Publisher Correction: Nanoscale percolation in doped BaZrO3 for high proton mobility.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Nanoscale percolation in doped BaZrO3 for high proton mobility.

Acceptor-doped barium zirconate is a promising proton-conducting oxide for various applications, for example, electrolysers, fuel cells or methane-conversion cells. Despite many experimental and theoretical investigations there is, however, only a limited understanding as to how to connect the complex microscopic proton motion and the macroscopic proton conductivity for the full range of acceptor levels, from diluted acceptors to concentrated solid solutions. Here we show that a combination of density functional theory calculations and kinetic Monte Carlo simulations enables this connection. At low concentrations, acceptors trap protons, which results in a decrease of the average proton mobility. With increasing concentration, however, acceptors form nanoscale percolation pathways with low proton migration energies, which leads to a strong increase of the proton mobility and conductivity. Comparing our simulated proton conductivities with experimental values for yttrium-doped barium zirconate yields excellent agreement. We then predict that ordered dopant structures would not only strongly enhance the proton conductivities, but would also enable one- or two-dimensional proton conduction in barium zirconate. Finally, we show how the properties of other dopants influence the proton conductivity.

Mechanistic origin of the time-dependence of the open-circuit voltage of a galvanic cell involving a ternary or higher compound.

It has previously been predicted [H.-I. Yoo and M. Martin, Phys. Chem. Chem. Phys., 2010, 12, 14699] and observed [E. Kim, et al., Solid State Ionics, 2013, 235, 22] that the open-circuit voltage U of a galvanic cell, involving a ternary or higher compound with more than one kind of mobile ionic carrier, is path- and time-dependent upon imposition or removal of the mobile components' chemical potential differences, in contradistinction to the cell involving a binary compound. This has been attributed [H.-I. Yoo and M. Martin, Phys. Chem. Chem. Phys., 2010, 12 14699; J.-Y. Yoon, et al., Solid State Ionics, 2012, 213, 22] to the decoupled redistributions of multiple mobile components or multi-fold relaxation. We hereby experimentally demonstrate with SrTi0.982Al0.018O3-Δ, known to have an appreciable water solubility depending on temperature, that introduction of a secondary ionic carrier H+ in addition to the native O2- indeed renders the otherwise time-independent U time-dependent; and that this phenomenon may, thus, be employed to probe the presence of a secondary ionic carrier, e.g., H+ in addition to the primary O2- in BaTi0.982Al0.018O3-Δ whose water solubility is yet to be known. The temporal behavior of U of SrTi0.982Al0.018O3-Δ subjected to the two fixed chemical potential differences, ΔµO and ΔµH, is precisely delineated in terms of two-fold relaxation of H and O, yielding their chemical diffusivity values, and consequently, the ambiguity with the EMF-method to determine the ionic transference numbers of a multinary compound is cleared away.

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 diffusion in amorphous and partially crystalline gallium oxide.

Oxygen transport in amorphous (a-GaO1.5) and partially crystalline (a/c-GaO1.5) gallium oxide was studied by means of 18O/16O isotope exchange experiments and time-of-flight secondary ion mass spectrometry (ToF-SIMS). Thin films of a-GaO1.5 were deposited by pulsed laser deposition (PLD) on alumina substrates at room temperature in an oxygen atmosphere. Oxygen tracer diffusion coefficients D* and oxygen surface exchange coefficients k* were determined as a function of temperature, 300 ≤ T/°C ≤ 370, and as a function of oxygen partial pressure, 2 ≤ p(O2)/mbar ≤ 500 at a temperature of T = 330 °C. The activation energy of oxygen tracer diffusion in amorphous gallium oxide was found to be EA = 0.8 eV. In addition, the time-temperature-transformation (TTT) diagram of crystallisation of amorphous gallium oxide was determined.

On the kinetic decomposition voltage of ternary oxides.

In a previous article the authors reported the kinetic unmixing and decomposition of the ternary oxide NiTiO3 by an externally applied voltage. It was found [J. Chun, et al., J. Appl. Phys., 117, 2015, 124504] that while kinetic unmixing occurred for all magnitudes of the applied voltage, kinetic decomposition occurred only above a certain threshold voltage U. The experimentally determined value of U, however, did not coincide with the thermodynamic expectation according to the definition by Gibbs (). In this work the kinetic decomposition voltage U of a ternary oxide ABOν is theoretically derived and compared with the experimental results. It turns out that U depends on the mobility ratio of the cations and agrees with observed results for the system of NiTiO3 within the error bounds.

