Defect equilibria and thermophysical properties of CeO2-x based on experimental data and density functional theory calculation result

Properties of CeO₂ were evaluated by density functional theory (DFT) simulation to determine bandgap, Frenkel defect formation energy, and defect migration energy. Bandgap and Frenkel defect formation energy were used to analyze defect equilibria. Oxygen partial pressure dependence of defect equilibria was evaluated based on oxygen potential experimental data and DFT calculation, and a Brouwer diagram was derived. The defect formation energies, including Frenkel defect, electron-hole pair, and so on, were determined and used to evaluate the properties, including oxygen diffusion coefficients, electrical conduction, heat capacity, and thermal conductivity. Mechanisms of various properties were discussed for a deeper understanding based on defect chemistry, and the relationship among properties was systematically described.     

Fermi level pinning in Co-doped BaTiO3: Part II. Defect chemistry models

A first-principles informed grand canonical defect chemistry model capable of accounting for non-stoichiometry and partial equilibration of different sub-lattices is developed and used to study Mg and Mn doped, and (Mg+Y) and (Mn+Y) co-doped BaTiO₃ to elucidate the role of Mn and Y in improving the resistivity and resistance degradation of BaTiO₃ as observed by Ryu et al. in Part I of this series of papers. The model qualitatively captures the behavior of the samples in all conditions, reproducing the observed carrier plateau and increased resistivity of (Mn+Y) co-doped BaTiO₃, and expected trends in the concentrations of free oxygen vacancies with doping. These trends reflect the observed differences in degradation characteristics, and help explain the substantially improved degradation resistance of the (Mn+Y) co-doped samples. Our model adds to the mechanism proposed by Yeoh et al. that the Fermi level is pinned by the multivalent character of Mn_Ti in (Mn+Y) co-doped BaTiO₃ by giving insight into the role of barium vacancies, the site preferences of the dopants, and defect complexes in this mechanism. These insights provide a set of criteria in the search for sets of co-dopants with similar behaviors.     

The effect of Fe-acceptor doping on the electrical properties of Na1/2Bi1/2TiO3 and 0.94 (Na1/2Bi1/2)TiO3–0.06 BaTiO3

Na_1/2Bi_1/2TiO₃ (NBT) based ceramics are amongst the most promising lead-free ferroelectric materials. It was expected that the defect chemistry and the effect of doping of NBT would be similar to that observed for lead based materials, however, acceptor doping does not lead to ferroelectric hardening. Instead, high oxygen ionic conductivity is induced. Nevertheless, for solid solutions with BaTiO₃ (BT), which are more relevant with respect to ferroelectric applications, such a drastic change of electrical properties has not been observed so far. To rationalize the difference in defect chemistry between NBT and its solid solution 94(Na_1/2Bi_1/2TiO₃)–0.06 BaTiO₃ (NBT–6BT) compositions with different concentrations of Fe-dopant were investigated. The study illustrates that the materials exhibit very similar behavior to NBT, and extraordinarily high oxygen ionic conductivity could also be induced in NBT–6BT. The key difference between NBT–6BT and NBT is the range of the dependence of ionic conductivity with dopant concentration. Previous studies of NBT–6BT have not reached sufficiently high dopant concentrations to observe high conductivity. In consequence, the same defect chemical model can be applied to both NBT and its solid solutions. This will help to rationalize the effect of doping on ferroelectric properties of NBT-ceramics and defect chemistry related degradation and fatigue.     

Evaluation of dielectric and piezoelectric behavior of unpoled and poled barium titanate polycrystals with oxygen vacancies using phase field method

This article studies the dielectric and piezoelectric behavior of unpoled and poled barium titanate (BaTiO₃) polycrystals with oxygen vacancies. A phase field model is employed for BaTiO₃ polycrystals, coupled with the time-dependent Ginzburg–Landau theory and the oxygen vacancies diffusion, to demonstrate the interaction between oxygen vacancies and domain evolutions. To generate grain structures, the phase field model for grain growth is also used. The hysteresis loop and butterfly curve are predicted at room and high temperatures. The permittivity, and longitudinal and transverse piezoelectric constants of the BaTiO₃ polycrystals are then examined for various grain sizes and oxygen vacancy densities.     

