The microscopic mechanism in the realization of ultra-wide temperature range stability in Bi³⁺,Na⁺,Zn²⁺,Nb⁵⁺ doped BaTiO₃ dielectric system

Abstract

A novel lead-free, ultra-wide temperature range stable dielectric ceramic with a high dielectric constant was prepared by a traditional solid-state reaction method. The microscopic mechanism, and the electric and dielectric properties of the Bi³⁺,Na⁺,Zn²⁺,Nb⁵⁺ doped BaTiO₃ dielectric system were investigated for the first time. X-ray diffraction revealed that Bi³⁺,Na⁺,Zn²⁺,Nb⁵⁺ and BaTiO₃ form a solid-solution with a pseudo-cubic structure. The thermal vibration and interactions between the dipoles contributing to the realization of an ultra-wide temperature range stability, were discussed. The microscopic model based on the bond energy and coordination number, was used to research the changes of the dielectric stability. In this paper, the relationship between microscopic mechanism and the macroscopic dielectric properties in the ultra-wide temperature range stable dielectric ceramics was established, thereby paving the way for achieving ultra-wide temperature range capacitors. In addition, fine dielectric properties of (Na_0.015Bi_0.3Ba_0.685)(Zn_0.2Nb_0.115Ti_0.685)O₃ with an ε_r of 700, and tan δ of 0.00535 can be obtained over an ultra-wide temperature range (−53 to 350 °C). These features give the ceramic system high practical value in miniaturization and increasing applications in harsh environments.

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1. Introduction

The rapid development of the electronics industry leads to higher requirements for the next generation of dielectric ceramic materials.^1–4 With the increasing integration of components, more circuits and devices are integrated in a limited space. A high dielectric constant is required for capacitors, so that they can meet the requirements of miniaturization. What’s more, the need for short circuit lengths forces us to make circuit modules near or directly in the work environment. Harsh working conditions, such as in automobile engines and rockets, as well as outer space, require that the components can be stable in an ultra-broad temperature scope.^1–4 The ceiling working temperature of the dielectric materials has been raised from 125 °C (Electronic Industries Alliance X7R) to 150 °C (EIA-X8R) and now reaches 200 °C (EIA-X9R).^5–9

With their high dielectric constants, excellent insulation properties, non-toxicity and low cost, BaTiO₃ based ceramics have become one of the major dielectric ceramic materials.¹⁰ The ceiling temperature of present BaTiO₃ based dielectric materials only reaches 125–200 °C. When the temperature increases to over 200 °C a sharp decline occurs. However, even X9R materials would not fulfill the requirements of some harsh conditions, such as in oil drilling, aerospace and automotive environments. For example, anti-lock brake system sensors on wheels are required to work at a temperature range of 150–250 °C and in the cylinder the ambient temperature is 200–300 °C.^11–13 The mismatch between the narrow effective temperature range (125–200 °C) and the high operating temperature requirements (over 200 °C) severely limits the use of dielectric components (e.g. MLCC). Thus, it is of great significance to develop temperature stable dielectric materials with a high dielectric constant, and low dielectric loss over a wide temperature range (−55 to 350 °C).^14–17

Currently, there is much research on the development of stable dielectric materials over a wide temperature range. However, few studies have been done on the microscopic mechanisms in the materials, which benefit the realization of ultra-wide temperature range stability. In this paper, we report a Bi³⁺,Na⁺,Zn²⁺,Nb⁵⁺ doped BaTiO₃ dielectric system, which had a high dielectric constant, and a low dielectric loss over a wide temperature range (−53 to 350 °C). The thermal vibrations and the interactions between the dipoles contributing to the realization of the ultra-wide temperature range stability are discussed. What’s more, the bond energy and coordination number model were used to research the movements of the stable temperature range. This work has high practical value in the development of ultra-wide temperature range stable dielectric ceramics.

