A number of technologies rely on the conversion of short laser pulses from one spectral domain to another. Efficient frequency conversion is currently obtained in ordered nonlinear optical materials and requires a periodic spatial modulation of their nonlinear coefficient which results in a narrow bandwidth. One can trade off efficiency for more spectral bandwidth by relaxing the strict phase-matching conditions and achieve nonlinear interaction in carefully engineered disordered crystalline aggregates, in a so-called random quasi-phase-matching (rQPM) process. In this dissertation, we examine appropriate fabrication pathways for (1-x)Pb(Mg1/3Nb2/3)O3-xPbTiO3 (PMN-PT) and ZnSe transparent ceramics for applications in the mid-IR. The main challenge associated with the fabrication of high transparency PMN-PT ceramics is to avoid the parasitic pyrochlore phase. The most effective method to suppress the formation of this undesired phase is to use magnesium niobate (MgNb2O6) as the starting material. We have found that, contrary to commercially available lead oxide powders, nanopowders synthesized in our lab by the combustion method help improve the densification of ceramics and their overall optical quality. The effects of dopants on the microstructure evolution and phase-purity control in PMN-PT ceramics are also investigated and show that La3+ helps control grain-growth and get a pure perovskite phase, thereby improving the samples transparency. With large second order susceptibility coefficients and wide transmission window from 0.45 to 21 μm, polycrystalline zinc selenide is also an ideal candidate material for accessing the MWIR spectrum through rQPM nonlinear interaction. We have investigated non-stoichiometric heat-treatment conditions necessary to develop adequate microstructure for rQPM from commercial CVD-grown ZnSe ceramics. We have been able to demonstrate the world's first optical parametric oscillation (OPO) based on rQPM in ZnSe transparent ceramic, enabling broadband frequency combs spanning 3-7.5 μm.

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In this dissertation I present computational studies that focus on the unique characteristics of metallic nanowires. We generated virtual nanowires of nanocrystalline nickel (nc-Ni) and single crystalline silver (Ag) in order to investigate particular nanoscale effects. Three-dimensional atomistic molecular dynamics studies were performed for each sample using the super computer System X located at Virginia Tech. Thermal grain growth simulations were performed on 4 nm grain size nc-Ni by observing grain sizes over time for temperatures from 800K to 1450K and we discovered grain growth to be linearly time-dependant, contrary to coarse grained materials with square root dependence. Strain induced grain growth studies consisted of straining the nanostructures in tension at a strain rate of 3.3 x 10^8 s⁻¹. Grain boundary movement was recorded to quantify grain boundary velocities and grain growth. It was shown that during deformation, there is interplay between dislocation-mediated plasticity and grain boundary accommodation of plasticity through grain boundary sliding. To further understand the effect of stress on nanocrystalline materials we performed tensile tests at different strain rates, varying from 2.22 x 10⁷ s⁻¹ to 1.33 x 10⁹ s⁻¹ for a 5 nm grain size nc-Ni nanowire with a 5 nm radius. The activation volume was given as ~2b³, where b is the Burger's vector and is consistent with a grain boundary dominate deformation mechanism. We expanded our research to 10 nm grain size nc-Ni nanowires with radii from 5 nm to 18 nm. Each wire was deformed 15% in tension or compression at a strain rate of 3.3 x 10⁸ s⁻¹. Asymmetry was observed for all radii, in which larger radii produced higher flow stresses for compression and small radii yielded higher flow stresses in tension. A cross over in the tension-compression asymmetry is found to occur at a radius of ~9 nm. A change in the dominate deformation mechanism in combination with the ease of grain boundary sliding contributes to the phenomena of the asymmetry. In the final chapter we focus on the energetic stability of multi-twinned Ag nanorods at the nanoscale. We used a combination of molecular statics and dynamics to find the local minimum energies for the multi-twinned nanorods and the non-twinned "bulk" materials and concluded that the stability of multi-twinned nanorods is highly influenced by the size of the sample and the existence of the ends. Using an analytical model we found the excess energy of the nanorods with ends and determined the critical aspect ratio below which five-twinned nanorods are stable. / Ph. D.