Defect mechanisms,oxygen vacancy trapping ability in rare-earth doped BaTiO3 from first-principles and thermodynamics

The defect mechanisms of rare earth (RE) doped BaTiO₃ have a strong impact on the electrical performance of the multilayer ceramics capacitors (MLCCs). Oxygen vacancy is the main reason for the device degradation over longtime use, while the effect of the doping strategy on controlling the oxygen vacancies is not yet quantitatively understood. In this work, the grand canonical thermodynamic defect model based on first-principle calculations is applied to evaluate the defect mechanism of RE-doped BaTiO₃ under practical experimental condition. The charge compensation and prior site occupancy of RE are found not only associated with ionic size but also exhibit transitions with oxygen partial pressure and doping concentration. Furthermore, the oxygen vacancy trapping ability of RE ions is evaluated from the perspectives of thermodynamics and kinetics. The migration barrier among first nearest oxygen sites dramatically changed depending on the RE site occupancy. The large trapping ability is contributed by the relatively large negative binding energy of the defect complex and comparable RE concentrations substituted on Ba and Ti sites. The two conditions can be achieved in amphoteric ions doped systems, while in pure donor doped BT only one of these conditions can be satisfied. Although the self-compensated defect complexes exhibit the highest binding energy, the trapping ability contributed by different defect complexes (${\mathrm{RE}}_{\mathrm{Ti}}^{{}^{\prime }}$, ${\mathrm{RE}}_{\mathrm{Ba}}^{·}$, RE_Ba − RE_Ti) is generally comparable in these systems. This feature of amphoteric RE ions accounts for the improvement of the lifetime and reliability of MLCCs.     

Analysis of defect mechanisms in nonstoichiometric ceria–zirconia by the microwave cavity perturbation method

In this microwave study, the defect chemistry of ceria–zirconia solid solutions (CZO, Ce_1−yZr_yO_2−δ) was investigated at high temperatures by a resonant microwave method. Specifically, the effects of temperature and Zr content on the dielectric properties and defect chemistry mechanisms in CZO were analyzed. Experiments were performed on a series of different CZO powders (y = 0.2, 0.33, 0.50, 0.67). Measurements at 600°C and different oxygen partial pressures (p_O2 = 10⁻²⁶–0.2 bar) confirm a dominant n-type conduction of small-polarons in CZO due to the preferred formation of oxygen vacancies, which is also supported by a multimodal analysis. Polarization losses were found to be negligible in the GHz range. Furthermore, an increased relative permittivity was observed in CZO, which correlates with the concentration of oxygen vacancies in CZO. Our microwave study is the first to provide a comprehensive data set for the dielectric properties of CZO powder sample in a wide range of different conditions. In addition, the connection of dielectric properties to CZO defect chemistry mechanisms is presented. The results are in good agreement with findings in the literature and may contribute to a better understanding of microwave-based state diagnosis of CZO-based materials, as it discussed for three-way catalysts.     

Blacklight sintering of BaTiO3 ceramics

Blacklight sintering has been used for rapid densification of ceramics. Compared to other methods, neither electrodes nor complex sample holders and dies are required, resulting in an effective technique for energy-efficient sintering. Still, the question remains whether excellent functional properties can be obtained by this method. Therefore, blacklight-sintered ferroelectric BaTiO₃ was investigated. Gradient-free microstructures and phase purity could be reached. Enhanced electrical conductivity was determined, indicating changes in defect chemistry and, most likely, an increase in oxygen vacancy concentration. Furthermore, measurements of ferroelectric properties confirmed leaky ferroelectric behavior, with migration and pinning of oxygen vacancies affecting the polarization loops. An additional short annealing step in an oxygen-rich atmosphere led to di/ferroelectric parameters equivalent to those of a conventionally sintered reference sample. Thus, the fabrication of ferroelectric ceramics by blacklight sintering is possible if the quenching effect caused by the freeze-in of defects during rapid cooling is considered.     

