Improved dielectric and nonlinear properties of CaCu3Ti4O12 ceramics with Cu-rich phase at grain boundary layers

The formation and compositions of grain boundary layers are very important factors to improve the electrical properties of CaCu₃Ti₄O₁₂ (CCTO) ceramics. In present work, the dielectric and nonlinear properties of the CCTO ceramics are enhanced by controlling the Cu-rich phase degree at grain boundary layers. The dense CCTO ceramics were prepared successfully through mixing the nanometer and micrometer powders and using the cold isostatic pressing process. The average grain size of these CCTO ceramics is about 30.71(±11.76) ∼ 62.01(±32.16) μm, and their grain microstructures show the Cu-rich phases at grain boundary layers. The CCTO ceramics with the mass ratios of nanometer and micrometer powders 7:3 display a giant dielectric constant of 5.4 × 10⁴, low dielectric loss of 0.048 at 10³ Hz, enhanced nonlinear coefficients of 11.12, as well as the noteworthy breakdown field of 4466.17 V/cm. The complex impedance spectroscopy results indicate that the giant dielectric behavior is due to the electrically heterogeneous grain/grain boundary characteristics from internal barrier layer capacitance (IBLC) model. The lower dielectric loss and the higher breakdown field are attributed to the high resistance grain boundary layers with the Cu-rich phase. The improved nonlinear properties are related to the increased Schottky barrier height at grain boundary. This work may provide a potential way to design the CCTO ceramics with excellent electrical properties from the viewpoint of controlling the response of the Cu-rich phase grain boundary.     

Electrical Conductivities of (CeO2)1−x(Y2O3)x Thin Films

Electrical properties of CeO₂ thin films of different Y₂O₃ dopant concentration as prepared earlier were studied using impedance spectroscopy. The ionic conductivities of the films were found to be dominated by grain boundaries of high conductivity as compared with that of the bulk ceramic of the same dopant concentration sintered at 1500°C. The film grain-boundary conductivities were investigated with regard to grain size, grain-boundary impurity segregation, space charge at grain boundaries, and grain-boundary microstructures. Because of the large grain boundary and surface area in thin films, the impurity concentration is insufficient to form a continuous highly resistive Si-rich glassy phase at grain boundaries, such that the resistivity associated with space-charge layers becomes important. The grain-boundary resistance may originate from oxygen-vacancy-trapping near grain boundaries from space-charge layers. High-resolution transmission electron microscopy coupled with a trans-boundary profile of electron energy loss spectroscopy gives strong credence to the space-charged layers. Since the conductivities of the films were observed to be independent of crystallographic texture, the interface misorientation contribution to the grain-boundary resistance is considered to be negligible with respect to those of the impurity layer and space-charge layers.     

Effects of sintering temperature on the internal barrier layer capacitor (IBLC) structure in CaCu3Ti4O12 (CCTO) ceramics

The formation of the internal barrier layer capacitor (IBLC) structure in CaCu₃Ti₄O₁₂ (CCTO) ceramics was found to be facilitated by the ceramic heat treatment. Electrically insulating grain boundary (GB) and semi-conducting grain interior areas were characterized by impedance spectroscopy to monitor the evolution of the IBLC structure with increasing sintering temperature T_S (975–1100 °C). The intrinsic bulk and GB permittivity increased by factors of ≈2 and 300, respectively and the bulk resistivity decreased by a factor of ≈10³. These trends were accompanied by increased Cu segregation from the CCTO ceramics as detected by scanning electron microscopy and quantitative energy dispersive analysis of X-rays. The chemical changes due to possible Cu-loss in CCTO ceramics with increasing T_S are small and beyond the detection limits of X-ray absorption spectroscopy near Cu and Ti K-edges and Raman Spectroscopy.     

Interfacial Segregation in Perovskites: III, Microstructure and Electrical Properties

A model is proposed to relate segregation of dopants with the development of fine ceramic microstructures and electrical properties in polycrystalline donor-doped BaTiO₃. As the average dopant concentration is increased, the dopant concentration at the grain boundary increases compared with the bulk. This has two important effects: (1) dopant incorporation at the grain boundary shifts from electronic to vacancy compensation and the formation of high-resistive layers, and (2) grain-boundary mobility is impeded and grain growth retarded with increased dopant additions. Thus, for high dopant concentrations, donor-doped BaTiO₃ becomes insulating. The model discusses in detail the nonequilibrium heterogeneous defect chemistry as a function of thermal-processing and accounts for barrier layer phenomena.     

