, Z. Xu, R. Chu, W. Li, D. Juan and F. Peng, Solid State Commun., 2015, 204, 19–22.
21. Q. Xu, M. T. Lanagan, X. Huang, J. Xie, L. Zhang and H. Hao, et al., Ceram. Int., 2016, 42(8), 9728–9736.
22. J. König, B. Jančar and D. Suvorov, J. Am. Ceram. Soc., 2007, 90(11), 3621–3627.
23. M. Spreitzer, J. König, B. Jančar and D. Suvorov, EEE Trans. Ultrason. Ferroelectrics Freq. Contr., 2007, 54(12), 2617–2622.
24. J. E. Daniels, W. Jo, J. Rödel, V. Honkimäki and J. L. Jones, Acta Mater., 2010, 58(6), 2103–2111.
25. E.-M. Anton, W. Jo, D. Damjanovic and J. R. Rödel, J. Appl. Phys., 2011, 110(9), 094108.
26. S.-T. Zhang, A. B. Kounga, E. Aulbach, T. Granzow, W. Jo and H.-J. Kleebe, et al., J. Appl. Phys., 2008, 103(3), 034107.
27. G. Viola, R. Mkinnon, V. Koval, A. Adomkevicius, S. Dunn and H. Yan, J. Phys. Chem. C, 2014, 118(16), 8564–8570.
28. W. Jo, S. Schaab, E. Sapper, L. A. Schmitt, H.-J. Kleebe and A. J. Bell, et al., J. Appl. Phys., 2011, 110(7), 074106.
29. C. Ma, X. Tan and H. J. Kleebe, J. Am. Ceram. Soc., 2011, 94(11), 4040–4044.
30. V. A. Khomchenko, V. V. Shvartsman, P. Borisov, W. Kleemann, D. A. Kiselev and I. K. Bdikin, et al., Acta Mater., 2009, 57(17), 5137–5145.
31. Q. Xu, M. Chen, W. Chen, H.-X. Liu, B.-H. Kim and B.-K. Ahn, Acta Mater., 2008, 56(3), 642–650.
32. M. Zhu, H. Hu, N. Lei, Y. Hou and H. Yan, Appl. Phys. Lett., 2009, 94(18), 182901.
33. K. Kumar and B. Kumar, Ceram. Int., 2012, 38(2), 1157–1165.
34. H. Y. Ma, X. M. Chen, J. Wang, K. T. Huo, H. L. Lian and P. Liu, Ceram. Int., 2013, 39(4), 3721–3729.
35. S.-T. Zhang, A. B. Kounga, E. Aulbach, W. Jo, T. Granzow and H. Ehrenberg, et al., J. Appl. Phys., 2008, 103(3), 034108.
36. J. East and D. C. Sinclair, J. Mater. Sci. Lett., 1997, 16(6), 422–425.
37. R. Dittmer, W. Jo, D. Damjanovic and J. R. Rödel, J. Appl. Phys., 2011, 109(3), 034107.
38. H. Hao, M. Liu, H. Liu, S. Zhang, X. Shu and T. Wang, et al., RSC Adv., 2015, 5(12), 8868–8876.
39. R. Rani, S. Sharma, R. Rai and A. L. Kholkin, Solid State Sci., 2013, 17, 46–53.
40. S. K. Rout, A. Hussian, J. S. Lee, I. W. Kim and S. I. Woo, J. Alloys Compd., 2009, 477(1–2), 706–711.
41. K. Prasad, K. Kumari Lily, K. P. Chandra, K. L. Yadav and S. Sen, Adv. Appl. Ceram., 2013, 106(5), 241–246.
42. J. S. Kim, A. Hussain, M.-H. Kim and T. K. Song, J. Korean Phys. Soc., 2012, 61(6), 951–955.
43. J. R. Macdonald, J. Non-Cryst. Solids, 1997, 210(1), 70–86.
44. A. K. Jonscher, Nature, 1977, 267(5613), 673–679.
45. A. K. Jonscher, Nature, 1975, 256(5518), 566–568.
46. A. K. Roy, A. Singh, K. Kumari, K. Amar Nath, A. Prasad and K. Prasad, ISRN Ceram., 2012, 2012, 1–10.
47. N. Ortega, A. Kumar, P. Bhattacharya, S. B. Majumder and R. S. Katiyar, Phys. Rev. B: Condens. Matter Mater. Phys., 2008, 77(1), 014111.