2. Experimental procedures

Reagent-grade BaTiO₃, Na₂CO₃, Bi₂O₃, ZnO, and Nb₂O₅ were used as raw materials. Firstly, reagent-grade oxides and carbonate of Bi₂O₃, ZnO and Nb₂O₅ were weighed with a mole ratio of 3 : 4 : 1 and mixed using ball-milling in deionized water for 4 h. Then the mixture was calcined in air at 800 °C to synthesize a Bi(Zn_2/3Nb_1/3)O₃ phase. Secondly, stoichiometric proportions of Na₂CO₃ and Nb₂O₅ were mixed by ball milling in deionized water for 4 h. The mixture was dried and calcined at 900 °C in a covered alumina crucible for 4 h to synthesize a NaNbO₃ phase. Bi(Zn_2/3Nb_1/3)O₃ and NaNbO₃ have a similar structure to BaTiO₃.^36,38–47 In the sintering process, it is more convenient for Bi³⁺, Na⁺, Zn²⁺, and Nb⁵⁺ to diffuse into the crystal lattice, rather than the oxide forms, such as Bi₂O₃, ZnO and Nb₂O₅. Subsequently, (1 − x)BaTiO₃–xBi(Zn_2/3Nb_1/3)O₃–0.015NaNbO₃ (0.22 ≤ x ≤ 0.30) powders were weighed and milled in deionized water using zirconia balls for 4 h. The locations of the compositions in the (1 − x)BaTiO₃–xBi(Zn_2/3Nb_1/3)O₃–0.015NaNbO₃ system are shown in Fig. 1. After drying, the mixed powders were added in 7 wt% binder wax, and then cold isostatically pressed into discs under a pressure of 200 MPa with a 20 mm diameter and 1 mm thickness. The samples were sintered at 1200 °C for 2 h. The samples with x = 0.22, 0.24, 0.0.27, and 0.30 were named sample 1, sample 2, sample 3, and sample 4, respectively.

Fig. 1 The locations of the compositions in the Bi³⁺,Na⁺,Zn²⁺,Nb⁵⁺ doped BaTiO₃ dielectric system.

The crystal structure of the samples was identified at room temperature using an X-ray diffractometer (D8-Focus, Bruker AXS GmbH, German). To reduce noise, all data have been smoothed by an adaptive smoothing method and had background deducted. All parameters including background, zero-point, scale factors for all phases, half-width, asymmetry parameters, unit-cell parameters, atomic positional coordinates, and temperature factors are refined step-by-step to avoid correlations by the soft-ware of Fullprof-suite. The microstructure of the ceramic samples was observed by field emission scanning electron microscopy (FE-SEM, S-4800, Hitachi, Ltd. Japan). Dielectric loss and capacitance were measured with the use of a capacitance meter (HP4278A) at 1 kHz to 1 MHz, with a temperature range of −55 °C to 350 °C. Insulation resistance was measured using a high resistance meter (Agilent 4339B) at room temperature.

3. Results and discussion

3.1 The micro-mechanism and the dielectric properties

Fig. 2(a–c) shows the temperature dependence of the dielectric constant and capacitance variation rate based on C_{25 °C} with various amounts of Bi³⁺,Na⁺,Zn²⁺,Nb⁵⁺, sintered at 1200 °C, and measured at 1 kHz to 1 MHz. As Fig. 2 shows, there is only one dielectric dispersion peak at low temperature (∼25 °C) and the dielectric constant varies with frequency, which is consistent with the relaxation ferroelectrics. The “modified Curie–Weiss law”³⁴ is a method commonly used in the study of ferroelectric materials, which is expressed by the following equation:
where ε is the relative permittivity, T_m is the temperature, ε_m is the maximum ε value at T = T_m, C is the modified Curie–Weiss constant, and r is a measurement of diffusivity. The material with r = 1 fits a normal ferroelectric behavior, with r = 2 it fits the ideal relaxation ferroelectric system,³⁵ and between 1 and 2 it indicates a diffuse ferroelectric characteristic, which has the characteristics of “relaxorlike” behavior. Fig. 2(d) shows that the diffuse exponent r is about 1.4–1.5 for the (1 − x)BaTiO₃–xBi(Zn_2/3Nb_1/3)O₃–0.015NaNbO₃ (0.22 ≤ x ≤ 0.30) ceramics, which confirmed that (1 − x)BaTiO₃–xBi(Zn_2/3Nb_1/3)O₃–0.015NaNbO₃ exhibit the “relaxorlike” behavior. It was the special structure—“relaxorlike”—that gives the Bi³⁺,Na⁺,Zn²⁺,Nb⁵⁺ doped BaTiO₃ dielectric system special dielectric properties. The details are shown below.³⁵

