Ionic conductivity of space charge layers in acceptor doped ceria

The ionic conductivity of acceptor doped ceria is strongly influenced by grain boundaries and interfaces. Most experiments show a decrease in ionic conductivity and an increase in electronic conductivity in these regions. Classical models explain this observation by the formation of space charge layers that are depleted of mobile ionic charge carriers and enriched in small polarons. However, some experiments demonstrate an increase in ionic conductivity and recent models show that the space charge layers can also be enriched in mobile ionic species. Because of these contradictions, it is still not clear whether nanocrystalline or thin film ceria can offer superior ionic conductivity or not. To aid this debate, we calculate the ionic conductivity of yttrium doped ceria in regions of net charge density using kinetic Monte Carlo simulations. Through an appropriate choice of the charge densities, these calculations allow to demarcate the possible conductivity gains from space charge layers.     

Effect of divalent cation addition on structure,conductivity and grain boundary properties in La doped ceria oxygen ion conductors

The aim of this work is to investigate the effect of divalent cations on the structure and electrical properties of Ce_0.85La_0.1D_0.05O_2-δ (D = Ca, Sr and Ba) oxygen ion conductors. The X-Ray structural analysis confirms the presence of CeDO₃ minor phase in addition to cubic fluorite phase of ceria in Sr²⁺ and Ba²⁺ added compositions. The lattice parameter of the compositions significantly depends on the ionic radius of dopants and the presence of D²⁺ ions in ceria lattice. The Ca²⁺ added composition shows the highest free oxygen vacancy concentration due to its lowest association energy and complete dissolution of Ca²⁺ ions into ceria lattice. The dopant-vacancy association energy and grain interior conductivity changes with the ionic radii of the divalent dopants. The grain boundary capacitance depends on dielectric constant, grain size and grain boundary thickness. The grain boundary conductivity shows 46% over total conductivity for Sr²⁺ added composition. The presence of CeDO₃ phase and space charge layer promotes the grain boundary resistances and affects the ion dynamics. Schematic models are proposed to understand the ion migration in grain boundaries. The scavenging effect is found to be highest in Sr²⁺ ions added composition. The defect structures, the presence of CeDO3 phase and electrical properties are correlated with each other.     

Grain size effect on the electrical properties of nanocrystalline ceria

The total and partial electronic conductivities of gadolinium doped ceria (Ce_0.95Gd_0.1O_1.95−δ: GDC) with nanometer grain size have been evaluated in an attempt to identify the nanosize effect in heavily doped ceria. Nanocrystalline GDC bulk specimens with relatively high densities (≥96% of theoretical density) and various grain sizes (70, 100, 170 nm) were successfully fabricated by a conventional solid-state sintering method. According to the measurements of total and partial electronic conductivity via AC-impedance and DC polarization methods, respectively, no significant grain size dependence appeared for either type of conductivity. Furthermore, both total and partial electronic conductivity were not significantly different from those of microcrystalline GDC, which indicated that, upon nanostructuring within the examined grain size range, nanostructured bulk GDC was not affected by any nanosize effect: either space charge layer effect or grain boundary blocking effect.     

The ionic conductivity of Sm-doped ceria

The oxygen ion conductivity of polycrystalline samples of Sm-doped ceria and of Gd-doped ceria is studied as a function of doping fraction and temperature using impedance spectroscopy allowing the separation of bulk and grain boundary conductivity. The introduction of a fine spacing for the Sm dopant fraction allows the clear identification of the dopant fraction leading to the largest bulk conductivity. At 267°C, the largest bulk conductivity is shown for Ce_0.93Sm_0.07O_1.965. With increasing temperature, indications of an increase in the dopant fraction, which leads to the maximum in conductivity, are found. For the grain boundary conductivity, the maximum appears at larger dopant fractions compared to the bulk conductivity. The largest total conductivity for both dopants is again found for Sm-doped ceria. In literature, different syntheses and sample preparation methods led to larger total conductivities for Gd-doped ceria. In this work, we demonstrate that the variation of sintering conditions leads to scattering in the conductivity over one order of magnitude. Finally, we demonstrate that, in nominally pure cerium oxide, impurities dominate the ionic conductivity.     

