Vacancy Diffusion Coefficient Research Articles

(Invited) Oxide Ion Conductivity and Oxide Vacancy Diffusion Coefficient of Stabilized ZrO2 and Doped CeO2 Discussed Based on Classical Defect Chemistry with Particular Focus on Valence State (2+, 3+, and 4+) of Doped Cations

So far tremendous works have been reported on the oxide-ion conductivity of fluorite-type oxides typically stabilized zirconia and doped ceria. It is well known that the oxide-ion conductivity vs. dopant concentration plot shows maximum around 10 mol percent dopant concentration and the maximum conductivity varies with the dopant species. Interests tend to be focused on the higher and the stabler conductivity. For the aim, explorations are made on the dopant survey and the phase stability of the solid solution.Generally, conductivity is considered proportional to the product of carrier concentration and carrier mobility. For the fluorite-type oxide ion conductors, it is considered that carrier is oxygen vacancy, V O ··, and mobility is proportional to oxygen vacancy diffusion coefficient, DV . However, such defect chemical approach to the fluorite-type oxides is not popular. When we assume that the mobility is constant following the classical hypothesis, we cannot explain the conductivity maximum.The author has been trying to discuss the oxide-ion conduction in fluorite-type oxide solid solutions in terms of oxygen vacancy concentration, cV ,and DV .Using the literature data on conductivity and composition relationship, the author has already calculated DV for some compositions of stabilized zirconia and doped ceria as a function of composition. The data have been published in a short review [1] and books [2,3]. However, the published graphical displays were so crowded that the physical meanings seem still unclear.In this presentation, discussion is made on the conductivity of stabilized zirconia and doped ceria in the following order to make clear the characteristic feature of DV with the variation of valence state and chemical species of dopant oxides.1: zirconia base solid solutions 1a: with divalent cation oxides 1b: with trivalent cation oxides2: ceria base solid solutions 2a: with divalent cation oxides 2b: with trivalent cation oxides3: stabilized zirconia – ceria solid solutions 3a: stabilized zirconia base solid compositions 3b: ceria base solid compositions 3c: trivalent cerium formation by partial reductionIt is clarified that DV of fluorite type oxide is affected by the dopant cation not only by different valent but also by the same valent cations.

Understanding atomic interaction between cuprous oxide film and aggressive chloride solution

Considering the structural complexity of actual copper (Cu) passive films consisting of Cu2O, the multiple roles of aggressive chloride anion (Cl–) on Cu2O are revealed through first-principles calculations. Despite different Cl– adsorption susceptibilities of various Cu2O surfaces, similar surface O vacancy formation mechanisms promoted by Cl– adsorption are elucidated, accompanying with further Cu vacancy propagation. Increasing surface Cu vacancy concentration and unchanged Cu vacancy diffusion coefficient induced by Cl– adsorption lead to increasing diffusion flux. These results reveal the atomic interaction between Cu2O film and Cl ion, which is helpful to understand the depassivation mechanism of Cu.

Void nucleation at dislocation boundaries aided by the synergy of multiple dislocation pile-ups

Void nucleation is of great significance in understanding ductile fracture. Recent experiments have shown that voids are nucleated via vacancy condensation and dislocation boundaries are the main nucleation sites. However, it is unclear what role is played exactly by dislocation boundaries in promoting void nucleation. Here we propose a new mechanism for dislocation boundary-induced void nucleation and develop a corresponding model based on the classical nucleation theory and vacancy diffusion theory. The model suggests that void nucleation is mainly influenced by hydrostatic stress, temperature, and relative vacancy concentration, whose contributions are systematically studied. It is also suggested that the vacancy formation energy and the interaction energy of hydrostatic stress and vacancy, which are absent in the previous models and introduced in ours, exhibit a clear tendency to lower the activation free energy barrier. Analysis of the nucleation kinetic suggests that the growth rate of void depends on the vacancy diffusion coefficient and vacancy concentration; the higher the values of these parameters, the faster the growth rate of the void. The kinetic feasibility of the newly proposed mechanism is examined using three-dimensional discrete dislocation dynamics simulations. The results predict that the size of incipient voids nucleated at the dislocation boundary is ∼35 nm, which is consistent with the experimental characterization value of ∼50 nm. Finally, when the relaxation of the dislocation boundary is considered, the synergistic effect is weakened.

