Masters Research - Master of Philosophy (Engineering) / Thermal conduction properties are of major concern for those metal/ceramic composite materials having applications in semiconductor devices and electronic packaging materials. A higher thermal conductivity to coefficient of thermal expansion ratio is an advantage for such materials employed in electronic devices due to the subjective high thermal loads. It is well known that the shape, size and distribution of the insulating phase have an effect on the overall thermal conductivity properties. But the details are lacking and well deserving of study. Metal/ceramic oxide interfaces are important in the strengthening mechanisms of dispersion strengthened materials. Accordingly, considerable attention has been given to recent investigations of oxygen diffusion characteristics and the bonding mechanisms at such interfaces. Susceptibility to oxidation can be studied by analysing several thicknesses of material. As an example, studying a thin film and a semi-infinite material subjected to a high oxygen partial pressure environment and a vacuum condition would help to determine the oxidation (in-diffusion) and de-oxidation (out-diffusion) processes respectively. Since metal/ceramic internal interfaces play a very important role in controlling the mechanical, thermal and electrical properties, it is timely to consider these diffusion processes for detailed study. In this Thesis, the two areas mentioned above were selected for detailed investigation. The Thesis also addresses the further development of a method for solving complex phenomenological diffusion problems. This method makes use of lattice-based random walks of virtual particles, directed according to the Monte Carlo method (the Lattice Monte Carlo method) which is then used to address various mass and thermal diffusion processes. Chapter 2 is concerned with using this method to determine the thermal conductivity of model composites. In that chapter, the Lattice Monte Carlo method is used to calculate the effective thermal conductivity of several models of a composite, where inclusions are arranged in square planar and cubic arrangements with periodic boundary conditions. Excellent agreement is found of the effective thermal conductivity with the century-old Maxwell-Garnett Equation. Chapter 3 is concerned with a phenomenological representation of oxygen diffusion and segregation in a model composite based on Ag/MgO. The Lattice Monte Carlo method is employed to address mass diffusion in this composite. Square and randomly distributed multiple inclusions were considered as shapes of the MgO inclusion phase. The time-dependence of oxygen concentration depth profiles and contour maps were determined. First, oxygen in-diffusion is considered from a constant surface source solely into the Ag metal matrix: oxygen depth profiles were in excellent agreement with exact results. Next, oxygen in-diffusion/segregation is simulated in the composite by permitting and restricting the mobility of oxygen in different scenarios involving the Ag-MgO interface. The (higher temperature) out-diffusion of oxygen from the composite was also simulated and corresponding results obtained for the oxygen depth profiles. In both cases, very good agreement was found between the results from the Lattice Monte Carlo method and analytical expressions.

Masters Research - Master of Philosophy (Engineering) / Thermal conduction properties are of major concern for those metal/ceramic composite materials having applications in semiconductor devices and electronic packaging materials. A higher thermal conductivity to coefficient of thermal expansion ratio is an advantage for such materials employed in electronic devices due to the subjective high thermal loads. It is well known that the shape, size and distribution of the insulating phase have an effect on the overall thermal conductivity properties. But the details are lacking and well deserving of study. Metal/ceramic oxide interfaces are important in the strengthening mechanisms of dispersion strengthened materials. Accordingly, considerable attention has been given to recent investigations of oxygen diffusion characteristics and the bonding mechanisms at such interfaces. Susceptibility to oxidation can be studied by analysing several thicknesses of material. As an example, studying a thin film and a semi-infinite material subjected to a high oxygen partial pressure environment and a vacuum condition would help to determine the oxidation (in-diffusion) and de-oxidation (out-diffusion) processes respectively. Since metal/ceramic internal interfaces play a very important role in controlling the mechanical, thermal and electrical properties, it is timely to consider these diffusion processes for detailed study. In this Thesis, the two areas mentioned above were selected for detailed investigation. The Thesis also addresses the further development of a method for solving complex phenomenological diffusion problems. This method makes use of lattice-based random walks of virtual particles, directed according to the Monte Carlo method (the Lattice Monte Carlo method) which is then used to address various mass and thermal diffusion processes. Chapter 2 is concerned with using this method to determine the thermal conductivity of model composites. In that chapter, the Lattice Monte Carlo method is used to calculate the effective thermal conductivity of several models of a composite, where inclusions are arranged in square planar and cubic arrangements with periodic boundary conditions. Excellent agreement is found of the effective thermal conductivity with the century-old Maxwell-Garnett Equation. Chapter 3 is concerned with a phenomenological representation of oxygen diffusion and segregation in a model composite based on Ag/MgO. The Lattice Monte Carlo method is employed to address mass diffusion in this composite. Square and randomly distributed multiple inclusions were considered as shapes of the MgO inclusion phase. The time-dependence of oxygen concentration depth profiles and contour maps were determined. First, oxygen in-diffusion is considered from a constant surface source solely into the Ag metal matrix: oxygen depth profiles were in excellent agreement with exact results. Next, oxygen in-diffusion/segregation is simulated in the composite by permitting and restricting the mobility of oxygen in different scenarios involving the Ag-MgO interface. The (higher temperature) out-diffusion of oxygen from the composite was also simulated and corresponding results obtained for the oxygen depth profiles. In both cases, very good agreement was found between the results from the Lattice Monte Carlo method and analytical expressions.