Crystal Structure–Ionic Conductivity Relationships in Doped Ceria Systems

In the past, it has been suggested that the maximum ionic conductivity is achieved in ceria, when doped with an acceptor cation that causes minimum distortion in the cubic fluorite crystal lattice. In the present work, this hypothesis is tested by measuring both the ionic conductivity and elastic lattice strain of 10 mol% trivalent cation-doped ceria systems at the same temperatures. A consistent set of ionic conductivity data is developed, where the samples are synthesized under similar experimental conditions. On comparing the grain ionic conductivity, Nd_0.10Ce_0.90O_2−δ exhibits the highest ionic conductivity among other doped ceria systems. The grain ionic conductivity is around 17% higher than that of Gd_0.10Ce_0.90O_2−δ at 500°C, in air. X-ray diffraction profiles are collected on the sintered powder of all the compositions, from room temperature to 600°C, in air. From the lattice expansion data at high temperatures, the minimal elastic strain due to the presence of dopant is observed in Dy_0.10Ce_0.90O_2−δ. Nd_0.10Ce_0.90O_2−δ exhibits larger elastic lattice strain than Dy_0.10Ce_0.90O_2−δ with better ionic conductivity at intermediate temperatures. Therefore, it is shown that the previously proposed crystal structure–ionic conductivity relationship based on minimum elastic strain is not sufficient to explain the ionic conductivity behavior in ceria-based system.     

高分子构象模拟研究中的Monte Carlo方法

介绍了Monte Carlo方法及其特点,进而分析了Monte Carlo用于高分子模拟的优势,并描述了两类模拟模型。论文重点综述了近年来Monte Carlo方法在高分子构象模拟中的一些研究与应用,并展望了Monte Carlo方法在高分子构象模拟中的发展趋势和前景。     

Monte Carlo studies of ion size effects in the diffuse double layer

Results from Monte Carlo (MC) simulations for restricted electrolytes are presented for both 1:1 and 2:1 electrolytes. It is shown that the potential drop across the diffuse layer for these systems may be expressed by a Taylors series in the Gouy-Chapman (GC) estimate of the same quantity. The coefficients of this series are defined in terms of the MSA volume fraction and the reciprocal thickness of the ionic atmosphere. The series model can also be used to estimate the differential capacity of the diffuse layer. The properties of unrestricted electrolytes are considered at or very close to the potential of zero charge.     

Influence of flash sintering on the ionic conductivity of 8 mol% yttria stabilized zirconia

The ionic conductivity of flash-sintered, polycrystalline 8 mol% yttria stabilized zirconia (8YSZ) was enhanced compared with that of conventionally-sintered specimens. Flash sintering was carried out at a furnace temperature of 850 °C with an electric field of 100 V cm^–1 to initiate flash. The current density limit was varied between 60 and 100 mA mm^–2. Post-flash impedance measurements over the range 215–900 °C showed that both bulk and grain boundary conductivities had increased with the increased current density limit which was set prior to flash. The conductivity increases post-flash were ionic, not electronic, although electronic conductivity probably occurred, in addition to ionic conductivity, during flash. The conductivity increases were not attributable to sample densification or microstructural changes. The higher ionic conductivities are attributed to a change in YSZ defect structure that led to an increased concentration of mobile charge carriers; possible explanations for this are discussed.     

