A coupled kinetic Monte Carlo – Finite Element Analysis (kMC–FEA) method is developed with a numerical implementation in the Scalable Implementation of Finite Elements at NASA (ScIFEN). This method is presented as a mesoscale model for Shape Memory Alloy (SMA) material systems. The model is based on Transition State Theory and predicts the nonlinear mechanical behavior of the 1st order solid–solid phase transformation between Austenite and Martensite in SMAs. The kMC–FEA modeling method presented in this work builds upon the work of Chen and Schuh [1, 2]. It represents a “bottom-up” approach to materials modeling and could serve as a bridge for future studies that attempt to link ab initio methods with phenomenological findings in SMA systems. This thesis presents the derivation of the kMC–FEA model, which is then used to probe the various responses expected in SMAs and verify the influence of model parameters on simulation behavior. In a departure from the work of Chen and Schuh, the thermodynamic derivation includes an elastic transformation energy term, which is found to be a significant fraction of the total transformation energy and play an important role in the evolution of a simulation. Theoretical predictions of the model behavior can be made from this derivation, including expected transformation stresses and temperatures. A convergence study is presented as verification that the new elastic energy term proposed in this model is a reasonable approximation. A parameter sensitivity study is also presented, showing good agreement between theoretical predictions and the results of a full-factorial numerical exploration of model outputs. Model simulation demonstrates the emergence of the shape memory effect, an important SMA behavior not shown by Chen and Schuh, along with the expected superelastic effect and thermal hysteresis. Further exploration of simulated model outputs presented in this work involves comparison with experimental data and predicted output values obtained from a separate phenomenological constitutive model. This comparison shows that the kMC–FEA method is capable of reproducing qualitative, but not yet quantitative, responses of real SMA material systems. Discussion of each model parameter and its effects on the behavior of the model are presented as guidelines for future studies of SMA materials. A complete implementation of the method is contained in a new finite element software package (ScIFEN) that is available for future

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The following dissertation is divided into two parts. Part I deals with the modeling of helium trapping at oxide-iron interfaces in nanostructured ferritic alloys (NFAs) using density functional theory (DFT). The modelling that has been performed serves to increase the knowledge and understanding of the theory underlying the prevention of helium embrittlement in materials. Although the focus is for nuclear reactor materials, the theory can be applied to any material that may be in an environment where helium embrittlement is of concern. In addition to an improved theoretical understanding of helium embrittlement, the following DFT models will provide valuable thermodynamic and kinetic information. This information can be utilized in the development of large-scale models (such as kinetic Monte Carlo simulations) of the microstructural evolution of reactor components. Accurate modelling is an essential tool for the development of new reactor materials, as experiments for components can span decades for the lifetime of the reactor. Part II of this dissertation deals with the development, and use of, kinetic Monte Carlo (KMC) simulations for improved efficiency in investigating catalytic chemical reactions on surfaces. An essential technique for the predictive development and discovery of catalysts relies on modelling of large-scale chemical reactions. This requires multi-scale modelling where a common sequence of techniques would require parameterization obtained from DFT, simulation of the chemical reactions for millions of conditions using KMC (requiring millions of separate simulations), and finally simulation of the large scale reactor environment using computational fluid dynamics. The tools that have been developed will aid in the predictive discovery, development and modelling of catalysts through the use of KMC simulations. The algorithms that have been developed are versatile and thus, they can be applied to nearly any KMC simulation that would seek to overcome similar challenges as those posed by investigating catalysis (such as the need for millions of simulations, long simulation time and large discrepancies in transition probabilities). / Ph. D.

