BaTiO3 Crystal Research Articles

Calculations of Ba(1-x)SrxTio3 structure and band gap properties by using density functional theory

TThe aim of this study is to simulate features using molecular modeling methods. The point is to show that it will accelerate research in material development studies by directing us, researchers, in terms of gaining time, material and workforce. In this study, the structural and electronic properties of undoped BaTiO3 and Sr-doped BaTiO3 were calculated by molecular modeling. In the study, energy calculations were made with the PBE and GGA (Generalized Gradient Approximation approach) developed by Perdew, Burke and Ernzerhof (PBE) using the density functional theory (DFT) calculation method, the CASTEP module of the Materials Studio program. First, the structural and electronic properties of the BaTiO3 crystal phase were calculated. Then, the lattice constants, band gap values and electron state densities of the Sr doped structure to BaTiO3 structure were calculated. The values in the literature were compared with the calculations made using the( DFT) density functional theory and it was determined that the calculations were in agreement with the values in the literature. It has been revealed that it will accelerate research in material development studies by giving direction to us researchers in terms of gaining from materials and workforce. As a result of geometric optimization of the non-stoichiometric Ba(1-x)SrXTiO3 structure and DFT calculations, it was determined that the electronic band gap shifted after %1 and %3Sr addition towards the conduction band and the band gap respectively decreased to 1,911 eV and 1.989eV.

Behavior of strain stripe networks in barium titanate nanocrystals on crossing its ferroelectric phase transition

Nanoscale strain networks are reported in BaTiO3 (BTO) crystals of 300 nm size using Bragg coherent diffractive imaging. BTO nanocrystals with clear facets were chosen to identify the crystallographic directions, allowing the strain field direction and periodicity to be studied in detail. Stripes of strain were observed, which were both stable and preserved in tetragonal and cubic phases at elevated temperatures, above the tetragonal-to-cubic phase transition. A finite element analysis approach was used to simulate the domain structures inside a BTO crystal and to understand the origins of the strain stripes as piezoelectric blocks. A 180∘ domain model gives a better qualitative match to the experimental images. Published by the American Physical Society 2024

Enhancing the upconversion of Er3+ incorporated BaTiO3 by introducing oxygen vacancies.

Lanthanide-incorporated crystals display the phenomenon of upconversion (UC), wherein near-infrared (NIR) light is converted into ultraviolet-visible (UV-Vis) emission with a narrow bandwidth. This unique photophysical property renders lanthanide UC materials highly promising for diverse applications. However, the limited quantum efficiency (∼3%) hinders the broader utilization of UC materials. Consequently, numerous studies have focused on overcoming this low efficiency. Notably, it has been observed that manipulation of the site symmetry in UC materials significantly enhances their UC efficiency. In this study, we investigate the UC enhancement of Er3+ incorporated BaTiO3 (E-BT) crystals through the introduction of oxygen vacancies (OV). The OV were created using a post-heat treatment method, and the annealing time was varied to control the quantity of OV. An optimal annealing time of 6 hours was determined for efficient OV generation, beyond which the OV content decreased. Remarkably, E-BT crystals with OV exhibited up to three-fold greater UC compared to those without OV. This outcome suggests that OV induce symmetry changes in the E-BT crystal structure. Furthermore, the degree of UC enhancement in E-BT was found to be proportional to the amount of OV present.

Bandgap Narrowing of BaTiO3-Based Ferroelectric Oxides through Cobalt Doping for Photovoltaic Applications.

Following the finding of power conversion efficiency above the Shockley-Queisser limit in BaTiO3 (BTO) crystals, ferroelectric oxides have attracted scientific interest in ferroelectric photovoltaics (FPV). However, since ferroelectric oxides have a huge bandgap (>3 eV), progress in this sector is constrained. This paper proposes and demonstrates a new ferroelectric BaTi1-xCoxO3 powder (0 ≤ x ≤ 0.08), abbreviated as BTCx, that exhibited a bandgap decrease with increased Co content. Notably, changing the composition from x = 0.0 to 0.08 caused the system to show a bandgap drop from 3.24 to 2.42 eV. The ideal design with x = 0.08 displayed an abnormal PV response. Raman spectroscopy measurements were used to investigate the cause of the bandgap decrease, and density functional theory was used to interpret the analyzed results. According to our findings, Co2+ doping and oxygen octahedral distortions enhance bandgap reduction. This research sheds light on how bandgap tuning developed and laid the way for investigating novel low-bandgap ferroelectric materials for developing next-generation photovoltaic applications.