Electrical Conductivities of (CeO2)1−x(Y2O3)x Thin Films

Electrical properties of CeO₂ thin films of different Y₂O₃ dopant concentration as prepared earlier were studied using impedance spectroscopy. The ionic conductivities of the films were found to be dominated by grain boundaries of high conductivity as compared with that of the bulk ceramic of the same dopant concentration sintered at 1500°C. The film grain-boundary conductivities were investigated with regard to grain size, grain-boundary impurity segregation, space charge at grain boundaries, and grain-boundary microstructures. Because of the large grain boundary and surface area in thin films, the impurity concentration is insufficient to form a continuous highly resistive Si-rich glassy phase at grain boundaries, such that the resistivity associated with space-charge layers becomes important. The grain-boundary resistance may originate from oxygen-vacancy-trapping near grain boundaries from space-charge layers. High-resolution transmission electron microscopy coupled with a trans-boundary profile of electron energy loss spectroscopy gives strong credence to the space-charged layers. Since the conductivities of the films were observed to be independent of crystallographic texture, the interface misorientation contribution to the grain-boundary resistance is considered to be negligible with respect to those of the impurity layer and space-charge layers.     

Three-Dimensional Simulation of Grain Growth in the Presence of Mobile Pores

A kinetic, three-dimensional Monte Carlo model for simulating grain growth in the presence of mobile pores is presented. The model was used to study grain growth and pore migration by surface diffusion in an idealized geometry that ensures constant driving force for grain growth. The driving forces, pore size, and pore mobilities were varied to study their effects on grain-boundary mobility and grain growth. The simulations captured a variety of complex behaviors, including reduced grain-boundary velocity due to pore drag that has been predicted by analytical theories. The model is capable of treating far more complex geometries, including polycrystals. We present the capabilities of this model and discuss its limitations.     

Thermodynamic Stability of Gadolinia-Doped Ceria Thin Film Electrolytes for Micro-Solid Oxide Fuel Cells

Next-generation micro-solid oxide fuel cells for portable devices require nanocrystalline thin-film electrolytes in order to allow fuel cell fabrication on chips at a low operation temperature and with high power outputs. In this study, nanocrystalline gadolinia-doped ceria (Ce_0.8Gd_0.2O_{1.9− x} ) thin-film electrolytes are fabricated and their electrical conductivity and thermodynamic stability are evaluated with respect to microstructure. Nanocrystalline gadolinia-doped ceria thin-film material (Ce_0.8Gd_0.2O_{1.9− x} ) exhibits a larger amount of defects due to strain in the film than state-of-the-art microcrystalline bulk material. This strain in the film decreases the ionic conductivity of this ionic O²⁻ conductor. The thermodynamic stability of a nanocrystalline ceria solid solution with 65 nm grain size is reduced compared with microcrystalline material with 3–5 μm grain size. Nanocrystalline spray-pyrolyzed and PLD Ce_0.8Gd_0.2O_{1.9− x} thin films with average grain sizes larger than 70 nm show predominantly ionic conductivity for temperatures lower than 700°C, which is high enough to be potentially used as electrolytes in low to intermediate-temperature micro-solid oxide fuel cells.     

Monte Carlo simulation of microstructure evolution in biphasic-systems

Over the past few decades, a variety of models have been proposed in order to investigate the grain growth kinetics and the development of crystallographic textures in polycrystalline materials. In particular, a full understanding of the microstructure evolution is a key issue for ceramic systems, since their mechanical or thermal behaviour is intimately related to their microstructure. Moreover, the development of appropriate simulative tools is crucial to reproduce, control and finally optimize the solid-state sintering process of ceramics. Monte Carlo simulations are particularly attractive because of their ability to reproduce the statistical behaviour of atoms and grain boundaries with time. However, Monte Carlo simulations applied to two-phase materials, such as many ceramic systems, result complex because both grain growth and diffusion processes should be taken into account. Here the Monte Carlo Potts model, which is widely used to investigate the crystallization kinetics for monophasic systems, is modified and extended to biphasic ones. The proposed model maps the microstructure onto a discrete lattice. Each lattice element contains a number representing its phase and its crystallographic orientation. The grain formation and growth are simulated by appropriate switching and reorientation attempts involving the lattice elements. The effect of temperature is also discussed.     