Simplified atomistic based kinetic model for swelling prediction

In this paper, simplified kinetics with several self-consistent models is proposed for swelling prediction. It is based on the rate theory and atomistic simulation, while focusing on the description of experimentally observed bubbles and voids evolution and swelling. In this way, several models are proposed. They include the self-consistent accounting for the vacancy diffusion coefficient and the formation energy, models of heterogeneous bubbles nucleation, interstitial cluster sink and spatial inhomogeneity of sinks. Parametrized model shows the reasonable agreement with experimental data on AISI CW 316 steel, irradiated at various temperatures and doses in fast reactor EBR-II. The influence of interstitial cluster sink and dislocation annealing on temperature dependence of swelling is discussed.

Modeling oxygen diffusion in barium titanate using molecular dynamics: Comparison between Mg and Sc dopants

In this study, the diffusion coefficient of oxygen vacancies in barium titanate doped with 2.0% Sc was calculated by using molecular dynamics. The temperature was varied from 1273 K to 2500 K, and the simulation box consisted of 10 × 10 × 10 unit cells subject to periodic boundary conditions. The Sc dopants were incorporated into the B-sublattice and compensated for by using the randomly distributed oxygen vacancies on the oxygen sublattice. The diffusivity of the vacancies was determined from the slope of the mean-squared displacement of the oxygen ions over time. The Arrhenius plot of the diffusion coefficient showed a clear linear behavior, with an activation energy of 0.84 eV. The results were interpreted by computing radial pair distribution functions for various correlations (e.g., Ti–O and Sc–O) and by static lattice (nudged elastic band) calculations of energy barriers for the migration of oxygen. While Mg-doped BaTiO3 exhibited a strong trend of the formation of defect associates between the acceptor dopant and the oxygen vacancies that lead to a clear reduction in the observed activation energy for oxygen transport with increasing temperature (non-linear Arrhenius behavior), defect-induced interactions (associates) in case of Sc doping were nearly negligibly small, and gave rise to a linear Arrhenius plot with a single activation energy.

Recrystallization effect on surface passivation of Hastelloy X alloy fabricated by laser powder bed fusion

Post-heat treatment is generally adopted in the additive manufacturing field due to its alleviation of high residual stress and modification of rapid-solidified multilevel heterogeneous microstructure, and the related performance of the heat-treated counterparts calls for a systemic investigation to build a criterion of the heat treatment procedure. In this work, we focus on the heat treatment effects on the recrystallization of the Hastelloy X alloy produced by the laser powder bed fusion (LPBF) method, and the related surface passivation of the heat-treated counterparts is meticulously assessed as well. Results show that the multilevel heterostructure for LPBF Hastelloy X alloy consists of sub-micro dislocation cell substructures with Cr/Mo elemental segregation, fine columnar grains, and periodically-distributed molten pools. After heat treatment, partially and fully recrystallized structures for LPBF Hastelloy X alloys were achieved at 1100 and 1200 °C for 1 h, respectively. Furthermore, the as-built LPBF Hastelloy X alloy shows superior corrosion resistance while the heat-treated one (1100 °C) exhibits the worst in the borate buffer solution. The growth of passive film exhibited a highly linear correlation with the nucleation process controlled by diffusion, and high dislocation density and low angle grain boundary decreased the diffusion coefficient of cation vacancies, augmenting the nucleation sites of the passive film and enhancing its growth rate. Moreover, the micro-galvanic effect resulting from the partially recrystallized microstructure actively facilitated the formation of inhomogeneous porous passive films, leading to the worst corrosion resistance.