Low Temperature Ionic Conductivity of an Acceptor‐Doped Perovskite: II. Impedance of Single‐Crystal BaTiO3

Low temperature conductivity mechanisms were identified in acceptor‐doped BaTiO₃ single crystals equilibrated and quenched from high temperature under different oxygen partial pressures. A range of acceptor ionization states were quenched into samples doped with manganese or iron. Using an appropriate equivalent circuit to interpret impedance spectroscopy data, room temperature conductivity mechanisms in the single crystal samples were identified, and the permittivity/temperature dependence was also shown to be self‐consistent with the nature of a first‐order ferroelectric phase transition. The primary, low temperature, conduction mechanism in acceptor‐doped BaTiO₃ was determined to be dominated by the migration of oxygen vacancies. The activation energy for oxygen vacancy migration was experimentally determined to have a value of nearly 0.7 eV. This activation energy represents an intrinsic value for vacancy hopping and confirms our previous work that revealed minimal interaction between acceptor dopants and oxygen vacancies in BaTiO₃ in contrast to the well‐documented evidence of defect association in SrTiO₃.     

Synthesis, spark plasma sintering and electrical conduction mechanism in BaTiO3-Cu composites

BaTiO₃-Cu composite powders were prepared via an alkoxide-mediated synthesis approach. As-synthesized BaTiO₃ nanoparticles were as small as 40 nm and coated partially larger Cu particles of approximately 1 μm in size. Thermogravimetric analysis (TGA) and dilatometry revealed a gradual increase in weight loss and retarded shrinkage with the increase of Cu addition. BaTiO₃-Cu composites were successfully densified by spark plasma sintering (SPS). The microstructures show an average grain-size for BaTiO₃ of around 100 nm and a crystallite size of about 1 μm for the Cu inclusions. The AC conductivity of the BaTiO₃-Cu composites increased with increasing Cu content or with temperature. The dominant electrical conduction mechanism in SPSed BaTiO₃-Cu composites changed from migration of oxygen vacancies to band conduction of trapped electrons in oxygen vacancies with the increase of Cu content.     

Effect of surface charges on the polarization of BaTiO3 thin films investigated by UHV‐SPM

Nanostructured BaTiO₃ polar thin films are increasingly critical to the function of future multilayer ceramic capacitors and related oxide‐based electronic devices. The effect of surface charges on BaTiO₃ polarization behavior is therefore investigated by ultra‐high vacuum scanning probe microscopy (UHV‐SPM) for 3 distinct morphologies—epitaxial, polycrystalline, and nanocrystalline films. Regardless of the film morphology, Kelvin probe force microscopy reveals that BaTiO₃ thin film surfaces exhibit positive charging after contact scanning by various noble AFM probes due to the work function difference between tip and specimen. According to piezoresponse force microscopy, these positive charges uniformly stabilize downward polarized domains. However, the hysteresis and concomitant surface charging behavior are strongly sensitive to microstructure and defects. In particular, the stability and switching behavior are influenced by bulk and interfacial defect distributions and hence correlated to film deposition methods and grain size. Such morphology dependent properties for BaTiO₃ films are revealed only through UHV measurements where screening charges from the ambient can be minimized, demonstrating the importance of UHV‐SPM for understanding ferroelectric thin films and nanostructures.     

