Fabrication of barium titanate nanoparticles‐polymethylmethacrylate composite films and their dielectric properties

A method for incorporating barium titanate (BT) nanoparticles into polymethylmethacrylate (PMMA) is proposed to prepare composite films with a high dielectric constant and high transparency. BT particles with particle sizes of 7.8–24.0 nm and crystal sizes of 8.60–17.7 nm were synthesized with a complex alkoxide method. Surface of the BT particles was modified with 3‐methacryloxypropyltrimethoxysilane to introduce double bonds that was grafted with PMMA. The PMMA‐grafted BT particles were suspended in PMMA/N‐methyl‐2‐pyrrodinone solution and spin‐coated onto glass substrates to prepare the PMMA/BT composite films. The surface modification gave composite films having smooth surfaces and high transparency. An increase in BT particle size and BT volume fraction in the film tended to increase the dielectric constant while keeping the dissipation factor around 5%. The dielectric constant of the film prepared for a particle size of 24.0 nm at 39 vol% attained a value of 19.8 that was around four times higher than that of the pure PMMA film. The dielectric constants of the BT particles estimated by the application of Lichtenecker's mixing model to the composite films were 75.3, 105.1, and 166.3 for particle sizes of 7.8, 11.0, and 24.0 nm, respectively. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers     

High dielectric constant SU8 composite photoresist for embedded capacitors

A novel, photodefinable, high dielectric constant (high‐k) nanocomposite material was developed for embedded capacitor applications. It consists of SU8 as the polymer matrix and barium titanate (BT) nanoparticles as the filler. The UV absorption characteristics of BT nanoparticles were studied with a UV‐Vis spectrophotometer. The effects of BT nanoparticle size, filler loading, and UV irradiation dose on SU8 photopolymerization were systematically investigated. The dielectric properties of the photodefined SU8 nanocomposites were characterized. Embedded capacitors using the novel high dielectric constant SU8 composite photoresist were demonstrated on a flexible polyimide substrate by the UV lithography method. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 103: 1523–1528, 2007     

Processing,Dynamic mechanical thermal analysis,and dielectric properties of barium titanate/cellulosic polymer nanocomposites

High dielectric constant BaTiO₃/ethyl cellulose (BT/EC) nanocomposites having BT loadings of up to 13 vol% were fabricated through a simple casting technique. The BT filler powder, synthesized through an ultrasonic‐assisted solid‐state route, was revealed by X‐ray powder diffractometry (XRD) and Raman spectroscopy to be dominantly tetragonal. Scanning electron microscopy (SEM) showed good dispersion of the BT nanoparticles in the EC polymer matrix at lower BT concentrations. However, at higher concentrations, the BT particles form a continuous phase or a “filler network” leading to weak BT/EC interactions. This finding is well supported by the results of the tensile strength and storage modulus. The dielectric properties of the BT/EC nanocomposites were investigated over wide ranges of frequency and temperature. The addition of BT significantly increased the permittivity (ε ′) and dielectric loss (ε ″) and improved the ionic conductivity of the EC. The electric modulus (M″ ) results were analyzed in terms of the Havriliak–Negami function through three distinct relaxation mechanisms (namely α, β*, and β relaxations) in the temperature range 30–150°C. The dc conductivity (σ _dc) results suggest that the BT/EC nanocomposites formed at low BT loading (up to 7.0 vol%) and a temperature of ≤60°C are good candidates for antistatic applications while those formed at higher concentrations and temperatures are recommended for use in electrostatic dissipation applications. POLYM. COMPOS., 38:893–907, 2017. © 2015 Society of Plastics Engineers     

Fabrication of highly refractive barium‐titanate‐incorporated polyimide nanocomposite films with high permittivity and thermal stability

Crystalline nanoparticles of barium titanate (BT) are incorporated into polyimide (PI) to fabricate highly refractive, anti‐UV‐degradable nanocomposite films with high permittivity and thermal stability. For homogeneous incorporation of BT nanoparticles into the PI matrix, the BT nanoparticles are surface modified by phthalimide with the aid of a silane coupling agent as a scaffold. The PI nanocomposites are prepared by in situ polymerization in which a diphthalic anhydride and a diamine are used to form the PI matrix in the presence of the surface‐modified nanoparticles. The refractive index of the transparent nanocomposite films reaches 1.85 at a nanoparticle content of 59 vol% with a high dielectric constant of ε = 37 and thermal stability up to 460 °C. Copyright © 2012 Society of Chemical Industry     

