One Stone, Two Birds: Using High Electric Fields to Enhance the Mobility and the Concentration of Point Defects in Ion-Conducting Solids.

Improving the ionic conductivity of outstanding, composition-optimized crystalline electrolytes is a major challenge. Achieving increases of orders of magnitude requires, conceivably, highly nonlinear effects. One known possibility is the use of high electric fields to increase point-defect mobility. In this study, we investigate quantitatively a second possibility that high electric fields can increase substantially point-defect concentrations. As a model system, we take a pyrochlore oxide (La2Zr2O7) for its combination of structural vacancies and dominant anti-Frenkel disorder; we perform molecular-dynamics simulations with many-body potentials as a function of temperature and applied electric field. Results within the linear regime yield the activation enthalpies and entropies of oxygen-vacancy and oxygen-interstitial migration, and from three independent methods, the enthalpy and entropy of anti-Frenkel disorder. Transport data for the nonlinear regime are consistent with field-enhanced defect concentrations and defect mobilities. A route for separating the two effects is shown, and an analytical expression for the quantitative prediction of the field-dependent anti-Frenkel equilibrium constant is derived. In summary, we demonstrate that the one stone of a nonlinear driving force can be used to hit two birds of defect behavior.

A Single Model for the Thermodynamics and Kinetics of Metal Exsolution from Perovskite Oxides.

Exsolution has emerged as an outstanding route for producing oxide-supported metal nanoparticles. For ABO3-perovskite oxides, various late transition-metal cations can be substituted into the lattice under oxidizing conditions and exsolved as metal nanoparticles after reduction. A consistent and comprehensive description of the point-defect thermodynamics and kinetics of this phenomenon is lacking, however. Herein, supported by hybrid density-functional-theory calculations, we propose a single model that explains diverse experimental observations, such as why substituent transition-metal cations (but not host cations) exsolve from perovskite oxides upon reduction; why different substituent transition-metal cations exsolve under different conditions; why the metal nanoparticles are embedded in the surface; why exsolution occurs surprisingly rapidly at relatively low temperatures; and why the reincorporation of exsolved species involves far longer times and much higher temperatures. Our model's foundation is that the substituent transition-metal cations are reduced to neutral species within the perovskite lattice as the Fermi level is shifted upward within the bandgap upon sample reduction. The calculations also indicate unconventional influences of oxygen vacancies and A-site vacancies. Our model thus provides a fundamental basis for improving existing, and creating new, exsolution-generated catalysts.

A general expression for the statistical error in a diffusion coefficient obtained from a solid-state molecular-dynamics simulation.

Analysis of the mean squared displacement of species k , r k 2 , as a function of simulation time t constitutes a powerful method for extracting, from a molecular-dynamics (MD) simulation, the tracer diffusion coefficient, D k * . The statistical error in D k * is seldom considered, and when it is done, the error is generally underestimated. In this study, we examined the statistics of r k 2 t curves generated by solid-state diffusion by means of kinetic Monte Carlo sampling. Our results indicate that the statistical error in D k * depends, in a strongly interrelated way, on the simulation time, the cell size, and the number of relevant point defects in the simulation cell. Reducing our results to one key quantity-the number of k particles that have jumped at least once-we derive a closed-form expression for the relative uncertainty in D k * . We confirm the accuracy of our expression through comparisons with self-generated MD diffusion data. With the expression, we formulate a set of simple rules that encourage the efficient use of computational resources for MD simulations.

Recipes for superior ionic conductivities in thin-film ceria-based electrolytes.

