High Permittivity Research Articles

Insights into a Defective Potassium Sulfido Cobaltate: Giant Magnetic Exchange Bias, Ionic Conductivity, and Electrical Permittivity

AbstractThe novel potassium sulfido cobaltate, K2[Co3S4] is introduced, with 25% vacancies of the cobalt positions within a layered anionic sublattice. The impedance and dielectric investigations indicate a remarkable ionic conductivity of 21.4 mS cm−1 at room temperature, which is in the range of highest ever reported values for potassium‐ions, as well as a high electrical permittivity of 2650 at 1 kHz, respectively. Magnetometry results indicate an antiferromagnetic structure with giant intrinsic exchange bias fields of 0.432 and 0.161 T at 3 and 20 K respectively, potentially induced by a combination of the interfacial effect of combined magnetic anionic and nonmagnetic cationic sublattices, as well as partial spin canting. The stability of the exchange bias behavior is confirmed by a training effect of less than 18% upon 10 hysteresis cycles. The semiconductivity of the material is determined, both experimentally and theoretically, with a bandgap energy of 1.68 eV. The findings render this material as a promising candidate for both, active electrode material in potassium‐ion batteries, and for spintronic applications.

Electrically induced and controlled piezoelectricity

The quasi-linear electromechanical effect, which resembles piezoelectricity, can be induced by strong electric field in any solid dielectric. This effect is defined as linearized electrostriction, which is observed in the biasing electric field and is proportional to the square of the dielectric permittivity. The present work analyses physical mechanisms of the occurrence of such an effect in the piezoelectrics, the paraelectrics and the relaxor ferroelectrics, taking into account the inertia of electromechanical response. Hysteresis-less electromechanical control of deformation is used in actuators and tuneable microwave devices. The efficiency of the induced piezoelectricity is maximal in dielectrics with high permittivity, while the efficiency is ensured by mechanisms of low-inertia quasi-elastic polarization. To assess the maximum performance of piezoelectric actuators made of different materials, the method of dielectric spectroscopy is used.

Doping-Induced piezoelectricity in Ba2Nb2-xFexO6-δ double perovskite oxides for efficient hydrogen peroxide production via piezocatalysis in pure water

Piezocatalysis has emerged as a sustainable alternative for hydrogen peroxide production. However, the current development of efficient piezocatalysts is predominantly focusing on those conventional piezoelectric ceramic oxides with high permittivity and limited catalytic activities. Therefore, innovative approaches to develop novel piezocatalysts in particular from these outstanding paraelectric semiconductors are highly required. In this work, by employing a feasible doping strategy, robust piezoelectric property is created on the Ba2Nb2-xFexO6-δ double perovskite oxides, typically characterized by a stable paraelectric cubic structure. Optimum Fe doping not only intensifies the double perovskite phase but also inspires a phase transition from a centrosymmetric cubic to a piezoelectric tetragonal phase, thereby achieving desirable piezoelectricity and enabling a series of favorable physical properties including redox activity, active sites of anion defects, reduced bandgap, and increased free charge density. All these are important factors to enhance piezocatalytic activity. As a result, Ba2NbFeO6-δ achieved by the optimum Fe doping demonstrated exceptional piezocatalytic H2O2 yield of 512 and 690 µmol g-1 h−1 under atmosphere and oxygen-purging conditions, respectively, without the presence of any sacrificial agents. Mechanistic investigations reveal that both water oxidation and oxygen reduction involve in the H2O2 production, wherein piezopotential plays a critical role not only in facilitating the charge carrier separation and transportation but also in modulating the band structure to enhance the catalyst redox capacity. This study offers a feasible and universal strategy for the design of novel piezocatalysts, expanding the windows for catalyst selection for piezocatalysis.

Sandwiched polymers modified with BaTiO3@polyfluorosiloxane for enhanced energy density

AbstractPolymer dielectrics have gained significant usage in electrical engineering due to their unique merits, such as good flexibility, easy processing, and low cost. However, it is a huge challenge that polymer dielectrics maintain high breakdown strength meanwhile high permittivity for enhanced energy density. Here, sandwiched polymer films are constructed for enhanced energy density. Increased permittivity has been achieved via blending BaTiO3@polyfluorosiloxane with a polymer as the top and bottom layer. Furthermore, the neat polymer as the middle layer is without critically sacrificing breakdown strength. The energy storage density increases from 7.8 J/cm3 of the neat polymer to 10.41 J/cm3 of the sandwich structure at 460 MV/m. This research offers a feasible route for fabricating capacitive films with enhanced energy density.