Determination of Inversion Temperature of Sb2O3-Doped BaTiO3 Positive Temperature Coefficient of Resistivity (PTCR) Ceramics by the Finite Difference Method

The effect of the cooling rate on the PTCR (positive temperature coefficient of resistivity) characteristics of 0.1 mol% Sb₂O₃-doped BaTiO₃ ceramics has been investigated. Resistances both below and above the Curie temperature were increased by slow cooling, which indicated that the resistive layer width at the grain boundary increased as the cooling rate decreased. Concentration profiles of the Ba vacancies as a function of distance from the grain boundary have been simulated by the finite difference method. The inversion temperature of the 0.1 mol% Sb₂O₃-doped BaTiO₃ system was determined to be 1160°C from the measured electrical properties and computed concentration profiles.     

Grain Boundary Defect Chemistry of Acceptor-Doped Titanates: Space Charge Layer Width

The grain boundary space charge depletion layers in acceptor-doped SrTiO₃ and BaTiO₃ ceramics were investigated by impedance spectroscopy in the time and frequency domain. Based on the layer width and its dependence on the acceptor concentration, the temperature, and the oxygen partial pressure during annealing, a suggestion for a refined Schottky model is proposed. The local distribution of the donor-type grain boundary states causing the depletion layer and the resulting band bending are discussed.     

Reactive FAST/SPS sintering of strontium titanate as a tool for grain boundary engineering

A high-pressure FAST/Spark Plasma Sintering method was used to produce dense SrTiO₃ ceramics at temperatures of 1050 °C, more than 250 °C below typical sintering temperatures. Combining SPS with solid-state reactive sintering further improves densification. The process resulted in fine-grained microstructures with grain sizes of ∼300 nm. STEM-EDS was utilized for analyzing cationic segregation at grain boundaries, revealing no cationic segregation at the GBs after SPS. Electrochemical impedance spectroscopy indicates the presence of a space charge layer. Space charge thicknesses were calculated according to the plate capacitor equation and the Mott-Schottky model. They fit the expected size range, yet the corresponding space charge potentials are lower than typical values of conventionally processed SrTiO₃. The low space charge potential was associated to low cationic GB segregation after SPS and likely results in better grain boundary conductivity. The findings offer a path to tailor grain boundary segregation and conductivity in perovskite ceramics.     

Microcontact Impedance Spectroscopy at Single Grain Boundaries in Fe-Doped SrTiO3 Polycrystals

Microcontacts on adjacent grains of polycrystalline Fe-doped SrTiO₃ samples have been used to locally investigate the properties of individual grain boundaries. Impedance spectroscopy was employed to separate bulk and grain boundary impedances. Experiments at about 30 different grain boundaries permit far-reaching conclusions on the distribution of grain boundary resistances, capacitances, and peak frequencies measured between adjacent grains. The rather narrow distribution of the grain boundary peak frequencies indicates a narrow distribution of grain boundary resistivities. All features (e.g., nonlinear current–voltage characteristics, grain boundary thickness, temperature dependence) are in accordance with the assumption of space charge depletion layers (double Schottky barriers) as the origin of the enhanced grain boundary resistivity. The average barrier height measured was about 630 mV. For comparison conventional (macroscopic) impedance measurements on a polycrystal were also performed and a brick layer model was used to extract effective properties. The reasonable agreement between these effective parameters and the average of the locally obtained parameters demonstrates that, in this case, a brick layer analysis of conventional impedance experiments yields satisfying estimates of the grain boundary properties.     

The impedance of ceramics with highly resistive grain boundaries: validity and limits of the brick layer model

Impedance spectroscopy is an important tool to investigate the electrical properties of grain boundaries. For the analysis of the impedance spectra cubic grains, laterally homogeneous grain boundaries and identical properties of all grain boundaries are usually assumed (brick layer model). However, in real ceramics these assumptions are generally violated. Using the finite element method we calculated the impedance of several polycrystals exhibiting highly resistive grain boundaries with microstructures and grain boundary properties deviating from the simple brick layer model. Detours around highly resistive regions (e.g. due to high grain boundary density or enhanced grain boundary resistivity) can play an important role and lead to grain-boundary semicircles depending on bulk properties and even to additional semicircles. Conditions are discussed within which the brick layer model allows for a reasonable evaluation of the spectra.     

