Vacancy Diffusion Research Articles

Nanoscale chemical and structural investigation of solid solution polyelemental transition metal oxide nanoparticles

Although it has been shown that configurational entropy can improve the structural stability in transition metal oxides (TMOs), little is known about the oxidation state of transition metals under random mixing of alloys. Such information is essential in understanding the chemical reactivity and properties of TMOs stabilized by configurational entropy. Herein, utilizing electron energy loss spectroscopy (EELS) technique in an aberration-corrected scanning transmission electron microscope (STEM), we systematically studied the oxidation state of binary (Mn,Fe)3O4, ternary (Mn, Fe, Ni)3O4, and quinary (Mn, Fe, Ni, Cu, Zn)3O4 solid solution polyelemental transition metal oxides (SSP-TMOs) nanoparticles. Our findings show that the random mixing of multiple elements in the form of solid solution phase not only promotes the entropy stabilization but also results in stable oxidation state in transition metals spanning from binary to quinary transition metal oxide nanoparticles.

An atomistic study of fundamental bulk and defect properties in [formula omitted]-uranium

Alpha-uranium plays an important role in the performance and structure evolution of metallic fuels under irradiation. It is a highly anisotropic material that demonstrates a complex microstructural response to irradiation dependent on the irradiation temperature, and the mechanisms that control this behavior are not well understood. In this work, fundamental bulk properties and energetic and thermodynamic properties of single point defects and di-defects in α-uranium are determined using molecular dynamics over the range of 400 K - 750 K. The constant pressure heat capacity, total volumetric thermal expansion, anisotropy of the thermal expansion, and single vacancy and single interstitial formation energies all agree well with previous experimental and ab initio results, lending support to the di-defect formation and binding energies and the diffusivity results. We find that the diffusion of vacancies and di-vacancies is strongly anisotropic, while interstitial and di-interstitial diffusion is slightly anisotropic, and the most rapidly migrating species changes depending on the temperature. The formation energy of vacancies and di-vacancies increases slightly with temperature, while the formation energy of interstitials and di-interstitials increases strongly with temperature. In addition, di-vacancies are very loosely bound over the entire temperature range, with an average binding energy of 0.017 eV. Conversely, di-interstitials are strongly bound (0.64 eV) until approximately 600 K, above which the binding energy decreases significantly, with an average binding energy of 0.31 eV. These results provide valuable new insights into the possible mechanisms of the complex irradiation damage behavior of α-uranium.

Probing the thermal degradation mechanism of polycrystalline and single-crystal Li(Ni0.8Co0.1Mn0.1)O2 cathodes from the perspective of oxygen vacancy diffusion

The Ni-rich cathode is one of the most promising materials for application in high-energy-density lithium-ion batteries. However, the inherent thermal instability of this material raises the risk of thermal runaway, which presents a significant obstacle to its eventual commercialization. At present, the in-depth mechanism of how grain structure affects the thermal stability of Ni-rich cathodes remains unclear. In this work, we study the thermal degradation behavior of polycrystalline and single-crystal NCM811 cathodes from multiple dimensions based on a series of state-of-the-art physicochemical characterization tools combined with theoretical calculations, report different degradation pathways of polycrystalline and single-crystal cathodes, and investigate the enhancement mechanism of single-crystal structure on the thermal stability of cathodes from the atomic scale. The larger grain size and better integrity of single-crystal NCM811 particle effectively retard the oxygen vacancy formation and increase oxygen vacancy diffusion paths at high temperatures. As a result, the diffusion of oxygen vacancies is kinetically unfavorable during heating, which delays the degradation of its lattice structure and the release of oxygen. This work provides insight into the thermal failure mechanisms of Ni-rich cathode materials with different grain structures and offers an essential theoretical basis for designing future thermally stable cathode materials.