Crystal Structure and Spectroscopic Characterization of a New Hybrid Compound, (C12H17N2)2[CdBr4], for Energy Storage Applications.

Organic-inorganic hybrid materials have recently found a vast variety of applications in the fields of energy storage and microelectronics due to their outstanding electric and dielectric characteristics, including high dielectric constant, low conductivity, and low dielectric loss. However, despite the promising properties of these materials, there remains a need to explore novel compounds with improved performance for practical applications. In this research paper, the focus is on addressing this scientific challenge by synthesizing and characterizing the new-centrosymmetric (C12H17N2)2[CdBr4] crystal. This compound offers potential advancements in energy storage technologies and microelectronics due to its unique structural and electronic properties. The chemical mentioned above crystallizes in the monoclinic system, and its protonated amine (C12H17N2)+ and isolated anion [CdBr4]2- are bound by C-H···π and N-H···Br hydrogen bonds to form its zero-dimensional structure. Through optical absorption analysis, the semiconductor nature of the material is verified, showcasing a band gap of around 2.9 eV. Furthermore, an in-depth examination of Nyquist plots reveals the material's electrical characteristics' sensitivity to frequency and temperature variations. By applying Jonscher's power law to analyze ac conductivity plots, it is observed that the variation in the exponent "s" accurately characterizes the conduction mechanism, aligning with CBH models. The compound exhibits low dielectric loss values and a high permittivity value (ε ∼ 105), making it a promising candidate for energy storage applications. By managing the scientific challenge of improving material performance for energy storage and microelectronics, this research contributes to advancing the field and opens avenues for further exploration and application of organic-inorganic hybrid materials.

Analytical Modeling of Wave Absorption Performance in Gradient Graphene/Polymer Nanocomposites.

Due to the low impedance matching caused by the high dielectric permittivity of graphene, the strong absorption of electromagnetic waves by graphene/polymer nanocomposites is challenging. In this paper, an analytical model for microwave absorption based on Maxwell's equation and the effective medium theory, considering the interface effect, was constructed to explore the effect of the gradient distribution of graphene in the polymer matrix on its microwave absorption performance. The outcome indicated that the impedance of the composites matched well with the air, and its attenuation ability for electromagnetic waves was obviously improved as the graphene concentration was distributed in a gradient form. For instance, when the thickness of the material is 10 mm, based on the optimal concentration of the homogeneous composites being 0.7 wt%, the graphene concentration range of the gradient composites is set to 0.7-0.9 wt% and distributed in three gradient forms of linear, parabolic, and 0.5 power. The results show that the microwave absorption performance is significantly improved compared with the homogeneous composites. Among them, the effective bandwidth on the 0.5 power distribution is 5.2 GHz, 0.5 GHz higher than that of the homogeneous composites. The minimum reflection loss (RL) is as low as -54.7 dB, which is 26.26 dB lower than that of the homogeneous composites. This paper contributes to the design and application of gradient absorbing structures.

Core-shell engineering of graphite nanosheets reinforced PVDF toward synchronously enhanced dielectric properties and thermal conductivity

Polymer composites integrating high dielectric permittivity (ε′) but low loss, large breakdown strength (Eb) and thermal conductivity (TC), have attracted widespread attention in electronic devices and power systems. To simultaneously achieve these properties in graphite nanosheet (GNS)/poly(vinylidene fluoride, PVDF), the GNS were first encapsulated by a layer of aluminum oxide (Al2O3), and then incorporated into PVDF, and the resulting PVDF nanocomposites’ dielectric properties and TC were explored in terms of the Al2O3 shell thickness and filler loading. The insulating Al2O3 shell serves as a barrier layer for the formation of leakage current and long-distance electron migration thus resulting in much lower dielectric loss and conductivity of the GNS@Al2O3/PVDF. It effectively mitigates the dielectric mismatch between the filler and host matrix, further introduces more traps that can capture charge carriers, and increases the barrier height for electron detrapping subsequently preventing the growth of electric trees and elevating the Eb. Moreover, the Al2O3 interlayer alleviates both the phonon density state and phonon impedance mismatches between the filler and matrix and facilitates the interfacial phonon transport thus leading to improved TC. The dielectric parameters and TC of the GNS@Al2O3/PVDF can be simultaneously modulated by optimizing the Al2O3′s thickness. This work offers an effective approach for designing and fabricating the polymeric nanodielectrics concurrently integrating high ε′ but low loss, enhanced Eb, and TC for prospective applications in power equipment and microelectronic devices.