We employed Molecular Dynamics (MD) and Metropolis Monte Carlo (MMC) simulations to determine the oxide-ion mobility uO in Ce1-yGdyO2-y/2 (y = 0.02, 0.1, 0.2) for the range of temperatures 1400 ≤ T/K ≤ 2000 and field strengths 0.6 ≤ E/MV cm-1 ≤ 15.0. Direct, unambiguous determination of uO(E) from MD simulations is shown to require examination of the ions' mean displacement as a function of time. MD simulations were performed for random distributions of Gd cations and equilibrium distributions obtained by MMC calculations. All uO(E,T,y) data obtained can be described by an (empirically augmented) analytical model with four zero-field parameters, a result that allows data to be extrapolated down to the temperatures of electrolyte operation. Specifically, the oxide-ion conductivity is predicted, for example at T = 700 K, (i) to be up to 101 higher for a random distribution of Gd than for an equilibrium distribution; and (ii) to be a factor of 100.8 higher for a 6 nm thin film than for a µm-thick sample under a potential difference of 1 V. By virtue of non-equilibrium deposition and nm-thick samples, thin films thus provide two new recipes for attaining even higher oxide-ion conductivities in ceria-based electrolytes.

Surface potentials of acceptor- and donor-doped CeO2 thin films and their relation to oxygen surface exchange.

Surface Fermi level positions, ionisation potentials, and work functions of acceptor-, donor-, and nominally undoped CeO2 have been determined by means of in situ photoelectron spectroscopy on films grown with different surface orientation and preparation conditions. The Fermi energy varies in accordance with the doping and oxygen activity. The ionisation potentials are largely unaffected by the preparation conditions and surface orientation. They are comparable for nominally undoped, 1% donor-doped, and 1% acceptor-doped films. The majority of the 10% Gd-doped films exhibit a 0.5 eV lower ionisation potential, which might be related to the presence of a surface space-charge region. The lower ionisation potential of the 10% Gd-doped films compensates for their lower Fermi energies and eventually results in work functions being largely independent on doping. Oxygen surface exchange coefficients determined using secondary ion mass spectrometry and conductivity relaxation experiments reveal similar magnitudes and are not strongly affected by doping type, concentration, and surface orientation. The results indicate that surface space-charge regions are crucial for oxygen surface exchange but do not allow to finally identify the rate determining step for oxygen incorporation into CeO2-based materials.

High oxide-ion conductivity in acceptor-doped Bi-based perovskites at modest doping levels.

A combination of impedance spectroscopy, time-of-flight secondary ion mass spectrometry and literature data are used to show that, (i) the bulk oxide ion conductivity of A-site, alkaline earth-doped BiFeO3 (BF) is independent of the ionic radius of the alkaline earth ion (Ca, Sr, Ba) and, (ii) despite very different A-site environments in (Na1/2Bi1/2)TiO3 and BF, similar high levels and optimisation of bulk oxide ion conductivity in these Bi-based tilted perovskites is achieved at modest acceptor doping levels of ∼1-10%. These results clearly demonstrate that optimisation of oxide ion conductivity in these materials requires concepts beyond a simple crystallochemical approach based on matching the ionic radii of acceptor dopant and host lattice ions.

The surprisingly high activation barrier for oxygen-vacancy migration in oxygen-excess manganite perovskites.

The current description of oxygen-vacancy behaviour in (La,Sr)MnO3 perovskite-type oxides, though widely accepted, ignores a pronounced discrepancy. Values of the activation enthalpy of oxygen-vacancy migration reported in experimental investigations (ΔHmig,v = 1.2-2.4 eV) are substantially higher than those predicted in computational work (ΔHmig,v = 0.5-1.0 eV). In this study we examine the origin of this discrepancy using molecular-dynamics simulations. Specifically we investigate the effect of various cation defects (Sr substituents, La vacancies, Mn vacancies, both types of cation antisites) on the diffusivity of oxygen vacancies (Dv) in orthorhombic LaMnO3. Our results indicate that the presence of cation vacancies can bring the computational values of ΔHmig,v into good agreement with experimental data. Applying an analytical model to our results, we predict that isothermal values of Dv in manganite perovskites containing cation vacancies will depend strongly on oxygen partial pressure (contrary to the standard assumption). The implications of our results for modelling the point-defect chemistry of, and oxygen diffusion in, manganite perovskites are discussed.

The usefulness of molecular-dynamics simulations in clarifying the activation enthalpy of oxygen-vacancy migration in the perovskite oxide BaTiO3.

We employed molecular-dynamics simulations with interatomic pair-potentials to examine oxygen-vacancy diffusion in the cubic phase of perovskite BaTiO3 as a function of temperature. By comparing the absolute rate of vacancy diffusion as well as its temperature dependence with experimental data, we are able to narrow down the activation enthalpy of migration to 0.70-0.76 eV.