Electrical conduction mechanisms and effect of atmosphere annealing on the electrical properties of BiFeO3-BaTiO3 ceramics

BiFeO₃-BaTiO₃ (BFBT) is a promising high temperature piezoelectric ceramic system, as it possesses both high electromechanical properties and high Curie temperature. However, pure BFBT commonly exhibits large electrical conductivity at high temperatures, and there is considerable disagreement on its electrical conduction mechanism. Here we investigated the electrical conduction mechanisms of 0.70BiFeO₃-0.30BaTiO₃ and 0.67BiFeO₃-0.33BaTiO₃ ceramics by systematic impedance spectroscopy measurements as a function of oxygen partial pressure and temperature. Both ceramics exhibit higher electrical conductivity with an increase of oxygen partial pressure, consistent with p-type semiconductor behaviors. Particularly, reduced conductivity and improved ferroelectric remanent polarization can be obtained in BFBT when annealed in inert atmosphere. This study provides fundamental basis for preparing insulating and high performance BFBT ceramics.     

Conduction Mechanisms in BaTiO3–Bi(Zn1/2Ti1/2)O3 Ceramics

Polycrystalline BaTiO₃–Bi(Zn_1/2Ti_1/2)O₃ (BT–BZT) ceramics have superior dielectric properties for high‐temperature and high‐energy density applications as compared to the existing materials. While it has been shown that the addition of BZT to BT leads to an improvement in resistivity by two orders of magnitude, in this study impedance spectroscopy is used to demonstrate a novel change in conduction mechanism. While nominally undoped BT exhibits extrinsic‐like p‐type conduction, it is reported that BT–BZT ceramics exhibit intrinsic n‐type conduction using atmosphere‐dependent conductivity measurements. Annealing studies and Seebeck measurements were performed and confirmed this result. For BT, resistivity values were higher for samples annealed in nitrogen as compared to oxygen, whereas the opposite responses were observed for BZT‐containing solid solutions. This suggests a fundamental change in the defect equilibrium conditions upon the addition of BZT to the solid solution that lowered the carrier concentration and changed the sign of the majority charge carrier. This is then also linked to the observed improvement in resistivity in BT–BZT ceramics as compared to undoped BT.     

Multi‐Site and Multi‐Ionization of Sn in the Doping of BaTiO3

This article considers the diverse substitutional effects of the Sn cations in the BaTiO₃ lattice and its impact on the electrical conduction as a function of A/B stoichiometry, oxygen partial pressure, and temperature. High‐density specimens were fabricated in the different oxygen partial pressures to control the valence state of Sn ion. Specifically, the nonstoichiometric materials were sintered in a low pO₂ atmosphere (10^?14 atm at 1320°C) and in a high pO₂ atmosphere (10^?0.21 atm at 1320°C), respectively. It is found that Sn occupying the Ti‐site acts as an acceptor dopant, and the electronic conductivity varies from a n‐type to p‐type transition, with increasing oxygen activity as mostly expected. However, there is an unusual case noted with Sn doping the A‐site where the conductivity, σ, is invariant at high pO₂'s, i.e., σ ~  with m ≈ 0 in the high pO₂ regime. The variation of the conductivity is explained by a valence changing of Sn ion from +2 to +3 to +4 with increasing oxygen partial pressure, and we model this data across all conditions within a self‐consistent defect chemistry model.     

Modification of grain boundary potential barriers by annealing treatments of PTCR ceramics with identical microstructure and room-temperature resistivity

Semiconducting BaTiO₃-based ceramics originating from the same starting powder batch were subjected to different oxidative post-sintering treatments at temperatures between 800 °C and 1200 °C. The annealing profiles were chosen in a way to result in ceramics with same room-temperature and microstructure. However, the different annealing procedures clearly affected the resulting PTCR characteristics above and below the phase transition temperature. Observed changes in electrical properties were investigated by capacitance-voltage measurements and x-ray diffraction. It was found that annealing treatments influence the grain boundary potential barrier height and width by modifying the equilibrium concentration of cation and oxygen vacancies. Moreover, oxidative annealing at 1100 °C appears to influence the temperature development of spontaneous polarization by filling up oxygen vacancies within the grain bulk. These findings not only extent existing knowledge about defect equilibria in barium titanate but also emphasize the strong impact of process parameters on electrical properties of electroceramics.     