Study of dielectric and interfacial properties of functional biopolymer-based electrolyte with enhanced conductivity for energy storage application

This study investigates sodium (Na+) ion-conductive biopolymer blend electrolytes with glycerol as a plasticizer for energy storage. Through FTIR, impedance spectroscopy, transference number measurement (TNM), and linear sweep voltammetry (LSV), we identify an optimal film for electric double layer capacitor (EDLC) application. Glycerol induces notable changes in polymer-salt interaction, evidenced by FTIR band shifts reflecting increased free ions. Impedance measurements show reduced bulk resistance with optimal plasticizer content, emphasizing the system's suitability for energy storage. The system exhibits high real permittivity relative to imaginary at lower frequencies, attributing to glycerol's dielectric constant and small bulk resistance. Loss tangent (tanδ) and Argand plots reveal the dominant ion conduction mechanism. Electrochemical assessments support the suitability of the film for EDLC applications, featuring a favorable transference number (tion = 0.94) and high decomposition voltage (2.6V). Cyclic voltammetry (CV) curves demonstrate effective EDLC device design with significant capacitance adaptability across varying scan rates (5.946 F/g to 24.074 F/g).

Assessing mechanical and stray magnetic field energy harvesting capabilities in lead-free PVDF/BCT-BZT composites integrated with metglas

The exploration of energy harvesting encompasses a wide array of sources, with a specific focus on recovering mechanical and magnetic energy from overlooked outlets, driving current research endeavours. In this study, we developed highly flexible Magneto-Mechano-Electric (MME) harvesters by combining poly(vinylidene fluoride) (PVDF)/barium calcium zirconium titanate (BCT-BZT) composite films with metglas. The flexible piezoelectric polymer-ceramic composite films were fabricated using a solvent casting technique. The high piezoelectric BCT-BZT fillers were synthesized through a sol-gel reaction route. A thorough analysis was carried out on these composites to evaluate their structural, functional, microstructural, and dielectric properties. The composite film loaded with 20 wt% BCT-BZT filler achieved a 78 % β-phase with a significant enhancement in the dielectric properties, resulting in a high permittivity∼40 and low dielectric loss. Employing these films, we engineered nanogenerators capable of converting mechanical energy into electrical energy, yielding an output voltage of 11 V. Thereafter, to harvest mechanical and stray magnetic fields, we developed a MME generator comprising a magnetic Metglas layer and PVDF-BCT-BZT composite and achieved an output voltage of 3.3 V with a power density of 85 μW/m2 when subjected to an AC magnetic field of 5 Oe. Furthermore, the MME generator has demonstrated the ability to charge various capacitors showcasing its potential for usage in self-powered, non-contact, and implantable devices.

Versatile Landscape of Low-k Polyimide: Theories, Synthesis, Synergistic Properties, and Industrial Integration.

The development of microelectronics and large-scale intelligence nowadays promotes the integration, miniaturization, and multifunctionality of electronic and devices but also leads to the increment of signal transmission delays, crosstalk, and energy consumption. The exploitation of materials with low permittivity (low-k) is crucial for realizing innovations in microelectronics. However, due to the high permittivity of conventional interlayer dielectric material (k ∼ 4.0), it is difficult to meet the demands of current microelectronic technology development (k < 3.0). Organic dielectric materials have attracted much attention because of their relatively low permittivity owing to their low material density and low single bond polarization. Polyimide (PI) exhibits better application potential based on its well permittivity tunability (k = 1.1-3.2), high thermal stability (>500 °C), and mechanical property (modulus of elasticity up to 3.0-4.0 GPa). In this review, based on the synergistic relationship of dielectric parameters of materials, the development of nearly 20 years on low-k PI is thoroughly summarized. Moreover, process strategies for modifying low-k PI at the molecular level, multiphase recombination, and interface engineering are discussed exhaustively. The industrial application, technological challenges, and future development of low-k PI are also analyzed, which will provide meaningful guidance for the design and practical application of multifunctional low-k materials.