The work presented in this doctoral thesis employs colloidal suspensions to explore key open problems in condensed matter physics. Colloidal suspensions, along with gels, polymers, emulsions and liquid crystals belong to a family of materials that are collectively labelled as soft matter. Compositionally, colloidal suspensions consist of particles whose size ranges from a few nanometers to a few microns, dispersed in a solvent. A hallmark feature of these systems is that they exhibit Brownian motion, which makes them suitable for investigating statistical mechanical phenomena. Over the last fifteen years or so, colloids have been used extensively as model systems to shed light on a wide array of such phenomena typically observed in atomic systems. The chief reason why colloids are good mimics of atomic systems is their large size and slow dynamics. Unlike atomic systems, the dynamics of colloids can be probed in real time with single-particle resolution, which allows one to establish the link between macroscopic behavior and the microscopic processes that give rise to it. Yet another important feature is that colloidal systems exhibit various phases of matter such as crystals, liquids and glasses, which makes them versatile model systems that can probe a broad class of condensed matter physics problems. The work described in this thesis takes advantage of these lucrative features of colloidal suspensions to gain deeper insights into the physics of glass formation as well as shear-induced anisotropic grain growth in polycrystalline materials. The thesis is organized into two preliminary chapters, four work chapters and a concluding chapter, as follows. Chapter 1 provides an introduction to colloidal suspensions and reviews the chief theo-retical concepts regarding glass formation and grain boundary dynamics that form an integral part of subsequent chapters. Chapter 2 describes the experimental methods used for performing the work presented in the thesis and consists of two parts. The first part describes the protocols followed for synthesizing the size-tunable poly (N-isoprolypacrylamide) (PNIPAm) particles used in our study of shear-induced grain growth. The second part describes the instrumentation and techniques, such as holographic optical tweezers, confocal microscopy, rheology and Bragg diffraction microscopy, used to perform the measurements described in the thesis. Chapter 3 deals with our work on the dynamical facilitation (DF) theory of glass forma-tion. Despite decades of research, it remains to be established whether the transformation of a liquid into a glass is fundamentally thermodynamic or dynamic in origin. While obser-vations of growing length scales are consistent with thermodynamic perspectives, the purely dynamic approach of the DF theory has thus far lacked experimental support. Further, for glass transitions induced by randomly freezing a subset of particles in the liquid phase, theory and simulations support the existence of an underlying thermodynamic phase transi-tion, whereas the DF theory remains unexplored. In Chapter 3, using video microscopy and holographic optical tweezers, we show that dynamical facilitation in a colloidal glass-forming liquid grows with density as well as the fraction of pinned particles. In addition, we observe that heterogeneous dynamics in the form of string-like cooperative motion, which is consid-ered to be consistent with thermodynamic theories, can also emerge naturally within the framework of facilitation. These findings suggest that a deeper understanding of the glass transition necessitates an amalgamation of existing theoretical approaches. In Chapter 4, we further explore the question of whether glass formation is an intrinsi-cally thermodynamic or dynamic phenomenon. A major obstacle in answering this question lies in determining whether relaxation close to the glass transition is dominated by activated hopping, as espoused by various thermodynamic theories, or by the correlated motion of localized excitations, as proposed in the Dynamical Facilitation (DF) approach. In Chapter 4, we surmount this central challenge by developing a scheme based on real space micro-scopic analysis of particle dynamics and applying it to ascertain the relative importance of hopping and facilitation in a colloidal glass-former. By analysing the spatial organization of excitations within cooperatively rearranging regions (CRRs) and examining their parti-tioning into shell-like and core-like regions, we establish the existence of a crossover from a facilitation-dominated regime at low area fractions to a hopping-dominated one close to the glass transition. Remarkably, this crossover coincides with the change in morphology of CRRs predicted by the Random First-Order Transition theory (RFOT), a prominent ther-modynamic framework. Further, we analyse the variation of the concentration of excitations with distance from an amorphous wall and find that the evolution of these concentration profiles with area fraction is consistent with the presence of a crossover in the relaxation mechanism. By identifying regimes dominated by distinct dynamical processes, our study offers microscopic insights into the nature of structural relaxation