Vacancy Diffusion Model Research Articles

Influence of cationic vacancy diffusion on the aging behavior of low-temperature SrCo1-xRuxO3 thermosensitive ceramics

The thermosensitive ceramics of negative temperature coefficient (NTC), SrCo1-xRuxO3 (0 ≤ x ≤ 0.8), were synthesized using the solid-phase method. The research systematically explored the phase structure, microstructure, elemental chemical states, electrical properties, and aging performance. X-ray diffraction (XRD) data indicates that with the increase of Ru content, the lattice parameter increases. Scanning electron microscopy (SEM) images reveal a dense and uniform microstructure. X-ray photoelectron spectroscopy (XPS) data indicates the presence of Co2+/Co3+ and Ru4+/Ru5+ ion pairs. Resistive temperature data indicates its potential use as a low-temperature thermosensitive resistance material in the range of 2–300 K. Fitting the resistance-temperature curve using the thermally activated band conduction model and Mott's 3D variable range hopping model. Proposed the Ru–O2--Co hopping model, elucidating the hole hopping transport mechanism in NTC ceramics. Impedance spectroscopy analysis indicates that grain boundary resistance dominates the overall resistance of the sample. After aging at 77 K for 864 h, the maximum aging drift rate of the ceramic material is 1.55 %. Proposed a novel cationic vacancy diffusion model to explain aging phenomena, offering a new perspective for designing high-stability low-temperature NTC thermistors.

Modeling vacancy-induced porosity in compositionally-graded complex alloys

A phase-field model of the void evolution is developed to investigate the vacancy-induced Kirkendall porosity within diffusion couples under isothermal annealing conditions. This model encapsulates a comprehensive computational framework for multicomponent diffusion, non-equilibrium vacancy diffusion, voids nucleation, and growth — integrating considerations for surface anisotropy and morphological instability. This novel thermodynamically consistent methodology combines the phase-field model with the vacancy diffusion model and uses thermodynamic and atomic mobility parameters defined by CALPHAD approach. The generalized nature of the method enables us to include both non-equilibrium and equilibrium vacancies, covering all cases of non-ideal/ideal sinks and sources for vacancies, whether at dislocations or void surfaces. Moreover, the model can deal with compositionally complex alloys such as Ni-based superalloys. Along with the full model, a fast variant is also suggested, providing long-time simulations at the experimentally relevant time and space scales valuable for both academic and industrial contexts. The model’s efficacy was demonstrated through precise simulation of voids evolution in a model AlCoCrTa/Ni diffusion couple, mirroring the experimental outcomes observed in the CMSX-10/Ni diffusion couple at 1525 K after 192 h of annealing. This encompassed accurate replication of diffusion profiles and tomographic analysis of voids. A very good agreement with the experimental data was observed, particularly in the distribution of pore volume-fractions and the delineation of void shapes.

Final‐stage densification kinetics of direct current–sintered ZrB2

AbstractFinal‐stage sintering was analyzed for nominally phase pure zirconium diboride synthesized by borothermal reduction of high‐purity ZrO2. Analysis was conducted on ZrB2 ceramics with relative densities greater than 90% using the Nabarro–Herring stress–directed vacancy diffusion model. Temperatures of 1900°C or above and an applied uniaxial pressure of 50 MPa were required to fully densify ZrB2 ceramics by direct current sintering. Ram travel data were collected and used to determine the relative density of the specimens during sintering. Specimens sintered between 1900 and 2100°C achieved relative densities greater than 97%, whereas specimens sintered below 1900°C failed to reach the final stage of sintering. The average grain size ranged from 1.0 to 14.7 μm. The activation energy was calculated from the slope of an Arrhenius plot that used the Kalish equation. The activation energy was 162 ± 34 kJ/mol, which is consistent with the activation energy for dislocation movement in ZrB2. The diffusion coefficients for dislocation motion that controls densification were 5.1 × 10−6 cm2/s at 1900°C and 5.1 × 10−5 cm2/s at 2100°C, as calculated from activation energy and average grain sizes. This study provides evidence that the dominant mechanism for final‐stage sintering of ZrB2 ceramics is dislocation motion.

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.