Tuning Ferroelectric Properties of Barium Titanate by Lateral Strain: A Molecular Dynamics Simulation Study

BaTiO3 (BT), a lead‐free ferroelectric material, is employed in energy‐conversion devices, including actuators and capacitors. However, its ferroelectric properties, such as the piezoelectric coefficient and Curie temperature, fall short of those of harmful lead‐based ferroelectrics, such as Pb(Zrx, Ti1−x)O3. In this study, a BT crystal is examined under biaxial strain (i.e., strain in the a‐ and b‐directions of the unit cell) to investigate the alterations in its ferroelectric properties. The piezoelectric coefficient, Curie temperature, polarization magnitude, and coercive electric field are calculated under varying biaxial strains using molecular dynamics simulations. The simulations utilize a core–shell‐type interatomic potential developed from first‐principles electronic structure calculations. In the findings, it is revealed that 1) the Curie temperature, polarization magnitude, and coercive electric field increase, whereas the piezoelectric coefficient in the c‐direction decreases under biaxial compression; 2) modifications in the ferroelectric properties depend on the area of ab‐plane and not on its aspect ratio. Comprehensive analyses of the Ti‐displacement distribution offer microscopic insights into strain‐induced shifts in ferroelectric properties.

BaTiO3 solid solutions co-doped with Gd3+ and Eu3+: Synthesis, structural evolution and dielectric properties

In this paper, the synthesis, structural evolution, and dielectric properties of BaTiO3 solid solutions co-doped with rare earth elements (Gd3+ and Eu3+) prepared using the solid-state reaction method are presented. Chemically pure precursor powders of BaCO3, TiO2, Gd2O3, and Eu2O3 were mixed in stoichiometric proportions, ground in an agate mortar before being uniaxially pressed at 250 MPa and sintered at 1300 °C in air atmosphere for 6 h to obtain Ba1–3xGd2xTi1–3xEu4xO3 (x = 0, 0.0015, 0.01 and 0.1). X-ray diffraction (XRD) and Rietveld's refinement results reveal the crystal phase ferroelectric tetragonal BaTiO3 for the samples with x = 0, 0.0015 and 0.01, as well as a consistent increment in the lattice parameters caused by the doping. The solubility limit of Gd3+ and Eu3+ in the BaTiO3 structure is reached for the sample with x > 0.01, and the orthorhombic Eu2TiO5 and monoclinic BaTi2O5 secondary phases were identified. The Raman results show the characteristic peaks of ferroelectric tetragonal BaTiO3 around 716 cm−1 (LO of A1 symmetry), 515 cm−1 (TO of A1 symmetry), and 305 cm−1 (B1). The maximum relative permittivity measured at 1 kHz was recorded to be 6151.8 for the sample with x = 0.0015, and a decrease in the Curie temperature to 105 °C with respect to the undoped sample was observed. The punctual microanalysis for the samples with x = 0.0015, 0.01, and 0.1 reveals grains composed of Ba, Ti, O, Gd, and Eu homogeneously distributed in the BaTiO3 structure. The Ba/Ti ratios for samples with x = 0.0015, 0.01 and 0.1 are 2.86, 2.91, and 0.68, respectively, indicating substitution at the Ti site for samples with x = 0.0015 and 0.01 and a substitution at the Ba site for the sample with x = 0.1.

An Operando Study of the Thermal Reduction of BaTiO3 Crystals: The Nature of the Insulator–Metal Transition of the Surface Layer

The insulator-to-metal transition upon the thermal reduction of perovskites is a well-known yet not completely understood phenomenon. By combining different surface-sensitive analysis techniques, we analyze the electronic transport properties, electronic structure, and chemical composition during the annealing and cooling of high-quality BaTiO3 single crystals under ultra-high-vacuum conditions. Our results reveal that dislocations in the surface layer of the crystal play a decisive role as they serve as easy reduction sites. In this way, conducting filaments evolve and allow for turning a macroscopic crystal into a state of metallic conductivity upon reduction, although only an extremely small amount of oxygen is released. After annealing at high temperatures, a valence change of the Ti ions in the surface layer occurs, which becomes pronounced upon the quenching of the crystal. This shows that the reduction-induced insulator-to-metal transition is a highly dynamic non-equilibrium process in which resegregation effects in the surface layer take place. Upon cooling to the ferroelectric phase, the metallicity can be preserved, creating a “ferroelectric metal.” Through a nanoscale analysis of the local conductivity and piezoelectricity, we submit that this phenomenon is not a bulk effect but originates from the simultaneous existence of dislocation-based metallic filaments and piezoelectrically active areas, which are spatially separated.