Unveiling the synergistic effects of Re-Mo alloying on diffusion behaviors in γ-Ni: From a theoretical perspective

Fine-tuning of alloy composition is crucial for improving the temperature capacity of Ni-based superalloys, which is required for deeper understanding of the strengthening mechanisms of complex alloying. However, the typical strengthening elements Re and Mo still lack clear physical explanations on their synergistic effects on diffusion behaviors. They directly control the dislocation climb and further influence the steady creep rate under high temperatures. In this work, we perform a theoretical investigation on the vacancy-mediated diffusion behaviors regulated by Re and Mo conjunctively in the γ-Ni phase. Combined with the high-accuracy first-principles calculations, a kinetic Monte Carlo model is applied to Ni-Re-Mo ternary systems to evaluate their diffusion kinetics for the first time. The results verify that the 1Re1Mo additions exhibit comparable hindering effects on vacancy formation. The most increased effects on Ni self-diffusion barrier have also been found for 1Mo1Re substitutions compared with 2Re and 2Mo cases. Besides, Mo could elevate the diffusion barriers of Re to some extent and Re would dramatically improve the diffusion barriers of Mo. Especially, the quantified predictions of vacancy diffusion constants of Ni-Rex-Moy (x + y = 5 at.%) systems vary slightly within ∼5% compared with Ni-Re5 system. From the viewpoints of diffusion kinetics, we provide the theoretical interpretations for the synergistic effects of Re–Mo co-alloying and verify the feasibility of partly substituting Mo for Re as an alloy design strategy.

Microstructural evolution of Ti2ZrHfV0.5Mo0.2 refractory multi-principal alloy under low-energy, high-flux He ion irradiation

The irradiation response of refractory multi-principal element alloys (RMPEAs) has gained increasing attention for the potential applications in future fusion devices. In controlled fusion reactors, plasma-facing materials have to suffer continuous low-energy high flux helium (He) ion irradiations. During high flux He irradiation, vacancy-interstitial pairs can be generated through trap mutation mechanism even without cascade collision. To simplify the model, Ti2ZrHfV0.5Mo0.2 RMPEA was irradiated with 50 eV He+ (less than the minimum He displacement energy of the alloy EdTi = 67 eV) under 1200 K to various fluences of 5 × 1024 - 1 × 1026 ions/m2, and the microstructural evolution was investigated. In the irradiated RMPEA, the intense sputtering of Ti, the growth and degradation of fuzz mainly composed of Zr, Hf elements on the surface, as well as the formation of V, Mo enriched band and high density large He cavities in the subsurface layer were observed. Although the sputtering threshold energy for He of V is similar to that of Ti (ETi = 24 eV, EV = 29 eV), V showed anomalous enrichment in the subsurface layer. Moreover, unlike the W fuzz growth process, the adatoms used to form fuzz in Ti2ZrHfV0.5Mo0.2 were derived from the Zr, Hf atoms diffusing through the vacancy-solute exchange mechanism, rather than from the atoms formed by the loop-punching mechanism. The anomalous enrichment of V atoms and the different fuzz growth mechanism were attributed to (i) different migration rates for different species of atoms in the alloy under vacancy diffusion mechanism and (ii) the formation of AB2 (A = Ti, Zr, Hf; B = V, Mo) phase blocking the continued formation of prismatic dislocation loops mainly composed of V and Mo.

Coupled chemo-mechanical modeling of point-defect diffusion in a crystal plasticity fast Fourier transform framework

Below the yield strength and at moderate-to-high homologous temperatures, the inelastic deformation of metals is mostly governed/rate-controlled by vacancy diffusion-mediated processes. As a function of grain size, stress, temperature and dislocation content, vacancies (or atoms) can adopt preferential diffusion paths across grain interiors, along grain boundaries, or towards and along dislocations, resulting in climb and self-climb. In the steady state and under constant load, grain boundary and grain bulk vacancy diffusion-mediated plasticity have been described in seminal works by Coble and by Nabarro and Herring, respectively. Yet, the interplay between all aforementioned potential diffusion pathways has not been comprehensively mapped. This work presents a thermodynamically-consistent full-field model integrated within a voxel-based elasto-viscoplastic fast Fourier transform framework, which considers the coupling between the diffusion-mediated plasticity mechanisms. In the proposed approach, the kinetics and kinematics of plastic deformation due to vacancy diffusion along grain boundaries and grain bulk, as well as the exchange between grain boundaries and bulk are described explicitly. A homogenization approach at the voxel level is further introduced to simultaneously consider bulk and grain boundary diffusion in a numerically efficient fashion. The new formulation predicts the expected strain rate dependencies and the scaling of the steady-state creep rate with respect to grain size, temperature, and stress. The model predicts the transition from grain bulk to grain boundary-dominated diffusion with reduction in grain size, a significant step towards capturing transitions in deformation behavior without any phenomenological or ad-hoc adjustments.