Le vieillissement statique est un concept important dans la métallurgie qui se réfère à un durcissement de la matière ayant subi une déformation plastique et est ensuite vieilli pendant une certaine période de temps. La théorie proposée dans les années 1940 par Cottrell et Bilby explique ce phénomène comme étant causé par l'épinglage des dislocations par les impuretés (par exemple, les atomes de carbone en solution solide) qui migrent au voisinage du défaut de ligne. Au cours de ce travail de thèse, le mécanisme atomistique responsable du phénomène du vieillissement statique dans le fer alpha a été étudié par des simulations numériques. Etant donné que la diffusion à l'état solide se déroule lentement, l'utilisation de la dynamique moléculaire à basse température (lorsque l'effet du champ de contraintes sur la dislocation de diffusion du carbone est plus prononcé) a été évitée, et nous avons utilisé préférentiellement le couplage de la statique moléculaire avec le Monte-Carlo cinétique atomistique. Trois points principaux ont été abordés dans cette thèse: (i) l'effet du champ de contraintes d'une dislocation coin ou vis sur un atome de carbone qui diffuse à proximité, (ii) la diffusion de l'atome de carbone dans le cour de la dislocation («pipe diffusion»), et (iii) la distribution d'équilibre des atomes de carbone dans une atmosphère de Cottrell. Le principal effet du champ de contrainte de la dislocation à l'extérieur du coeur est de biaiser la diffusion de l'impurité, de sorte que certains sauts (transitions) deviennent plus probables que d'autres. Cet effet va conduire aux premiers stades de la formation de l'atmosphère de Cottrell, lorsque l'interaction mutuelle entre atomes de carbone est négligeable. Au cœur de la dislocation, comme prévu, nos résultats indiquent que le carbone diffuse plus vite que dans le volume. La concentration de carbone dans le voisinage d'une dislocation coin ou vis a été modélisée par une approche de physique statistique en utilisant les énergies de liaison calculées par la statique moléculaire. Cette approche est en bon accord avec les données expérimentales. / Static strain aging is an important concept in metalurgy that refers to the hardening of a material that has undergone plastic deformation and then is aged for a certain period of time. A theory proposed in the late 1940s by Cottrell and Bilby explains this phenomenon as being caused by the pinning of dislocations by impurities (e.g., carbon atoms in solid solution) that migrate to the vicinity of the line defect. In the course of this PhD work, the atomistic mechanism behind the static strain aging phenomenon in bcc iron has been studied by means of computer simulations. Given the fact that diffusion in the solid state proceeds slowly, thus preventing the use of molecular dynamics at low temperatures (when the effect of the dislocation stress field on carbon diffusion is more pronounced), we have preferentially employed a method coupling molecular statics with atomistic kinetic Monte Carlo. Three major points have been addressed by this thesis: (i) the effect of the stress field of an edge or screw dislocation on a carbon atom diffusing nearby; (ii) the diffusion of a carbon atom in the tight channel found in the dislocation core (pipe diffusion); and (iii) the equilibrium carbon distribution in a Cottrell atmosphere. The main effect of the dislocation stress field outside the dislocation core consists of biasing carbon diffusion, such that some transitions become more likely than others. This effect is expected to drive the early stages of Cottrell atmosphere formation, when the mutual interaction between carbon atoms is negligible. Right in the dislocation core, as expected, carbon was seen to diffuse faster than in the bulk. Carbon concentration in the neighborhood of an edge or a screw dislocation was modeled by an approach based in statistical physics using the binding energies calculated by molecular statics, revealing a good agreement with experimental data obtained by atom probe techniques.