Bandgap engineered BaTiO3-based ferroelectric oxides for photovoltaic applications

Ferroelectric oxides have gained research attention in the field of ferroelectric photovoltaics (PV) after the discovery of power conversion efficiency exceeding the Shockley–Queisser limit in BaTiO3 (BTO) crystals. However, advancement in this field is hindered by the wide bandgap (>3 eV) nature of ferroelectric oxides. In this work, a novel lead-free ferroelectric (1 − x)BTO − xBi(Ni2/3Nb1/3)O3 system was proposed and demonstrated to show bandgap reduction without compromising the polarization. Notably, the system displayed a bandgap reduction from 3.1 to 2.4 eV upon varying the composition from x = 0.0 to 0.05. Particularly, the optimal composition x = 0.02 showed enhancement in polarization (Pmax = 16 μC/cm2) and anomalous PV response with an open-circuit voltage of 6 V at 300 K. The origin of the bandgap reduction and polarization retention is explored experimentally by Raman spectroscopic measurements and analyzed theoretically by density functional theory. Our results revealed that the oxygen octahedral distortions and Ni2+ doping favor bandgap lowering, and Bi3+ ions stabilize the ferroelectric polarization. This study provides insight into the origin of bandgap tuning and paves the route for exploring new low-bandgap ferroelectric material with room temperature polarization.

Enhancement of the piezocatalytic properties of BaTiO3 dendrite by annealing modulation

Annealing treatment is believed to improve the catalytic performance of crystal structure and alter the ferroelectric properties of piezoelectric catalysts. However, nano-catalysts easily agglomerate during the calcination process, which lead to a sharp drop in catalytic performance. Herein, we synthesized BaTiO3 dendrite catalyst and modulated its crystal structure and ferroelectric properties via annealing treatment. A diagram of the crystal structure change mechanism at different annealing temperatures was drawn. The results show compared with unannealed BaTiO3 crystals, BaTiO3 crystals exhibit the improved piezocatalytic performance when the annealing temperature is 700–800 ℃, respectively. However, the piezocatalytic activities of the samples decreased with the increase of the annealing temperature over 800 ℃, which is mainly attributed to the random distribution of electric domains in BaTiO3 polycrystalline crystals. This work provides the references for improving the piezocatalyst’s activity via a simple method.

Superelastic ferroelectric micropillar with large hysteresis and super-durability

Hysteresis and durability are generally on the opposite sides of a trade-off for superelastic materials. We herein break this trade-off and report that BaTiO3 (BT) micropillars present size-dependent superelasticity and possess simultaneous large hysteresis and super-durability, sustaining up to 108 superelastic cycles without functional degradation and structural failure. TEM results reveal that the as-fabricated BT pillars are composed of inner BT crystal part and surface BT amorphous layer. In addition, it is found that after high temperature annealing, the BT pillar with cross sectional side length d of 2 µm loses superelasticity. Based on these results, a model was developed to explain the size dependent behavior of BT pillars by considering the constitutive behavior difference of BT crystal and BT in amorphous phase, and their interaction during compressive stress loading and unloading. The super-durability was attributed to the small ferroelastic switching stress, which are much smaller than the dislocation nucleation activation stress and the compression strength of BT pillars, and the moderate mismatch stress between different ferroelectric variants as well as the stress relaxation by the high surface area of the small volume BT pillar. These discoveries enable ferroelectric micropillars many promising applications such as microdampers, and also provide significant insight into developing superelastic materials with enhanced durability.