Study on Diffusion Kinetics and Law of Chromium on the Surface of Low-Carbon Steel

Cr/low-carbon steel surface composites were prepared by aqueous solution co-deposition and high-temperature solid-state diffusion technology, and the macro rule of the solid-state diffusion of chromium on the surface of low-carbon steel was analyzed. The molecular dynamics (MD) method was used to simulate and calculate the diffusion process of the Cr/Fe interface, and the macro and micro diffusion mechanisms were analyzed. The results show that the diffusion of the chromium in iron is the combined action of the temperature, crystal structure and lattice distortion, and the diffusion coefficients of chromium in α-Fe and γ-Fe have little difference. The vacancy diffusion mechanism of the first adjacent transition is the main diffusion mode. In practice, chromium atoms diffuse along the grain boundaries of the low-carbon steel matrix and provide pinning at the grain boundaries to prevent grain growth. The simulation law is in good agreement with the experimental law. The variation law of the average diffusion coefficient of chromium atoms with temperature is obtained. The diffusion rate of chromium in the bcc crystal structure is obviously higher than that in the fcc crystal structure. In the same crystal structure, the diffusion coefficient of chromium increases with the increase in temperature. However, in the lattice transition temperature region, the diffusion coefficient of chromium gradually decreases with the increase in temperature until the end of the transformation.

Gradual conductance modulation by defect reorganization in amorphous oxide memristors.

Amorphous oxides show great prospects in revolutionizing memristors benefiting from their abundant non-stoichiometric composition. However, an in-depth investigation of the memristive characteristics in amorphous oxides is inadequate and the resistive switching mechanism is still controversial. In this study, aiming to clearly understand the gradual conductance modulation that is deeply bound to the evolution of defects-mainly oxygen vacancies, forming-free memristors based on amorphous ZnAlSnO are fabricated, which exhibit high reproducibility with an initial low-resistance state. Pulse depression reveals the logarithmic-exponential mixed relaxation during RESET owing to the diffusion of oxygen vacancies in orthogonal directions. The remnants of conductive filaments formed through aggregation of oxygen vacancies induced by high-electric-field are identified using ex situ TEM. Especially, the conductance of the filament, including the remnant filament, is larger than that of the hopping conductive channel derived from the diffusion of oxygen vacancies. The Fermi level in the conduction band rationalizes the decay of the high resistance state. Rare oxidation-migration of Au occurs upon device failure, resulting in numerous gold nanoclusters in the functional layer. These comprehensive revelations on the reorganization of oxygen vacancies could provide original ideas for the design of memristors.

A novel phase of superionic conductor β'-Na3PS4 with a large band gap and a low migration barrier.

Na3PS4 crystals with high ionic conductivity are promising solid-state electrolytes. Here, a novel phase of Na3PS4 (β'-NPS) crystallizing in a cubic lattice with a space group of P4̄3m was systematically investigated using first-principles calculations. First of all, β'-NPS is determined to be thermodynamically, dynamically and mechanically stable. The phase transition from tetragonal Na3PS4(α-NPS) to a cubic β'-NPS system occurs at approximately 480 K, suggesting high feasibility of experimental access. Moreover, the β'-NPS is an insulator with a large band gap of 4.05 eV and a low migration energy barrier of 0.10 eV for an interstitial Na ion. Significantly, a novel Na ion diffusion mechanism, that is, interstitial diffusion, is proposed, in contrast to traditional vacancy diffusion or kick-off diffusion as observed in most solid electrolytes. This work proposes β'-NPS as a promising superionic conductor for sodium ion batteries and provides theoretical guidance towards designing future ideal solid-state electrolytes.

