Ab initio thermodynamics of intrinsic oxygen vacancies in ceria

Nonstoichiometric ceria(CeO$_{2-\delta}$) is a candidate reaction medium to facilitate two step water splitting cycles and generate hydrogen. Improving upon its thermodynamic suitability through doping requires an understanding of its vacancy thermodynamics. Using density functional theory(DFT) calculations and a cluster expansion based Monte Carlo simulations, we have studied the high temperature thermodynamics of intrinsic oxygen vacancies in ceria. The DFT+$U$ approach was used to get the ground state energies of various vacancy configurations in ceria, which were subsequently fit to a cluster expansion Hamiltonian to efficiently model the configurational dependence of energy. The effect of lattice vibrations was incorporated through a temperature dependent cluster expansion. Lattice Monte Carlo simulations using the cluster expansion Hamiltonian were able to detect the miscibility gap in the phase diagram of ceria. The inclusion of vibrational and electronic entropy effects made the agreement with experiments quantitative. The deviation from an ideal solution model was quantified by calculating as a function of nonstoichiometry, a) the solid state entropy from Monte Carlo simulations and b) Warren-Cowley short range order parameters of various pair clusters

Ab-Initio and Experimental Techniques for Studying Non-Stoichiometry and Oxygen Transport in Mixed Conducting Oxides