Fabrication and Characterization of the Piezoelectric Ceramic–Polymer Composites

The modified sol–gel method was used to synthesize lead zirconate titanate nanoparticles, and the lead zirconate titanate nanoparticles and polyvinylidene fluoride were used to prepare piezoelectric nano‐ceramic–polymer composites with 0–3 connectivity type. The composites were successfully prepared by cold‐pressing and curing‐molding methods. X‐ray diffraction and scanning electron microscopy were adopted to characterize the microstructure of the obtained lead zirconate titanate nanoparticles and composites. The normal vibration modes of the lead zirconate titanate nanoparticles were investigated by Fourier transform infrared spectroscopy. The dielectric and piezoelectric properties of the composites were analyzed in detail with respect to different volume fractions of the lead zirconate titanate nanoparticles. It demonstrated that the values of d₃₃ and ε increased with the increase in the content of lead zirconate titanate. The results here pointed to potential and simple methods to fabricate the lead zirconate titanate nanoparticles and the piezoelectric ceramic–polymer composites for piezoelectric applications.     

Fabrication of barium titanate nanoparticles‐epoxy resin composite films and their dielectric properties

A method for fabricating epoxy resin films dispersing the surface‐modified barium titanate (BT) particles (BT‐epoxy resin composite films) are proposed. BT particles with a size of 7.8 nm and a crystal size of 8.6 nm were synthesized with a complex alkoxide method. To introduce epoxy groups on the BT particle surface, the BT particles were surface‐modified with 2‐(3,4‐epoxycyclohexyl)‐ethyltrimethoxysilane. A precursor solution, which was prepared by prereacting 2,2‐bis(4‐glycidyloxyphenyl)propane (BGPP) and phthalic anhydride in 4‐butyrolactone and adding the surface‐modified BT particles to the prereacting solution, was spin‐coated on glass substrates to fabricate the composite films. An increase in BT volume fraction in film increased dielectric constant of the composite film while keeping dissipation factor below 0.03. The dielectric constant attained 10.8 at a BT volume fraction of 30% in film that was around twice higher than pure epoxy resin film. POLYM. COMPOS., 31:1179–1183, 2010. © 2009 Society of Plastics Engineers     

Reduced sedimentation of barium titanate nanoparticles in poly(vinylidene fluoride) films during solution casting by surface modification

Reduced sedimentation of barium titanate (BaTiO₃, BT) nanoparticles during solution casting to prepare the BT/poly(vinylidene fluoride) (PVDF) films is systematically investigated by surface modification of the BT nanoparticles. The surface of BT nanoparticles is hydroxylated by hydrogen peroxide (H₂O₂) or aminated by γ‐aminopropyl triethoxysilane (γ‐APS). It is found that the compatibility between the fillers and polymer matrix is remarkably improved by such surface treatments. As a result, the agglomeration and sedimentation of BT nanoparticles in the BT/PVDF composite films are significantly reduced, which is supported by morphology observation. Better dielectric properties such as higher dielectric constant, higher breakdown strength, and lower dielectric loss are also obtained for the composite films with surface‐modified fillers than those with raw fillers. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015 , 132, 42662.     

Multifunctional Properties of Multistage Spark Plasma Sintered HA–BaTiO3‐Based Piezobiocomposites for Bone Replacement Applications

This work reports the processing–microstructure–property correlation of novel HA–BaTiO₃‐based piezobiocomposites, which demonstrated the bone‐mimicking functional properties. A series of composites of hydroxyapatite (HA) with varying amounts of piezoelectric BaTiO₃ (BT) were optimally processed using uniquely designed multistage spark plasma sintering (SPS) route. Transmission electron microscopy imaging during in situ heating provides complementary information on the real‐time observation of sintering behavior. Ultrafine grains (≤0.50 μm) of HA and BT phases were predominantly retained in the SPSed samples. The experimental results revealed that dielectric constant, AC conductivity, piezoelectric strain coefficient, compressive strength, and modulus values of HA‐40 wt% BT closely resembles with that of the natural bone. The addition of 40 wt% BT enhances the long‐crack fracture toughness, compressive strength, and modulus by 132%, 200%, and 165%, respectively, with respect to HA. The above‐mentioned exceptional combination of functional properties potentially establishes HA‐40 wt% BT piezocomposite as a new‐generation composite for orthopedic implant applications.     

