<p>Grain structure and secondary phases play a critical role in determining the mechanical properties of industrial alloys. The spatial variation of such phases is very closely correlated to the liquid pooling established during late stage solidification and grain boundary coalescence. Obtaining a theory that correlates the evolution of length scales during grain boundary coalescence is a critical step toward the optimization of commercial alloys. This thesis highlights various phenomena that enter such a theory. They include coarsening and coalescence of dendrites, nucleation mechanisms and changes in composition of inter-dendritic liquid where second phases tend to initially form. Quantitative phase field models of solidification to simulate casting conditions and microstructure evolution are used in combination with characterization techniques to illustrate the connection between number, size, and distribution of liquid pools. Characterization techniques include spectral analysis, and clustering analysis by way of the Hoshen-Kopleman algorithm. By characterizing late-stage liquid pools, this thesis aims to be a first step towards developing a statistical scaling theory of length scale of liquid pooling.</p> / Master of Applied Science (MASc)

<p>Free solidification molecular dynamics simulations were used to study solute trapping behaviour in the Ni-Cu alloy system. The segregation coefficient, K, as a function of crys- tallization rate was compared with several theories of trapping and, in agreement with a model proposed by Sobolev, it was found that complete trapping (K=1) occurs at a finite velocity. In order to gain further insight into the thermodynamic and kinetic factors affect- ing solute trapping, forced velocity phase field crystal (PFC) simulations were performed on a model binary alloy. We find that the complete trapping limit only occurs if a com- bination of wave-like and diffusive dynamics equation of motion of the PFC alloy model. Finally, an amplitude expansion analysis of the PFC formulation for constant velocity so- lidification was performed and an analytic expression for the complete trapping limit and solute drag was obtained.</p> / Doctor of Philosophy (PhD)

<p>Rapid solidification is a well established method to produce novel materials with improved mechanical or electrical properties. The sharp-interface kinetics of rapid solidification for a binary alloy is summarized. A Phase Field model mapping to this sharp interface model is summarized and solved by a new adaptive mesh refinement algorithm. Simulation results are consistent with experiments: The solidification velocity increases in power-law like fashion at low undercooling and approximately linearly at high undercooling; The solid/liquid interface undergoes a transition from four-fold dendritic to circular crystal structures; Solute trapping emerges and the solute partitioning approaches unity as the solidification velocity increases. Our Phase Field simulations are the first self -consistent predictions of velocity selection and morphological selection at both low and high undercoolings and also the first independent check of the solute trapping model in two dimensions.</p> / Thesis / Master of Applied Science (MASc)

This thesis develops a new quantitative multi-phase field model for polycrystalline solidification of binary alloys. We extend the thin interface formalism of Karma and co-workers to multiple order parameters. This makes it possible to model segregation and interface kinetics during equiaxed dendritic growth quantitatively, a feature presently lacking from polycrystalline or multi-phase solidification models. We study dendrite tip speed convergence as a function of interface width during free dendritic growth. We then analyze the steady state and grain coalescence properties of the model. It is shown that the model captures the correct physics of back diffusion and repulsive grain boundary coalescence as outlined by Rappaz and co-workers. Finally, the model is applied to simulate solidification and coarsening in delta-ferrite solidification. / Thesis / Master of Applied Science (MASc)

A one-dimensional model of a heterogeneous material consisting of a matrix with embedded separated particles is considered, and the melting or solidification of the particles is investigated. The matrix is in imperfect contact with the particles, and the lumped capacity approximation applies to each individual particle. Heat is generated inside the particles or is transferred from the matrix to the particles coupled through a contact conductance. The matrix is not allowed to change phase and energy is either generated inside the matrix or transferred from the boundaries, which is initially conducted through the matrix material. The physical model of this coupled, two-step heat transfer process is solved using the energy method. The investigation is conducted in several phases using a building block approach. First, a lumped capacity system during phase transition is studied, then a one-dimensional homogeneous material during phase change is investigated, and finally the one-dimensional heterogeneous material is analyzed. A numerical solution based on the finite difference method is used to solve the model equations. This method allows for any kind of boundary conditions, any combination of material properties, particle sizes and contact conductance. In addition, computer programs, using Mathematica, are developed for the lumped capacity system, homogeneous material, and heterogeneous material. Results show the effects of control volume thickness, time step, contact conductance, material properties, internal sources, and external sources. / Master of Science