Selon la théorie de Cottrell et Bilby, les dislocations à travers leur champ de contrainte interagissent avec les atomes de soluté qui s’agrègent au cœur et autour des dislocations (atmosphère de Cottrell). Ces atmosphères « bloquent » les dislocations et fragilisent le matériau. Dans cette thèse, les techniques de simulations à l’échelle atomique telles que la Dynamique Moléculaire, les simulations Monte Carlo Cinétique, Monte Carlo Métropolis ont été développées qui permettent de prendre en compte les interactions entre plusieurs centaines d’atomes de carbone et la dislocation, pour étudier la cinétique de formation ainsi que la structure d’une atmosphère de Cottrell. Par ailleurs, la technique de simulation est appliquée à deux autres problématiques: premièrement, il est connu que les atomes de C dans la ferrite se mettent en ordre (mise en ordre de Zener). La stabilité de cette phase est étudiée en fonction de la température et la concentration de C. Deuxièmement, la ségrégation des atomes de soluté dans les nano-cristaux de Ni ainsi que la stabilité des nano-cristaux avec les atomes de soluté dans les joints de grain à haute température est étudiée. / The objective of the thesis was to understand the microscopic features at the origin of ageing in metals. The originality of this contribution was the com- bination of three complementary computational techniques : (1) Metropolis Monte Carlo (MMC), (2) Atomic Kinetic Monte Carlo (AKMC), and, (3) Molecular Dynamics (MD). It consisted of four main sections : Firstly the ordering occurring in bulk alpha-iron via MMC and MD was studied. Various carbon contents and temperatures were investigated in order to obtain a “phase diagram”. Secondly, the generation of systems containing a dislocation interacting with many carbon atoms, namely a Cottrell Atmosphere, with MMC technique was described. The equilibrium structure of the atmosphere and the stress field around the atmospheres proves that the stress field around the dislocation was affected but not cancelled out by the atmosphere. Thirdly, the kinetics of the carbon migration and Cottrell atmosphere evolution were investigated via AKMC. The activation energies for carbon atom migration were calculated from the local stress field and the arrangement of the neigh- bouring carbon atoms. Lastly, an application of the combined use of MMC and MD to describe grain boundary segregation of solute atoms in fcc nickel was presented. The grain growth was inhibited due to the solute atoms in the grain boundary.

Molecular beam epitaxy has recently been applied to the growth and self assembly of nanostructures on crystal substrates. This highlights the importance of understanding how microscopic rules of atomic motion and assembly lead to macroscopic surface shapes. In this thesis, we present results from two computational studies of these mechanisms. We identify a kinetic mechanism responsible for the emergence of low-angle facets in recent epitaxial regrowth experiments on patterned surfaces. Kinetic Monte Carlo simulations of vicinal surfaces show that the preferred slope of the facets matches the threshold slope for the transition between step flow and growth by island nucleation. At this crossover slope, the surface step density is minimized and the adatom density is maximized, respectively. A model is developed that predicts the temperature dependence of the crossover slope and hence the facet slope. We also examine the "step bunching" instability thought to be present in step flow growth on surfaces with a downhill diffusion bias. One mechanism thought to produce the necessary bias is the inverse Ehrlich Schwoebel (ES) barrier. Using continuum, stochastic, and hybrid models of one dimensional step flow, we show that an inverse ES barrier to adatom migration is an insufficient condition to destabilize a surface against step bunching.

LTA-type zeolites with narrow window apertures coinciding with the approximate size of small gaseous molecules such as CO2 and N2 are interesting candidates for adsorbents with swing adsorption technologies due to their molecular sieving capabilities and otherwise attractive properties. These sieving capabilities are dependent on the energy barriers of diffusion between the zeolite pores, which can be fine-tuned by altering the framework composition. An ab initio level of theory is necessary to accurately describe specific gas-zeolite interaction and diffusion properties, while it is desirable to predict the macroscopic scale diffusion for industrial applications. Hence, a multiscale modeling approach is necessary to describe the molecular sieving phenomena exhaustively. In this thesis, we use several different modeling methods on