Diffusion of Hydroxylated Si Vacancies in Olivine, and Its Relevance to Si Diffusion

AbstractThe diffusion coefficient associated with the 3,612 cm−1 infrared absorbance band in H‐bearing olivine, attributed to a defect involving a vacant Si site balanced by four H+ (i.e., ), was determined in H in‐diffusion experiments at 1200°C–1400°C and 1.5–3.0 GPa in piston‐cylinder and multi‐anvil apparatuses. The retrieved values are in good agreement with experimentally determined diffusion coefficients ascribed to the same process from previous experiments, despite those being conducted at atmospheric pressure and representing out‐diffusion rather than in‐diffusion. Overall, the diffusivity of the Si vacancy is several orders of magnitude lower than that of the M‐site vacancy (∼4 orders of magnitude at 1000°C), with a higher activation energy (∼450–500 vs. 200–250 kJ mol−1), when both are charge‐compensated solely by H+. From these data, the diffusion coefficient of Si in H‐bearing olivine can be estimated using the relationship between vacancy concentration, vacancy diffusivity, and diffusivity of an ion moving by a vacancy mechanism. However, these diffusivities are inconsistent with published results for Si diffusivity, with a considerable discrepancy of around two orders of magnitude. This suggests that simple relationships between diffusion coefficients of vacancies and species moving by vacancy diffusion mechanisms may be inappropriate, highlighting again the complexity of H incorporation and diffusion mechanisms in olivine.

Impact of the pulse induced current on the microstructure and mechanical properties of the 7075-T6 aluminum alloy

The effect of the pulse induced current on the mechanical properties and microstructure of the 7075-T6 aluminum alloy was thoroughly studied by transmission electron microscopy, X-ray diffraction, and electron backscattered diffraction measurements. The experimental results demonstrated that the strength of the alloy decreases slightly, whereas the elongation increases significantly. On top of that, after the application of the induced electro-pulsing treatment, the dislocation density of the alloy decreases, while the grain size and the second phase particles grow slightly. In addition, the induced current also causes the Cube, Copper and S textures to decrease. On the other hand, the Goss texture is enhanced. The current density and the local temperature distribution of the sample were simulated by employing the ANSYS software. From the acquired outcomes, we can draw the conclusion that the recorded changes in the mechanical properties and microstructure of our sample can be attributed to the combination of the joule phenomenon and the pure electric effects of the current. The Joule heat and current increase the vacancy concentration and diffusion coefficient of solute atoms and promote dislocation recovery, precipitation phase growth, and grain rotation. • Induced electro-pulsing treatment (IEPT) is used to change the properties of 7075-T6 aluminum alloy. • After IEPT, the plasticity of the alloy is significantly improved while the strength is slightly decreased. • It is found that induced current can reduce dislocation density, promote grain rotation and change texture type.

Concentrations and diffusion coefficients of thermal equilibrium point defects in silicon crystals

The dependencies of concentrations of thermal equilibrium vacancies and interstitials on temperatures in Si crystals are determined directly, which has been a long-standing issue since the 1950s. They are evaluated by combining the formation energies and self-diffusion entropies deduced from the analyses of self-diffusion coefficients, and migration entropies deduced from diffusion coefficients of point defects. The concentrations as the number density of thermal equilibrium vacancies and interstitials at temperature T (K) are determined to be 5 × 1022exp(6.5)exp(–3.85 eV/k B T) and 5 × 1022exp(10.6)exp(–4.3 eV/k B T) cm−3, respectively. The diffusion coefficients of vacancies and interstitials are determined to be 2.7 × 10−3exp(–0.45 eV/k B T) and 2.5 × 10−2 exp(–0.49 eV/k B T) cm2 s−1, respectively. The results are discussed in comparison with those reported experimentally.