A hybrid stochastic-deterministic algorithm for lattice-gas models of catalytic reactions and the computation of TPD spectra

We present a hybrid numerical approach for modeling surface reactions in the framework of a lattice-gas model with lateral interactions between adsorbed particles. A hybrid multiscale algorithm, which we refer to as Quasi-Equilibrium Kinetic Monte Carlo (QE-KMC), comprises traditional Metropolis Monte Carlo (MMC) simulations of equilibrium systems and standard numerical methods for deterministic ordinary differential equations (ODEs). The functional dependence of these ODEs on the macroscopic state variables (adsorbate coverages) is not explicitly known, but their right-hand sides can be evaluated “on the fly” with prescribed accuracy by means of the MMC simulations. At the time scale of these ODEs it is assumed that an equilibrium statistical distribution of adsorbed particles on an infinite lattice is attained at every moment in time due to infinitely fast surface diffusion. QE-KMC and conventional KMC simulations are used to study the temperature-programmed desorption (TPD) spectra of adsorbed particles. We critically discuss results of previous studies that applied Monte Carlo simulations to describe the TPD spectra in the case of fast adsorbate diffusion and strong lateral interactions. We show that the quasi-equilibrium TPD spectra can be quickly and accurately estimated by the QE-KMC algorithm, while the KMC simulations require much more extensive computational resources to obtain the same results.     

Oxygen Ion Conduction in Bulk and Grain Boundaries of Nominally Donor‐Doped Lead Zirconate Titanate (PZT): A Combined Impedance and Tracer Diffusion Study

Oxygen ion conduction in Nd³⁺‐doped Pb(Zr_xTi_1?x)O₃ (PZT) was investigated by impedance spectroscopy and ¹⁸O‐tracer diffusion with subsequent secondary ion mass spectrometry (SIMS) analysis. Ion blocking electrodes lead to a second relaxation feature in impedance spectra at temperatures above 600°C. This allowed analysis of ionic and electronic partial conductivities. Between 600°C and 700°C those are in the same order of magnitude (10^?5–10^?4 S/cm) though very differently activated (2.4 eV vs. 1.2 eV for ions and electron holes, respectively). Oxygen tracer experiments showed that ion transport mainly takes place along grain boundaries with partly very high local ionic conductivities. Numerical analysis of the tracer profiles, including a near‐surface space charge zone, revealed bulk and grain‐boundary diffusion coefficients. Calculation of an effective ionic conductivity from these diffusion coefficients showed good agreement with conductivity values determined from impedance measurements. Based on these data oxygen vacancy concentrations in grain boundary and bulk could be estimated. Annealing at high temperatures caused a decrease in the grain‐boundary ionic conductivity and onset of additional defect chemical processes near the surface, most probably due to cation diffusion.     

Effects of microstructure on electrochemical reactivity and conductivity in nanostructured ceria thin films

The proton conductivity in functional oxides is crucial in determining electrochemistry and transport phenomena in a number of applications such as catalytic devices and fuel cells. However, single characterization techniques are usually limited in detecting the ionic dynamics at the full range of environmental conditions. In this report, we probe and uncover the links between the microstructure of nanostructured ceria (NC) and parameters that govern its electrochemical reaction and proton transport, by coupling experimental data obtained with time‐resolved Kelvin probe force microscopy (tr‐KPFM), electrochemical impedance spectroscopy (EIS), and finite element analysis. It is found that surface morphology determines the water splitting rate and proton conductivity at 25°C and wet conditions, when protons are mainly generated and transported within surface physisorbed water layers. However, at higher temperature (i.e., ≥125°C) and dry conditions, when physisorbed water evaporates, grain size, and crystallographic orientation become significant factors. Specifically, the proton generation rate is negatively correlated with the grain size, whereas proton diffusivity is facilitated by surface {111} planes and additional conduction pathways offered by cracks and open pores connected to the surface.     