different length and time scales to describe the diffusion driven uptake and separation of CO2 and N2 in Zeolite NaKA. A combination of classical force field based modeling methods are used to show the importance of taking into account both thermodynamic, as well as, kinetic effects when modeling gas uptake in narrow pore zeolites where the gas diffusion is to some extent hindered. For a more detailed investigation of the gas molecules’ pore-to-pore dynamics in the material, we present a procedure to compute the free energy barriers of diffusion using spatially constrained ab initio Molecular Dynamics. With this procedure, we seek to identify diffusion rate determining local properties of the Zeolite NaKA pores, including the Na+-to-K+ exchange at different ion sites and the presence of additional CO2 molecules in the pores. This energy barrier information is then used as input for the Kinetic Monte Carlo method, allowing us to simulate and compare these and other effects on the diffusion driven uptake using a realistic powder particle model on macroscopic timescales. / <p>At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 4: Manuscript.</p>

Molecular beam epitaxy has recently been applied to the growth and self assembly of nanostructures on crystal substrates. This highlights the importance of understanding how microscopic rules of atomic motion and assembly lead to macroscopic surface shapes. In this thesis, we present results from two computational studies of these mechanisms. We identify a kinetic mechanism responsible for the emergence of low-angle facets in recent epitaxial regrowth experiments on patterned surfaces. Kinetic Monte Carlo simulations of vicinal surfaces show that the preferred slope of the facets matches the threshold slope for the transition between step flow and growth by island nucleation. At this crossover slope, the surface step density is minimized and the adatom density is maximized, respectively. A model is developed that predicts the temperature dependence of the crossover slope and hence the facet slope. We also examine the "step bunching" instability thought to be present in step flow growth on surfaces with a downhill diffusion bias. One mechanism thought to produce the necessary bias is the inverse Ehrlich Schwoebel (ES) barrier. Using continuum, stochastic, and hybrid models of one dimensional step flow, we show that an inverse ES barrier to adatom migration is an insufficient condition to destabilize a surface against step bunching.

The ageing state of the world's nuclear power infrastructure, and the need to reduce humanity s dependency on fossil fuels, requires that this electrical energy generating capacity is replaced. Economic factors, and its physical and chemical properties, make high purity iron-chromium binary alloys a strong candidate for use in the construction of the pressure vessels of the next generation of nuclear reactors. This relatively inexpensive metal retains the oxidation resistance property of so-called stainless steel alloys, and has demonstrated dimensional stability and low degradation under harsh experimental environments of temperature and radiation. In this work, we consider radiation induced interstitial damage to the atomic lattices of iron-chromium binary alloys using the atomistic modelling methods, Molecular Dynamics and Adaptive Kinetic Monte Carlo, simulating collision cascade sequences, and the migration of defects in the aftermath. Variations in chromium content does not effect the initial damage production in terms of the number of Frenkel pairs produced, but iron and chromium atoms are not evenly distributed in defect atoms with respect to the bulk concentration. In simulations conducted at low temperature, chromium is under-represented, and at high temperature, a greater proportion of interstitial atoms are chromium than in the lattice overall. The latter phenomena is most strongly pronounced in systems of low bulk chromium content. During the simulation of post-cascade defect migration, interstitials atoms are observed to form temporary clusters and vacancies align along adjacent lattice sites, with the two types of defect also migrating to annihilate by recombination. Calculating the energy spectra of cascade events corresponding to an example experimental configuration using the SRIM package, we investigated the evolution of lattice systems in which a sequence of multiple cascade events occurred, both with and without a physically representative time gap between events. These simulations gave us the opportunity to observe the behaviour of cascades in the proximity of damage remaining from previous events, such as the promotion of defect clustering when this occurs.