close to the glass transi-tion. In Chapter 5, we extend our investigation of the glass transition to systems composed of anisotropic particles. The primary motivation for this is to bridge a long-standing di-vide between theories and simulations on one hand, and experiments on molecular liquids on the other. In particular, theories and simulations predominantly focus on simple glass-formers composed of spherical particles interacting via isotropic interactions. Indeed, even the prominent theory of Dynamical Facilitation has not even been formulated to account for anisotropic shapes or interactions. On the other hand, an overwhelming majority of liquids possess considerable anisotropy, both in particle shape as well as interactions. In Chapter 5, we mitigate this situation by developing the DF theory further and applying it to systems with orientational degrees of freedom as well as anisotropic attractive interactions. By analyzing data from experiments on colloidal ellipsoids, we show that facilitation plays a pivotal role in translational as well as orientational relaxation. Further, we demonstrate that the introduction of attractive interactions leads to spatial decoupling of translational and rotational facilitation, which subsequently results in the decoupling of dynamical het-erogeneities. Most strikingly, the DF theory can predict the existence of reentrant glass transitions based on the statistics of localized dynamical events, called excitations, whose duration is substantially smaller than the structural relaxation time. Our findings pave the way for systematically testing the DF approach in complex glass-formers and also establish the significance of facilitation in governing structural relaxation in supercooled liquids. In Chapter 6, we turn our attention away from the glass transition and address the problem of grain growth in sheared polycrystalline materials. The fabrication of functional materials via grain growth engineering implicitly relies on altering the mobilities of grain boundaries (GBs) by applying external fields. While computer simulations have alluded to kinetic roughening as a potential mechanism for modifying GB mobilities, its implications for grain growth have remained largely unexplored owing to difficulties in bridging the disparate length and time scales involved. In Chapter 6, by imaging GB particle dynamics as well as grain network evolution under shear, we present direct evidence for kinetic roughening of GBs and unravel its connection to grain growth in driven colloidal polycrystals. The capillary fluctuation method allows us to quantitatively extract shear-dependent effective mobilities. Remarkably, our experiments reveal that for sufficiently large strains, GBs with normals parallel to shear undergo preferential kinetic roughening resulting in anisotropic enhancement of effective mobilities and hence directional grain growth. Single-particle level analysis shows that the anisotropy in mobility emerges from strain-induced directional enhancement of activated particle hops normal to the GB plane. Finally, in Chapter 7, we present our conclusions and discuss possible future directions.

Les propriétés des matériaux métalliques sont très liées à leurs caractéristiques microstructurales. Par exemple il est bien connu que la taille de grains joue sur la limite élastique du matériau ainsi que sur ses capacités d'écrouissage. Ainsi, la compréhension et la modélisation de l'évolution de la microstructure d'un métal pendant un traitement thermomécanique est d'une importance primordiale afin de prédire finement son comportement ainsi que ses propriétés finales. Dans le cadre de cette thèse, nous nous sommes concentrés sur la modélisation, à l'échelle d'un agrégat polycristallin, de la plasticité cristalline, de la recristallisation statique et de la croissance des grains dans un contexte de mobilité et d'énergie d'interface isotrope. Un modèle à champ complet dans un cadre éléments finis (EF) est proposé. Les grains sont représentés grâce à un formalisme level-set. L'étude EF développée peut être divisée en trois grandes parties: la génération statistique de microstructures digitales, la modélisation de la plasticité cristalline et la modélisation de la migration des joins de grains en régime de recristallisation statique. Concernant la génération statistique des microstructures digitales, une étude comparative entre deux méthodes de génération (Voronoï et Laguerre-Voronoï) a été réalisée. La capacité de la deuxième approche à respecter une microstructure basée sur des données expérimentales est mise en valeur en 2D et en 3D. Dans une deuxième étape, la plasticité cristalline des matériaux métalliques est étudiée. Deux modèles d'écrouissage ont été implémentés et validés : un premier modèle considérant uniquement les densités de dislocations totales, et un deuxième modèle différenciant les dislocations statistiquement stockées (SSDs) des dislocations géométriquement nécessaires (GNDs). Afin de valider l'implémentation de ces deux modèles issus de la littérature deux cas ont été étudiés : le premier correspond à l'étude à chaud d'un essai de compression plane d'un acier 304L, et le deuxième correspond à l'étude d'un essai à froid de