Modeling space charge layer interaction and conductivity enhancement in nanoionic composites

Potential conductivity enhancement due to formation of space charge layers in nanoionic composites was computed numerically for several structures of non-conducting nanoparticles in a bulk ionic conductor. Optimum loading fractions were extracted from simulation results and found to depend strongly on the thickness of the space charge layer relative to the size of the particles. This behavior agreed well with an approximate analytical expression derived herein. In certain cases, significant conductivity enhancement was predicted, even for nanoparticle loadings as small as 0.5 volume %. The model was also applied to a space charge layer depletion scenario, and found to be in good agreement with results from a recent experimental study.     

Fabrication and Characterization of High-Conductivity Bilayer Electrolytes for Intermediate-Temperature Solid Oxide Fuel Cells

A stable bilayer electrolyte with high ionic conductivity was developed for intermediate-temperature solid oxide fuel cell operation. The bilayer structure improved the limited thermodynamic stability of bismuth oxides and prevented electronic conductivity of ceria-based oxides in reducing atmosphere. Bilayer electrolytes were formed by depositing thin and thick layers of erbia-stabilized bismuth oxide (ESB) on samaria-doped ceria (SDC) substrates, via pulsed laser deposition and dip-coating techniques. Scanning electron microscope (SEM) images of the ESB/SDC samples showed dense ESB layers and excellent adherence between both ESB and SDC phases. Interdiffusion between the two phases was not detected by X-ray diffraction and EDX. Measurements of the conductivity of SDC coated with ESB exhibited slightly higher total conductance than SDC.     

Re-examination of bulk and grain boundary conductivities of Ce1−xGdxO2−δ ceramics

Powders of gadolinium-doped ceria solid solutions, Ce_1−xGd_xO_2−δ (x = 0.05, 0.1, 0.2, 0.3 and 0.4), were prepared by a freeze-drying precursor route. Dense ceramic pellets with average grain sizes in the range of several microns were obtained after sintering at 1600 °C. Cobalt nitrate was added to the powders to obtain dense ceramic samples with grain sizes in the submicrometer range at 1150 °C. The ionic conduction was analysed by impedance spectroscopy in air, to de-convolute the bulk and grain boundary contributions. The bulk conductivity at low temperature clearly decreases with increasing content of Gd whereas the activation energy increases. An alternative method is proposed to analyse the extent of defect interactions on conduction. For samples without addition of Co, the specific grain boundary conductivity increases with increasing Gd content. Addition of cobalt does not alter the bulk properties but produces an important increase in the specific grain boundary conductivity, mainly in samples with lower Gd-concentration (x = 0.05 and 0.1). Segregation of Gd and its strong interaction with charge carriers may explain the blocking effects of grain boundaries.     

The grain-boundary resistance of CeO2 ceramics: A combined microscopy-spectroscopy-simulation study of a dilute solution

Weakly acceptor-doped ceria ceramics were characterized structurally and compositionally with advanced transmission electron microscopy (TEM) techniques and electrically with electrochemical impedance spectroscopy (EIS). The grain boundaries studied with TEM were found to be free of second phases. The impedance spectra, acquired in the range 703 ≤ T/K ≤ 893 in air, showed several arcs that were analyzed in terms of bulk, grain-boundary, and electrode responses. We ascribed the grain-boundary resistance to the presence of space-charge layers. Continuum-level simulations were used to calculate charge-carrier distributions (of acceptor cations, oxygen vacancies, and electrons) in these space-charge layers. The acceptor cations were assumed to be mobile at high (sintering) temperatures but immobile at the temperatures of the EIS measurements. Space-charge formation was assumed to be driven by the segregation of oxygen vacancies to the grain-boundary core. Comparisons of data from the simulations and from the EIS measurements yielded space-charge potentials and the segregation energy of vacancies to the grain-boundary core. The space-charge potentials from the simulations are compared with values obtained by applying the standard, analytical (Mott–Schottky and Gouy–Chapman) expressions. The importance of modelling space-charge layers from the thermodynamic level is demonstrated.