Fig. 2 (a) and (b) Temperature dependence of dielectric constant and capacitance variation rate based on C_{25 °C} for samples with various amounts of Bi(Zn_2/3Nb_1/3)O₃, sintered at 1200 °C, and measured at 1 kHz; (c) the sample doped with x = 0.27 of (1 − x)BaTiO₃–xBi(Zn_2/3Nb_1/3)O₃–0.015NaNbO₃ system, sintered at 1200 °C, measured at 1 kHz to 1 MHz; (d) plot of ln(1/ε − 1/ε_m) as a function of ln(T − T_m) for (1 − x)BaTiO₃–xBi(Zn_2/3Nb_1/3)O₃–0.015NaNbO₃ (x = 0.22, 0.24, 0.27, and 0.30, sintered at 1200 °C) at 1 kHz.

Spontaneous polarization occurred in the ferroelectric BaTiO₃ and the long-range interactions between the dipoles promoted the dipoles to form ferroelectric domains. When an external electric field was applied, the ferroelectric domains would be extended along the external electric field, which is the reason for a high dielectric constant in BaTiO₃. Meanwhile, long-range interactions between dipoles were destroyed by the doping of external additives. The macroscopic ferroelectric domains gradually decreased and randomly distributed micro-domains formed.^18–20 Fig. 3 shows a micro-mechanism in the Bi³⁺,Na⁺,Zn²⁺,Nb⁵⁺ doped BaTiO₃ dielectric system, which benefits the realization of an ultra-wide temperature range stability.

Fig. 3 The micro-mechanism in the Bi³⁺,Na⁺,Zn²⁺,Nb⁵⁺ doped BaTiO₃ dielectric system, which benefits the realization of an ultra-wide temperature range stability.

When an external electric field was applied, there were three forces involved in the phase change process, the external electric field force (F_e), the interaction between the polarized micro-domains (F_i) and the thermal vibration force (F_v), which occurred throughout the whole temperature range. The interaction between the polarized micro-domains and the thermal vibration make the polarized micro-domains distribute randomly and macroscopic polarization is reduced. Meanwhile, the external electric field force (F_e) makes the polarized micro-domains distribute along the external electric field and the macroscopic polarization is increased. Local polarization regions formed at the Burns temperature (T_d). At ambient temperatures, T ≫ T_d, no polarization existed and the dielectric system was in a paraelectric phase. The Burns temperature is generally higher than the temperature T_c of the maximum dielectric constant.^21,22

In a high temperature range (T ≤ T_d), thermal vibration is very strong. The interactions of different polarization regions (F_i) are so weak they can be ignored. The thermal vibration force (F_v) is greater than the external electric field force (F_e). The polarized micro-domains can vibrate in several equivalent directions. The orientation of each polarized micro-domain is insulated from the others. The macroscopic polarization was close to zero.

In the temperature region of T_c < T ≪ T_d, the polarized micro-domains gradually increased. The thermal vibration (F_v) reduced and gradually became less than the external electric field force (F_e). The interactions of different polarization regions (F_i) remain so weak that they can be ignored. Since the temperature is still relatively high, the degree of freedom of the polarized micro-domains is high and the external electric field force (F_e) makes the polarized micro-domains distribute along the external electric field quickly. As a result, the dielectric constant increases and the relaxivity is low.

In the temperature region of T_f ≪ T < T_c, the polarized micro-domains are large, and the interaction between the polarized micro-domains is strong. Because the temperature is relatively low, the thermal vibration energy is small and it can be ignored. The polarized micro-domains gradually increase and the interactions of micro-domains strengthen as the temperature declines. The electric field directional force (F_e) gradually becomes lower than the interaction between the polarized micro-domains (F_i). As a result, the dielectric constant is decreased, and dielectric loss and relaxivity are enhanced.

In the temperature region of T ≥ T_f, the polarized micro-domains become larger and the interaction between the dipoles (polarized micro-domains) (F_i) is larger than the electric field directional force (F_e) which leads to the dipoles being distributing randomly. The ambient temperature is so low that thermal vibration can be ignored. As a result, the macroscopic polarization is close to zero.