Effect of PO2 on Bulk and Grain Boundary Resistance of n-Type BaTiO3 at Cryogenic Temperatures

Complex impedance analysis at cryogenic temperatures has revealed that the bulk and grain boundary properties of BaTiO₃ polycrystals are very sensitive to the oxygen partial pressure during sintering. Polycrystals sintered at P _O2 as low as 10⁻¹⁵ atm were already electrically heterogeneous. The activation energy of the bulk conductivity in the rhombohedral phase was found to be close to that of the reduced undoped single crystal (i.e., 0.093 eV). The activation energy of the grain boundary conductivity increases with the temperature of the postsinter oxidation treatment from 0.064 to 0.113 eV. Analysis of polycrystalline BaTiO₃ sintered in reducing atmosphere and then annealed at P _O2= 0.2 atm has shown that the onset of the PTCR effect occurs at much higher temperatures than expected in the framework of the oxygen chemisorption model. The EPR intensity of barium and titanium vacancies increases after oxidation at T > 1000°C. A substantial PTCR effect is achieved only after prolonged annealing of the ceramic in air at temperatures as high as 1200–1250°C. This result suggests that the PTCR effect in polycrystalline BaTiO₃ is associated with interfacial segregation of cation vacancies during oxidation of the grain boundaries.     

Electrical Conduction and Dielectric Properties of the Rb‐doped CaCu3Ti4O12

Ca_1?xRb_xCu₃Ti₄O₁₂ (x = 0, 0.03, and 0.05) ceramics were synthesized by the sol‐gel method. Their microstructure and electrical properties were investigated. In the Rb‐doped samples, the Cu‐rich and Ti‐poor grain‐boundary layers are formed, and electrical properties are also changed by doping: With the increase in doping concentration, the grain resistivity and the grain‐boundary Schottky potential barrier are changed, the grain‐boundary resistivity is enhanced, and the low‐frequency dielectric constants and loss are reduced. These results were discussed in terms of the internal barrier layer capacitor (IBLC) mechanism, particularly focusing on the electrical properties in grains and the cationic nonstoichiometry at grain boundaries.     

Direct Characterization of Grain-Boundary Electrical Activity in Doped (Ba0.6Sr0.4)TiO3 by Combined Imaging of Electron-Beam-Induced Current and Electron-Backscattered Diffraction

Simultaneous measurements of remote electron beam induced current (REBIC) and orientation imaging microscopy (OIM) in a scanning electron microscope (SEM) have been applied to a polycrystalline (Ba_0.6Sr_0.4)TiO₃ with a positive temperature coefficient of resistivity (PTCR) to elucidate a grain-boundary character dependence of the potential barrier formation. The absence of electrical activity in a coherent Σ3 twin boundary is clearly imaged. The resistivity of individual grain boundaries estimated from a resistive contrast image is interpreted in terms of geometrical coherency, which is defined by the degree of coincidence in the reciprocal lattice points.     

Direct Observation of the Double Schottky Barrier in Niobium-Doped Barium Titanate by the Charge-Collection Current Method

Charge-collection (CC) current was measured at a single grain boundary, which exhibited positive temperature coefficient of resistivity (PTCR) effects, in 0.1-mol%-Nb-doped BaTiO₃. The CC current systematically reversed across the grain boundary above the Curie point, which indicated the presence of a double Schottky barrier (DSB) at the grain boundary. In contrast, the CC current was constant across the grain boundary below the Curie temperature. The result obtained from the CC current measurement agrees with the classical DSB model in donor-doped BaTiO₃, indicating the PTCR effects.     

DC Electric Field‐Enhanced Grain‐Boundary Mobility in Magnesium Aluminate During Annealing

Magnesium aluminate spinel was sintered and annealed at 1300°C under an applied 1000 V/cm DC electric field. The experiment was designed such that current could be removed as a variable and just the effect of a noncontact electric field was studied. Enhanced grain growth was observed for both samples that were sintered or annealed after densification in the presence of an electric field. Grain‐boundary character distributions revealed that no microstructural changes were induced due to the field. However, the electric field was found to enhance the kinetic movement of cations within the lattice. Energy‐loss spectroscopy experiments revealed cation segregation resulting in regions of Mg‐rich and Al‐rich layers adjacent the grain‐boundary cores. The defects generated during segregation supported the generation of a space charge gradient radiating from the grain‐boundary core out into the bulk, which was significantly affected by the applied field. The interaction between the field and space charges effectively reduced the activation energy for cation movement across boundaries thereby enhanced grain‐boundary mobility and resultant grain growth.     