First-principles simulation of neutral and charged oxygen vacancies in m-ZrO2: an origin of filamentary type resistive switching

Metal oxide ZrO2 has been widely explored for resistive switching application due to excellent properties like high ON/OFF ratio, superior data retention, and low operating voltage. However, the conduction mechanism at the atomistic level is still under debate. Therefore, we have performed comprehensive insights into the role of neutral and charged oxygen vacancies in conduction filament (CF) formation and rupture, which are demonstrated using the atomistic simulation based on density functional theory (DFT). Formation energy demonstrated that the fourfold coordinated oxygen vacancy is more stable. In addition, the electronic properties of the defect included supercell confirm the improvement in electrical conductivity due to the presence of additional energy states near Fermi energy. The CF formation and rupture using threefold and fourfold oxygen vacancies are demonstrated through cohesive energy, electron localization function, and band structure. Cohesive energy analysis confirms the cohesive nature of neutral oxygen vacancies while the isolated behavior for +2 charged oxygen vacancies in the CF. In addition, nudged elastic band calculation is also performed to analyze the oxygen vacancy diffusion energy under different paths. Moreover, we have computed the diffusion coefficient and drift velocity of oxygen vacancies to understand the CF. This DFT study described detailed insight into filamentary type resistive switching observed in the experimentally fabricated device. Therefore, this fundamental study provides the platform to explore the switching mechanism of other oxide materials used for memristor device application.

INFLUENCE OF ADATOMS ON THE VACANCY GROWTH OF FACETED PORES IN A CRYSTAL UNDER MECHANICAL LOAD

The process of growth of faceted pores in a crystal under the influence of an applied mechanical load is considered in the framework of the classical Barton-Cabrera-Frank model, taking into account the presence of adatoms on the surface of pore faces. The growth is caused by the flow of excess vacancies from the bulk of the crystal, which arise due to tensile stresses. The recombination of advacancies and adatoms on the surface of pores is taken into account, and it is shown that as a result, a flow of adatoms from steps and fissures to the terrace can occur. This additional flow contributes to the growth of pores under load and, under certain conditions, can be the predominant mechanism of mass transfer, which must be taken into account for a correct assessment of the growth rate and lifetime of the crystal under load before failure. Expressions are obtained for the dependence of the pore growth rate on the applied mechanical load, the diffusion coefficients of vacancies and adatoms, and the rate of their recombination.

Dislocation loop evolution in Kr‐irradiated ThO2

AbstractThe early stage of microstructural evolution of ThO2, under krypton irradiation at 600, 800, and 1000°C, was investigated using in situ transmission electron microscopy (TEM). Dislocation loops grew faster, whereas their number density decreased with increasing irradiation temperature. Loop density was found to decrease with ion dose. Interstitial dislocation loops, including Frank loops with Burgers vector of a/3〈111〉 and perfect loops with Burgers vector of a/2〈110〉, were determined by traditional TEM and atomic resolution–scanning TEM techniques. Atomistic and mesoscale level modeling are performed to interpret experimental observations. The migration energy barriers of defects in ThO2 were calculated using density‐functional theory. The energetics of different dislocation loop types were studied using molecular dynamics simulations. Loop density and diameter were analyzed using a kinetic rate theory model that considers stoichiometric loop evolution. This analysis reveals that loop growth is governed by the mobility of cation interstitials, whereas loop nucleation is determined by the mobility of anion defects. Lastly, a rate theory model was used to extract the diffusion coefficients of thorium interstitials, oxygen interstitials, and vacancies.

What controls electrostatic vs electrochemical response in electrolyte-gated materials? A perspective on critical materials factors

Electrolyte-gate transistors are a powerful platform for control of material properties, spanning semiconducting behavior, insulator-metal transitions, superconductivity, magnetism, optical properties, etc. When applied to magnetic materials, for example, electrolyte-gate devices are promising for magnetoionics, wherein voltage-driven ionic motion enables low-power control of magnetic order and properties. The mechanisms of electrolyte gating with ionic liquids and gels vary from predominantly electrostatic to entirely electrochemical, however, sometimes even in single material families, for reasons that remain unclear. In this Perspective, we compare literature ionic liquid and ion gel gating data on two rather different material classes—perovskite oxides and pyrite-structure sulfides—seeking to understand which material factors dictate the electrostatic vs electrochemical gate response. From these comparisons, we argue that the ambient-temperature anion vacancy diffusion coefficient (not the vacancy formation energy) is a critical factor controlling electrostatic vs electrochemical mechanisms in electrolyte gating of these materials. We, in fact, suggest that the diffusivity of lowest-formation-energy defects may often dictate the electrostatic vs electrochemical response in electrolyte-gated inorganic materials, thereby advancing a concrete hypothesis for further exploration in a broader range of materials.