Semiconductor nanocrystals, also known as quantum dots (QDs), are an important class of materials that are being extensively studied for a wide variety of potential applications, such as medical diagnostics, photovoltaics, and solid-state lighting. The optical and electronic properties of these nanocrystals are different from their bulk properties and depend on the size of the QDs. Therefore an important requirement in their synthesis is a proper control on the final nanoparticle size. Recently, a technique has been developed for synthesizing zinc selenide (ZnSe) QDs using microemulsion droplets as templates. In these systems, a fixed amount of a reactant is dissolved in each droplet and a second reactant is supplied by diffusion through the interface. Spontaneous reaction between the two reactants at the droplet interface forms ZnSe nuclei, whose subsequent diffusion and coalescence into clusters ultimately leads to the formation of a single particle in each droplet. The size of the final particle can be adjusted by changing the initial concentration of the reactant that is dissolved in the dispersed phase of the microemulsion. In this thesis we use a modeling and simulation approach to study the phenomena underlying the formation of QDs in the droplets of a microemulsion. A Lattice Monte-Carlo model was developed to describe Brownian diffusion of a Zn-containing precursor (reactant) inside a droplet, formation of ZnSe nuclei via an irreversible reaction with a Se-containing precursor at the droplet interface, Brownian diffusion and coalescence of nuclei into clusters ultimately leading to the formation of a single nanoparticle inside the droplet. The time required for forming a single particle was found to initially increase as the final particle size was increased by increasing the initial concentration of the reactant in the droplet, but it quickly passed through a maximum, and subsequently decreased. The simulations revealed that this seemingly anomalous result can be explained by studying the intermediate cluster populations that show the formation of a large intermediate "sweeper" cluster. This sweeper cluster is a more effective collision partner to smaller ones and accelerates the coalescence process that eventually leads to the formation of a single particle. A generalized dimensionless equation was obtained that relates the formation time of the final particle to its size for various droplet sizes and diffusivities of the reactant and clusters in the droplet. A parametric study revealed that the final particle formation time is more sensitive to changes in the cluster coalescence probability than in the probability of nucleation. We subsequently compared these results with those obtained by simulating the coalescence of nuclei that are assumed to be formed spontaneously inside a droplet and to be initially uniformly dispersed in it. Comparison of the time required for forming a single final particle for the two cases revealed that for ZnSe particles with diameter smaller than 3.5 nm the predicted formation times were approximately the same. Surprisingly, for particles larger than 3.5 nm, the scenario that required diffusion of a reactant to the interface and formation of nuclei via a reaction at the interface led to the formation of a single particle faster than the scenario that started with nuclei uniformly dispersed in the droplet. Analysis of intermediate cluster populations indicates that the "sweeper" clusters are more effective in accelerating cluster coalescence when the nuclei are supplied gradually, as in the first scenario, compared to spontaneous nucleation throughout the domain. Generalized equations were obtained that describe the evolution of the number of different cluster sizes during coalescence starting from an initially monodispersed population of nuclei thus extending the classical theory of coalescence of monodisperse aerosols in an infinite domain to include coalescence in finite spherical domains with reflective boundaries. Finally, a generalized phenomenological model describing an energy balance during coalescence of two nanoparticles was developed. The reduction in the surface area of the coalescing system was modeled to be the source of thermal energy released due to the formation of additional bonds in the bulk of the coalesced particles. The temperature rise of the coalescing system was predicted for adiabatic coalescence and for coalescence with energy dissipation to a surrounding medium. Generalized equations were developed by scaling the temperature rise with its maximum value that corresponds to adiabatic conditions and the time with a characteristic time for coalescence obtained from the literature that depends on the mechanism (e.g., viscous flow, bulk diffusion, or surface diffusion). As a case study, the effects of the size of coalescing ZnSe nanoparticles on the temperature evolution of the coalescing system were studied by assuming that surface diffusion is the predominant mechanism for coalescence in this system. This modeling and simulation study of nanoparticle nucleation and coalescence presented in this thesis has revealed new phenomena and led to generalized models that can be used for studying such systems. Our work extended the classical theory for coalescence in an infinite domain to include finite spherical domains with reflective boundaries and provided a generalized approach for the analysis of transient thermal effects occurring during coalescence of two nanoparticles.