compression simple d'un oligocristal de tantale composé de 6 grains. Les résultats numériques obtenus sont comparés avec les données expérimentales des deux essais. La migration des joints de grains est étudiée dans le contexte des régimes de recristallisation statique et de croissance de grains. Par rapport aux travaux pre-existants dans un cadre level-set, l'accent est mis sur la prise en compte des forces capillaires. La croissance des grains pure est en effet développée dans le formalisme éléments finis/level set considéré, et des validations à partir de résultats analytiques connus sont présentées. De plus, un travail d'analyse de modèles de croissance des grains à champ moyen existant dans la littérature est réalisé. Deux modèles en particuliers sont étudiés : celui de Burke et Turnbull et celui de Hillert/Abbruzzese. En comparant ces modèles avec les résultats obtenus par l'approche en champ complet développée, il est mis en évidence que le modèle simple de Burke et Turnbull n'est pas approprié pour décrire la croissance de grains pour tout type de distribution initiale de taille de grains. La recristallisation statique est ensuite abordée, avec une prise en compte des deux forces motrices liées (i) aux gradients d'énergies stockées sous la forme de dislocations, et (ii) aux effets capillaires. L'influence des effets de capillarité apparaît comme fortement liée à la distribution spatiale des nouveaux germes. Finalement, les résultats des simulations réalisées en plasticité cristalline sont utilisés comme données d'entrée du modèle de recristallisation statique développé. La comparaison des prédictions obtenues comparativement aux résultats expérimentaux sur 304L permet d'illustrer la pertinence d'une approche de type SSD/GND afin de prédire les sites de germination potentiels. / Mechanical and functional properties of metals are strongly related to their microstructures, which are themselves inherited from thermal and mechanical processing. For example, the material grain size distribution plays an important role on the material yield limit and work hardening. The understanding of these microstructure evolutions during thermo-mechanical processes is of prime importance for a better prediction and control of the material mechanical properties. During this Ph.D., we have worked on the modelling of crystal plasticity, static recrystallization and grain growth at the mesoscopic scale in the context of isotropic mobility and interface energy. The full field model developed is based on a finite element formulation combined with a level set framework used to describe the granular structure. This Ph.D. thesis is divided in three main parts: statistical generation of digital microstructures, crystal plasticity modelling and grain boundary migration modelling. In what concerns the digital microstructures statistical generation, a comparative study between two methods (Voronoï and Laguerre-Voronoï) is presented. The ability of the second approach to respect a given grain size distribution is highlighted in 2D and 3D. Secondly, the metallic materials crystal plasticity is studied. Two hardening laws have been implemented and validated: the first one considering the total dislocation density and a second one that differentiates the statistically stored dislocations (SSD) from geometrically necessary dislocations (GNDs). Two different tests cases are used in order to validate the implementation of both hardening laws in the considered crystal plasticity model. The first one corresponds to a planar hot compression test (channel die test) on a 304L stainless steel whereas the second one corresponds to a simple cold compression test on a tantalum olygocrystal composed by six different grains. The obtained results are compared to experimental data for both cases. Grain boundary migration is studied for static recrystallization and grain growth phenomena. Compared to previous work in the considered level-set framework, the focus is on the consideration of capillary forces. Indeed pure grain growth is developed in the considered finite elements/level set formalism and this algorithm is validated using well-known analytical results. Moreover, the results of the developed full field grain growth model are compared in 2D with several well-known mean field grain growth models (Burke and Turbull model and Hillert/Abbruzzese model). The results obtained illustrate that only the Hillert/Abbruzzese model accurately describes grain growth kinetics for all initial grain size distributions. The validity of the Burke and Turnbull model is, on the contrary, restricted to specific distributions. Static recrystallization is then discussed considering both driving forces: (i) internal energy gradient and (ii) grain boundaries capillarity effects. The influence of capillary effects appears to be strongly related to the spatial distribution of the new grains. Finally, the crystal plasticity numerical results are used as input data of the developed static recrystallization full field model. The comparison of the numerical predictions obtained with 304L experimental results allows illustrating the relevance of the SSDs/GNDs formalism used concerning the prediction of the nuclei potential position.