Real-Time Capturing of Microscale Events Controlling the Sintering of Lead-Free Piezoelectric Potassium-Sodium Niobate.

Sintering is a very important process in materials science and technological applications. Despite breakthroughs in achieving optimized piezoelectric properties, fundamentals of K0.5 Na0.5 NbO3 (KNN) sintering are not yet fully understood, facing densification versus grain growth competition. At present, microscale events during KNN sintering under reducing atmospheres are real-time monitored using a High Temperature-Environmental Scanning Electron Microscope. A two contacting KNN particles model satisfying the Kingery and Berg's bulk diffusion model is reported. Dynamic events like individual grain growth and grain elimination process are explored through a postanalysis of recorded image series. The diffusion coefficient for oxygen vacancies of 10-8 cm2 s-1 and average boundary mobility of 10-9 cm4 J-1 s-1 are reported for the KNN ceramics. Moreover, the local pore shrinkage is consistent with the Kingery and François's concept of pore stability except that pore curvatures are not all concave, convex or flat due to anisotropic grain-boundary energies. The global grain growth kinetics are described using parabolic and/or cubic laws. The effect of atmospheres and microstructure evolution on the intrinsic and extrinsic contributions to the dielectric response using Rayleigh's law is also explored. These results bring a new breath for KNN sintering studies in order to adapt the sintering process.

Onset of electronic conductivity in nanometer thick films of yttria stabilized zirconia (YSZ) at high electric fields

Electrochemical cells were prepared on a silicon wafer consisting of a 100 nm thick solid electrolyte of yttria stabilized zirconia (YSZ) prepared by atomic layer deposition (ALD), a bottom Ruthenium and an upper Gold electrode. Constant voltages were applied to the cells and currents were measured at temperatures between 120 °C and 170 °C. After an incubation time stationary currents were measured corresponding to conductivities well above the ionic one of the YSZ. After the polarization an open circuit voltage remained, which was reduced to zero by passing a constant depolarization current through the cell. All results were explained qualitatively and quantitatively assuming reactions with the electrodes and internal reactions within the YSZ. The latter lead to virtual electrodes with high electronic conductivity between which unreacted YSZ exists, i.e. a n/i/p junction forms. A stationary flux of single charged vacancies through the unreacted YSZ is assumed leading to the final stationary current. The calculated characteristic time for reaching this steady state is shown to be the incubation time, which in agreement with the experiment is inverse proportional to both the second power of electric field strength and the diffusion coefficient of oxygen vacancies.

An influence of mechanical stresses on the magnitude of the internal field in lead zirconate titanate thin films

In self-polarized lead zirconate titanate thin films formed on platinized silicon substrates, a significant increase in the internal electric field was observed as a result of long-term aging. To explain this phenomenon, a mechanism is proposed for the formation of the internal field associated with the diffusion of charged oxygen vacancies, which, in turn, is due to the action of a mechanical stress gradient. The diffusion coefficient of charged oxygen vacancies was estimated to be ~ 3·10-16 cm2/s. Keywords: thin films, lead zirconate titanate, internal field, Gorsky effect.

Влияние механических напряжений на величину внутреннего поля в тонких пленках цирконата-титаната свинца

In self-polarized lead zirconate titanate thin films formed on platinized silicon substrates, a significant increase in the internal electric field was observed as a result of long-term aging. To explain this phenomenon, a mechanism is proposed for the formation of the internal field associated with the diffusion of charged oxygen vacancies, which, in turn, is due to the action of a mechanical stress gradient. The diffusion coefficient of charged oxygen vacancies was estimated to be ∼ 3 × 10–16 cm2/s.

Doping- and Strain-Dependent Electrolyte-Gate-Induced Perovskite to Brownmillerite Transformation in Epitaxial La1-xSrxCoO3-δ Films.