The ability of cerium oxide (CeO2-δ, also called ceria), to vary its oxygen stoichiometry in response to changes in temperature or oxygen activity is key to many of its applications in catalysis and electrochemical energy storage and conversion. This thesis explores ab initio and experimental approaches to study the fundamental thermodynamic and oxygen transport properties of ceria (MxCe1-xOO2-δ), but the methods are applicable to other mixed conducting oxides as well. In the first part of the thesis, a computational thermodynamics approach that integrates quantum mechanical and statistical ensemble-based simulations is used to calculate the reduction-oxidation thermodynamics of non-stoichiometric ceria entirely from first principles. This procedure is well understood and has been successfully implemented for metallic alloys, but has not been extended to correlated electron systems such as ceria, for which the physics of electronic structure calculations is significantly more complicated. Density functional calculations were used to obtain the ground state energies of ceria with vacancy concentrations ranging from fully stoichiometric up to δ=0.25$. For each δ, numerous vacancy configurations were sampled to capture the interactions between vacancies and other atoms. Using the frozen phonon method, lattice dynamical calculations of phonon density of states were performed for various δ. Based on the ground state energies of nearly 40 structures, a cluster expansion Hamiltonian was used to parametrize the energy as a polynomial in occupation variables. The vibrational energies were used to make the Hamiltoninan temperature dependent. Lattice Monte Carlo (MC) simulations using the cluster expansion Hamiltonian were then used to study, for the first time, the effect of temperature and chemical potential on the vacancy concentration in ceria from first principles. The temperature composition phase diagram constructed from the MC simulations successfully reproduced the experimentally reported miscibility gap. The inclusion of vibrational and electronic contributions to the entropy made the agreement quantitative. Further, the partial molar enthalpy and entropy of reduction as a function of δ were extracted and found to deviate significantly from those of an ideally behaved system. The deviations were quantified by calculating the Warren-Cowley short range order parameters. This was the first demonstration of an ab initio approach being used to accurately model the defect thermodynamics of a correlated electron system without resorting to experimental inputs. Using ceria as benchmark material, this project lays the groundwork for a computational approach to screen new oxides for thermochemical cycling. The rest of the thesis describes experimental investigations of oxygen transport and non-stoichiometry in doped and undoped ceria. Oxygen transport studies were performed using electrical conductivity relaxation (ECR). In ECR, a small step change in pO2 forces the sample non-stoichiometry δ, and other dependent properties such as electrical conductivity, to equilibrate to a new value. The rate of this re-equilibration is governed by the bulk oxygen diffusivity, DChem, and surface reaction rate constant, kS -- the two principal kinetic properties. By fitting the solution to Fick's second law, with the appropriate boundary conditions, to the conductivity relaxation profile, DChem and kS can be extracted. The instrumental capability for performing electrical conductivity relaxation experiments was set up and a systematic data analysis procedure was developed to reliably and accurately extract DChem and or kS. The experimental and data analytical methodologies were successfully benchmarked with 15 mol% Sm doped ceria, for which approximate values of the two principal transport properties, bulk oxygen diffusivity, DChem, and surface reaction rate constant, kS, can be found in the literature. An unexpectedly high p-type electronic transference number enabled ECR measurements under oxidizing conditions. A systematic data analysis procedure was developed to permit reliable extraction of the kinetic parameters even in the general case of simultaneous bulk and surface limitation. When the surface kinetics were too sluggish compared to bulk diffusion, Pt catalyst nanoparticles were sputtered to catalyze the surface reaction and enable extraction of DChem. The DChem from this study showed excellent qualitative and quantitative agreement with expected values, falling in the range from ~ 2 x 10-5 to 2 x 10-4 cm2/s. The surface reaction constant under H2/H2O mixtures also showed good agreement with literature results. Remarkably, this value increased by a factor of 40 under mixtures of CO/CO2 or O2/Ar. This observation suggests kinetic advantages for production of CO rather than H2 in a two-step solar-driven thermochemical process based on samarium doped ceria. Using ECR, the effect of 20% Zr addition on the electrical conductivity and oxygen transport properties of ceria as a function of pO2 and T was investigated. Under oxidizing conditions, both CeO2-δ and Zr0.2Ce0.8O2-δ(ZDC20) showed n type, mixed conduction. The conductivity of ZDC20 was two orders of magnitude higher than that of undoped ceria. Contrary to previous studies, we found that Zr addition does not change the electronic mobility in this pO2 regime. The enhancement in conductivity is a consequence of higher vacancy concentration in ZDC20 under identical conditions compared to ceria. Under reducing conditions, while the n-type conductivity of ceria continued to increase with decreasing pO2, that of ZDC20 reached a broad maximum, eventually decreasing with pO2 (p-type) despite increasing carrier concentration. We show that the electronic mobility becomes strongly concentration dependent at high oxygen non-stoichiometry. This leads to a marked decrease in mobility with increase in δ, causing the conductivity to roll over from n to p type. The chemical diffusion coefficient and surface reaction rate constant of both ceria and ZDC20 showed strong dependence on pO2 under oxidizing conditions, decreasing by nearly an order of magnitude between 10-2 atm and 10-5 atm. The unexpectedly high sensitivity to pO2 was ascribed to the effect of extrinsic vacancies generated by trace quantities of lower valence cation impurities, that dramatically increase both the absolute value of the thermodynamic factor and its sensitivity to pO2 close to stoichiometry. Overall, the addition of Zr lowers the DChem and kS of ceria in the temperature and oxygen partial pressure range of this study, the effect being more pronounced under reducing conditions. Beyond its relevance to ceria, this work demonstrates the potential of ECR to isolate the effect of kinetics from thermodynamics of the real thermochemical cycle, reveal the limiting transport parameters, and ultimately guide microstructure design for maximizing the rate of fuel production. Lastly, we improve upon an existing formalism to calculate the oxygen non-stoichiometry in thin films of mixed conducting oxides using AC impedance spectroscopy. Cerium oxide was once again chosen as the benchmarking material, since it shows both ideal and non-ideal thermodynamic behavior under different conditions, and has been well studied in its bulk form. In this method, the impedance response of dense, thin films of CeO2-δ deposited on a Y0.84Zr0.16O1.92> (YSZ) substrate was measured using AC impedance spectroscopy. To explore potential grain boundary effects on bulk thermodynamic properties. A physically derived equivalent circuit model was fit to the impedance response to extract a quantity called the 'chemical capacitance', which was subsequently related to the non-stoichiometry. Previous studies employing this method were restricted to systems that can be described using ideal solution thermodynamics, which allows simplifications to the theoretical treatment of their capacitance. Apart from extending this technique to a non-ideally behaved oxide, we report excellent agreement between the non-stoichiometry of single crystal and polycrystalline films and that of bulk ceria. By virtue of using thin films, equilibration times are dramatically decreased, enabling faster measurements compared to bulk techniques like thermogravimetry and coulometric titration. Further, the electrochemical method is ideal for thin films, for which the mass changes are below the detection limits of bulk techniques.</p