<div>Understanding grain growth in dielectric ceramics is essential to controlling the electrical and mechanical properties necessary to produce ceramic capacitors and sensors. The effect of alloying barium titanate with strontium titanate on the equilibrium crystal shape was investigated in order to determine possible impacts on grain growth. The equilibrium crystal shape was studied through three experimental methods to identify possible changes in grain boundary energy or anisotropy with changing composition.</div><div>The first method was by imaging intergranular pores to observe faceting behavior and relative interfacial energies. Intergranular pores were reconstructed to determine the relative surface energies of the identified facets. The second method was to perform atomic force microscopy on surface facets to collect topography data. The topography data was combined with orientation data obtained by EBSD analysis from the same region, and used to calculate the normal vector of the surface facets. These datasets were plotted in a stereographic projection to study the faceting anisotropy. The third method involved collecting EBSD orientation data and images of surface faceting behavior. The surface faceting behavior of each grain was categorized by type of facet and plotted on a stereographic projection at the corresponding orientation. This allowed for the analysis of faceting transitions and the differentiation of faceted and continuous regions of the equilibrium crystal shape. The analysis of faceting behavior across compositions has implications on grain growth of the barium titanate/strontium titanate system.</div>

Les alliages à base Nickel polycristallins sont largement utilisés pour les pièces aéronautiques soumises à des sollicitations extrêmes en service. Des objectifs toujours plus ambitieux en termes de rendement énergétique des moteurs d’avions ont conduit les constructeurs à augmenter leur température de fonctionnement. Les nuances utilisées jusqu’alors dans les parties chaudes, tels que l’Inconel 718, n’ont pas une tenue mécanique suffisante à ces températures. Le René 65 est un nouvel alliage à microstructure γ-γ’ élaboré spécifiquement pour ces applications. Il a été retenu par Safran Aircraft Engines comme constituant des disques de turbine basse pression du nouveau turboréacteur LEAP. Pour garantir la bonne tenue des disques, une microstructure fine et homogène est requise. Le procédé de forgeage de ces pièces est une séquence d’étapes de déformation à chaud et de traitements thermiques, durant lesquelles la microstructure évolue. Si les phénomènes physiques gouvernant les évolutions microstructurales sont connus, leurs mécanismes exacts et leurs cinétiques varient d’un alliage à l’autre.Des essais de déformation à chaud ont été réalisés en laboratoire dans différentes conditions de température, vitesse et taux de déformation représentatifs des procédés industriels. L’étude précise des mécanismes de recristallisation dynamique, ainsi que de leurs cinétiques, constitue la première partie de ce travail. La caractérisation fine des microstructures déformées a permis de mettre en évidence un nouveau mécanisme de recristallisation, dit de recristallisation en hétéroépitaxie, qui se superpose aux autres mécanismes conventionnels. L’interaction entre ces différents mécanismes ainsi que leurs cinétiques relatives ont été établies dans une vaste gamme de conditions de déformation. Il est démontré que ce mécanisme de recristallisation s'applique également à d'autres alliages γ-γ’. La deuxième partie de l’étude est consacrée à la stabilité des microstructures déformées lors de leur exposition à haute température. L'alliage René 65, comme d’autres alliages à base Nickel, est sensible à un phénomène indésirable dit de croissance sélective de grains. Ses conditions de déclenchement ont été déterminées, de manière à délimiter une fenêtre de forgeage critique. Les mécanismes microstructuraux à l’origine de ce phénomène ont été discutés, ainsi que la possibilité d’une solution préventive. / Polycrystalline Nickel-based alloys are widely used as components for rotative parts of jet engines submitted to extreme conditions. Endlessly increasing objectives in terms of energy efficiency have led the engine manufacturers to increase their service temperature. As a consequence, Inconel 718 and similar alloys -that were used until now- cannot withstand such severe conditions anymore, and lack mechanical resistance at the increased temperature. René 65 is a new γ-γ’ superalloy which has been designed specifically for that purpose by General Electric. It has been selected by Safran Aircraft Engines as the material for low-pressure turbine disks in the new LEAP engine. To reach the desired mechanical properties, a fine and homogeneous microstructure is required. The forging process is a complex sequence which involves various hot deformation stages and thermal treatments, during which the microstructure evolves. Although the underlying mechanisms governing the microstructure evolutions are quite known, their specific mechanism and kinetics may vary depending on the alloy.Interrupted compression tests were conducted at laboratory scale under thermomechanical conditions (temperature, strain and strain rate) in accordance with the industrial process. In the first part, the focus is placed on the dynamic recrystallization mechanisms. Accurate characterization of the deformed microstructures has enabled to highlight a new recrystallization mechanism which superimposes with more conventional ones. It was named heteroepitaxial recrystallization. The interactions between those mechanisms as well as their relative kinetics have been established in a wide range of deformation conditions. . It is demonstrated that this mechanism occurs in other γ-γ’ Nickel-based alloys. The second part of the study is dedicated to the stability of deformed microstructures when exposed to high temperature thermal treatments. René 65, as many other Nickel-based alloys, is subjected to the undesirable phenomenon of selective grain growth, which leads to very heterogeneous microstructures containing abnormally large grains in a fine matrix. Critical deformation conditions leading to heterogeneous microstructures during subsequent annealing have been determined in an aim to identify the critical forging window which should be avoided. The microstructural mechanisms responsible of this phenomenon have been investigated, and the possibility of a preventive solution is discussed.