La fabrication de jonctions implique de nombreux défis technologiques à mesure que les dispositifs se rétrécissent. Afin de mitiger les problèmes liés à la diminution agressive des dimensions des transistors, des substrats SOI ainsi que du silicium-germanium (SiGe) contraint ont été introduits dans les nœuds avancés. Ces nœuds nécessitent toutefois une jonction abrupte fortement activée, qui est réalisable avec la recristallisation en phase solide (SPER) et un faible budget thermique (500°C-5h).Dans ce manuscrit, la SPER du silicium, germanium et d’alliages SiGe est étudiée avec des méthodes atomistiques telles que le Monte Carlo Cinétique (KMC) et la dynamique moléculaire (MD). Le modèle KMC de SPER se base sur une équation d'Arrhenius et distingue des configurations locales à l'interface amorphe-cristal pour simuler la dépendance de la vitesse de SPER par rapport à l’orientation de substrat. Les simulations en dynamique moléculaire montrent que la vitesse de SPER sur les orientations de {111} est fortement dépendante de la taille de la cellule ainsi que de la température et du temps de recuit.Le modèle KMC est de plus étendu afin de considérer l'effet du bore pendant la SPER. Le bore peut en effet créer des complexes à la fois dans l’amorphe et le cristal et augmenter la vitesse de SPER. Cette augmentation est toutefois saturée lorsque le bore atteint de trop fortes concentrations. Un modèle de réaction de défauts traitant les complexes a été adjoint au modèle de SPER afin de correctement simuler la vitesse de SPER pour toutes les concentrations de bore. Dans les alliages (100)SiGe relaxés, l'énergie d'activation de la SPER possède un maximum à 40% de concentration de Ge.Le modèle KMC doit introduire en plus des liaisons Si-Si et Ge-Ge, la liaison Si-Ge pour simuler correctement la recristallisation des alliages. Le modèle est également utilisé pour émettre des hypothèses sur la vitesse de SPER sur d'autres orientations. Les simulations en dynamique moléculaire confirment également le comportement de l’énergie d'activation dans les alliages SiGe.Des expériences de diffractions par rayons-X suivant en temps réel la recristallisation d’alliages de SiGe contraints ont été réalisées avec un rayonnement synchrotron. La contrainte est perdue dans les alliages riches en Ge et la température de recuit semble avoir un rôle sur la relaxation. La rugosité de l'interface pourrait être le lien entre la relaxation de la contrainte et la température, du fait que des simulations en dynamique moléculaires révèlent l’influence de la température de recuit sur la rugosité de l'interface et que les défauts relaxant la contrainte ont été associés à une interface rugueuse.En résumé, le SPER et ses diverses dépendances ont été étudiées dans ce manuscrit par des approches atomistiques. Les conclusions tirées améliorent la compréhension actuelle de la SPER, permettant ainsi une meilleure optimisation de la fabrication des jonctions. / The junction fabrication involve numerous technological challenges as the devices shrink. To alleviate issues brought by the aggressive device scaling, Fully Depleted SOI substrates as well as strained silicon-germanium (SiGe) have been introduced in advanced nodes. They however require a highly-activated abrupt junction achievable with solid phase epitaxial regrowth (SPER) and a low thermal budget (500$^circ$C-5h).In this manuscript, the SPER of silicon, germanium and SiGe alloys is investigated using Kinetic Monte Carlo (KMC) and Molecular Dynamics (MD) methods. The KMC model of SPER uses an Arrhenius equation and distinguishes local configurations at the amorphous-crystalline interface to simulate the SPER rate dependence on substrate orientations. In MD simulations, the SPER rate on {111} orientations is found to heavily depends on the cell size, anneal temperature and time.The KMC model is furthermore refined to consider the effect of boron during SPER. Boron is known to create complexes in both amorphous and crystalline phases and increase the SPER rate. This increase however saturates at high boron concentrations. A defect reaction model handling the complexes has been conjoined to the SPER model to correctly simulate the SPER rate behaviour for all boron concentrations.In relaxed (100)SiGe alloys, the SPER activation energy possesses a maximum at 40% of Ge concentration. The KMC model introduces in addition to Si-Si and Ge-Ge bonds, the Si-Ge bond to correctly simulate alloy recrystallisation. The model is also used to hypothesise the rates on other orientations. MD simulations also confirm the activation energy behaviour in SiGe alloys.Finally, X-ray diffractions following in real-time the recrystallisation of strained SiGe alloys are performed with synchrotron radiations. The strain is lost in Ge-rich alloys. The strain relaxation can be related to the anneal temperature. The interface roughness could be the link between the strain relaxation and the temperature, as MD simulations exhibit an influence of the anneal temperature on the interface roughness and strain relaxing defects are associated to a rough interface.In summary, the SPER and its several dependencies are investigated in this manuscript with atomistic approaches. The drawn conclusions increase the current understanding of SPER, allowing a better optimisation of junction fabrication.