Temperature Dependent Anion Rotational Dynamics Correlated to Cation Transport in Cluster Ion Anti-Perovskites

As fast-ion conductors, cluster-ion anti-perovskites (APs) are attractive for potential new mechanisms of conduction whereby cation and anion motion is highly correlated. Cluster-ion APs, like perovskites, have a framework that accommodates diverse atomic substitutions. Furthermore, the potential for cluster-ion substitution onto one or both anion sites (A and B in X3AB) provides additional compositional degrees of freedom. We have synthesized and characterized a series of compositions Na3-x(NH2)xO1-x(BH4), a unique sodium ion conductor with two chemically distinct cluster anions, in order to further understand the correlation between anion rotation and cation translation. We are particularly interested in the x = 1 composition which shows a positive deviation from conductivity trends as predicted by a vacancy diffusion model, shown in Figure 1. This presentation will discuss the synthesis and characterization of Na2(NH2)(BH4) via XRD, neutron diffraction, NMR, and AIMD, aimed at understanding the temperature dependent rotational dynamics of the cluster anions and their effects on cation transport.This work was supported as part of the Joint Center for Energy Storage Research, an Energy Innovation Hub funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences.Figure 1. The (a) atomistic model and (b) ionic conductivity of Na3-x(NH2)xO1-x(BH4) cluster-ion APs Figure 1

Simulation of Diffusion Bonding of Different Heat Resistant Nickel-Base Alloys

Currently, an important fundamental problem of practical importance is the production of high-quality solid-phase compounds of various metals. This paper presents a theoretical model that allows one to study the diffusion process in nickel-base refractory alloys. As an example, a two-dimensional model of ternary alloy is considered to model diffusion bonding of the alloys with different compositions. The main idea is to divide the alloy components into three groups: (i) the base element Ni, (ii) the intermetallic forming elements Al and Ti and (iii) the alloying elements. This approach allows one to consider multi-component alloys as ternary alloys, which greatly simplifies the analysis. The calculations are carried out within the framework of the hard sphere model when describing interatomic interactions by pair potentials. The energy of any configuration of a given system is written in terms of order parameters and ordering energies. A vacancy diffusion model is described, which takes into account the gain/loss of potential energy due to a vacancy jump and temperature. Diffusion bonding of two dissimilar refractory alloys is modeled. The concentration profiles of the components and order parameters are analyzed at different times. The results obtained indicate that the ternary alloy model is efficient in modeling the diffusion bonding of dissimilar Ni-base refractory alloys.

Tracer Diffusion Coefficients of Li Ions in LixMn2O4 Thin Films Observed by Isotope Exchange Secondary Ion Mass Spectrometry

Tracer diffusion coefficients D* of lithium ions in LixMn2O4 (0.2 < x < 1) thin films were measured as a function of the composition x by using secondary ion mass spectrometry. For this purpose, a new “step-isotope-exchange method” was developed to observe the time dependence of the 6Li isotope concentration ratio in the LixMn2O4 film which is in contact with a 6Li-enriched electrolyte to exchange Li+ ions. A steep decrease in D* depending on the Li composition was observed for LixMn2O4, with D* = 8 × 10–13 cm2 s–1 for x = 0.2 and decreasing to 1.5 × 10–17 cm2 s–1 for x = 1.0 (bulk diffusion coefficient, Db*). This behavior is well explained by a vacancy diffusion model for the α phase on LixMn2O4 (0.77 < x < 1.0). Chemical diffusion coefficients D̃ were also measured in the range of 0.2 < x < 1.0 by an electrochemical method, which was compared with the D* to evaluate the effect of thermodynamic factors. The thermodynamic factors and interactions between Li+ ions were found to strongly influence the chemical diffusion coefficient. The tracer diffusion measurements are important to understand the charge–discharge mechanism in the electrodes of lithium-ion batteries.

Comparative study of aluminum and nickel contact electrodes for indium–tin–zinc oxide thin film transistors using oxygen vacancy diffusion model