abstract: Fuel cells, particularly solid oxide fuel cells (SOFC), are important for the future of greener and more efficient energy sources. Although SOFCs have been in existence for over fifty years, they have not been deployed extensively because they need to be operated at a high temperature (∼1000 °C), are expensive, and have slow response to changes in energy demands. One important need for commercialization of SOFCs is a lowering of their operating temperature, which requires an electrolyte that can operate at lower temperatures. Doped ceria is one such candidate. For this dissertation work I have studied different types of doped ceria to understand the mechanism of oxygen vacancy diffusion through the bulk. Doped ceria is important because they have high ionic conductivities thus making them attractive candidates for the electrolytes of solid oxide fuel cells. In particular, I have studied how the ionic conductivities are improved in these doped materials by studying the oxygen-vacancy formations and migrations. In this dissertation I describe the application of density functional theory (DFT) and Kinetic Lattice Monte Carlo (KLMC) simulations to calculate the vacancy diffusion and ionic conductivities in doped ceria. The dopants used are praseodymium (Pr), gadolinium (Gd), and neodymium (Nd), all belonging to the lanthanide series. The activation energies for vacancy migration between different nearest neighbor (relative to the dopant) positions were calculated using the commercial DFT code VASP (Vienna Ab-initio Simulation Package). These activation energies were then used as inputs to the KLMC code that I co-developed. The KLMC code was run for different temperatures (673 K to 1073 K) and for different dopant concentrations (0 to 40%). These simulations have resulted in the prediction of dopant concentrations for maximum ionic conductivity at a given temperature. / Dissertation/Thesis / Ph.D. Materials Science and Engineering 2011

Lattice Monte Carlo methods are used to investigate far from and out-of-equilibrium systems, including surface growth, spin systems and solid mixtures. Applications range from the determination of universal growth or aging behaviors to palpable systems, where coarsening of nanocomposites or self-organization of functional nanostructures are of interest. Such studies require observations of large systems over long times scales, to allow structures to grow over orders of magnitude, which necessitates massively parallel simulations. This work addresses the problem of parallel processing introducing correlations in Monte Carlo updates and proposes a virtually correlation-free domain decomposition scheme to solve it. The effect of correlations on scaling and dynamical properties of surface growth systems and related lattice gases is investigated further by comparing results obtained by correlation-free and intrinsically correlated but highly efficient simulations using a stochastic cellular automaton (SCA). Efficient massively parallel implementations on graphics processing units (GPUs) were developed, which enable large-scale simulations leading to unprecedented precision in the final results. The primary subject of study is the Kardar–Parisi–Zhang (KPZ) surface growth in (2 + 1) dimensions, which is simulated using a dimer lattice gas and the restricted solid-on-solid model (RSOS) model. Using extensive simulations, conjectures regard- ing growth, autocorrelation and autoresponse properties are tested and new precise numerical predictions for several universal parameters are made.:1. Introduction 1.1. Motivations and Goals 1.2. Overview 2. Methods and Models 2.1. Estimation of Scaling Exponents and Error Margins 2.2. From Continuum- to Atomistic Models 2.3. Models for Phase Ordering and Nanostructure Evolution 2.3.1. The Kinetic Metropolis Lattice Monte-Carlo Method 2.3.2. The Potts Model 