Accordingly, the dielectric constant increased firstly and then decreased, and significant dielectric relaxation appeared in the low temperature region.

3.2 Bond energy and coordination number relaxor model and the dielectric stability

In the Bi³⁺,Na⁺,Zn²⁺,Nb⁵⁺ doped BaTiO₃ dielectric system, relaxation arises from the inert substitution of A, B site ions. Bi³⁺,Na⁺,Zn²⁺,Nb⁵⁺ diffuses into the cell and the dielectric system changes from normal ferroelectric to diffuse ferroelectric. The relaxation behavior can be described by the relationship of Vogel–Fulcher:f: the measurement frequency; f₀: Debye frequency; k: Boltzmann’s constant; T_c: the temperature corresponding to the maximum dielectric; E_a: activation energy of the transition in micro-domains; T_f: freezing temperature of the transition.

According to the bond energy and coordination number model, the Vogel–Fulcher formula can be expressed as follows:^23,24

〈〉: statistics average; τ: relaxation time; E: the interaction between neighboring dipoles; Z: the number of neighboring dipoles.

In the crystal of BaTiO3, one Ti⁴⁺ ion and six O²⁻ ions form the special octahedral structure of [TiO₆], which can be seen in the Fig. 1. In the octahedron, Ti⁴⁺ deviates from the center position of the octahedron and a dipole forms. So, each [TiO₆] octahedron can be seen as one dipole.

In the Bi³⁺,Na⁺,Zn²⁺,Nb⁵⁺ doped BaTiO₃ dielectric system, Bi³⁺,Na⁺,Zn²⁺,Nb⁵⁺ diffuses into the cell. Because of the different radii and valence with Ba²⁺ and Ti⁴⁺, the doping ions (Zn²⁺,Nb⁵⁺) locate at the center of the oxygen octahedra. As a result, a dipole cannot form.

What’s more, the original polarized [TiO₆] octahedra in BaTiO₃ are separated by the non-polarized area (the doping area). As a result, the interactions between the dipoles are weakened.

In summary, the inert substitution of A, B site ions makes the number of neighboring dipoles decrease and the interactions (which we call bond energy in this paper) between the dipoles weaken. Due to the non-uniform distribution of dopant ions,³⁷ each different dipole has its own surroundings. Thus, the coordination number and bond energy of each dipole can be described as follows:

Z = Z₀ + ΔZ (4)

E = E₀ + ΔE (5)

Z₀: the average coordination number of each dipole in the whole system; ΔZ: fluctuations in the coordination number of local areas due to the non-uniform distribution of dopant ions; E₀: the average bond energy of each dipole in the whole system; ΔE: fluctuations in the bond energy of the local areas due to the non-uniform distribution of dopant ions.

When the bond energy and coordination number follow Gaussian distribution²⁵

ΔE/E₀ = γ·ΔZ/Z₀ (7)

When γ = 1, formula (7) can be expressed as²⁶

In the Bi³⁺,Na⁺,Zn²⁺,Nb⁵⁺ doped BaTiO₃ dielectric system, the substitution of doping ions within the crystal is non-uniform.³⁷ The non-uniform distribution of the crystals inside leads to large fluctuations in bond energy (ΔE). From eqn (8), we can conclude that relaxation behavior will be enhanced with the increase of doping content.

What’s more, due to the non-uniform distribution of the substitutional ions, the surroundings of each dipole are different. Different areas have their own activation energy. So, different areas have different responses to temperature. As a result, the dielectric peak was broadened and dielectric stability was enhanced. The mechanism is shown in Fig. 2.

The results of Fig. 2 and 3 and Table 1 are consistent with the discussion above. Fig. 2 and Table 1 show that from sample 1 to sample 4, the dielectric stability gradually increased from the range of −55 to 245 °C, to −53 to 350 °C. What’s more, according to eqn (8), if the measuring frequency (f) remains constant, T_c will move to a higher temperature with the increasing of the doping content (ΔE is increased). Table 1 shows the dielectric properties of samples 1–4. When the doping content increased from x = 0.24 to x = 0.30, T_c increased from ∼25 °C to ∼50 °C. The movement of T_c makes the temperature stable range move to a higher temperature which we can see from Fig. 2 and Table 1.