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.

Understanding the ionic conductivity maximum in doped ceria: trapping and blocking.

Materials with high oxygen ion conductivity and low electronic conductivity are required for electrolytes in solid oxide fuel cells (SOFC) and high-temperature electrolysis (SOEC). A potential candidate for the electrolytes, which separate oxidation and reduction processes, is rare-earth doped ceria. The prediction of the ionic conductivity of the electrolytes and a better understanding of the underlying atomistic mechanisms provide an important contribution to the future of sustainable and efficient energy conversion and storage. The central aim of this paper is the detailed investigation of the relationship between defect interactions at the microscopic level and the macroscopic oxygen ion conductivity in the bulk of doped ceria. By combining ab initio density functional theory (DFT) with Kinetic Monte Carlo (KMC) simulations, the oxygen ion conductivity is predicted as a function of the doping concentration. Migration barriers are analyzed for energy contributions, which are caused by the interactions of dopants and vacancies with the migrating oxygen vacancy. We clearly distinguish between energy contributions that are either uniform for forward and backward jumps or favor one migration direction over the reverse direction. If the presence of a dopant changes the migration energy identically for forward and backward jumps, the resulting energy contribution is referred to as blocking. If the change in migration energy due to doping is different for forward and backward jumps of a specific ionic configuration, the resulting energy contributions are referred to as trapping. The influence of both effects on the ionic conductivity is analyzed: blocking determines the dopant fraction where the ionic conductivity exhibits the maximum. Trapping limits the maximum ionic conductivity value. In this way, a deeper understanding of the underlying mechanisms determining the influence of dopants on the ionic conductivity is obtained and the ionic conductivity is predicted more accurately. The detailed results and insights obtained here for doped ceria can be generalized and applied to other ion conductors that are important for SOFCs and SOECs as well as solid state batteries.

Ab initio calculation of the attempt frequency of oxygen diffusion in pure and samarium doped ceria.

The rate of oxygen ion jumps in a solid oxide depends not only on the activation energy but also on the pre-exponential factor of diffusion. In order to allow a fully ab initio prediction of the oxygen ion conductivity in pure and samarium doped ceria, we calculated the attempt frequency for an oxygen ion jump from first principles combining DFT+U, the NEB method, phonon calculations and the transition state theory. Different definitions of the jump attempt frequency are presented. The equivalence of the Eyring and the Vineyard method is shown without restriction to the Gamma point. Convergence checks of the phonon mesh reveal that the common reduction to the Gamma point is not sufficient to calculate the attempt frequency. Calculations of Sm doped ceria revealed an increase of the prefactor. The attempt frequency for the constant pressure case in quasi-harmonic approximation is larger than the attempt frequency at constant volume in harmonic approximation. The calculated electronic energies, enthalpies and entropies of migration are in agreement with the experimental diffusion coefficients and activation energies.

Association of defects in doped non-stoichiometric ceria from first principles.

We investigate the interaction and distribution of defects in doped non-stoichometric ceria Ce1-xRExO2-x/2-δ (with RE = Lu, Y, Gd, Sm, Nd, and La) by combining DFT+U calculations and Monte Carlo simulations. The concentrated solution of defects in ceria is described by the pair interactions of dopant ions, oxygen vacancies, and small polarons. The calculated interaction energies for polarons and oxygen vacancies are in agreement with experimental results and previously reported calculations. Simulations reveal that in thermodynamic equilibrium the configurational energy decreases with increasing non-stoichiometry as well as increasing dopant fraction similar to the observed behavior of the enthalpy of reduction in experiments. This effect is attributed to the attractive interaction of oxygen vacancies with polarons and dopant ions.

Comment on "How to interpret Onsager cross terms in mixed ionic electronic conductors" by I. Riess, Phys. Chem. Chem. Phys., 2014, 16, 22513.