High Performance Indium-Tin-Oxide Schottky Diodes for Terahertz Band Operation.

Schottky diode, capable of ultrahigh frequency operation, plays a critical role in modern communication systems. To develop cost-effective and widely applicable high-speed diodes, researchers have delved into thin-film semiconductors. However, a performance gap persists between thin-film diodes and conventional bulk semiconductor-based ones. Featuring high mobility and low permittivity, indium-tin-oxide has emerged to bridge this gap. Nevertheless, due to its high carrier concentration, indium-tin-oxide has predominantly been utilized as electrode rather than semiconductor. In this study, a remarkable quantum confinement induced dedoping phenomenon was discovered during the aggressive indium-tin-oxide thickness downscaling. By leveraging such a feature to change indium-tin-oxide from metal-like into semiconductor-like, in conjunction with a novel heterogeneous lateral design facilitated by an innovative digital etch, we demonstrated an indium-tin-oxide Schottky diode with a cutoff frequency reaching terahertz band. By pushing the boundaries of thin-film Schottky diodes, our research offers a potential enabler for future fifth-generation/sixth-generation networks, empowering diverse applications.

Ionic Liquid Enabled Transparent Heterogeneous Elastomers for Soft Electronics

AbstractDielectric elastomer (DE), as an electrically active soft material, has enabled stretchable electronics, electronic skins, artificial muscles, biomimetic soft robots, and non‐magnetic motors. High permittivity is urgently desired for increasing the sensitivity of DE sensors and lowering the driving voltage of DE actuators. However, existing efforts for significantly enhanced permittivity is usually achieved at the expense of transparency of the DE by compositing external fillers, which limits the applications in optoelectronics, such as displays, touch screens, artificial eyes, etc. Here, by utilizing of transparent functional filler, ionic liquid micro‐droplet, and precise matching the refractive index with polydimethylsiloxane (PDMS) elastomer matrix, heterogeneous composites with high transparency and high permittivity are obtained simultaneously. The composites are transparent in the visible range (transmittance, 80%–95%). The permittivity reaches up to 22, which is more than seven times higher than the original value of the elastomer matrix. Moreover, the arbitrary deformability of ionic liquid filler endows the composites with better stretchability (300%) and much lower elastic modulus (0.5 MPa, about a quarter the value of PDMS), which is beneficial for soft electronics. Based on the as‐prepared high‐performance composites, high sensitivity and transparent soft sensors and touch panels have been realized, as well as wireless transmission of sensing signals.

Innovative and Cost-Effective Fabrication Technique for Dielectric Composite Material

In this paper, the fabrication process of epoxy resin and nanocomposite barium titanate using a cost-effective apparatus is presented along with measurements of complex permittivity. The material is prepared by mixing epoxy resin and barium titanate powder which has high permittivity. Measurement of complex permittivity of materials is performed using a waveguide technique in the G-band with a frequency between 4 and 6 GHz. The results are then compared with the previous works that use advanced and precision instrumentation. The results indicate that the material’s permittivity, determined using our proposed technique, performs admirably. Specifically, at a frequency of 5 GHz, the permittivity is 7.32 with a loss tangent of 0.025 for a filler concentration of 20%. These values not only meet but also closely match those obtained with high-end equipment. Therefore, the proposed technique could be a good potential as an alternative technique for dielectric material preparation which is suitable to be used as a substrate antenna.

Lead‐Free High Permittivity Quasi‐Linear Dielectrics for Giant Energy Storage Multilayer Ceramic Capacitors with Broad Temperature Stability

AbstractElectrostatic energy storage capacitors are essential passive components for power electronics and prioritize dielectric ceramics over polymer counterparts due to their potential to operate more reliably at &gt; 100 ˚C. Most work has focused on non‐linear dielectrics compositions in which polarization (P)/electric displacement (D) and maximum field (Emax) are optimized to give values of energy density, 6≤U≤21 J cm−3. In each case however, either saturation (dP/dE = 0, AFE) or “partial” saturation (dP/dE → 0, RFE) of P limits the value of U which can be achieved before breakdown. It is proposed that U can be further improved with respect to relaxors (RFEs) and anti‐ferroelectrics (AFEs) by designing high permittivity quasi‐linear dielectric (QLD) behaviour in which dP/dE remains constant up to ultrahigh Emax. QLD multilayer capacitor prototypes with dielectric layers composed of 0.88NaNb0.9Ta0.1O3‐0.10SrTiO3‐0.02La(Mg1/2Ti1/2)O3 deliver room temperature U ≈ 43.5 J cm−3, supporting an extremely‐large Emax ≈ 280 MV m−1, both of which exceed current state‐of‐art by a factor of two for devices based on powder, tape‐cast technology. Importantly QLD capacitors exhibit scant variation in U (≈15 J cm−3) up to &gt; 200 ˚C and robust resistance to cyclic degradation, offering a promising new approach for the development of sustainable technology.