Table 1 Comparisons of varying amounts of Bi(Zn_2/3Nb_1/3)O₃ (x = 0.25, 0.275, 0.3, 0.325) sintered at 1200 °C

Sample	εr at 25 °C	tan δ	ΔC/C25 °C (%) ≤ ±15%		Curie temperature (Tc/°C)	Bulk density (g cm^−3)	Insulation resistance (ρv 10^10 Ω cm)
1	721	0.00539	−55 °C	245 °C	25	5.729	2.78
2	704	0.00773	−50 °C	250 °C	25	5.727	3.74
3	678	0.01005	−50 °C	300 °C	25	5.817	1.41
4	630	0.01069	−53 °C	350 °C	50	5.777	4.25

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3.3 Structure of Bi³⁺,Zn²⁺,Nb⁵⁺ doped BaTiO₃ solid solution

Fig. 4(a) shows the X-ray diffraction patterns of (1 − x)BaTiO₃–xBi(Zn_2/3Nb_1/3)O₃–0.015NaNbO₃ doped with varying content of Bi(Zn_2/3Nb_1/3)O₃ and sintered at 1200 °C. All samples show a perovskite phase, which means that there is formation of a solid solution between Bi³⁺,Na⁺,Zn²⁺,Nb⁵⁺ and BaTiO₃. No second phase exists. The enlarged XRD patterns in the range of 2θ from 44° to 46° are illustrated in Fig. 4(b). It is clearly visible that there is a merging of the (002)/(200) (2θ = 45°) diffraction peaks of the pure barium titanate into a single (200) peak, indicating a transformation from a tetragonal phase (P4mm) to pseudocubic symmetry. Just as we can see from the dielectric constant–temperature curve mentioned above, the Curie peak at ∼120 °C (pure BaTiO₃) disappeared. In addition, the dielectric anomaly peak occurs at the low temperature of ∼25 °C. With the increase of the doping concentration of Bi(Zn_2/3Nb_1/3)O₃, the (200) diffraction peak shifted toward lower angles firstly (from x = 0.22 to x = 0.24) and then the (200) diffraction peak shifted higher accompanied by gradually enhancing Bi(Zn_2/3Nb_1/3)O₃ concentration (from x = 0.24 to x = 0.27, and x = 0.30). This behavior demonstrates that the lattice parameters of solid solutions increased firstly and then decreased slightly. According to the principles of crystal chemistry and the radius-matching rule,^30,31 the incorporation of the radii of Na⁺ (1.39 Å) and Bi³⁺ (1.30 Å) is nearly comparable to the value of Ba²⁺ (1.61 Å) owing to the 12-fold coordination in the A-site.²⁷ Meanwhile, the B-site ions Zn²⁺ (0.74 Å) and Nb⁵⁺ (0.64 Å) have considerably larger radii than that of Ti⁴⁺ (0.605 Å) in a six-fold coordination.^28,32 The substitution of the B-site is the main influencing factor on the crystal lattice in this paper. When there is a further increase in Bi(Zn_2/3Nb_1/3)O₃ (e.g. sample 3), the content of Zn²⁺ and Nb⁵⁺ that diffuses into the cell is abnormally reduced. This phenomenon is due to the produced pinning effect by the heavily doped Bi(Zn_2/3Nb_1/3)O₃, which inhibits the grains’ growth. What’s more, excessive increase in the content of Bi(Zn_2/3Nb_1/3)O₃ (e.g. sample 4) will generate a lot of liquid phase in the sintering process; the content of Zn²⁺ and Nb⁵⁺ that diffuses into the lattice will increase. The lattice parameters (a and c) of the Bi³⁺,Na⁺,Zn²⁺,Nb⁵⁺ doped BaTiO₃ solid solution are calculated based on XRD results using High-Score plus software. Fig. 4(c) illustrates the compositional dependence of the tetragonality factor (c/a). The c/a ratio reduced from 1.011 for x = 0 to 1.0002 for x = 0.27 and 0.9971 for x = 0.30, and became equal to 1. The decreased c/a is inherently associated with the lower tolerance factor of Zn²⁺ and Nb⁵⁺, which is significantly lower than Ti⁴⁺ for the pure BaTiO₃.

