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 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.

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.

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.

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.

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.

Oxygen Surface Exchange and Tracer Diffusion in Differently Oriented Thin Films of Gd-Doped CeO2.

The exchange of 18O between gaseous molecular oxygen and thin-film samples of Ce0.99Gd0.01O1.995 with two different, nominal surface orientations [(111) and (110)] was studied. Oxygen isotope exchange experiments were conducted in the temperature range of 573 ≤ T/K ≤ 673 at an oxygen activity of aO2 = 0.2. Subsequently, secondary ion mass spectrometry (SIMS) measurements were performed on the thin-film samples to obtain 18O isotope depth profiles. All 18O diffusion profiles showed two features, suggesting spatially nonuniform oxygen tracer diffusion coefficients in the samples. A numerical solution to the diffusion equation was used to describe the experimental profiles and yielded oxygen tracer diffusion coefficients D* and oxygen surface exchange coefficients k*. Values of D* obtained were found, surprisingly, to be different for the two orientations and also orders of magnitude lower than values for ceramic samples in this temperature range. As possible explanations, we examine quantitatively the effect of halide anion impurities and the effect of ultrasmall columnar grains on oxygen tracer diffusion. Surface exchange coefficients for the (111) oriented surface were found to be roughly 1 order of magnitude higher than those for (110). We discuss two possible explanations for the observed behavior: the enrichment of anion impurities at the surface and the interaction between the surface and vapor water in the gas phase.

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.

Unraveling the Origin and Mechanism of Nanofilament Formation in Polycrystalline SrTiO3 Resistive Switching Memories.

Three central themes in the study of the phenomenon of resistive switching are the nature of the conducting phase, why it forms, and how it forms. In this study, the answers to all three questions are provided by performing switching experiments in situ in a transmission electron microscope on thin films of the model system polycrystalline SrTiO3 . On the basis of high-resolution transmission electron microscopy, electron-energy-loss spectroscopy and in situ current-voltage measurements, the conducting phase is identified to be SrTi11 O20 . This phase is only observed at specific grain boundaries, and a Ruddlesden-Popper phase, Sr3 Ti2 O7 , is typically observed adjacent to the conducting phase. These results allow not only the proposal that filament formation in this system has a thermodynamic origin-it is driven by electrochemical polarization and the local oxygen activity in the film decreasing below a critical value-but also the deduction of a phase diagram for strongly reduced SrTiO3 . Furthermore, why many conducting filaments are nucleated at one electrode but only one filament wins the race to the opposite electrode is also explained. The work thus provides detailed insights into the origin and mechanisms of filament generation and rupture.

Probing vacancy behavior across complex oxide heterointerfaces.

Oxygen vacancies ( V O • • ) play a critical role as defects in complex oxides in establishing functionality in systems including memristors, all-oxide electronics, and electrochemical cells that comprise metal-insulator-metal or complex oxide heterostructure configurations. Improving oxide-oxide interfaces necessitates a direct, spatial understanding of vacancy distributions that define electrochemically active regions. We show vacancies deplete over micrometer-level distances in Nb-doped SrTiO3 (Nb:SrTiO3) substrates due to deposition and post-annealing processes. We convert the surface potential across a strontium titanate/yttria-stabilized zirconia (STO/YSZ) heterostructured film to spatial (<100 nm) vacancy profiles within STO using (T = 500°C) in situ scanning probes and semiconductor analysis. Oxygen scavenging occurring during pulsed laser deposition reduces Nb:STO substantially, which partially reoxidizes in an oxygen-rich environment upon cooling. These results (i) introduce the means to spatially resolve quantitative vacancy distributions across oxide films and (ii) indicate the mechanisms by which oxide thin films enhance and then deplete vacancies within the underlying substrate.

Iodide-ion conduction in methylammonium lead iodide perovskite: some extraordinary aspects.

A recent model of iodide-ion conduction in methylammonium lead iodide perovskite (CH3NH3PbI3) is discussed. Issues include the low activation barrier of vacancy migration and the high diffusivities of iodine vacancies and interstitials. Comparisons are also made with the behaviour of point defects in the oxide perovskite SrTiO3.

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.

Oxygen Exchange Processes between Oxide Memristive Devices and Water Molecules.

Resistive switching based on transition metal oxide memristive devices is suspected to be caused by the electric-field-driven motion and internal redistribution of oxygen vacancies. Deriving the detailed mechanistic picture of the switching process is complicated, however, by the frequently observed influence of the surrounding atmosphere. Specifically, the presence or absence of water vapor in the atmosphere has a strong impact on the switching properties, but the redox reactions between water and the active layer have yet to be clarified. To investigate the role of oxygen and water species during resistive switching in greater detail, isotope labeling experiments in a N2 /H218 O tracer gas atmosphere combined with time-of-flight secondary-ion mass spectrometry are used. It is explicitly demonstrated that during the RESET operation in resistive switching SrTiO3 -based memristive devices, oxygen is incorporated directly from water molecules or oxygen molecules into the active layer. In humid atmospheres, the reaction pathway via water molecules predominates. These findings clearly resolve the role of humidity as both oxidizing agent and source of protonic defects during the RESET operation.

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.

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).