ROMP‐based boron nitride composites

The present work focuses on the investigation of the thermal and dielectric properties of composites obtained by surface‐modified hexagonal boron nitride (hBN) and ring‐opening metathesis polymerization (ROMP) based polymer. A new kind of high performance composites was developed based on using amino silane functionalized hBN (AS‐hBN) and bromine functional group possessing homo and copolymers synthesized via ROMP pathway. Aminosilane capped boron nitride (BN) and bromine bearing polymer backbone enhance the interaction between filler and the polymer chains. The effects of surface‐modified BN (AS‐hBN) and its content on the dielectric properties, and thermal resistance of composites, are systematically investigated and discussed. The resultant composites possess high electrical break over voltages. While all of the ROMP‐based films exhibit low ?′ value in a wide frequency range, in the case of the composite with 20% AS‐hBN and poly(bromooxanorbornene‐co‐cyclooctadiene) (ROMP‐BN‐6) displays very low dielectric constants in around 1.5 up to 1 MHz at 20 °C. This value is significantly lower than that of common polymer dielectrics, which is usually in the range of 3–6. Besides the lowest dielectric constant of ROMP‐BN‐6, it has also the smallest dielectric loss tangent even at high temperatures. Tan δ of ROMP‐BN‐6 is 0.003 and 0.0067 at 10 Hz–1 MHz at 20 °C, respectively. Thermal stability of polymers was also improved by introducing surface‐modified hBN. Polymers bearing 20% AS‐hBN are highly thermally stable up to ～350 °C and gave 25% char yield at 800 °C. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2018 , 135, 45658.     

Constructing the core–shell structured island domain in polymer blends to achieve high dielectric constant and low loss

Carbon nanotubes (CNTs) and barium titanate (BaTiO₃) (BT) were simultaneously introduced into the immiscible blend poly(ethylene‐co‐vinyl acetate)/thermoplastic urethane (EVA/TPU), and the EVA/TPU/CNT/BT quaternary polymer composite blends with core–shell structured island TPU domain were successfully prepared, in which CNTs in the TPU domain act as the core and the BT spheres at the interface of the TPU and EVA act as the shell. A core–shell structured island can lead to the formation of micro‐capacitors and further accumulate electron storage owing to the incorporation of CNTs and BT; on the other hand, a BT shell can be assembled along the TPU spheres, reducing the possibility of formation of a conductive CNT network, resulting in suppressed dielectric loss. Therefore, CNTs and BT were tailor‐made into blend composites with a core–shell structured domain, which can achieve an increased dielectric constant by 176% and decreased low dielectric loss by 80% compared with the blend composites with only CNTs in the TPU domain. © 2019 Society of Chemical Industry     

Enhancement of mechanical strength associated with interfacial tension between barium titanate and acrylonitrile–butadiene rubber with different acrylonitrile contents by surface modification

Acrylonitrile–butadiene rubber (NBR) with different acrylonitrile (ACN) contents was filled with barium titanate (BT) to prepare the polymer dielectrics. The neat NBR, NBR/untreated BT, and NBR/bis‐(γ‐triethoxysilylpropyl)‐tetrasulfide (silane coupling agent KH845‐4) modified BT (MBT) composites were prepared. At low ACN content (ACN content 20 wt %), the tensile strength of the NBR/MBT composites increased by 173.6% from 2.69 to 7.36 MPa compared to the neat NBR. The pleasing results were not found in those composites with high ACN content. Both surface modifications of BT and NBR with low ACN content would result in lower interfacial tension between BT and NBR. A strong interfacial adhesion was observed between MBT and NBR with 20 wt % ACN content. The interfacial adhesion had great contribution to the mechanical strength of composites. Moreover, the dielectric properties of composites were also investigated in detail. The addition of BT enhanced the dielectric constant of composites markedly. This study can be applied in manufacturing electronic devices, which are subjected to oily environments for a long time. At the same time, the study can provide some help for researchers to select the polymer matrix and the appropriate surface modification agent of functional filler. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2018 , 135, 45936.     