Double Paddle‐Wheel Enhanced Sodium Ion Conduction in an Antiperovskite Solid Electrolyte

AbstractAntiperovskite structure compounds (X3AB, where X is an alkali cation and A and B are anions) have the potential for highly correlated motion between the cation and a cluster anion on the A or B site. This so‐called “paddle‐wheel” mechanism may be the basis for enhanced cation mobility in solid electrolytes. Through combined experiments and modeling, the first instance of a double paddle‐wheel mechanism, leading to fast sodium ion conduction in the antiperovskite Na3−xO1−x(NH2)x(BH4), is shown. As the concentration of amide (NH2−) cluster anions is increased, large positive deviations in ionic conductivity above that predicted from a vacancy diffusion model are observed. Using electrochemical impedance spectroscopy, powder X‐ray diffraction, synchrotron X‐ray diffraction, neutron diffraction, ab initio molecular dynamics simulations, and NMR, the cluster anion rotational dynamics are characterized and it is found that cation mobility is influenced by the rotation of both NH2− and BH4− species, resulting in sodium ion conductivity a factor of 102 higher at x = 1 than expected for the vacancy mechanism alone. Generalization of this phenomenon to other compounds could accelerate fast ion conductor exploration and design.

Kinetics and Pore Formation of the Sodium Metal Anode on NASICON‐Type Na3.4Zr2Si2.4P0.6O12 for Sodium Solid‐State Batteries

AbstractIn recent years, many efforts have been made to introduce reversible alkali metal anodes using solid electrolytes in order to increase the energy density of next‐generation batteries. In this respect, Na3.4Zr2Si2.4P0.6O12 is a promising solid electrolyte for solid‐state sodium batteries, due to its high ionic conductivity and apparent stability versus sodium metal. The formation of a kinetically stable interphase in contact with sodium metal is revealed by time‐resolved impedance analysis, in situ X‐ray photoelectron spectroscopy, and transmission electron microscopy. Based on pressure‐ and temperature‐dependent impedance analyses, it is concluded that the Na|Na3.4Zr2Si2.4P0.6O12 interface kinetics is dominated by current constriction rather than by charge transfer. Cross‐sections of the interface after anodic dissolution at various mechanical loads visualize the formed pore structure due to the accumulation of vacancies near the interface. The temporal evolution of the pore morphology after anodic dissolution is monitored by time‐resolved impedance analysis. Equilibration of the interface is observed even under extremely low external mechanical load, which is attributed to fast vacancy diffusion in sodium metal, while equilibration is faster and mainly caused by creep at increased external load. The presented information provides useful insights into a more profound evaluation of the sodium metal anode in solid‐state batteries.

Unveiling surface stability and oxygen diffusion of rare‐earth zirconate pyrochlores by density functional theory

AbstractThe surface structures, bond variations, and segregation of oxygen vacancies play crucial roles in the structural stability and functionality of nanocrystalline rare‐earth zirconate pyrochlores. In this work, the stabilities of (1 0 0), (1 1 0), and (1 1 1) surfaces of pyrochlore A2Zr2O7 (A = La, Ce, Pr, Nd, Pm, Sm, Eu, or Gd) are investigated by first‐principles calculations. Surface reconstruction occurs on (1 1 0) surface with a transition of ZrO6 octahedron to ZrO4 tetrahedron, leading to their large relaxation energies. In combination with the small amount of broken bonds during the surface formation process, the (1 1 0) surfaces are identified having the lowest surface formation energies than the (1 0 0) and (1 1 1) surfaces. Moreover, the reconstructed (1 1 0) surface has characteristics of the segregation of oxygen vacancies. The surface oxygen vacancies have the low migration barriers (<1.2 eV), which are comparable with those in bulk and ensure the long‐distance diffusion of oxygen vacancies in A2Zr2O7. These discoveries provide fundamental insight to the surface structure and related oxygen vacancy behavior, which are expected to guide the optimization of the surface related properties for nanocrystalline rare‐earth zirconates.

Optical, thermal properties, and hydrolysis resistance of transparent YF3-doped CaO ceramics fabricated by vacuum sintering

Transparent calcium oxide (CaO) ceramic was successfully fabricated by pressureless vacuum sintering technique with 0.5 at% YF3 as the sintering additive. In consideration of the hydrolysis of CaO, the precursor powders were calcined at 600 °C. Within the sintering temperature range of 1150–1450 °C, the effect of YF3 additive on the phase structure, relative density, transmittance, and microstructure of CaO ceramics was studied. Benefiting from the assisted liquid-phase sintering mechanism and vacancy diffusion mechanism of YF3, full-dense (3.35 g/cm3) YF3-doped CaO transparent ceramic was fabricated at 1350 °C with high thermal conductivity of 15.42 W/(m·K). The in-line transmittance attained 47.10% at the wavelength of 1200 nm. Moreover, the hydrolysis resistance was extremely enhanced due to the pore-free structure. Compared to the CaO ceramic with low relative density of 78.66%, the weight gain of full-dense CaO ceramic greatly decreased from 22% to 1.2% within 35 days.