Influence of Ca doping in structural, electronic, optical and mechanical properties of Ba1−xCaxTiO3 perovskite from first-principles investigation

Nowadays, perovskite materials are well known for electronics and optoelectronics applications. We have investigated a potential candidate for those applications to compare the applicability in optoelectronics, photorefractive and photovoltaic (PV) devices. The systematic comparative study of the structural, electronic, optical, mechanical, and thermodynamic properties of pure BaTiO3 and Ca doped BaTiO3 (Ba1−xCaxTiO3 where x = 0.125, 0.25, 0.375, 0.500, 0.625) perovskite have been carried out using first-principles and density-functional-theory calculations as recently this material was mostly experimented. The measured structural parameters from the geometrically optimized structure of cubic BT ceramic compared with the other theoretical values. A crystal phase transition occurs when doping content x = 0.25. The electronic band structure shows that the nature of the bandgap is changed from indirect bandgap to direct bandgap energy at G-point after doping the Ca atom into BaTiO3 (BT) crystal. Doping of Ca into BT has led to bandstructure modification including conduction band (CB) shifting toward the higher energy level. Electronic properties have been reported to examine the contribution of different orbitals to the CB and to the valance band (VB). This study investigated the modification of optical properties such as absorption, reflectivity, refractive index, extinction coefficient, conductivity, dielectric function and loss function at the energy range from 0 to 30 eV. The prominent absorption peak and optical energy were observed at the UV light energy region. Based on the optical behavior of the material this theoretical research suggests that the doped BT solution is a suitable candidate for photorefractive and optoelectronic devices. Different elastic constants reveal mechanical stability and the existence of the covalent bond of those compounds. Debye temperature increases with doping content. Hence modification of BaTiO3 crystal by Ca atom significantly develop various properties that led it to multifunctional applications.

Anisotropic behavior of mechanical properties for the a- and c-domains in a (001) BaTiO3 single crystal

Barium titanate (BaTiO3) single crystal with a tetragonal phase was characterized by nanoindentation. Elastic and elastic–plastic deformation regimes were obtained. The main objective was the evaluation of the anisotropic behavior related to mechanical properties associated with the cross-section of the ferroelectric a- and c-domains (In-plane and out-of-plane) in (001) configuration domains. This behavior was evaluated along a line perpendicular to the between domains, which demonstrated that the mechanical properties of the BaTiO3 single crystal depend on the distance from due to the effect of the influence of the neighbor domain. A three-dimensional (3D) finite element (FE) model was developed to simulate mechanical effects revealed by the nanoindentations test. The FE simulation demonstrated that there is no simple isotropic mechanical behavior associated with the domain type. Numerical simulations and experiments performed to study ferroelastic switching domains in BaTiO3 crystals revealed the interaction of the 90°-ca domain with the indentation position.

DFT investigation of lattice parameters, spontaneous polarization, and refractive indices of tetragonal BaTiO3 and PbTiO3

In the present work, we study the structural, electrical and optical properties of barium titanate (BaTiO3) and lead titanate (PbTiO3) using the plane wave pseudopotential method and the PBESOL approximation in the framework of density functional theory (DFT). We use the open-source program Quantum Espresso to perform the calculation of optimized lattice parameters, spontaneous polarization and refractive indices of tetragonal BaTiO3 and PbTiO3 single crystals. In the calculations, all types of pseudopotentials were considered: ultrasoft pseudopotentials (USPP), norm-conserving pseudopotentials (NCPP) and projector-augmented wave (PAW). The calculated values of the optimized lattice parameters, the spontaneous polarization and the refractive indices of the tetragonal BaTiO3 and PbTiO3 show a good agreement with the experimental values, especially for the USPP and PAW pseudopotentials.

Microscopic Hamiltonian and chaotic behavior for Barium Titanate nanoparticles revealed by photonic tunneling model

In order to understand the microscopic properties of the ferroelectric nanoparticles, we review concepts of the attractive BaTiO3 crystals where a photon field from its constituent electrons and ions are considered. We present an associated Hamiltonian and extended potential which are the bases of the physical description of the system from certain geometry of the semiquantal space with the specific phonon mode. Furthermore, we formulate the nonlinear dynamics equation of the systems with the famous microscopic Hamiltonian and Heisenberg equation of motion. In addition, we interest ourselves to a system of BaTiO3 crystals and hypothesis leading to order-disorder nature of phase transitions. The latter are linked to the cooperative phenomenon of chains. The numerical simulations reveal that complex behaviors propagate in such system that can be useful for future application of Barium Titanate crystals in modern electronic technologies.

