(PHD, 2015)

Abstract:

The ability of cerium oxide (CeO_{2-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 (M_{x}Ce_{1-x}OO_{2-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 _{p}O_{2} 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, D_{Chem}, and surface reaction rate constant, k_{S} – the two principal kinetic properties. By fitting the solution to Fick’s second law, with the appropriate boundary conditions, to the conductivity relaxation profile, D_{Chem} and k_{S} 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 D_{Chem} and or k_{S}. 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, D_{Chem}, and surface reaction rate constant, k_{S}, 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 D_{Chem}. The D_{Chem} 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} cm^{2}/s. The surface reaction constant under H_{2}/H_{2}O 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.

Using ECR, the effect of 20% Zr addition on the electrical conductivity and oxygen transport properties of ceria as a function of _{p}O_{2} and T was investigated. Under oxidizing conditions, both CeO_{2-δ} and Zr_{0.2}Ce_{0.8}O_{2-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 _{p}O_{2} 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 _{p}O_{2}, that of ZDC20 reached a broad maximum, eventually decreasing with _{p}O_{2} (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 _{p}O_{2} under oxidizing conditions, decreasing by nearly an order of magnitude between 10^{-2} atm and 10^{-5} atm. The unexpectedly high sensitivity to _{p}O_{2} 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 _{p}O_{2} close to stoichiometry. Overall, the addition of Zr lowers the D_{Chem} and k_{S} 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 CeO_{2-δ} deposited on a Y_{0.84}Zr_{0.16}O_{1.92>} (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.

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(PHD, 2015)

Abstract:

Melting temperature calculation has important applications in the theoretical study of phase diagrams and computational materials screenings. In this thesis, we present two new methods, i.e., the improved Widom’s particle insertion method and the small-cell coexistence method, which we developed in order to capture melting temperatures both accurately and quickly.

We propose a scheme that drastically improves the efficiency of Widom’s particle insertion method by efficiently sampling cavities while calculating the integrals providing the chemical potentials of a physical system. This idea enables us to calculate chemical potentials of liquids directly from first-principles without the help of any reference system, which is necessary in the commonly used thermodynamic integration method. As an example, we apply our scheme, combined with the density functional formalism, to the calculation of the chemical potential of liquid copper. The calculated chemical potential is further used to locate the melting temperature. The calculated results closely agree with experiments.

We propose the small-cell coexistence method based on the statistical analysis of small-size coexistence MD simulations. It eliminates the risk of a metastable superheated solid in the fast-heating method, while also significantly reducing the computer cost relative to the traditional large-scale coexistence method. Using empirical potentials, we validate the method and systematically study the finite-size effect on the calculated melting points. The method converges to the exact result in the limit of a large system size. An accuracy within 100 K in melting temperature is usually achieved when the simulation contains more than 100 atoms. DFT examples of Tantalum, high-pressure Sodium, and ionic material NaCl are shown to demonstrate the accuracy and flexibility of the method in its practical applications. The method serves as a promising approach for large-scale automated material screening in which the melting temperature is a design criterion.

We present in detail two examples of refractory materials. First, we demonstrate how key material properties that provide guidance in the design of refractory materials can be accurately determined via ab initio thermodynamic calculations in conjunction with experimental techniques based on synchrotron X-ray diffraction and thermal analysis under laser-heated aerodynamic levitation. The properties considered include melting point, heat of fusion, heat capacity, thermal expansion coefficients, thermal stability, and sublattice disordering, as illustrated in a motivating example of lanthanum zirconate (La_{2}Zr_{2}O_{7}). The close agreement with experiment in the known but structurally complex compound La_{2}Zr_{2}O_{7} provides good indication that the computation methods described can be used within a computational screening framework to identify novel refractory materials. Second, we report an extensive investigation into the melting temperatures of the Hf-C and Hf-Ta-C systems using ab initio calculations. With melting points above 4000 K, hafnium carbide (HfC) and tantalum carbide (TaC) are among the most refractory binary compounds known to date. Their mixture, with a general formula Ta_{x}Hf_{1-x}C_{y}, is known to have a melting point of 4215 K at the composition Ta_{4}HfC_{5}, which has long been considered as the highest melting temperature for any solid. Very few measurements of melting point in tantalum and hafnium carbides have been documented, because of the obvious experimental difficulties at extreme temperatures. The investigation lets us identify three major chemical factors that contribute to the high melting temperatures. Based on these three factors, we propose and explore a new class of materials, which, according to our ab initio calculations, may possess even higher melting temperatures than Ta-Hf-C. This example also demonstrates the feasibility of materials screening and discovery via ab initio calculations for the optimization of “higher-level” properties whose determination requires extensive sampling of atomic configuration space.

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(PHD, 2014)

Abstract:

In this work we chiefly deal with two broad classes of problems in computational materials science, determining the doping mechanism in a semiconductor and developing an extreme condition equation of state. While solving certain aspects of these questions is well-trodden ground, both require extending the reach of existing methods to fully answer them. Here we choose to build upon the framework of density functional theory (DFT) which provides an efficient means to investigate a system from a quantum mechanics description.

Zinc Phosphide (Zn_{3}P_{2}) could be the basis for cheap and highly efficient solar cells. Its use in this regard is limited by the difficulty in n-type doping the material. In an effort to understand the mechanism behind this, the energetics and electronic structure of intrinsic point defects in zinc phosphide are studied using generalized Kohn-Sham theory and utilizing the Heyd, Scuseria, and Ernzerhof (HSE) hybrid functional for exchange and correlation. Novel ‘perturbation extrapolation’ is utilized to extend the use of the computationally expensive HSE functional to this large-scale defect system. According to calculations, the formation energy of charged phosphorus interstitial defects are very low in n-type Zn_{3}P_{2} and act as ‘electron sinks’, nullifying the desired doping and lowering the fermi-level back towards the p-type regime. Going forward, this insight provides clues to fabricating useful zinc phosphide based devices. In addition, the methodology developed for this work can be applied to further doping studies in other systems.