48. A. Roy, K. Prasad and A. Prasad, Process. Appl. Ceram., 2013, 7(2), 81–91.
49. A. K. Roy, K. Prasad and A. Prasad, ISRN Ceram., 2013, 2013, 1–12.
50. B. Parija and S. Panigrahi, Ferroelectr., Lett. Sect., 2012, 39(1–3), 38–55.
51. K. Funke, Prog. Solid State Chem., 1993, 22(2), 111–195.
52. A. A. A. Youssef, Z. Naturforsch., A: Phys. Sci., 2002, 57(5), 263–269.
53. S. Kumar and K. B. R. Varma, Curr. Appl. Phys., 2011, 11(2), 203–210.
54. B. K. Barick, K. K. Mishra, A. K. Arora, R. N. P. Choudhary and D. K. Pradhan, J. Phys. D: Appl. Phys., 2011, 44(35), 355402.
55. D. P. Almond, A. R. West and R. J. Grant, Solid State Commun., 1982, 44(8), 1277–1280.
56. J. Zang, M. Li, D. C. Sinclair, W. Jo, J. Rödel and S. Zhang, J. Am. Ceram. Soc., 2014, 97(5), 1523–1529.
57. Z. Song, S. Zhang, H. Liu, H. Hao, M. Cao and Q. Li, et al., J. Am. Ceram. Soc., 2015, 98(10), 3212–3222.
58. A. Hussain, J. S. Kim, J. U. Rahman, A. Maqbool, T. K. Song and W. J. Kim, et al., Ferroelectrics, 2014, 464(1), 107–115.
59. J. Portelles, N. S. Almodovar, J. Fuentes, O. Raymond, J. Heiras and J. M. Siqueiros, J. Appl. Phys., 2008, 104(7), 073511.
60. M. A. Rafiq, M. E. Costa, A. Tkach and P. M. Vilarinho, Cryst. Growth Des., 2015, 15(3), 1289–1294.
61. Q. Xu, M. T. Lanagan, W. Luo, L. Zhang, J. Xie and H. Hao, et al., J. Eur. Ceram. Soc., 2016, 36(10), 2469–2477.
62. K. S. Rao, K. C. V. Rajulu, B. Tilak and A. Swathi, Nat. Sci., 2010, 2(4), 357–367.
63. J. Zang, M. Li, D. C. Sinclair, T. Frömling, W. Jo and J. Rödel, et al., J. Am. Ceram. Soc., 2014, 97(9), 2825–2831.
64. M. Bousquet, J. R. Ducleère, E. Orhan, A. Boulle, C. Bachelet and C. Champeaux, J. Appl. Phys., 2010, 107(10), 104107.
65. M. Cernea, A. C. Galca, M. C. Cioangher, C. Dragoi and G. Ioncea, J. Mater. Sci., 2011, 46(17), 5621–5627.
66. M. Cernea, L. Trupina, C. Dragoi, A.-C. Galca and L. Trinca, J. Mater. Sci., 2012, 47(19), 6966–6971.
67. N. H. Fletcher, A. D. Hilton and B. W. Ricketts, J. Phys. D: Appl. Phys., 1996, 29(1), 253–258.
68. M. Yao, Y. Pu, H. Zheng, L. Zhang, M. Chen and Y. Cui, Ceram. Int., 2016, 42(7), 8974–8979.

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