Electronic structure and optical properties of tin (IV) doped transparent perovskite crystal BaTiO3 for efficient visible optoelectronic devices and solar cells

The electronic structure and optical properties of BaSnxTi1−xO3 (BSnT, 0 ≤ x ≤ 0.375) perovskite crystals have been investigated using the newly developed PBEsol and nKTBmBJ approaches within the full potential linear augmented plane wave (FPLAPW) method for potential applications in optoelectronics. The lattice parameter showed a0 a quasi-linear increase with Sn content (with a bowing parameter of ∼ 0.048 Å). The calculated formation energy indicates that BSnT crystals are thermodynamically stable. BSnT exhibits a direct bandgap within the Sn composition range of ∼ 0.03–0.375, which can cover the emission wavelengths within the UV–visible spectrum region of ∼ 375–442 nm. The addition of Sn dopants into BaTiO3 results in a significant increase in the bandgap (by ∼ 496 meV, up to x = 0.375) due to the resonant interaction between O_2p orbitals and Sn_4d states in the upper valence band. Furthermore, the dielectric functions (ε1, ε2), refractive index n, extinction coefficient k, reflectivity R, and absorption coefficient α were determined for the radiation range of 0–12 eV and were found to be in close agreement with experimental spectra. BSnT exhibits good absorption within the ultraviolet spectrum while remaining transparent within the visible spectrum. Sn-doped BaTiO3 holds great promise as a transparent and/or active layer in the development of modern/low-cost solar cells and light-emitting diodes (LEDs) for visible light communication (VLC).

Rejuvenation of giant electrostrain in doped barium titanate single crystals

Engineering materials through the introduction of point defects has resulted in significant advances in semiconductor processing and, more recently, the observation of novel phenomena such as large reconfigurable strains in ferroelectrics as a result of defect dipole complexes. Up to 0.8% strain has been demonstrated in BaTiO3 crystals dilutely doped with iron. However, the defect dipole pinning sites and the corresponding achievable strains are found to degrade as the crystal is electrically cycled as part of the measurement process. The strain degradation rate is dependent on the applied field values but shows an exponential change in materials properties regardless of the electric field. This behavior, plus a change in impedance with number of times cycled, suggests these changes are due to electric field induced oxygen migration—similar to the cause of the resistance degradation effect. Despite this, effective piezoelectric coefficients of over 4700 pm/V were recorded with 1.5 kV/cm fields, one of the largest values for a lead-free piezoelectric material thus far. In addition, the defect dipole-aligned state and the high strains can be repeatably recovered by a subsequent heat treatment step after cycling. Potential paths to exploiting the defect dipole induced effects and large piezoelectric coefficient in these dilutely doped systems are proposed.

Stoichiometric Control and Optical Properties of BaTiO3 Thin Films Grown by Hybrid MBE

AbstractBaTiO3 is a technologically relevant material in the perovskite oxide class with above‐room‐temperature ferroelectricity and a very large electro‐optical coefficient, making it highly suitable for emerging electronic and photonic devices. An easy, robust, straightforward, and scalable growth method is required to synthesize epitaxial BaTiO3 thin films with sufficient control over the film's stoichiometry to achieve reproducible thin film properties. Here the growth of BaTiO3 thin films by hybrid molecular beam epitaxy is reported. A self‐regulated growth window is identified using complementary information obtained from reflection high energy electron diffraction, the intrinsic film lattice parameter, film surface morphology, and scanning transmission electron microscopy. Subsequent optical characterization of the BaTiO3 films by spectroscopic ellipsometry revealed refractive index and extinction coefficient values closely resembling those of stoichiometric bulk BaTiO3 crystals for films grown inside the growth window. Even in the absence of a lattice parameter change of BaTiO3 thin films, degradation of optical properties is observed, accompanied by the appearance of a wide optical absorption peak in the IR spectrum, attributed to optical transitions involving defect states present. Therefore, the optical properties of BaTiO3 can be utilized as a much finer and more straightforward probe to determine the stoichiometry level present in BaTiO3 films.