A quantitative analysis of two-fold electrical conductivity relaxation behaviour in mixed proton-oxide-ion-electron conductors upon hydration.

Electrical conductivity relaxation experiments on oxides with three mobile charge carriers, H+, O2- and e-, yield in (de-)hydration experiments kinetic parameters (diffusion coefficients and surface reaction constants). In addition, three amplitude factors are obtained, but they have not been given further consideration because quantitative expressions for their forms are lacking. In this study, the forms of the amplitude factors are derived for a diffusion-limited and a surface-reaction-limited case and a mixed case. In order to demonstrate the benefits of the approach, the electrical conductivity relaxation behaviour of lanthanum tungstate (La5.4WO11.1, LaWO54) was investigated experimentally over the temperature range 923 ≤T/K ≤ 1223. A switch from two-fold non-monotonic relaxation behaviour at high temperatures to two-fold monotonic behaviour at low temperatures upon hydration was observed. The switch in sign of the fast kinetics' amplitude factor can be assigned to the electrochemical mobility of protons surpassing the electron-hole mobility with decreasing temperature.

The blocking effect of surface dislocations on oxygen tracer diffusion in SrTiO3.

The existence of a polishing-induced damaged zone at the surface of standard, nominally undoped, single-crystal SrTiO3 is exploited in diffusion studies in order to investigate the interaction between oxygen vacancies and dislocations. Tracer diffusion profiles for such crystals are proposed to exhibit three features: a short feature arising from a surface space-charge layer; an intermediate, longer feature arising from the high density of dislocations in the damaged zone; and finally, a much longer feature corresponding to diffusion in the homogeneous bulk crystal. Quantitative information is provided by finite-element-method calculations. First, the distribution of oxygen vacancies in a sample in which space-charge zones depleted of oxygen vacancies form at dislocations and at the sample surface is calculated; subsequently, oxygen tracer diffusion profiles for such vacancy distributions are simulated. The proposed model is experimentally validated by performing conventional oxygen isotope exchange and depth-profiling experiments on commercial single-crystal SrTiO3. In this way, we confirm directly that arrays of dislocations in acceptor-doped SrTiO3, by virtue of the attendant space-charge tubes, hinder the diffusion of oxygen. Finally, in order to aid the prediction of oxygen tracer diffusion profiles in polished perovskite single-crystal substrates, we suggest a one-dimensional continuum approach that takes account of the complex, three-dimensional diffusion problem posed by dislocation arrays with depletion space-charge tubes.

Correction: Oxygen diffusion in single crystal barium titanate.

Correction for 'Oxygen diffusion in single crystal barium titanate' by Markus Kessel et al., Phys. Chem. Chem. Phys., 2015, 17, 12587-12597.

A Space-Charge Treatment of the Increased Concentration of Reactive Species at the Surface of a Ceria Solid Solution.

A space-charge theory applicable to concentrated solid solutions (Poisson-Cahn theory) was applied to describe quantitatively as a function of temperature and oxygen partial pressure published data obtained by in situ X-ray photoelectron spectroscopy (XPS) for the concentration of Ce3+ (the reactive species) at the surface of the oxide catalyst Ce0.8 Sm0.2 O1.9 . In contrast to previous theoretical treatments, these calculations clearly indicate that the surface is positively charged and compensated by an attendant negative space-charge zone. The high space-charge potential that develops at the surface (>0.8 V) is demonstrated to be hardly detectable by XPS measurements because of the short extent of the space-charge layer. This approach emphasizes the need to take into account defect interactions and to allow deviations from local charge neutrality when considering the surfaces of oxide catalysts.

Oxygen diffusion and surface exchange in the mixed conducting oxides SrTi1-yFeyO3-δ.