Accurate determination of high pressure and temperature equations of state is fundamental in a variety of fields. However, it is often very difficult to cover a wide range of temperatures and pressures in an laboratory setting. Here we develop methods to determine a multi-phase equation of state for Ta through computation. The typical means of investigating thermodynamic properties is via ’classical’ molecular dynamics where the atomic motion is calculated from Newtonian mechanics with the electronic effects abstracted away into an interatomic potential function. For our purposes, a ’first principles’ approach such as DFT is useful as a classical potential is typically valid for only a portion of the phase diagram (i.e. whatever part it has been fit to). Furthermore, for extremes of temperature and pressure quantum effects become critical to accurately capture an equation of state and are very hard to capture in even complex model potentials. This requires extending the inherently zero temperature DFT to predict the finite temperature response of the system. Statistical modelling and thermodynamic integration is used to extend our results over all phases, as well as phase-coexistence regions which are at the limits of typical DFT validity. We deliver the most comprehensive and accurate equation of state that has been done for Ta. This work also lends insights that can be applied to further equation of state work in many other materials.

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(PHD, 2013)

Abstract:

The Zn-Sb binary phase system has been of interest for many years in the search for efficient and low-cost thermoelectric materials. Of primary interest has been the Zn_{4}Sb_{3} phase which exhibits a thermoelectric figure of merit, *zT*, in excess of 1 in an intermediate temperature range. In this study, Zn_{4}Sb_{3} is shown to be entropically stabilized with respect to decomposition to Zn and ZnSb through the effects of configurational disorder and phonon free energy. Single-phase stability is predicted for a range of compositions and temperatures. Retrograde solubility of Zn is predicted on the two-phase boundary region between Zn_{4}Sb_{3} and Zn. The complex temperature-dependent solubility can be used to explain the variety of nanoparticle formation observed in the system: formation of ZnSb on the Sb-rich side, Zn on the far Zn-rich side, and nano-void formation due to Zn precipitates being reabsorbed at lower temperatures.

A new binary compound, Zn_{8}Sb_{7}, known only in nanoparticulate form, is also studied using density functional calculations. The free energies of formation, including effects from vibrations and configurational disorder, are calculated to compare with the relevant phases ZnSb, Zn, and Zn_{4}Sb_{3}, yielding insight into the phase stability of Zn_{8}Sb_{7}. Band structure calculations predict Zn_{8}Sb_{7}, much like ZnSb and Zn_{4}Sb_{3}, to be an intermetallic semiconductor with similar thermoelectric properties. If sufficient entropy or surface energy exists to stabilize the bulk material, it would be stable in a limited temperature window at high temperature.

In the AZn_{2}Sb_{2} series of materials—A = Ca, Sr, Yb, and Eu—I show that a large concentration of thermodynamically stable cation vacancies leads to high extrinsic carrier concentrations. The stable defect level depends on the choice of A, and is consistent with experimentally observed carrier concentrations in these materials. These results demonstrate that point defects are the primary mechanism by which the covalency of the cation bond can influence carrier concentration in nominally valence-precise AZn_{2}Sb_{2}compounds. This mechanism may be generally applicable to other Zintl phases, perhaps explaining similar trends seen in A_{14}MSb_{11}, A_{2}MSb_{2} (A=2+ cation, M = 2+ or 3+ metal),and similar materials.

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(PHD, 2012)

Abstract:

This thesis deals with achieving more realistic atomistic simulations of materials, by developing accurate and robust force-fields, and algorithms for practical time scales.

I develop a formalism for generating interatomic potentials for simulating atomistic phenomena occurring at energy scales ranging from lattice vibrations to crystal defects to high-energy collisions. This is done by fitting against an extensive database of ab initio results, as well as to experimental measurements for mixed oxide nuclear fuels. The applicability of these interactions to a variety of mixed environments beyond the fitting domain is also assessed. The employed formalism makes these potentials applicable across all interatomic distances without the need for any ambiguous splining to the well-established short-range Ziegler-Biersack-Littmark universal pair potential. We expect these to be reliable potentials for carrying out damage simulations (and molecular dynamics simulations in general) in nuclear fuels of varying compositions for all relevant atomic collision energies.

A hybrid stochastic and deterministic algorithm is proposed that while maintaining fully atomistic resolution, allows one to achieve milliseconds and longer time scales for several thousands of atoms. The method exploits the rare event nature of the dynamics like other such methods, but goes beyond them by (i) not having to pick a scheme for biasing the energy landscape, (ii) providing control on the accuracy of the boosted time scale, (iii) not assuming any harmonic transition state theory (HTST), and (iv) not having to identify collective coordinates or interesting degrees of freedom. The method is validated by calculating diffusion constants for vacancy-mediated diffusion in iron metal at low temperatures, and comparing against brute-force high temperature molecular dynamics. We also calculate diffusion constants for vacancy diffusion in tantalum metal, where we compare against low-temperature HTST as well. The robustness of the algorithm with respect to the only free parameter it involves is ascertained.

The method is then applied to perform tensile tests on gold nanopillars on strain rates as low as 100/s, bringing out the perils of high strain-rate molecular dynamics calculations. We also calculate temperature and stress dependence of activation free energy for surface nucleation of dislocations in pristine gold nanopillars under realistic loads. While maintaining fully atomistic resolution, we reach the fraction-of-a-second time scale regime. It is found that the activation free energy depends significantly and nonlinearly on the driving force (stress or strain) and temperature, leading to very high activation entropies for surface dislocation nucleation.

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