Structural and optical properties of Sb–BaTiO3 and Y– BaTiO3 doped ceramics prepared by solid-state reaction

Barium titanate ceramics synthesized employing the solid-state method were investigated for their optical properties and phase transition characteristics. X-ray diffraction method and Scanning electronic microscopy were used to reveal a typical perovskite structure. The average grain size of (Sb or Y) doped barium titanate ceramics falls considerably as the concentration of Sb2O3 or Y2O3 increases. XRD investigation revealed the creation of cubic crystal structure. The impact of (Sb, Y) concentration on structure, including the appearance of various tetragonal phases, grain size reduction, and microstructure development, was investigated. The cell parameters of the formed phases decrease from 4.05418 to 3.99385 and from 4.05418 to 3.98605 as the doping rate increases Ba1-x SbxTiO3 and Ba1-xYxTiO3 ceramics respectively,where (x = 0.00,x = 0.05, x = 0.1, x = 0.15 and x = 0.20).Crystallites sizes of Sb-doped BaTiO3 crystals changes from 34.59 to 40.47 nm when dopant concentration is changed from 0.05 to 0.20. For Y doped BaTiO3 crystallite change in size from 28.92 to 29.10 nm. Additionally, assessed were the absorption coefficient (α), extinction coefficient (k), and refractive index (n). When the concentration of Sb3+ or Y3+ ions is increased from 0.05 to 20%, the values of the energy bandgaps for Ba1-x SbxTiO3 and Ba1-xYxTiO3 increase from 3.11 to 3.17 eV and 3.07–3.14 eV, respectively. It is found that the refractive index(n) rises as wavelength rises. It has been shown that the absorption coefficient (α) increases when photon energy increases. It is found that the extinction coefficient (k) decreases with wavelength. The extinction coefficient (k) and the absorption coefficient (α) are both observed to decrease with increasing concentration for all compositions.

Four modifications of the Jahn-Teller effects. The problem of observables: spin-orbit interaction, tunneling splitting, and orientational polarization of solids.

In a semi-review paper, we first show that Landau's fundamental idea of the origin of spontaneous symmetry breaking (SSB) in atomic matter due to electronic degeneracy, termed the Jahn-Teller effect (JTE) and further developed into the pseudo-JTE (PJTE), was appended recently with two more modifications, the hidden JTE (h-JTE) and hidden PJTE (h-PJTE). All four versions of JTEs are defined in the adiabatic approximation by their adiabatic potential energy surfaces (APES), which possess a common feature - the lack of a minimum in the high-symmetry configuration, thus confirming (and extending) the Landau idea of SSB. However, although serving as a qualitative indication of the SSB and consequent possible (virtual) properties of the system, the APES by themselves are not experimentally observable directly, and this important feature of JTEs is often ignored. Taking spin-orbit interaction as an example, we show that just perturbation of the APES does not reveal its observable reduction by the JTE, which emerges only after solving the Schrödinger equation with this APES. Following the multi-minimum nature of the latter, this leads to tunneling splitting of the vibrational states in the minima wells or over-the-barrier (hindered) rotations, resulting in novel properties, one of them being the reduction of the spin-orbit coupling. We demonstrate the methodology of solving such problems by using the example of electric field polarization of the BaTiO3 crystal, which leads to a novel effect: orientational polarization of solids.

Effect of yttrium (Y) substitution on the structure and dielectric properties of BaTiO3

As the rate of application of multilayer ceramic capacitors (MLCCs) in small electronic devices increases, the use of the raw material barium titanate (BaTiO3) with a small particle size and excellent dielectric properties becomes needed. Due to the size effect, small-sized BaTiO3 generally has a cubic phase structure with a low dielectric constant, which limits its use in MLCCs. We report the preparation of small cubic phase Y-doped BaTiO3 (BYT) nanoparticles by a hydrothermal method and the preparation of highly dielectric tetragonal phase BYT ceramics based on this method. XRD and Raman analysis showed that the BYT nanoparticles are in substable cubic phases. The particle size of the BYT nanoparticles, measured by TEM, XRD, and BET, was approximately 35 nm. The dielectric properties of the BYT ceramics were tested by an impedance analyzer, and the dielectric constant of the BYT ceramics was 7547 when the Y3+ doping amount was 0.5 mol%. In addition, the substitution mechanism of Y3+ doping in BaTiO3 crystals was proposed from XPS and EPR analysis. The results demonstrate for the first time that the 50 nm cubic phase BaTiO3 powder can meet the needs of next-generation high-capacity MLCCs. This work provides a reference for small cubic phase BaTiO3 as a dielectric material for high-capacity MLCCs.