Here we show that the Onsager cross terms for ion-electron interactions are not an artifact, but the necessity to phenomenologically and completely describe the mass/charge transport of a mixed ionic-electronic conductor in terms of mobile charged components which are the only experimentally operable species. The use of an appropriate comprehensive defect model may help to reduce the cross terms (which depend on the choice of formal charge of the mobile defects), but it cannot obviate them if long-range Coulombic interactions are in action among the defects.

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.

A combined DFT + U and Monte Carlo study on rare earth doped ceria.

We investigate the dopant distribution and its influence on the oxygen ion conductivity of ceria doped with rare earth oxides by combining density functional theory and Monte Carlo simulations. We calculate the association energies of dopant pairs, oxygen vacancy pairs and between dopant ions and oxygen vacancies by means of DFT + U including finite size corrections. The cation coordination numbers from ensuing Metropolis Monte Carlo simulations show remarkable agreement with experimental data. Combining Metropolis and Kinetic Monte Carlo simulations we find a distinct dependence of the ionic conductivity on the dopant distribution and predict long term degradation of electrolytes based on doped ceria.

Molecular Beam Epitaxy of ß-(InxGa1-x)2O3 on ß-Ga2O3 (010): Compositional Control, Layer Quality, Anisotropic Strain Relaxation, and Prospects for Two-Dimensional Electron Gas Confinement.

In this work, we investigate the growth of monoclinic ß-(InxGa1-x)2O3 alloys on top of (010) ß-Ga2O3 substrates via plasma-assisted molecular beam epitaxy. In particular, using different in situ (reflection high-energy electron diffraction) and ex situ (atomic force microscopy, X-ray diffraction, time-of-flight secondary ion mass spectrometry, and transmission electron microscopy) characterization techniques, we discuss (i) the growth parameters that allow for In incorporation and (ii) the obtainable structural quality of the deposited layers as a function of the alloy composition. In particular, we give experimental evidence of the possibility of coherently growing (010) ß-(InxGa1-x)2O3 layers on ß-Ga2O3 with good structural quality for x up to ≈ 0.1. Moreover, we show that the monoclinic structure of the underlying (010) ß-Ga2O3 substrate can be preserved in the ß-(InxGa1-x)2O3 layers for wider concentrations of In (x ≤ 0.19). Nonetheless, the formation of a large amount of structural defects, like unexpected (102̅) oriented twin domains and partial segregation of In is suggested for x > 0.1. Strain relaxes anisotropically, maintaining an elastically strained unit cell along the a* direction vs plastic relaxation along the c* direction. This study provides important guidelines for the low-end side tunability of the energy bandgap of ß-Ga2O3-based alloys and provides an estimate of its potential in increasing the confined carrier concentration of two-dimensional electron gases in ß-(InxGa1-x)2O3/(AlyGa1-y)2O3 heterostructures.

Entropies of defect formation in ceria from first principles.

We calculate entropies of formation for fully charged point defects, including the small polaron Ce'(Ce), in undoped fluorite-structured ceria by means of density functional theory in the GGA + U approximation. We discuss the behaviour of the entropy for the constant volume and the constant pressure case. Our results for constant pressure (p = 0) suggest that the change in volume, due to the formation of defects, dominates the entropy of formation. From the individual entropies of formation the entropies of Frenkel, anti-Frenkel and Schottky disorder as well as the entropy of reduction of ceria are obtained. At temperatures of about 1000 K the entropic contributions to the Gibbs energy are up to 0.9 eV per defect and thus are no longer negligible. For our calculated entropy of reduction of about 17 kB we find a remarkable agreement with experimental data from the literature.

1H-NMR measurements of proton mobility in nano-crystalline YSZ.

We report nuclear magnetic resonance (NMR) results on water saturated, dense, nano-crystalline YSZ samples (9.5 mol% yttria doped zirconia) which exhibit proton conductivity at temperatures as low as room temperature. (1)H-NMR spectra recorded under static and magic angle spinning conditions show two distinct signals. Their temperature-dependent behavior and their linewidths suggest that one can be attributed to (free) water adsorbed on the surface of the sample and the other one to mobile protons within the sample. This interpretation is supported by comparison with measurements on a single-crystalline sample. For the nano-crystalline samples motional narrowing is observed for the signal originating from protons in the sample interior. For these protons, the analysis of temperature and field dependent spin-lattice relaxation time T1 points towards diffusion in a confined two-dimensional geometry. We attribute this quasi two-dimensional motion to protons that are mobile along internal interfaces or nanopores of nano-crystalline YSZ.