An electrical conductivity relaxation study of oxygen transport in samarium doped ceria

The efficacy of the electrical conductivity relaxation (ECR) technique for investigating the oxygen transport properties of mixed conducting oxides has been evaluated. Fifteen mol% samarium doped ceria (SDC15), for which approximate values of the two principal transport properties, bulk oxygen diffusivity, D_(Chem), and surface reaction rate constant, kS, can be found in the literature, was chosen as the benchmark material against which to validate the methodology. Measurements were carried out at temperatures between 750 and 850 °C and over a wide range of oxygen partial pressures. An unexpectedly high p-type electronic transference number enabled ECR measurements under oxidizing conditions. A systematic data analysis procedure was developed to permit reliable extraction of the kinetic parameters even in the general case of simultaneous bulk and surface limitation. The D_(Chem) from this study showed excellent qualitative and quantitative agreement with expected values, falling in the range from ~2 × 10^(−5) to 2 × 10^(−4) cm^2 s^(−1). The surface reaction constant under H_2–H_2O mixtures also showed good agreement with literature results. Remarkably, this value increased by a factor of 40 under mixtures of CO–CO_2 or O_2–Ar. This observation suggests kinetic advantages for production of CO rather than H_2 in a two-step solar-driven thermochemical process based on samarium doped ceria

Extreme high temperature redox kinetics in ceria: exploration of the transition from gas-phase to material-kinetic limitations

The redox kinetics of undoped ceria (CeO_(2−δ)) are investigated by the electrical conductivity relaxation method in the oxygen partial pressure range of −4.3 ≤ log(pO_2/atm) ≤ −2.0 at 1400 °C. It is demonstrated that extremely large gas flow rates, relative to the mass of the oxide, are required in order to overcome gas phase limitations and access the material kinetic properties. Using these high flow rate conditions, the surface reaction rate constant k_(chem) is found to obey the correlation log(k_(chem)/cm s^(−1)) = (0.84 ± 0.02) × log(pO_2/atm) − (0.99 ± 0.05) and increases with oxygen partial pressure. This increase contrasts the known behavior of the dominant defect species, oxygen vacancies and free electrons, which decrease in concentration with increasing oxygen partial pressure. For the sample geometries employed, diffusion was too fast to be detected. At low gas flow rates, the relaxation process becomes limited by the capacity of the sweep gas to supply/remove oxygen to/from the oxide. An analytical expression is derived for the relaxation in the gas-phase limited regime, and the result reveals an exponential decay profile, identical in form to that known for a surface reaction limited process. Thus, measurements under varied gas flow rates are required to differentiate between surface reaction limited and gas flow limited behavior

Surface oxygen nonstoichiometry depends non-monotonically on biaxial strain in ultrathin ceria films