Much recent attention has focused on the voltage-driven reversible topotactic transformation between the ferromagnetic metallic perovskite (P) SrCoO3-δ and oxygen-vacancy-ordered antiferromagnetic insulating brownmillerite (BM) SrCoO2.5. This is emerging as a paradigmatic example of the power of electrochemical gating (using, e.g., ionic liquids/gels), the wide modulation of electronic, magnetic, and optical properties generating clear application potential. SrCoO3 films are challenging with respect to stability, however, and there has been little exploration of alternate compositions. Here, we present the first study of ion-gel-gating-induced P → BM transformations across almost the entire La1-xSrxCoO3 phase diagram (0 ≤ x ≤ 0.70), under both tensile and compressive epitaxial strain. Electronic transport, magnetometry, and operando synchrotron X-ray diffraction establish that voltage-induced P → BM transformations are possible at essentially all x, including x ≤ 0.50, where both P and BM phases are highly stable. Under small compressive strain, the transformation threshold voltage decreases from approximately +2.7 V at x = 0 to negligible at x = 0.70. Both larger compressive strain and tensile strain induce further threshold voltage lowering, particularly at low x. The P → BM threshold voltage is thus tunable, via both composition and strain. At x = 0.50, voltage-controlled ferromagnetism, transport, and optical transmittance are then demonstrated, achieving Curie temperature and resistivity modulations of ∼220 K and at least 5 orders of magnitude, respectively, and enabling estimation of the voltage-dependent Co valence. The results are analyzed in the context of doping- and strain-dependent oxygen vacancy formation energies and diffusion coefficients, establishing that it is thermodynamic factors, not kinetics, that underpin the decrease in the threshold voltage with x, that is, with increasing formal Co valence. These findings substantially advance the practical and mechanistic understanding of this voltage-driven transformation, with fundamental and technological implications.

Effect of an external electric field on the diffusion of oxygen ions in zirconium dioxide doped with yttrium oxide. Molecular dynamics study

The influence of an external electric field on the character of ion motion, diffusion coefficients, and diffusion activation energies in cubic ZrO2 doped with Y2O3 with varying dopant content, temperature, and electric field strength has been studied by the molecular dynamics method. The diffusion coefficient of oxygen vacancies for models with different Y2O3 contents in the temperature range 873–1273 K without an imposed field decreases with an increase in the molar fraction of yttrium oxide in the crystal, while the dependence of the diffusion coefficient of O2− ions has a maximum (2.4∙10−11 m2/s) with an yttrium oxide content of 3 mol%. The activation energy of ionic conductivity, estimated in the absence of a field on the basis of diffusion of O2− ions, increases from 0.45 eV at a Y2O3 content of 4.6 mol% to 0.61 eV at a dopant content of 15.7 mol%. An external electric field of 0.02–0.08 V/Å noticeably changes the frequency of jumps of oxygen ions. At the electric field strength of 0.08 V/Å, a dopant content of 4.6 mol%, and a temperature of 1073 K, the О2− diffusion coefficient increases to 1.41∙10−9 m2/s. The dependence of diffusion coefficients on the field strength is close to quadratic.

Microstructural evolution and corrosion behavior of Ti–6Al–4V alloy fabricated by laser metal deposition for dental applications

In this study, microstructural evolution and corrosion behavior of Ti–6Al–4V (TC4) alloy fabricated by laser metal deposition (LMD) were investigated in simulated saliva at 37 °C as a function of scanning strategies. One-way scanning possessed a higher corrosion resistance than cross-scanning, but both of those were inferior to the wrought one. Compared with conventional wrought counterpart, the higher content of β phase improved the corrosion resistance. Results of Mott–Schottky and potentiostatic tests indicated that the passive film upon the surfaces of all the samples exhibited an N-type semiconductor structure and instantaneous nucleation. Of these, the LMD-ed parts displayed a lower donor concentration, higher vacancy diffusion coefficient, and thicker passive film than the wrought samples. XPS analysis revealed that the double-layer structure of passive film leads to a dense protective layer on the surface while the oxide contents of the three were different.