2.4. The Kardar–Parisi–Zhang and Edwards–Wilkinson Universality Classes 2.4.0.1. Physical Aging 2.4.1. The Octahedron Model 2.4.2. The Restricted Solid on Solid Model 3. Parallel Implementation: Towards Large-Scale Simulations 3.1. Parallel Architectures and Programming Models 3.1.1. CPU 3.1.2. GPU 3.1.3. Heterogeneous Parallelism and MPI 3.1.4. Bit-Coding of Lattice Sites 3.2. Domain Decomposition for Stochastic Lattice Models 3.2.1. DD for Asynchronous Updates 3.2.1.1. Dead border (DB) 3.2.1.2. Double tiling (DT) 3.2.1.3. DT DD with random origin (DTr) 3.2.1.4. Implementation 3.2.2. Second DD Layer on GPUs 3.2.2.1. Single-Hit DT 3.2.2.2. Single-Hit dead border (DB) 3.2.2.3. DD Parameters for the Octahedron Model 3.2.3. Performance 3.3. Lattice Level DD: Stochastic Cellular Automaton 3.3.1. Local Approach for the Octahedron Model 3.3.2. Non-Local Approach for the Octahedron Model 3.3.2.1. Bit-Vectorized GPU Implementation 3.3.3. Performance of SCA Implementations 3.4. The Multi-Surface Coding Approach 3.4.0.1. Vectorization 3.4.0.2. Scalar Updates 3.4.0.3. Domain Decomposition 3.4.1. Implementation: SkyMC 3.4.1.1. 2d Restricted Solid on Solid Model 3.4.1.2. 2d and 3d Potts Model 3.4.1.3. Sequential CPU Reference 3.4.2. SkyMC Benchmarks 3.5. Measurements 3.5.0.1. Measurement Intervals 3.5.0.2. Measuring using Heterogeneous Resources 4. Monte-Carlo Investigation of the Kardar–Parisi–Zhang Universality Class 4.1. Evolution of Surface Roughness 4.1.1. Comparison of Parallel Implementations of the Octahedron Model 4.1.1.1. The Growth Regime 4.1.1.2. Distribution of Interface Heights in the Growth Regime 4.1.1.3. KPZ Ansatz for the Growth Regime 4.1.1.4. The Steady State 4.1.2. Investigations using RSOS 4.1.2.1. The Growth Regime 4.1.2.2. The Steady State 4.1.2.3. Consistency of Fine-Size Scaling with Respect to DD 4.1.3. Results for Growth Phase and Steady State 4.2. Autocorrelation Functions 4.2.1. Comparison of DD Methods for RS Dynamics 4.2.1.1. Device-Layer DD 4.2.1.2. Block-Layer DD 4.2.2. Autocorrelation Properties under RS Dynamics 4.2.3. Autocorrelation Properties under SCA Dynamics 4.2.3.1. Autocorrelation of Heights 4.2.3.2. Autocorrelation of Slopes 4.2.4. Autocorrelation in the SCA Steady State 4.2.5. Autocorrelation in the EW Case under SCA 4.2.5.1. Autocorrelation of Heights 4.2.5.2. Autocorrelations of Slopes 4.3. Autoresponse Functions 4.3.1. Autoresponse Properties 4.3.1.1. Autoresponse of Heights 4.3.1.2. Autoresponse of Slopes 4.3.1.3. Self-Averaging 4.4. Summary 5. Further Topics 5.1. Investigations of the Potts Model 5.1.1. Testing Results from the Parallel Implementations 5.1.2. Domain Growth in Disordered Potts Models 5.2. Local Scale Invariance in KPZ Surface Growth 6. Conclusions and Outlook Acknowledgements A. Coding Details A.1. Bit-Coding A.2. Packing and Unpacking Signed Integers A.3. Random Number Generation / Gitter-Monte-Carlo-Methoden werden zur Untersuchung von Systemen wie Oberflächenwachstum, Spinsystemen oder gemischten Feststoffen verwendet, welche fern eines Gleichgewichtes bleiben oder zu einem streben. Die Anwendungen reichen von der Bestimmung universellen Wachstums- und Alterungsverhaltens hin zu konkreten Systemen, in denen die Reifung von Nanokompositmaterialien oder die Selbstorganisation von funktionalen Nanostrukturen von Interesse sind. In solchen Studien müssen große Systemen über lange Zeiträume betrachtet werden, um Strukturwachstum über mehrere Größenordnungen zu erlauben. Dies erfordert massivparallele Simulationen. Diese Arbeit adressiert das Problem, dass parallele Verarbeitung Korrelationen in Monte-Carlo-Updates verursachen und entwickelt eine praktisch korrelationsfreie Domänenzerlegungsmethode, um es zu lösen. Der Einfluss von Korrelationen auf Skalierungs- und dynamische Eigenschaften von Oberflächenwachtums- sowie verwandten Gittergassystemen wird weitergehend durch