We fabricate amorphous indium–tin–zinc oxide (ITZO) thin film transistors (TFTs), in which the source/drain (S/D) electrodes are composed of metallic Al and nickel Ni. We experimentally investigate the contact characteristics of Al and Ni S/D electrodes using the transmission line method. The ITZO with Al exhibits low field-effect mobility (≤4.8 cm2/Vs) and behaves like a conductor at short channel lengths. Even with a short channel length, the ITZO with Ni exhibits typical field-effect TFT behavior and high field-effect mobility (≥8.1 cm2/Vs), required for a high-resolution display. We present a mechanism to dope oxygen vacancies in the S/D regions to account for the differences in the properties of the ITZO TFTs with Al and Ni electrodes. Using a technology computer-aided design (TCAD) simulation, we show that the oxygen vacancies (VO+) could diffuse from the Al and Ni S/D electrodes at a substrate temperature of 350 °C in 30 min, and find that their diffusion coefficient and activation energy are 2.8 × 10−8 cm2/s and 0.45 eV, respectively. Further, the S/D doping concentrations of VO+ are 3.47 × 1019 and 1.55 × 1017/cm3 at the Al and Ni interfaces, respectively. The lateral diffusion profiles of VO+ are different for the Al and Ni electrodes, which caused a difference in the drain current to gate voltage transfer characteristics of each electrode.

Mean first passage times reconstruct the slowest relaxations in potential energy landscapes of nanoclusters.

Relaxation modes are the collective modes in which all probability deviations from equilibrium states decay with the same relaxation rates. In contrast, a first passage time is the required time for arriving for the first time from one state to another. In this paper, we discuss how and why the slowest relaxation rates of relaxation modes are reconstructed from the first passage times. As an illustrative model, we use a continuous-time Markov state model of vacancy diffusion in KCl nanoclusters. Using this model, we reveal that all characteristics of the relaxations in KCl nanoclusters come from the fact that they are hybrids of two kinetically different regions of the fast surface and slow bulk diffusions. The origin of the different diffusivities turns out to come from the heterogeneity of the activation energies on the potential energy landscapes. We also develop a stationary population method to compute the mean first passage times as mean times required for pair annihilations of particle-hole pairs, which enables us to obtain the symmetric results of relaxation rates under the exchange of the sinks and the sources. With this symmetric method, we finally show why the slowest relaxation times can be reconstructed from the mean first passage times.

Mechanism for Propagation of Intergranular Corrosion in Pipeline Steel

"High-pH" (pH 8 to 10.5) stress corrosion cracking (SCC) and intergranular corrosion (IGC) of low-carbon pipeline steels both occur in the active-passive transition potential region, suggesting that both processes are driven by metal dissolution (1). In non-sensitized pipeline steels, there are no grain boundary (GB) precipitates and no consensus on the mechanism of IGC. IGC in non-sensitized steels forms triangular wedges of corrosion product around GBs (2,3). The wedges display characteristic angles determined by enhanced rates of dissolution at the GB compared to that of the grain surface (2,3). Recently we reported the formation of such corrosion product wedges around GB triple junctions during high-pH IGC of X70 pipeline steel in 1 M sodium bicarbonate solution (4). Nanoindentation measurements detected reduced hardness in the metal around corroded GBs, which was suggested to arise from softening by vacancies produced by anodic oxidation of reactive Si solute atoms (5). In the present work, a mathematical model was developed for evolution of GB morphology during IGC of pipeline steel. The model incorporates generation of vacancies at the dissolving steel interface and vacancy diffusion to GBs. The vacancy concentration at the corroding surface is taken to be the same as that of Si solute, 0.77 at. %. Vacancies reaching GBs are assumed to diffuse rapidly to the steel surface and contribute to GB recession, thus accounting for enhanced penetration of corrosion along the boundary. Finite-element simulations were performed to predict GB shape evolution. The predicted shapes were compared with measurements from cross sections of X70 steel samples corroded in 1 M NaHCO3at -0.521 V vs Ag/AgCl. Short corrosion exposures of 2 hr produced GB wedges with flat triangular sides having angles of 120o- 140o(5). Calculations with the vacancy diffusion model showed that these angles are consistent with a vacancy diffusivity of 3 x 10-18m2/s, one order of magnitude smaller than the diffusivity of 6 x 10-17m2/s obtained by extrapolation from high-temperature measurements in bcc Fe (6). The lower diffusivity in ferritic steel is considered reasonable in view of likely vacancy trapping in the alloy. For longer corrosion exposures of 5 hr, the current density decreased by two orders of magnitude due to the formation of a precipitated corrosion product on the outer steel surface. Pronounced sharpening of the GB wedges was observed to angles of 20o- 30o. For comparison, calculations with the vacancy diffusion model incorporated the diffusivity from short-time experiments and included the transient decay of the corrosion rate. The calculations demonstrated dramatic sharpening of the GB wedges in quantitative agreement with experiment (Fig. 1). Sharpening is caused by an enhanced contribution to GB morphology evolution from vacancy diffusion at low current densities, relative to that from grain surface corrosion. Further, sample cross sections after long corrosion exposures showed evidence of GB crack initiation. It is suggested that wedge angle sharpening leads to intensification of tensile wedging stress due to GB corrosion product (5), which eventually initiates cracks. Therefore, the vacancy diffusion model explains IGC morphology evolution and also provides an explanation for the transition of IGC to early-stage SCC. REFERENCES R. N. Parkins, S. Zhou, Corros. Sci., 52, 347 (1996). B. Gwinner et al., Corros. Sci., 107, 60 (2016). L. Beaunier, M. Froment, C. Vigneaud, Electrochim. Acta, 25, 1239 (1980). D. Yavas et al., Electrochem. Commun., 88, 88 (2018). D. Yavas et al., Electrochim. Acta, 285, 336 (2018). M. I. Mendelev, Y. Mishin. Phys. Rev. B, 80, 144111 (2009). ACKNOWLEDGMENTS Support was provided by the USDoT PHMSA under Competitive Academic Agreement Program No. DTPH5614HCAP03 and DTPH5614HCAP01. Figure 1. Grain boundary wedge apex angle variations over time. Curves (a), (b) and (c) are calculated from the FE simulation using time-dependent corrosion rates from experimental current transients. Data points (a), (b) and (c) are experimental wedge angles from the same corrosion experiments. Error bars represent standard deviations of measured wedge angles in each experiment. Figure 1