X‐ray diffraction and differential scanning calorimetry studies of a BaTiO3/polyvinylidene fluoride composites

Barium titanate/polyvinylidene fluoride (BaTiO₃)_x (PVDF)_100–x composite samples were prepared and characterized using X‐ray diffraction (XRD) and differential scanning calorimetry (DSC) techniques. In this work, the ratio of the constituents of this composite was altered, and the structural and thermal changes were studied. Also, the variation of tetragonality of BaTiO₃ (BT) in the composite samples as a function of BT content was studied for the first time. The results show that all the samples are in the α‐phase, and the hindrance to the PVDF crystallization increases with the increase of BaTiO₃ (BT) ratio in the composite. Tetragonal distortion of BT nanoparticles in the composite increases with the increase in BT ratio up to 30%, where it gets a saturation value. Also, it seems that stretching the samples enhances the BT tetragonality. Both melting and crystallization behaviors of the composite samples show double‐melting endotherms (reorganization) and crystallization exotherms. The inclusion of BT in the composite samples results in a decrease in the melting temperature of the samples. POLYM. ENG. SCI., 52:1945–1950, 2012. © 2012 Society of Plastics Engineers     

Fabrication of highly refractive,transparent BaTiO3/poly(methyl methacrylate) composite films with high permittivities

Incorporation of crystalline barium titanate (BT) nanoparticles into poly(methyl methacrylate) (PMMA) was carried out to prepare highly refractive polymer nanocomposite films that have transparency and high permittivities. The BT nanoparticles were prepared by hydrolysis of a barium/titanium complex alkoxide in 2‐methoxyethanol, then surface‐modified with a silane coupling agent (3‐methacryloxypropyltrimethoxysilane) to improve their affinity for PMMA. The incorporation of the surface‐modified nanoparticles into PMMA was performed up to a nanoparticle content almost equivalent to particle close‐packing state. The refractive index of the composite films increased with nanoparticle incorporation, keeping the relative transmittance normalized with PMMA film above 90%. A high refractive index of 1.82 was reached at a nanoparticle content of 53 vol% with a dielectric constant as high as 36 and a dissipation factor as low as 0.05. The results demonstrate that the crystalline BT nanoparticles are useful fillers for effectively increasing both refractive index and dielectric constant of polymer nanocomposites. Copyright © 2011 Society of Chemical Industry     

Dielectric property of modified barium titanate/polyamide 11 nanocomposites with different surfactants

Barium titanate/polyamide 11 (BT/PA11) nanocomposites were prepared by modifying BT nanoparticles with dry surface modification process, which had well dispersion, high dielectric constant, and low dielectric loss. Various methods were reported to improve dispersion and compatibility with complex process and high cost. Herein, three surfactants [ γ- aminopropyl triethoxy silane (KH550), sorbitan monostearate (SP60), and octadecyl phosphate ester (OPE)] were chosen to modify BT nanoparticles. Then modified-BT nanoparticles were blended with PA11. The structure was characterized by Fourier transform infrared, scanning electron microscope, and wide angle X-ray diffraction. Dielectric property was studied by broadband dielectric spectroscopy. The frequency dependence and temperature dependence of dielectric constant, dielectric loss, and dielectric modulus were analyzed. In general, dielectric property has strong frequency and temperature dependence. Furthermore, dielectric spectra shows that modified BT/PA11 nanocomposites have higher dielectric constant, lower dielectric loss, fewer interface polarization, and more dipole polarization. In contrast to three surfactants, OPE-BT nanoparticles have better effects, whose dielectric constant increases from 19 to 28 at 1 Hz, and dielectric loss decreases from 0.36 to 0.23. Meanwhile, mechanical property was characterized by universal testing machine. In all, the work improves dispersion of BT nanoparticles and dielectric property with easy process and low cost. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019 , 136, 47447.     