Machine learning based on-the-fly kinetic Monte Carlo simulations of sluggish diffusion in Ni-Fe concentrated alloys

Defect diffusion in concentrated alloys plays a key role on governing their unique mechanical and physical properties. In such alloys, defect diffusion depends on its complex local atomic environment and varies from site to site due to the chemical disorder. On-the-fly determination of the defect migration barrier at every site using the standard nudged elastic band (NEB) method is computationally expensive and often impractical. In this work, we couple machine learning and kinetic Monte Carlo (KMC) to study vacancy-mediated sluggish diffusion in concentrated Ni-Fe model alloys. Based on about 32,000 pre-calculated NEB barriers, an artificial neural network (ANN) based machine learning model is developed to accurately predict the vacancy migration barriers for arbitrary local atomic environments, including both random solution configurations and alloys with short-range orders. The ANN model is then coupled with KMC (ANN-KMC) to determine the vacancy migration barriers on-the-fly, enabling an efficient study of the vacancy diffusion in the full composition range at a wide range of temperatures. In addition, a composition and temperature dependent jump attempt frequency model is developed. Upon calibration, the ANN-KMC modeling can predict nearly identical vacancy diffusivities as those obtained from independent molecular dynamics (MD) and temperature accelerated dynamics (TAD) simulations at their accessible temperatures. The sluggish diffusion mechanisms in this specific alloy system at both high and low temperatures are discussed based on the ANN-KMC results.

Crystal plane-orientation dependent phase evolution from precursor to porous intermediate phase in the vapor phase dealloying of a Co-Zn alloy

Understanding phase transitions and pore formation during vapor phase dealloying (VPD) is essential to optimize the microstructure and composition of nanoporous metals for versatile applications. Nevertheless, the underlying atomic mechanisms of phase formation and pore evolution during VPD are unknown. Using a binary γ-CoZn precursor alloy as a prototype system, we found a two-step dealloying process. The microsized porous β-CoZn intermediate phase that formed at the dealloying front facilitated the subsequent growth of completely dealloyed hierarchical nanoporous α-Co with the micropore structure of the intermediate phase. Combining aberration-corrected scanning transmission electron microscopy with energy dispersion X-ray spectrometry, we found that the intermediate phase preferentially formed on specific crystal planes of the precursor, and the vacancies generated by sublimation of Zn atoms diffused dominantly on the {110} planes of the precursor close to the intermediate phase. Theoretical calculations indicated that the energy barrier to the diffusion of Zn vacancies on the low-index {110} plane was lower than on other planes. The atomic-scale phase evolution play a key role in the subsequent evolution of the porous structure and provide deep insight into the phase transition during VPD. This insight may provide a new approach to tune the pore structure and composition of nanoporous metals by designing and regulating their intermediate phases.

Effect of the temperature on the passivity of the modified martensitic stainless steels

ABSTRACT The limits and nature of the passive behavior exhibited by modified martensitic stainless steels (MMSS) is studied in brine solutions at different temperatures using electrochemical methods and the point defect model (PDM), in an environment at pH is 3 and temperatures up to 150°C, using autoclaves with CO2 gas up to 2.8 MPa. The results show that passivity on the MMSS is characterized by the metal cation vacancy diffusivity (D) which indicates that the passivity up to temperatures of 75°C is more stable than at higher temperatures up to 150°C. The value of D is used to describe the transition between the passive layers at the threshold temperature of 75°C; at which exhibits the largest stability. MMSS specimens passivated at 75°C exhibit higher passivity stability in experiments performed at 25°C, when compared the pre passivation, suggesting that the change experienced at 75°C is at least partially irreversible.