Electrical properties of calcia-stabilised zirconia ceramics

The electrical properties of cubic, calcia-stabilised zirconia ceramics, Ca_xZr_1-xO_2-x: 0.12 ≤ x ≤ 0.18 have been investigated using impedance spectroscopy to separate bulk, grain boundary and electrode contact impedances. The most appropriate equivalent circuit to characterise the bulk response required inclusion of a dielectric component, represented by a series RC element, in parallel with the oxide ion conductivity represented by a parallel combination of a resistance, capacitance and constant phase element. The dielectric component may be attributed to defect complexes involving immobile oxygen vacancy pairs whereas long range conduction involves single oxygen vacancies.     

XPS and UPS in situ study of oxygen thermal desorption from nanocrystalline diamond surface oxidized by different process

The chemistry of oxygen bonding on the diamond surface is a rich area of surface science research. It is well known that different surface terminations lead to strong variation of the material work function. This effect in diamond assumes peculiar consequences. In fact the oxidized diamond surface is hydrophilic, due to the high work function it shows a positive electron affinity and it is non conductive. On the contrary hydrogenation completely changes the orientation of the surface dipoles, the surface becomes hydrophobic, the work function lowers leading to a negative electron affinity. In addition hydrogen induces subsurface carriers which render the diamond surface semiconducting. These distinctive electronic properties make the diamond surface very interesting for the fabrication of surface field effect transistors just playing with the oxygen/hydrogen chemistry. Hydrogenation is generally obtained during the diamond synthesis in plasma reactors. Differently, the diamond surface oxidation may be accomplished with different processes (wet chemistry, plasma, UV irradiation).The realization of electronic devices calls for a complete understanding of the carbon-oxygen interactions, their stability and their influence on the electronic properties of diamond. Aim of this work is to explore the properties of diamond surfaces oxidized with piranha mixture, with O₂ plasma and with UV irradiation in a pure O₂ atmosphere. Each of these oxidized surfaces were annealed in situ at different temperatures and analyzed with photoelectron spectroscopies. Decreases of the oxygen concentration obtained via thermal desorption are then correlated with variations of the electronic properties obtained from UPS analyses.     

Modeling and analysis of hydrogen permeation in mixed proton-electronic conductors

A rigorous model for hydrogen permeation through dense mixed conductors was derived using the formalism of non-equilibrium thermodynamics for various operating modes and process conditions. The concentrations of charge carriers were rigorously included in this model through defect equilibria with the chemical environment at each membrane surface and through balance equations and a virtual pressure formalism within the membrane. Hydrogen permeation rates through proton-electron-hole mixed conductors were simulated using this framework under open-circuit, short-circuited, and applied potential operating modes. The sensitivity of H₂ permeation rates to the reduction-oxidation potentials at each side of the membrane and to the membrane properties (e.g. electron/hole diffusivity, oxygen binding energy) was examined in terms of the mobility and concentration of each charge carrier in order to identify rate-limiting steps for H₂ transport. These simulations showed that electronic transport controls H₂ permeation rates in proton-electron-hole mixed conductors typically used for H₂ permeation, especially when hydrogen chemical potentials are significantly different in the two sides of the membrane. These electronic conduction limitations arise from a region of very low electronic conductivity within the membrane, caused by a shift in the predominant charge carriers from electron to holes with decreasing hydrogen chemical potential. Under these asymmetrical conditions, H₂ permeation rates increase more markedly when an external electron-conducting path is introduced than at lower chemical potential gradients. Such interplay between rate-controlling variables leads to complex effects of H₂ chemical potential gradients on permeation rates. The effects of intrinsic membrane properties on H₂ permeation were examined by systematic changes in the defect equilibrium constants. A decrease in oxygen binding energy, manifested in a stronger tendency for reduction of the oxide membrane material, leads to higher electron concentrations and to higher rates for open-circuit operation, during which electron conduction limits H₂ transport rates.     