Enhanced thermal and electrical insulation properties of polyimide films determined via a two‐dimensional layered double hydroxide–potassium perfluorooctane sulfonate material

Polyimide (PI) films used in aerospace and rail applications are degraded by thermal, chemical, and electric power under the effect of insulation aging. To prevent these types of degradation, we prepared nanocomposite films of PI and layered double hydroxide (LDH) modified with the potassium perfluorooctane sulfonate (FS) by an in situ method. On the whole, the glass‐transition temperature, dielectric constant (?′), and corona‐resistance lifetime of the nanocomposite films increased over those of the pure PI film, but the temperature at 10 wt % weight loss, breakdown strength, and volume resistance decreased correspondingly as a whole. The PI matrix was protected by the inorganic material of LDH–FS with a high ?′ from corona corrosion. Furthermore, the heat and chemical interactions of the composite films improved the corona‐resistance lifetime, despite the decrease in the breakdown strength; this should result in promising applications for insulation parts of variable‐frequency motors. © 2018 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2018 , 135, 46528.     

Enhancement of dielectric constants of epoxy thermosets via a fine dispersion of barium titanate nanoparticles

In this study, we examined a facile approach for achieving a fine dispersion of barium titanate (BT) nanoparticles (NPs) in epoxy thermosets. First, the surfaces of BT NPs were modified with poly(ε‐caprolactone) (PCL) via a surface‐initiated ring‐opening polymerization approach. We found that the PCL‐grafted BT NPs were easily dispersed in epoxy thermosets. The fine dispersion of the PCL‐grafted BT NPs in the epoxy thermosets was evidenced by transmission electron microscopy and dynamic mechanical thermal analysis. We found that the organic–inorganic nanocomposites displayed significantly enhanced dielectric constants and low dielectric loss compared to the control epoxy. The nanocomposites containing 14.1 wt % BT NPs possessed dielectric constants as high as at a frequency of 10³ Hz. The dielectric loss was measured to be 0.002 at a frequency of 10³ Hz. The improved dielectric properties are accounted for the fine dispersion of the BT NPs in the epoxy thermosets. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 43322.     

Effect of BaTiO3 on the microwave absorbing properties of Co‐doped Ni‐Zn ferrite nanocomposites

Coprecipitation and hydrothermal method were utilized for the synthesis of Co‐doped Ni‐Zn ferrite and barium titanate nanoparticles. The microwave absorption properties of Co‐doped Ni‐Zn ferrite/barium titanate nanocomposites with single layer structure were studied in the frequency range of 8.2–12.4 GHz.The spectroscopic characterizations of the nanocomposites were examined using X‐ ray diffraction, scanning electron microscopy, transmission electron microscopy and dynamic light scattering measurement. Thermogravimetric analysis indicated the high thermal stabilities of the composites. The composite materials showed brilliant microwave absorbing properties in a wide range of frequency in the X‐band region with the minimum return loss of ?42.53 dB at 11.81 GHz when sample thickness was 2 mm and the mechanisms of microwave absorption are happening mainly due to the dielectric loss. Compared with pure Co‐doped Ni‐Zn ferrite, Co‐doped Ni‐Zn ferrite/BaTiO₃ composites exhibited enhanced absorbing properties. The microwave absorbing properties can be modulated by controlling the BaTiO₃ content of the absorbers and also by changing the sample thicknesses. Therefore, these composites can be used as lightweight and highly effective microwave absorbers. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014 , 131, 39926.     

Remarkable piezoelectricity and stable high‐temperature dielectric properties of quenched BiFeO3–BaTiO3 ceramics