Oxygen transport in the mixed ionic-electronic conducting perovskite-oxides SrTi1-yFeyO3-δ (with y = 0.5 and y = 1.0) was studied by oxygen isotope exchange measurements. Experiments were performed on thin-film samples that were grown by Pulsed Laser Deposition (PLD) on MgO substrates. Isotope penetration profiles were introduced by 18O2/16O2 exchanges into the plane of the films at various temperatures in the range 773 < T/K < 973 at an oxygen activity aO2 = 0.5. Isotope profiles were determined subsequently by Time-of-Flight Secondary Ion Mass Spectrometry (ToF-SIMS), and their analysis yielded tracer diffusion coefficients D* and oxygen surface exchange coefficients k*. Activation energies for oxygen diffusion ΔHD* and surface exchange ΔHk* were obtained. Isothermal values of D* and values of ΔHD* are compared with literature data as a function of Fe content. D* is seen to increase monotonically with Fe content; ΔHD* shows more complex behaviour. D* and ΔHD* are also compared with the predictions of defect-chemical models. Analogous comparisons with literature data for k* and ΔHk* indicate, in contrast to prior studies, no mechanistic difference between electron-poor and electron-rich materials. It is concluded that the single operative mechanism of surface exchange for the entire series of STF compositions requires conduction-band electrons (minority electronic charge-carriers).

A family of oxide ion conductors based on the ferroelectric perovskite Na0.5Bi0.5TiO3.

Oxide ion conductors find important technical applications in electrochemical devices such as solid-oxide fuel cells (SOFCs), oxygen separation membranes and sensors. Na0.5Bi0.5TiO3 (NBT) is a well-known lead-free piezoelectric material; however, it is often reported to possess high leakage conductivity that is problematic for its piezo- and ferroelectric applications. Here we report this high leakage to be oxide ion conduction due to Bi-deficiency and oxygen vacancies induced during materials processing. Mg-doping on the Ti-site increases the ionic conductivity to ~0.01 S cm(-1) at 600 °C, improves the electrolyte stability in reducing atmospheres and lowers the sintering temperature. This study not only demonstrates how to adjust the nominal NBT composition for dielectric-based applications, but also, more importantly, gives NBT-based materials an unexpected role as a completely new family of oxide ion conductors with potential applications in intermediate-temperature SOFCs and opens up a new direction to design oxide ion conductors in perovskite oxides.

Oxygen diffusion in single crystal barium titanate.

Oxygen diffusion in cubic, nominally undoped, (100) oriented BaTiO3 single crystals has been studied by means of (18)O2/(16)O2 isotope exchange annealing and subsequent determination of the isotope profiles in the solid by time-of-flight secondary ion mass spectrometry (ToF-SIMS). Experiments were carried out as a function of temperature 973 < T/K < 1173, at an oxygen activity of aO2 = 0.200, and as a function of oxygen activity 0.009 < aO2 < 0.900 at T = 1073 K. The oxygen isotope profiles comprise two parts: slow diffusion through a space-charge zone at the surface depleted of oxygen vacancies followed by faster diffusion in a homogeneous bulk phase. The entire isotope profile can be described by a single solution to the diffusion equation involving only three fitting parameters: the surface exchange coefficient ks*, the space-charge potential Φ0 and the bulk diffusion coefficient D*(∞). Analysis of the temperature and oxygen activity dependencies of D*(∞) and Φ0 yields a consistent picture of both the bulk and the interfacial defect chemistry of BaTiO3. Values of the oxygen vacancy diffusion coefficient DV extracted from measured D*(∞) data are compared with literature data; consequently a global expression for the vacancy diffusivity in BaTiO3 for the temperature range 466 < T/K < 1273 is obtained, with an activation enthalpy of vacancy migration, ΔHmig,V = (0.70 ± 0.04) eV.

Complex behaviour of vacancy point-defects in SrRuO3 thin films.