Tuning electrical properties of BaTiO3 with iron modification

BaTiO₃ plays an important role in advanced functional devices owing to its fascinating properties. Though it is an excellent ferroelectric material, its magnetism can be switchable via suitable modification. In this report, we have studied iron-modified BaTiO₃, which has been prepared using cost-effective high-temperature solid-state reaction techniques. The Fe-modified BaTiO₃ maintains its crystallinity in the tetragonal phase with P4mm space group with a slight variation of tetragonality ratio to 1.002 from 1.008 of BaTiO₃ of the identical synthesis method. This is confirmed by Rietveld refinement. Field emission scanning electron microscopy (FESEM) and EDX (energy dispersive X-rays) spectrum along with an elemental mapping analysis has provided the feature of the Fe-modifed BaTiO₃. Atomic force microscope (AFM) has been employed to get the detailed surface topology (2D and 3D) and surface roughness of the developed systems. This deformation caused by the incorporation of Fe significantly modifies the electrical properties of barium titanate. The ferroelectric-paraelectric phase transition temperature (T_c) of Fe-modified BaTiO₃ has been diffused and shifted to 300 °C from 120 °C of pure BaTiO₃, suggesting the materials for the high-temperature capacitive application. The room temperature M-H hysteresis of Fe-modified BaTiO₃ indicates the ferromagnetism developed in the BaTiO₃ with the introduction of Fe. The ac conductivity is in the order of 10⁻⁴ Ω⁻¹cm⁻¹, and its frequency response obeys Jonscher's power law. Different charge carriers are responsible for diverse conduction processes in different temperature ranges confirmed by the Arrhenius plot. Impedance spectroscopy studies reveal the existence of NTCR characteristics of the developed system. Well defined ferroelectric hysteresis loop indicates the existence of ferroelectricity in the developed system. The analysis of various electrical parameters has provided information on the material's dielectric relaxation and conduction mechanisms for possible application in functional devices.     

The significance of defect chemistry for the rate of gas–solid reactions: three examples

Three examples are revisited in which the reaction rate could be reliably correlated with point defect chemistry highlighting the role of point defects as acid–base active centers. In the case of dehydrohalogenation of tertiary butyl chloride, AgCl becomes increasingly active as heterogeneous catalyst, if AgCl is homogeneously or heterogeneously doped. By such a procedure the silver vacancy concentration is adequately increased. The oxygen incorporation into SrTiO₃ offers an example in which the surface mechanism in terms of adsorbed species, oxygen vacancies and electronic centers has been elucidated. Appropriate surface coatings give rise to significant catalytic effects. Increasing iron (acceptor) doping not only changes the point defect chemistry but also the nature of the rate determining step. Lastly, the electrocatalytic function of Sr-doped LaMnO₃ is considered as regards oxygen reduction reaction and O²⁻ incorporation into Y-doped ZrO₂ in the context of solid oxide fuel cells. Again the defect chemistry is of prime importance for the reaction rate.     

Effect of doping method on microstructural and defect profile of Sb–BaTiO3

Electrical properties in BaTiO₃ based ceramics are strongly dependent on composition and microstructural development. In this work, we studied the effect of the particle coating as doping method on microstructure and electrical properties of Sb-doped BaTiO₃. The advanced doping method involved surface-coated BaTiO₃ particles with a thin film of a metal-organic precursor solution. Results were compared with the performance obtained on conventional doping method. The particle coating as doping method led to an effective grain growth inhibition as well as significant microstructure improvement.The incorporation of dopant into the perovskite lattice is influenced by the doping method. Results suggested that Sb acted as donor dopant on A or/and B sites, and also as acceptor on B sites, modifying the grain boundaries structure characteristics. Dopant incorporation method affected the defect structure, and therefore, the donor dopant concentration for the semiconductor insulator transition in BaTiO₃ ceramics.