A concerted migration mechanism of mixed oxide ion and electron conduction in reduced ceria studied by first-principles density functional theory.

Ceria based oxides are regarded as key oxide materials for energy and environmental applications, such as solid oxide fuel cells, oxygen permeation membranes, fuel cell electrodes, oxygen storage, or heterogeneous catalysis. This great versatility in applications is rendered possible by the fact that rare earth-doped ceria is a pure oxygen ion conductor while undoped ceria, CeO(2-δ), is a mixed oxygen ion-electron conductor. To get deeper insight into the mixed conduction mechanism of oxygen ions and electrons from atomistic and electronic level viewpoints we have applied first-principles density functional theory (DFT + U method). The calculation results show that oxygen vacancies strongly attract localized electrons, forming associates between them. The migration energy of an oxygen vacancy in such an associate is substantially lowered compared to the unassociated case due to the simultaneous positional rearrangement of localized electrons during the ionic jump process. Accordingly, we propose a concerted migration mechanism of oxygen vacancies and localized electrons in reduced ceria; this mechanism results in an increased diffusivity of oxygen vacancies supported by localized electrons compared with that in pure oxide ion conductors.

Electrochemical activation of molecular nitrogen at the Ir/YSZ interface.

Nitrogen is often used as an inert background atmosphere in solid state studies of electrode and reaction kinetics, of solid state studies of transport phenomena, and in applications e.g. solid oxide fuel cells (SOFC), sensors and membranes. Thus, chemical and electrochemical reactions of oxides related to or with dinitrogen are not supposed and in general not considered. We demonstrate by a steady state electrochemical polarisation experiments complemented with in situ photoelectron spectroscopy (XPS) that at a temperature of 450 °C dinitrogen can be electrochemically activated at the three phase boundary between N(2), a metal microelectrode and one of the most widely used solid oxide electrolytes--yttria stabilized zirconia (YSZ)--at potentials more negative than E = -1.25 V. The process is neither related to a reduction of the electrolyte nor to an adsorption process or a purely chemical reaction but is electrochemical in nature. Only at potentials more negative than E = -2 V did new components of Zr 3d and Y 3d signals with a lower formal charge appear, thus indicating electrochemical reduction of the electrolyte matrix. Theoretical model calculations suggest the presence of anionic intermediates with delocalized electrons at the electrode/electrolyte reaction interface. The ex situ SIMS analysis confirmed that nitrogen is incorporated and migrates into the electrolyte beneath the electrode.

Transition between bipolar and abnormal bipolar resistive switching in amorphous oxides with a mobility edge.

Resistive switching is an important phenomenon for future memory devices such as resistance random access memories or neuronal networks. While there are different types of resistive switching, such as filament or interface switching, this work focuses on bulk switching in amorphous, binary oxides. Bulk switching was found experimentally in different oxides, for example in amorphous gallium oxide. The forms of the observed current-voltage curves differ, however, fundamentally. Even within the same material, both abnormal bipolar and normal bipolar resistive switching were found. Here, we use a new drift-diffusion model to theoretically investigate bulk switching in amorphous oxides where the electronic conductivity can be described by Mott's concept of a mobility edge. We show not only that a strong, non-linear dependence of the electronic conductivity on the oxygen content is necessary for bulk switching but also that changing the geometry of the memristive device causes the transition between abnormal and normal bipolar switching.

On the path-dependence of the open-cell voltage of a galvanic cell involving a ternary or multinary compound with multiple mobile ionic species under multiple chemical potential gradients.

It is well known that the open-cell voltage (U) of a galvanic cell involving a binary compound, or a multinary compound with a single kind of mobile ionic species, is a state property under a gradient of chemical potential of the mobile component. It is not so transparent, however, whether U is still a state property when involving a ternary or multinary compound with two or more kinds of mobile ions under multiple chemical potential gradients of those mobile components. We clarify this issue with a multinary oxide that conducts oxide ions, protons and electron holes and is exposed to the chemical potential gradients of both water and oxygen. We show that U is path- and history-dependent, and manifests itself along the diffusion paths of the two mobile components H and O under given boundary conditions.