The behaviour of point defects in thin, epitaxial films of the oxide electrode SrRuO3 was probed by means of diffusion measurements. Thin-film SrRuO3 was deposited by means of pulsed laser deposition (PLD) on (100) oriented, undoped single crystal SrTiO3 substrates. (16)O/(18)O exchange anneals were employed to probe the behavior of oxygen vacancies. Anneals were performed in the temperature range 850 ≤T/K≤ 1100 at an oxygen partial pressure of pO2 = 500 mbar. Samples were subsequently analyzed by means of Time-of-Flight Secondary Ion Mass Spectrometry (ToF-SIMS). The measured oxygen isotope penetration profiles comprised, surprisingly, two features. Oxygen tracer diffusion coefficients determined for thin-film SrRuO3 are amongst the lowest measured for nominally undoped perovskite-type oxides. The activation enthalpy of oxygen tracer diffusion was found to be ≈ 2 eV. Diffusion of Ti from the SrTiO3 substrates into the SrRuO3 thin films, probing the cation defects, was also observed in ToF-SIMS profiles; here, too, the diffusion profiles showed two features. The activation enthalpy of titanium diffusion was found to be ΔHDTi≈ 4 eV. We propose a model-cation sublattice equilibration-that accounts for the appearance of two features in both anion and cation diffusion profiles. We suggest that the observed complex behavior arises from the metastable defect structure of PLD thin films and the unusual defect structure of SrRuO3.

Complex diffusion behavior of oxygen in nanocrystalline BaTiO3 ceramics.

(18)O/(16)O exchange annealing and subsequent Time-of-Flight Secondary Ion Mass Spectrometry (ToF-SIMS) analysis is used to investigate oxygen transport in dense, nanocrystalline (average grain size d ≈ 300 nm) ceramics of nominally un-doped BaTiO3. Isotope penetration profiles are obtained as a function of temperature, 973 < T/K < 1173, at an oxygen activity aO2 = 0.20 and as a function of oxygen activity, 0.002 < aO2 < 0.20, at T = 1073 K. All isotope profiles show the same unusual shape: a flattened profile over the first ∼10(2) nm, followed by a short, conventional diffusion profile. We demonstrate that the entire isotope profile can be described quantitatively by a numerical solution to the diffusion equation based on an increase in the local oxygen diffusion coefficient close to the surface. This position-dependent increase is attributed to additional oxygen vacancies that are generated by diffusion of chlorine impurities out of the ceramics. The presence of chlorine derives from the chemical route necessary to produce nanometric powders: it thus indicates a new manner in which nanocrystalline ceramics may differ from their microcrystalline counterparts.

Hydration Entropy and Enthalpy of a Perovskite Oxide from Oxygen Tracer Diffusion Experiments.

Water incorporation into perovskite oxides generates protonic defects in the form of hydroxide ions. In this study, an indirect method to probe the thermodynamics of water incorporation is demonstrated. Acceptor-doped single-crystal samples of SrTiO3 were subjected to H218O/H216O exchange annealing at temperatures of 723 < T/K < 1023 at a water partial pressure of pH2O = 0.1 bar; from 18O diffusion profiles, measured by secondary ion mass spectrometry, oxygen tracer diffusion coefficients DO* were obtained. The decreased values of DO* for wet (relative to dry) conditions yielded ΔhydH = -(73 ± 15) kJ mol-1 and ΔhydS = -(148 ± 18) J mol-1 K-1 as the hydration enthalpy and entropy of SrTiO3. For T < 1023 K and this pH2O, the experiments also indicate that oxygen exchange from H2O(g) is faster than that from O2(g) (with a lower activation enthalpy) and that the surface space-charge potential is decreased under wet conditions.

Caution! Static Supercell Calculations of Defect Migration in Higher Symmetry ABX3 Perovskite Halides May Be Unreliable: A Case Study of Methylammonium Lead Iodide.

Activation energies of defect migration in ABX3 perovskite halides are widely obtained through static supercell calculations with the nudged-elastic-band method. Taking methylammonium lead iodide (CH3NH3PbI3, MAPbI3) as an example, we demonstrate that such calculations are unreliable for the higher symmetry structures adopted by the material at temperatures relevant to device operation (tetragonal and cubic MAPbI3) because, in addition to ion relaxation around the point defects, local structural modifications characteristic of the ground-state (orthorhombic) structure occur. In this way, we offer a simple explanation of why calculated activation energies of defect migration in MAPbI3 suffer from surprisingly large scatter. We propose a robust test to determine whether static supercell calculations of point-defect processes in ABX3 perovskite systems are reliable.