den Vergleich von Ergebnissen aus korrelationsfreien und intrinsisch korrelierten Simulationen mit einem stochastischen zellulären Automaten untersucht. Effiziente massiv parallele Implementationen auf Grafikkarten wurden entwickelt, welche großskalige Simulationen und damit präzedenzlos genaue Ergebnisse ermöglichen. Das primäre Studienobjekt ist das (2 + 1)-dimensionale Kardar–Parisi–Zhang- Oberflächenwachstum, welches durch ein Dimer-Gittergas und das Kim-Kosterlitz-Modell simuliert wird. Durch massive Simulationen werden Thesen über Wachstums-, Autokorrelations- und Antworteigenschaften getestet und neue, präzise numerische Vorhersagen zu einigen universellen Parametern getroffen.:1. Introduction 1.1. Motivations and Goals 1.2. Overview 2. Methods and Models 2.1. Estimation of Scaling Exponents and Error Margins 2.2. From Continuum- to Atomistic Models 2.3. Models for Phase Ordering and Nanostructure Evolution 2.3.1. The Kinetic Metropolis Lattice Monte-Carlo Method 2.3.2. The Potts Model 2.4. The Kardar–Parisi–Zhang and Edwards–Wilkinson Universality Classes 2.4.0.1. Physical Aging 2.4.1. The Octahedron Model 2.4.2. The Restricted Solid on Solid Model 3. Parallel Implementation: Towards Large-Scale Simulations 3.1. Parallel Architectures and Programming Models 3.1.1. CPU 3.1.2. GPU 3.1.3. Heterogeneous Parallelism and MPI 3.1.4. Bit-Coding of Lattice Sites 3.2. Domain Decomposition for Stochastic Lattice Models 3.2.1. DD for Asynchronous Updates 3.2.1.1. Dead border (DB) 3.2.1.2. Double tiling (DT) 3.2.1.3. DT DD with random origin (DTr) 3.2.1.4. Implementation 3.2.2. Second DD Layer on GPUs 3.2.2.1. Single-Hit DT 3.2.2.2. Single-Hit dead border (DB) 3.2.2.3. DD Parameters for the Octahedron Model 3.2.3. Performance 3.3. Lattice Level DD: Stochastic Cellular Automaton 3.3.1. Local Approach for the Octahedron Model 3.3.2. Non-Local Approach for the Octahedron Model 3.3.2.1. Bit-Vectorized GPU Implementation 3.3.3. Performance of SCA Implementations 3.4. The Multi-Surface Coding Approach 3.4.0.1. Vectorization 3.4.0.2. Scalar Updates 3.4.0.3. Domain Decomposition 3.4.1. Implementation: SkyMC 3.4.1.1. 2d Restricted Solid on Solid Model 3.4.1.2. 2d and 3d Potts Model 3.4.1.3. Sequential CPU Reference 3.4.2. SkyMC Benchmarks 3.5. Measurements 3.5.0.1. Measurement Intervals 3.5.0.2. Measuring using Heterogeneous Resources 4. Monte-Carlo Investigation of the Kardar–Parisi–Zhang Universality Class 4.1. Evolution of Surface Roughness 4.1.1. Comparison of Parallel Implementations of the Octahedron Model 4.1.1.1. The Growth Regime 4.1.1.2. Distribution of Interface Heights in the Growth Regime 4.1.1.3. KPZ Ansatz for the Growth Regime 4.1.1.4. The Steady State 4.1.2. Investigations using RSOS 4.1.2.1. The Growth Regime 4.1.2.2. The Steady State 4.1.2.3. Consistency of Fine-Size Scaling with Respect to DD 4.1.3. Results for Growth Phase and Steady State 4.2. Autocorrelation Functions 4.2.1. Comparison of DD Methods for RS Dynamics 4.2.1.1. Device-Layer DD 4.2.1.2. Block-Layer DD 4.2.2. Autocorrelation Properties under RS Dynamics 4.2.3. Autocorrelation Properties under SCA Dynamics 4.2.3.1. Autocorrelation of Heights 4.2.3.2. Autocorrelation of Slopes 4.2.4. Autocorrelation in the SCA Steady State 4.2.5. Autocorrelation in the EW Case under SCA 4.2.5.1. Autocorrelation of Heights 4.2.5.2. Autocorrelations of Slopes 4.3. Autoresponse Functions 4.3.1. Autoresponse Properties 4.3.1.1. Autoresponse of Heights 4.3.1.2. Autoresponse of Slopes 4.3.1.3. Self-Averaging 4.4. Summary 5. Further Topics 5.1. Investigations of the Potts Model 5.1.1. Testing Results from the Parallel Implementations 5.1.2. Domain Growth in Disordered Potts Models 5.2. Local Scale Invariance in KPZ Surface Growth 6. Conclusions and Outlook Acknowledgements A. Coding Details A.1. Bit-Coding A.2. Packing and Unpacking Signed Integers A.3. Random Number Generation