In dieser Arbeit wird eine detaillierte Analysis des konsistenten kinetischen Modells zum Kornwachstum von Fradkov durchgeführt. Dieses Modell beschreibt - basierend auf dem von Neumann--Mullins Gesetz - die Flächenänderung eines Korns abhängig von seiner Topologieklasse, d.h. der Anzahl der Kanten. Topologieänderungen werden durch Kopplungsterme zwischen den Gleichungen für die Anzahldichten der verschiedenen Topologieklassen beschrieben. Daraus resultiert ein unendlich-dimensionales System von Transportgleichungen mit tridiagonaler Kopplungsstruktur. Durch eine spezielle Wahl des Kopplungsgewichts, welche die Gleichungen nichtlinear und räumlich nichtlokal macht, wird das Modell konsistent. Nach einer Einführung wird das Modell von Fradkov im zweiten Kapitel hergeleitet; formale Rechnungen zeigen die Konsistenz des Modells auf. Im dritten Kapitel wird das Kopplungsgewicht a priori beschränkt. Dadurch kann im ersten Teil des vierten Kapitels Existenz und Eindeutigkeit von Lösungen für endlich-dimensionale Systeme gezeigt werden. Weitere Schranken an die Anzahldichten im fünften Kapitel ermöglichen den Grenzübergang hinsichtlich der Anzahl der Gleichungen im zweiten Teil des vierten Kapitels. Die Existenz von Lösungen des unendlich-dimensionalen Systems wird somit über eine geeignete Approximation gezeigt. Energiemethoden liefern Eindeutigkeit und stetige Abhängigkeit von den Daten. Im sechsten Kapitel wird das Langzeitverhalten untersucht. Besonderes Augenmerk liegt dabei auf stationären Lösungen eines reskalierten Systems als Kandidaten für selbstähnliche Lösungen. Abschließend wird das Lewis''sche Gesetz asymptotisch verifiziert. / The subject matter of this thesis is a detailed analysis of the self--consistent kinetic model for grain growth introduced by Fradkov. The model is based on the von Neumann--Mullins law describing the change of area of grains according to their topological class, i.e. the number of edges they have. Topological events are performed by coupling terms between equations for the number densities of different topological classes. The resulting system of transport equations is infinite-dimensional with a tridiagonal coupling structure. Self-consistency of this kinetic model is achieved by introducing a coupling''s weight making the equations nonlinear and nonlocal in space. We start with an introduction in the first chapter. Afterwards in the second chapter we derive Fradkov''s model and carry out formal calculations to illustrate self-consistency. In the third chapter we present a priori calculations mainly allowing us to bound the nonlinearity. This enables us to prove existence and uniqueness of solutions to finite-dimensional systems in the first part of the fourth chapter. Further bounds on the number densities established in the fifth chapter allow for passing to the limit concerning the number of equations in the second part of the fourth chapter. Therefore we prove existence of solutions to the infinite-dimensional system by a suitable approximation procedure. Uniqueness and continuous dependence on the data is then provided by energy methods. The sixth chapter focusses on long-time behaviour and mainly on stationary solutions of a rescaled system as candidates for self-similar solutions. Finally we prove Lewis'' law asymptotically.