Strain engineering provides a ‘dopant-free’ alternative to tailor the electronic, defect chemical and catalytic properties of mixed ion and electron conducting (MIEC) oxides. By perturbing the crystallographic symmetry of an oxide, strain can dramatically alter both the position and degeneracy of electronic energy levels, which directly impact the defect chemistry of the oxide. In this work, we employed ambient pressure X-ray photoelectron spectroscopy (APXPS) to probe the valence and core levels of ultra thin films of cerium oxide, a prototypical MIEC, subject to an elastic strain. Coherently strained CeO2 films were grown on atomically flat (001) Y0.16Zr0.84O1.92 (5.5 % compressive strain) and SrTiO3 (2.1 % tensile strain) single crystal substrates. Aberration-corrected transmission electron microscopy revealed an CeO2/substrate interface free of cation diffusion and devoid of misfit dislocations. While equilibrium theory predicts that a coherently ceria/YSZ interface is unlikely because of the large lattice mismatch, we demonstrate a stable, redox active coherent ceria film up to 3 nm in thickness on YSZ. Surface sensitive APXPS performed at 450°C and 550°C under various oxygen partial pressures revealed that the surfaces of the strained ultrathin oxide films, both compressive and tensile, exhibited higher surface polaron concentration (and by extension, oxygen vacancies) compared to the bulk-like, unstrained films. This remarkable result is at odds with the conventional view that the reduction enthalpy decreases monotonically with strain. We systematically performed depth resolved XPS measurements on films of different thicknesses to deconvolve strain effect on the surface redox capacity from that of substrate induced chemical and electrostatic effects. We hypothesize that elastic biaxial strain has a two-pronged effect on the redox capacity. By its coupling with oxygen chemical potential through chemical expansion, tensile and compressive strain will have a monotonic effect on the oxygen nonstoichiometry. However, the symmetry breaking induced by the tetragonal distortion – irrespective of compression or tension - predisposes the oxide away from cubic symmetry. In turn, this favors the reduced oxide (3+ oxidation state of Ce) in its hexagonal sesquioxide environment. The latter effect leads to a non-monotonic dependence of redox properties on biaxial strain. This work expands our understanding of the behavior of highly strained MIEC oxide films under catalytically relevant conditions. The knowledge of non-monotonic oxygen nonstoichiometry dependence could be extremely useful for strain-engineered heterolayers for memristive applications and surface coatings for pseudocapacitive energy storage

Solar thermochemical water splitting: Advances in materials and methods

Photoelectrochemical (PEC) water splitting, termed artificial photosynthesis, converts solar energy into hydrogen by harvesting a narrow spectrum of visible light using photovoltaics integrated with water-splitting electrocatalysts. While conceptually attractive, critical materials issues currently challenge technology development(1) and economic viability(2). Despite decades of active research, this approach has not been demonstrated at power levels above a few watts, or for more than a few days of operation. High-temperature solar thermochemical (STCH) water splitting is an alternative approach that converts solar energy into hydrogen by using the deceptively simple metal oxide-based thermochemical cycle presented in figure 1. The STCH process requires very high temperatures, achieved by collecting and concentrating solar energy. Unlike PEC, two-step metal oxide water-splitting cycles have been demonstrated at the 100kW scale(3), and continuous operation at even higher power levels is nearing pre-commercial demonstration (HYDROSOL-3D). Nonetheless STCH, like PEC, faces critical materials issues that must be addressed for this technology to achieve commercial success. Please click Additional Files below to see the full abstract

py4DSTEM: a software package for multimodal analysis of four-dimensional scanning transmission electron microscopy datasets

Scanning transmission electron microscopy (STEM) allows for imaging, diffraction, and spectroscopy of materials on length scales ranging from microns to atoms. By using a high-speed, direct electron detector, it is now possible to record a full 2D image of the diffracted electron beam at each probe position, typically a 2D grid of probe positions. These 4D-STEM datasets are rich in information, including signatures of the local structure, orientation, deformation, electromagnetic fields and other sample-dependent properties. However, extracting this information requires complex analysis pipelines, from data wrangling to calibration to analysis to visualization, all while maintaining robustness against imaging distortions and artifacts. In this paper, we present py4DSTEM, an analysis toolkit for measuring material properties from 4D-STEM datasets, written in the Python language and released with an open source license. We describe the algorithmic steps for dataset calibration and various 4D-STEM property measurements in detail, and present results from several experimental datasets. We have also implemented a simple and universal file format appropriate for electron microscopy data in py4DSTEM, which uses the open source HDF5 standard. We hope this tool will benefit the research community, helps to move the developing standards for data and computational methods in electron microscopy, and invite the community to contribute to this ongoing, fully open-source project

The Materials Research Platform: Defining the Requirements from User Stories

A recent meeting focused on accelerated materials design and discovery examined user requirements for a general, collaborative, integrative, and on-demand materials research platform