Extremely enhanced thermal stability of Y2/3Cu3Ti4O12 ceramics by a Pechini method

AbstractY2/3Cu3Ti4O12 ceramic is a novel semiconductor with potential applications in electronic devices. However, its resistance drift and surface structure defects limit the application for negative temperature coefficient thermistor devices. A comparative study of solid‐phase and a Pechini processing of Y2/3Cu3Ti4O12 is presented in this paper, in the particular comparative study of stability. The Pechini method is found to be effective in lowering sintering temperature and improving thermal stability (ΔR/R0 < 0.3％) in comparison with solid‐phase method. The origin of the stability deterioration is related to the oxidation state of Cu ions and the migration of sublattice. The Pechini method overcomes stoichiometric ratio deviations and cation vacancy diffusion, thus reducing metal ion segregation in a continuous high‐temperature environment and thereby showing unique insensitivity to oxygen. The important role of the Pechini method in improving thermal stability is revealed, which is expected to be used in the preparation of high stability electron devices.

Robustness of Passivated ALD Zinc Tin Oxide TFTs to Aging and Bias Stress

Thin-film electronics fabricated with amorphous oxide semiconductors (AOS) are being studied for beyond-display technologies because of their superior electron transport. To widen the commercial applications, robust devices fabricated using scalable deposition techniques are required. Here, we fabricate bottom-gate, top contact thin-film transistors (TFTs) using zinc tin oxide, an AOS deposited by atomic layer deposition (ALD), and study robustness to aging and bias stress for devices stored in a dark air ambient with and without Al2O3 passivation. All samples exhibit excellent mobility ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu _{\text {FE}}$ </tex-math></inline-formula> ) and subthreshold swing (SS) robustness to aging. Most of the device aging occurs within the first 25 days, after which the performance stabilizes. Changes due to positive bias stress, which are dominated by interactions with ambient molecules, are greatly reduced by passivation. Passivation, however, results in an increase in contact resistance ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${R}_{C}$ </tex-math></inline-formula> ), SS, and negative bias illumination stress (NBIS) instability. The increase in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${R}_{C}$ </tex-math></inline-formula> is attributed to the diffusion of oxygen vacancies that occurs during the passivation process, while the increase in SS and NBIS instability is attributed to subgap interface defects. The experimental results are compared to Silvaco ATLAS simulations to confirm the proposed physical mechanisms and allow quantification of the associated defects and non-idealities.

Electrolyte-gate-driven carrier density modulation and metal–insulator transition in semiconducting epitaxial CdO films

CdO has drawn much recent interest as a high-room-temperature-mobility oxide semiconductor with exciting potential for mid-infrared photonics and plasmonics. Wide-range modulation of carrier density in CdO is of interest both for fundamental reasons (to explore transport mechanisms in single samples) and for applications (in tunable photonic devices). Here, we thus apply ion-gel-based electrolyte gating to ultrathin epitaxial CdO(001) films, using transport, x-ray diffraction, and atomic force microscopy to deduce a reversible electrostatic gate response from −4 to +2 V, followed by rapid film degradation at higher gate voltage. Further advancing the mechanistic understanding of electrolyte gating, these observations are explained in terms of low oxygen vacancy diffusivity and high acid etchability in CdO. Most importantly, the 6-V-wide reversible electrostatic gating window is shown to enable ten-fold modulation of the Hall electron density, a striking voltage-induced metal–insulator transition, and 15-fold variation of the electron mobility. Such modulations, which are limited only by unintentional doping levels in ultrathin films, are of exceptional interest for voltage-tunable devices.

Oxygen transport at a ferroelastic domain wall in CaTiO3

The formation and migration of charged oxygen vacancies at a ${90}^{\ensuremath{\circ}}(100)[001]$ domain wall in orthorhombic ${\mathrm{CaTiO}}_{3}$ were studied by means of atomistic simulation techniques. The segregation-energy profiles of an oxygen vacancy across the wall were revealed through careful discrimination to display hyperbolic secant forms, with a domain-wall width consistent with that obtained from a tilt-angle analysis. Equilibrium distributions of oxygen vacancies across the ferroelastic domain wall in a nominally undoped (weakly acceptor-doped) sample were calculated self-consistently (assuming a sech segregation-energy profile) for various temperatures. The calculations indicate a positively charged domain wall, arising from high vacancy concentrations, compensated by negative space-charge layers, in which vacancies are depleted. The activation barriers for oxygen-vacancy migration along the domain wall, determined from nudged-elastic-band calculations, revealed that the long-range diffusion of oxygen vacancies along the wall is neither strongly enhanced nor strongly hindered.