Effects of quenching process on dielectric, ferroelectric, and piezoelectric properties of 0.71BiFeO₃?0.29BaTiO₃ ceramics with Mn modification (BF–BT?xmol%Mn) were investigated. The dielectric, ferroelectric, and piezoelectric properties of BF–BT?xmol%Mn were improved by quenching, especially to the BF–BT?0.3 mol%Mn ceramics. The dielectric loss tanδ of quenched BF–BT?0.3 mol%Mn ceramics was only 0.28 at 500°C, which was half of the slow cooling one. Meanwhile, the remnant polarization P_r of quenched BF–BT?0.3 mol%Mn ceramics increased to 21 μC/cm². It was notable that the piezoelectric constant d₃₃ of quenched BF–BT?0.3 mol%Mn ceramics reached up to 191 pC/N, while the T_C was 530°C, showing excellent compatible properties. The BF–BT?xmol%Mn system ceramics showed to obey the Rayleigh law within suitable field regions. The Rayleigh law results indicated that the extrinsic contributions to the dielectric and piezoelectric responses of quenched BF–BT?xmol%Mn ceramics were larger than the unquenched ceramics. These results presented that the quenched BF–BT?xmol%Mn ceramics were promising candidates for high‐temperature piezoelectric devices.     

Flexible /PET/batio3/ layer–layer composite film with enhanced dielectric properties fabricated by highly loaded /batio3/ coating with acrylic resin as binder

Flexible layer–layer poly(ethylene phthalate) (PET)/BaTiO₃ composite films with enhanced dielectric permittivity were fabricated by spin coating method, consisting of PET substrate film layer and modified BaTiO₃/acrylic resin hybrid coating layer. The thickness of coating layer was less than 3 μm (about 2% of PET film thickness), and therefore, the PET/barium titanate (BT) composite films remained flexible even at high volume fraction of BaTiO₃ fillers. The volume contents of BaTiO₃ were varied from 0 to 80%, and the solid contents of BaTiO₃/acrylic resin were in the range of 51.8–72.9%. Scanning electron microscopy showed strong interaction of finely dispersed BaTiO₃ particles with acrylic resin. Morphological profile also displayed uniform coating layer of modified BaTiO₃/acrylic resin and its strong adhesion with PET film. The dielectric constant of the PET/BaTiO₃ composite films increased by about 26% at 60 vol % BaTiO₃ loading when compared with the pristine PET film, whereas the dielectric loss decreased slightly. In addition, PET‐grafted poly(hydroxylethyl methacrylate) brushes were used as substrate to introduce covalent bonding with the coating layer. Further enhancement of dielectric constant and reduction of dielectric loss were realized when compared with the composite films with bare PET substrate. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015 , 132, 42508.     

Microstructure and Electrical Properties of Nonstoichiometric 0.94(Na0.5Bi0.5+x)TiO3–0.06BaTiO3 Lead‐Free Ceramics

0.94(Na_0.5Bi_0.5+x)TiO₃–0.06BaTiO₃ (x = ?0.04, 0, 0.02; named NB_0.46T‐6BT, NB_0.50T‐6BT, NB_0.52T‐6BT, respectively) lead‐free piezoelectric ceramics were prepared via the solid‐state reaction method. Effects of Bi³⁺ nonstoichiometry on microstructure, dielectric, ferroelectric, and piezoelectric properties were studied. All ceramics show typical X‐ray diffraction peaks of ABO₃ perovskite structure. The lattice parameters increase with the increase in the Bi³⁺ content. The electron probe microanalysis demonstrates that the excess Bi₂O₃ in the starting composition can compensate the Bi₂O₃ loss induced during sample processing. The size and shape of grains are closely related to the Bi³⁺ content. For the unpoled NB_0.50T‐6BT and NB_0.52T‐6BT, there are two dielectric anomalies in the dielectric constant–temperature curves. The unpoled NB_0.46T‐6BT shows one dielectric anomaly accompanied by high dielectric constant and dielectric loss at low frequencies. After poling, a new dielectric anomaly appears around depolarization temperature (T_d) for all ceramics and the T_d values increase with the Bi³⁺ amount decreasing from excess to deficiency. The diffuse phase transition character was studied via the Curie–Weiss law and modified Curie–Weiss law. The activation energy values obtained via the impedance analysis are 0.69, 1.05, and 1.16 eV for NB_0.46T‐6BT, NB_0.50T‐6BT and NB_0.52T‐6BT, respectively, implying the change in oxygen vacancy concentration in the ceramics. The piezoelectric constant, polarization, and coercive field of the ceramics change with the variation in the Bi³⁺ content. The Rayleigh analysis suggests that the change in electrical properties of the ceramics with the variation in the Bi³⁺ amount is related to the effect of oxygen vacancies.