Fig. 4 (a) X-ray diffraction patterns of (1 − x)BaTiO₃–xBi(Zn_2/3Nb_1/3)O₃–0.015NaNbO₃ ceramics with x = 0.22, 0.24, 0.27, and 0.30 at room temperature; (b) the (002)/(200) diffraction patterns of the sample in the range 44–46°; (c) compositional dependence of the tetragonality factor (c/a).

3.4 Microstructure of the BaTiO₃–Bi(Zn_2/3Nb_1/3)O₃–NaNbO₃ ceramics

Fig. 5 shows the relationships between sintering temperatures and densities of all the studied samples. It can be observed that increasing the Bi(Zn_2/3Nb_1/3)O₃ content could increase the density while no significant change occurred in the sintering temperature. Fig. 6 shows the SEM micrographs for the Bi³⁺,Na⁺,Zn²⁺,Nb⁵⁺ doped BaTiO₃ dielectric system. As shown here, the grains are well developed in all the samples. All of the samples show a uniform grain distribution and the size of the grain is about 2–3 μm. There is no second phase in this report. Fig. 7 shows the distribution of the grain size obtained by the software of Nano measure. Just as we can see, with the increase of the Bi(Zn_2/3Nb_1/3)O₃ content, the densification and the grain size increased firstly, then decreased, and increased finally. As mentioned above, the Zn²⁺ ions will enter into the lattice to substitute for Ti⁴⁺ ions; the imbalance of ion valence will lead to the creation of oxygen vacancies,^32,33 which enhances the transfer of mass and energy between the reactants. This improved the sintering process inducing an increase in the densification of grain distribution. However, a further increase in Bi(Zn_2/3Nb_1/3)O₃ (x = 0.30) has an adverse effect on the densification of the samples, as illustrated in Fig. 6(c). This phenomenon is due to the produced pinning effect. When the doping amount is less, the distribution of Bi³⁺,Na⁺,Zn²⁺,Nb⁵⁺ is uniform. However, when the doping increases, an increase in the number of substitutional ions and lattice distortion occurs which is harmful to the diffusion process. Fig. 6(d) shows that the densification and the grain size increased again. This may be due to excess doping. A large amount of liquid phase occurred in the sintering process and accumulated in the grain boundaries. The right amount of liquid benefits the dissolution/precipitation process.^27–29,33

Fig. 5 The relationships between sintering temperatures and densities of all studied samples.

Fig. 6 SEM micrographs of natural surfaces for (1 − x)BaTiO₃–xBi(Zn_2/3Nb_1/3)O₃–0.015NaNbO₃ ceramics with x = 0.22, 0.24, 0.27, and 0.30: (a)–(d).

Fig. 7 (a)–(d) The distribution of the grain size in (1 − x)BaTiO₃–xBi(Zn_2/3Nb_1/3)O₃–0.015NaNbO₃ ceramics with x = 0.22, 0.24, 0.27, and 0.30; (e) compositional dependence of the grain size.

4. Conclusion

The crystal structure and dielectric properties of Bi³⁺,Na⁺,Zn²⁺,Nb⁵⁺ doped BaTiO₃ dielectric systems were investigated. The relationship between the microscopic structure and the dielectric properties was discussed systematically. The microscopic model based on bond energy and coordination number, was proposed and used to investigate the changes of the dielectric stability in the Bi³⁺,Na⁺,Zn²⁺,Nb⁵⁺ doped BaTiO₃ dielectric systems. The obtained results indicated that doping with Bi³⁺,Na⁺,Zn²⁺,Nb⁵⁺ can alter the temperature dependence of the dielectric constant markedly both in the high and low temperature range, which played a decisive role in the realization of wide temperature range stability. Dielectric measurements showed that doping with Bi³⁺,Na⁺,Zn²⁺,Nb⁵⁺ can make the dielectric system change from a normal ferroelectric to a diffusive ferroelectric (1 < r < 2) system, which has the characteristics of a normal ferroelectric system and ideal relaxation. The temperature coefficient of capacitance was flat in the temperature range of −53 to 350 °C. Moreover, the system had a relatively higher dielectric constant and lower dielectric loss (ε_r = ∼700, tan δ = 0.00535) over an ultra-wide temperature range. These features suggest that the ceramic system can be considered as a promising candidate material for the next generation of MLCCs used in harsh conditions (over 300 °C).

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