Suppressed conductive loss of flower-like NiCo2O4-wrapped flaky FeSiAl for excellent low-frequency microwave absorption

Flaky FeSiAl is a high potential absorbent for low-frequency microwave applications. However, impedance mismatching due to its excessively high complex permittivity presents a challenge. Herein, inspired by the surface modification strategy, flaky FeSiAl wrapped with flower-like NiCo2O4 (NiCo2O4@flaky FeSiAl) was developed via a hydrothermal method. The introduction of a surface NiCo2O4 insulating layer was expected to reduce the complex permittivity and increase the high complex permeability in the NiCo2O4@flaky FeSiAl composite. Subsequently, an excellent low-frequency microwave absorption performance was achieved. The designed NiCo2O4@flaky FeSiAl displayed a robust minimum refection loss (RL min) of −33.41 dB at 6.32 GHz and increased the effective absorption bandwidth (EAB, RL < −10 dB) to 4.08 GHz when the matching thickness was 1.6 mm. The enhanced low-frequency microwave absorption performance was mainly attributed to the improvement in impedance matching, which originated from the collaborative regulation of electromagnetic parameters. This study provides a promising approach for designing flaky FeSiAl-based composites and high-performance low-frequency microwave absorbents.

Flexocatalysis of nanoscale titanium dioxide

Piezocatalysis emerges as a distinctive approach for producing free radicals to drive catalysis. However, the piezoelectric effect exclusively manifests in non-centrosymmetric materials, which largely constraints the use of materials with centrosymmetry. To address this challenge, the concept of flexocatalysis is explored to bypass the structural constraints of materials by harnessing strain-gradient-induced polarization, taking advantage of universality of flexoelectricity. As an exemplar of flexocatalysis, centrosymmetric rutile titanium dioxide (TiO2) nano particles are selected due to its high permittivity, non-toxicity, biocompatibility, and wide-ranging utility. The effectiveness of flexocatalysis in generating free radicals (·H, and ·OH) is validated through hydrogen generation (∼2380 μmolg−1h−1 in pure water) and Rhodamine B dye degradation. Additionally, the size effect on flexoelectricity is examined both experimentally and theoretically, revealing that materials at nanoscale exhibit greatly enhanced flexoelectricity that can rival the traditional piezoelectricity. This work endows TiO2 with novel capabilities and broadens material’s selection in mechanochemistry applications.

Superscattering of electromagnetic waves from subwavelength dielectric structures

Superscattering, corresponding to the scattering cross section of a scatterer being significantly larger than its single-channel limit, has attracted increasing attention due to its huge potential for practical applications. The realization of superscattering relies on the overlapping of multiple resonance modes in a scatterer. Accordingly, superscattering phenomena have been observed primarily in alternating plasmonic/dielectric layered structures which support surface plasmons. However, such systems suffer from high Ohmic loss due to the excitation of surface plasmons, hindering broader application of the plasmonic/dielectric hybrid systems. On the other hand, subwavelength structures based on high permittivity dielectric materials (such as ferroelectric ceramics) offer expansive opportunities to realize electric and magnetic resonances at microwave and THz frequencies. Here, based on optimization methods involving mode analysis, we numerically demonstrate superscattering from individual multilayered dielectric cylinders. The maximum scattering cross section achieved is determined by the collective contributions from several resonance modes excited in a complex cylinder. Our results reveal that a combination of mode analysis and a custom optimization method can enable efficient designs of complex dielectric structures exhibiting exotic scattering responses.