Diffusion and Equilibration of Site-Preferences Following Transmutation of Tracer Atoms

Using the method of perturbed angular correlation of gamma rays, diffusional jump-frequencies of probe atoms can be measured through relaxation of the nuclear quadrupole interaction. This was first shown in 2004 for jumps of tracer atoms that lead to reorientation of the local electric field-gradient, such as jumps on the connected a-sublattice in the L12 crystal structure. Studies on many such phases using the 111In/Cd PAC probe are reviewed in this paper. A major finding from a 2009 study of indides of rare-earth elements, In3R, was the apparent observation of two diffusional regimes: one dominant for heavy-lanthanide phases, R= Lu, Tm, Er, Dy, Tb, Gd, that was consistent with a simple model of vacancy diffusion on the In a-sublattice, and another for light-lanthanides, R= La, Ce, Pr, Nd, that had no obvious explanation but for which several alternative diffusion mechanisms were suggested. It is herein proposed that the latter regime arises not from a diffusion mechanism but from transfer of Cd-probes from In-sites where they originate to R-sites as a consequence of a change in site-preference of 111Cd-daughter atoms from In-sites to R-sites following transmutation of 111In. Support for this transfer mechanism comes from a study of site-preferences and jump-frequencies of 111In/Cd probes in Pd3R phases. Possible mechanisms for transfer are described, with the most likely mechanism identified as one in which Cd-probes on a-sites transfer to interstitial sites, diffuse interstitially, and then react with vacancies on b-sites. Implications of this proposal are discussed. For indides of heavy-lanthanide elements, the Cd-tracer remains on the In-sublattice and relaxation gives the diffusional jump-frequency.

Lithium diffusion coefficient in LiMn2O4 thin films measured by secondary ion mass spectrometry with ion-exchange method

In this study, the lithium tracer diffusion coefficient (DLi∗) in spinel-type LiMn2O4 thin films is measured by secondary ion mass spectroscopy (SIMS) in the temperature range from 200 to 550 °C. An ion-exchange method is employed to prepare diffusion couples consisting of the stable isotopes 6Li and 7Li. The isotope profiles were measured by SIMS analysis to determine DLi∗ in the LiMn2O4 films. The DLi∗ value was 1.4 × 10−10 cm2/s at 300 °C and the activation energy was 0.52 eV, which is consistent with that of bulk LiMn2O4. The extrapolated value of DLi∗ at 25 °C was on the order of 10−14 cm2/s, which is smaller than the chemical diffusion coefficient of LixMn2O4 measured by electrochemical methods. The temperature dependence of DLi∗ can be explained by the vacancy diffusion model, in which the extrinsic and intrinsic regions of diffusion exist in the low- and high-temperature regions, respectively.