Interfacial Segregation in Perovskites: I, Theory

Based on thermodynamic principles a theory for equilibrium interfacial segregation is proposed for perovskite materials, and this theory is applied to BaTiO₃. An approach developed by Frenkel and refined by Kliewer and Koehler is extended to undoped ternary oxide materials such as BaTiO₃. The approach uses regular solution approximations and considers space charge effects as the major driving force for segregation. The analysis based on this model indicates the presence of a negative space charge potential (−0.1 V at 800°C) at the surface of pure BaTiO₃. The model also predicts cation enrichment at the interface. The thickness of the space charge layer decreases with increasing temperature, and calculated values agree well with experimental results. Since both elastic and electrostatic driving forces are important for dopant/impurity segregation, an approach where the grain boundary is considered to be a two-dimensional phase, in equilibrium with the three-dimensional phase of the grain, proves useful. Solving for the impurity/dopant segregation ratio is case specific and requires knowledge of the charge neutrality conditions as well as the strain energy contribution.     

Piezoresistivity in PTCR Barium Titanate Ceramics: II, Mathematical Modeling

A modified grain boundary potential barrier model for positive temperature coefficient of resistance (PTCR) barium titanate is developed. It is based on Heywang's double Schottky barrier model, together with Devonshire's thermodynamic phenomenology of polarization behavior. Modifications are made to address the nonlinearity of the dielectric response with respect to electric field in the depletion region adjacent to the grain boundary, and the circular dependence of these quantities with the height of the barrier. Piezoresistivities are calculated for various PTCR compositions and sintering conditions, and these are compared to experimental results from the preceding paper.     

Characterization of the Firing Schedule for Positive Temperature Coefficient of Resistance BaTiO3

The development of positive temperature coefficient of resistance (PTCR) behavior during the firing procedure of semiconducting BaTiO₃ was characterized. The PTCR properties of BaTiO₃ were shown to be sensitive to the material's microstructure, liquid-phase distribution, and extent of grain-boundary oxidation. The PTCR behavior first became pronounced as the material cooled from the sintering stage at 1350°C to the annealing stage at 1175°C. Within this region, rapid oxidation of the grain boundaries occurred, which resulted in significant formation of charge carrier traps and a potential barrier. The rapid oxidation of the grain boundaries corresponded with the redistribution and solidification of the liquid phases. Once the carrier traps were established, the magnitude and slope of the PTCR jump increased during the annealing and cool-down stages of the firing procedure because of further oxidation of the grain boundaries.     

Electrically Active and Inactive Single Grain Boundaries in Semiconducting BaTiO3

Bi‐crystal specimens were prepared from Nb and Mn‐doped BaTiO₃ poly‐crystals with giant grains of millimeter order in size, and the resistance (R) versus temperature (T) characteristics of these individual grain boundaries was investigated. The electrically active grain boundaries that show normal positive temperature coefficient resistor (PTCR) behavior had no second phases or they were partially distributed along boundaries. On the other hand, electrically inactive grain boundaries that show flat R‐T characteristics were also observed, where continuous Ti‐rich second phases of Ba₄Ti₁₂O₂₇ could be detected. Different interface state density and its resultant R–T characteristics were observed for each individual active boundary, which indicates the degree of oxidation and the formation of potential barrier can be different depending on the character of the grain‐boundary plane. The resistance of inactive boundaries was determined by that of insulating second phase showing negative temperature coefficient resistor (NTCR) behavior. These results demonstrate that continuous second phase surrounding a grain deactivates the electrical properties of grain boundary, and thus should be distinguished from insulating depletion layer near grain boundary.     

Space Charge Segregation at Grain Boundaries in Titanium Dioxide: II, Model Experiments

A quantitative study of space charge solute segregation at grain boundaries in TiO₂ is conducted, using a new STEM method for the measurement of aliovalent solute accumulation. It is shown that the electrostatic potential at grain boundaries can be varied in sign and magnitude with doping, oxygen pressure, and temperature, and that the isoelectric point lies in slightly donor-doped compositions for samples annealed in air. The experimental results closely fit the space charge model in Part I. Space charge solute segregation is found even in defect regimes of high electron concentration. Approximately one in ten grain boundaries are "special" in exhibiting no detectable segregation; in one such instance a twin boundary is identified. Among boundaries with significant amounts of segregation, clear differences in potential also exist. From the potential determined in acceptor- and donor-doped compositions, the Frenkel energy (assumed to be lower than the Schottky energy in TiO₂) can be separated into its individual terms. An average value for the titanium vacancy formation energy of g_vTi = 2.4 eV and an upper limit to the titanium interstitial formation energy of g_Tii = 2.6 eV are obtained.     

PTCR陶瓷复阻抗图谱拟合结果分析

采用砖形结构模型(brick wall model)分析了PTCR陶瓷的电显微结构,通过公式推导得到复阻抗图谱的宏观拟合结果与陶瓷单个晶粒和晶界电性能的对应关系.