Enhanced Magnetic and Dielectric Properties of YFeO3 Ceramics via Formation of Solid‐Solution with Sr2Bi4Ti5O18 and ZnSnO3 Oxides

In the present investigation, magnetic and dielectric properties of solid‐solution formed between the YFeO3 with the similar crystal structure of other oxide materials are focused on. Orthorhombic crystal structure of YFeO3 (YFO), Sr2Bi4Ti5O18 (SBT), and ZnSnO3 (ZS) nanomaterials are considered to prepare the solid solutions at 1150 °C/3 h. YFO and solid solutions exhibit the orthorhombic crystal structure, which is conformed through Rietveld refinement using X‐Ray powder diffraction pattern. The decreased average grain size is observed for the solid solution (3.0 μm for YFO and ZS and 2.6 μm for YFO and SBT) when compared to YFO (3.4 μm) through scanning electron microscopy. Oxidation state of each atom/ion/element present in the YFO and solid solutions are conformed through X‐Ray photoelectron spectroscopy studies. The solid solution formed between the YFO and SBT exhibits high magnetization value (2.92 emu g−1) and high coercive filed (67.5 Oe) when compared to solid solution formed between the YFO and ZS (magnetization value = 2.48 emu g−1, and coercive filed = 46.4 Oe) and YFO (magnetization value = 1.91 emu g−1, and coercive filed = 61.8 Oe). High dielectric permittivity (εr), low dielectric loss (tan δ), and low conductivity are observed for the solid solution formed between the YFO and SBT, when compared to other materials in this study.

Optimization of dielectric response in BiFeO3–CoFe2O4 nanocomposites for high frequency energy storage devices

The rapid development of smart and sophisticated miniaturized electronic devices put a high demand for high permittivity material. In the current report, we analyze structural, morphological, and dielectric response of spinel-perovskite composites consisting of CoFe2O4 (CFO) as the spinel phase and BiFeO3 (BFO) as the perovskites phase. Here pristine BFO and CFO are fabricated using Sol—Gel auto-combustion route and their composites with a recipe (1-x) BiFeO3 - (x) CoFe2O4 (x = 0.0, 0.1, 0.2 and 0.3) using solid-state reaction technique. Structural investigation identifies presence of rhombohedral perovskite phase of BFO and cubic spinel phase of CFO and thus guarantees the formation of the composite. The crystallite size increases from 16 to 36 nm for BFO and 39.5–54 nm for CFO. The distribution of well-shaped particles with a reduction in grain size in range of 50–400 nm is witnessed in morphological analysis with the increment of CFO contents in composites. Elemental purity and the presence of various elements according to their stoichiometric ratio are witnessed during elemental investigation. A detailed analysis of the dielectric permittivity, electric modulus, and impedance of these compositions is carried out to investigate their suitability for electronic and energy storage devices. The nanocomposites under study exhibit a dielectric constant of 1126 at 100 Hz for x = 0.3, which decreases to 102 at 1 MHz. Concurrently, the tangent loss for x = 0.3 is observed to be 3.37 at 100 Hz, decreasing to 0.31 at 1 MHz. However, a decrease in dielectric loss and increase in impedance is noticed when the concentration of CFO in BFO nano-composite is increased which reflects the reduction in power losses and better control in electronic conductivity and thus highlights the role of these compositions for advanced energy storage electronic devices.

Tungsten-bronze-type BaNd2Ti4O12 ceramics with high permittivity and ultra-low dielectric loss under low frequency

High dielectric constant and ultra-low dielectric loss are important for electronic device applications of dielectrics. In this work, the novel ceramic BaNd2Ti4O12, synthesized via solid-state reaction, exhibits remarkable dielectric stability, with excellent dielectric properties (ε′ = 117 and tanδ = 6.27 × 10−4, at 1 kHz) and high dielectric strength (Eb = 260 kV/cm). By exploring its polarization behavior and loss mechanisms at low frequencies for the first time, we found that the sustained high dielectric constant is attributed to the synergy of defect dipole polarization and interface polarization, while the observed exponential increase of dielectric loss is primarily caused by the conduction loss, with a minor contribution from the anelastic relaxation loss. In the low-temperature range of 50∼350 °C, the relaxation behavior is governed by the aggregation and subsequent thermal ionization of the oxygen vacancies, whereas at temperatures above 350 °C, it is predominated by the long-range motion of the doubly ionized oxygen vacancies. These findings provide valuable insights for the potential electronic device applications of BaNd2Ti4O12.