3D discrete dislocation dynamics study of creep behavior in Ni-base single crystal superalloys by a combined dislocation climb and vacancy diffusion model

A three-dimensional (3D) discrete dislocation dynamics (DDD) creep model is developed to investigate creep behavior under uniaxial tensile stress along the crystallographic [001] direction in Ni-base single crystal superalloys, which takes explicitly account of dislocation glide, climb and vacancy diffusion, but neglects phase transformation like rafting of γ′ precipitates. The vacancy diffusion model takes internal stresses by dislocations and mismatch strains into account and it is coupled to the dislocation dynamics model in a numerically efficient way. This model is helpful for understanding the fundamental creep mechanisms in superalloys and clarifying the effects of dislocation glide and climb on creep deformation. In cases where the precipitate cutting rarely occurs, e.g. due to the high anti-phase boundary energy and the lack of superdislocations, the dislocation glide in the γ matrix and the dislocation climb along the γ/γ′ interface dominate plastic deformation. The simulation results show that a high temperature or a high stress both promote dislocation motion and multiplication, so as to cause a large creep strain. Dislocation climb accelerated by high temperature only produces a small plastic strain, but relaxes the hardening caused by the filling γ channels and lets dislocations further glide and multiply. The strongest variation of vacancy concentration occurs in the horizontal channels, where more mixed dislocations exit and tend to climb. The increasing internal stresses due to the increasing dislocation density are easily overcome by dislocations under a high external stress that leads to a long-term dislocation glide accompanied by multiplication.

Precipitation in a copper matrix modeled byab initiocalculations and atomistic kinetic Monte Carlo simulations

A kinetic Monte Carlo approach is used to study the influence of Cr, Fe, Al, or Mg addition on the precipitation in a Cu–Ni–Si alloy. The simulation method is based on a vacancy diffusion model. The crucial parameters of this method are the pairwise mixing energies of all contained elements which are determined by ab initio calculations. The number of dissolved atoms in equilibrium state is used to estimate the influence of Cr, Fe, Al, or Mg on the electrical conductivity. In order to estimate the influence of the alloying elements on strength ab initio calculations of misfit strain at the Cu/Ni3Si interface are performed. The atomistic kinetic Monte Carlo (AKMC) simulations reveal that Cr, Fe, Al, and Mg atoms are located at different positions: Mg and Al atoms are preferably located at the interface of Ni–Si precipitates and Cu matrix, Cr atoms diffuse into Ni–Si precipitates, and Fe atoms form Fe clusters surrounded by Ni–Si shells. Cr addition leads to a significantly reduced fraction of atoms dissolved in the matrix which indicates an increase of electrical conductivity, whereas Mg addition results in a high misfit strain at the Cu/Ni3Si interface which can contribute to increased strength.

Tensile stress and plastic deformation in aluminum induced by aqueous corrosion

Measurement of near-surface stress generated by metallic corrosion can reveal defects and material property changes relevant to structural degradation by stress corrosion cracking. In this study, stress and topography evolution were characterized during alkaline corrosion of high-purity aluminum. In situ stress measurements revealed tensile increases of the force per width (stress integrated over depth) that scale directly with the sample yield stress. Spectral analysis of the uniform dimpled surface pattern produced by corrosion showed that transient changes of its characteristic wavelength track closely with the force per width. Together, the stress and topography measurements imply that corrosion creates a plastically deformed metal layer. Tensile stress is attributed to the lattice contraction associated with metal vacancies introduced during dissolution. In agreement with this hypothesis, a vacancy diffusion model successfully predicted the time dependence and magnitude of the force response, as well as the observed scaling relation between plastic layer thickness and pattern wavelength. The driving force for vacancy formation is thought to arise from high hydrogen and low aluminum chemical potentials near the corroding surface, the latter imposed by the high dissolution potential relative to the equilibrium potential of aluminum.

Research Progress in Gasochromics Mechanism of Tungsten Oxide Thin Films

The gasochromic effect and its potential applications of tungsten oxide (WO3) thin films are introduced. The research progress in gasochromics mechanism of WO3films is reviewed and various mechanism models are summarized and discussed. The double injection model, oxygen vacancy diffusion model and localized water molecules model are extensively used to explain the gasochromic coloration of WO3films. A perspective on the gasochromics mechanism development of WO3films is tended to fabricate WO3film with single crystal and regular structure, which may simply the quantitative characterizations induced by the complicated structure. Elucidating gasochromics mechanism of WO3films not only helps to understand gasochromic coloration phenomenon well but also improves the performance of gasochromic coloration devices. It also accelerates the development of the relative science, such as gas detector, atom/ion transport material, surface catalysis of semiconductor, and so on.

Precipitation in α $\alpha$ -Fe based Fe-Cu-Ni-Mn-alloys: behaviour of Ni and Mn modelled by ab initio and kinetic Monte Carlo simulations

A kinetic Monte Carlo approach is used to study the behaviour of Ni and Mn solutes in $\alpha$ -Fe containing Cu, Ni and Mn foreign atoms. The simulation method is based on a vacancy diffusion model. Regarding precipitation, the crucial parameters of this method are the mixing energies of all contained elements. These are determined using ab initio calculations taking into account temperature by varying the lattice constant. It is found that the behaviour of Ni and Mn solutes which can form NiMn-precipitates, NiMn-shells around Cu precipitates or stay in solution changes significantly with small changes in the mixing energies.

Molecular simulation of structural relaxation in ultrathin polymer films

Structural relaxation and physical aging in glassy polymer films have attracted much attention in the past two decades due to their strong correlation with the lifetime of polymer-based nano-devices. Currently, the observed physical aging in polymer films was explained on the basis of a free volume diffusion model (FVDM) that has not yet been validated by simulations at the molecular level. Here we performed a Monte Carlo simulation by introducing the vacancy diffusion mechanism (similar to FVDM) to investigate the structural relaxation in ultrathin polymer films. The results show that the local average density of segments increases linearly with the logarithm of time, similar to the fluorescence intensity and dielectric strength measurements in experiments. The responses of relaxation rates in ultrathin films to temperatures are consistent with that for glassy polymer thin films in experiments. The emergence of a peak of relaxation rates with decreasing temperature can be attributed to the competition of two mechanisms (segment mobility and accurate initial vacancy concentration) from the molecular levels. Our results demonstrate that the simulations with a vacancy diffusion model could indeed provide new insights from the molecular levels to understand the structural relaxation and physical aging in ultrathin polymer films.

Predicting the optimal dopant concentration in gadolinium doped ceria: a kinetic lattice Monte Carlo approach

Gadolinium doped ceria (GDC) is a promising alternative electrolyte material for solid oxide fuel cells that offers the possibility of operation in the intermediate temperature range (773–1073 K). To determine the optimal dopant concentration in GDC, we have employed a systematic approach of applying a 3D kinetic lattice Monte Carlo (KLMC) model of vacancy diffusion in conjunction with previously calculated activation energies for vacancy migration in GDC as inputs. KLMC simulations were performed including the vacancy repelling effects in GDC. Increasing the dopant concentration increases the vacancy concentration, which increases the ionic conductivity. However, at higher concentrations, vacancy–vacancy repulsion impedes vacancy diffusion, and together with vacancy trapping by dopants decreases the ionic conductivity. The maximum ionic conductivity is predicted to occur at ≈20% to 25% mole fraction of Gd dopant. Placing Gd dopants in pairs, instead of randomly, was found to decrease the conductivity by ≈50%. Overall, the trends in ionic conductivity results obtained using the KLMC model developed in this work are in reasonable agreement with the available experimental data. This KLMC model can be applied to a variety of ceria-based electrolyte materials for predicting the optimum dopant concentration.

Beyond the Cahn-Hilliard Equation: a Vacancy-Based Kinetic Theory

A Self-Consistent Mean Field (SCMF) kinetic theory including an explicit description ofthe vacancy diffusion mechanism is developed. The present theory goes beyond the usual local equi-librium hypothesis. It is applied to the study of the early time spinodal decomposition in alloys. Theresulting analytical expression of the structure function highlights the contribution of the vacancydiffusion mechanism. Instead of the single amplification rate of the Cahn-Hillard linear theory, thelinearized SCMF kinetic equations involve three constant rates, first one describing the vacancy re-laxation kinetics, second one related to the kinetic coupling between local concentrations and paircorrelations and the third one representing the spinodal amplification rate. Starting from the same va-cancy diffusion model, we perform kineticMonte Carlo simulations of a Body Centered Cubic (BCC)demixting alloy. The resulting spherically averaged structure function is compared to the SCMF pre-dictions. Both qualitative and quantitative agreements are satisfying.