Résumé : La mesure des profils transitoires et de la vitesse de solidification sont deux données importantes pour le contrôle de procédés industriels impliquant un changement de phase. Dans le cas de l’électrolyse de l’aluminium, ce processus de solidification assure la protection du système et influe sur la performance énergétique du procédé de fabrication. Malheureusement, ces données se révèlent, dans la plupart des cas, difficilement accessibles. Ce travail de thèse porte sur le développement de nouveaux outils permettant l’étude et la caractérisation de la solidification de matériaux à changement de phase et à haute température. L’objectif est de développer un système de mesure du front de solidification de matériaux à changement de phase non destructif et ne perturbant pas le milieu de mesure, tout en assurant une précision et une réponse suffisamment rapide pour exploiter de nouvelles stratégies de contrôle dans les cuves d’électrolyse. Ce travail couple une étude expérimentale fondamentale de la solidification de la cryolithe avec une modélisation numérique de phénomène de changement de phase solide-liquide dans des conditions proches du fonctionnement de cuves d’électrolyse. // Abstract : Measurement of transient solidification fronts and of solidification rate are two important data for controlling industrial processes involving a solid-liquid phase change. In the case of aluminium electrolysis, this solidification process protects the system and affects the energy performance of the manufacturing process. Unfortunately, these data are not easy to obtain in most cases. This thesis focuses on the development of new tools for the study and on the solidification characterization of phase change materials at high temperature. The goal is to develop a nondestructive solidification front measurement system for phase change materials without disturbing the measurement medium, while ensuring accuracy and a fast enough response time to exploit new control strategies in electrolysis cells. This work couples a fundamental experimental study of the cryolite solidification with numerical modeling of solid-liquid phase change phenomenon under conditions close to those during normal operation of electrolytic cells.

Nous avons étudié in situ et en temps réel la structure de grains du silicium multi-cristallin issue de la solidification dirigée en utilisant l’imagerie X synchrotron. La radiographie X permet de suivre l’évolution de l’interface solide/liquide et de caractériser sa dynamique et sa morphologie. La topographie X nous donne des informations sur la structure de grains formée, les contraintes et les défauts issus de la solidification. Nous avons montré l’importance la préparation de l’état initial de la solidification en particulier pour les expériences de reprise sur germe. L’analyse de la morphologie de l’interface solide/liquide nous a permis de caractériser la surfusion cinétique du front de solidification, de comprendre l’évolution des sillons de joints de grains et d’analyser les mécanismes de compétition de grains ainsi que de révéler l’impact des impuretés sur la structure de grains formée à l’issue de la solidification. Le phénomène de maclage a aussi été observé dans nos expériences et nous avons démontré que les macles dans le silicium multi-cristallin peuvent être des macles de croissance. Deux types de macles ont été identifiés et le phénomène de compétition de grains en présence de macles étudié. / We studied in situ and real-time the grain structure of multi-crystalline silicon from directional solidification using synchrotron X-ray imaging techniques. X-ray Radiography gives information on the evolution, dynamics and morphology of the solid/liquid interface. X- ray Topography gives more information on the grain structure, strains and defects that occur during solidification step. We showed the importance of the preparation of the initial stage of solidification in particular in the experiments where solidification is initiated from seed. The analysis of the solid/liquid interface morphology allowed us to characterize the kinetic undercooling of the solidification front, to understand the evolution of the grains boundary grooves and to analyze the mechanisms of grain competition and also to reveal the impurities impact on the grain structure formed at the end of the solidification. We also observed twinning phenomenon in our experiments and we demonstrated that twins in multi-crystalline silicon can be growth twins. Two kinds of silicon twins have been identified and the grain competition phenomenon with twins studied.

Cette étude s’intéresse à la modélisation de la ségrégation des impuretés lors des procédés de solidification dirigée du silicium pour l’industrie photovoltaïque. Il s’agit d’un problème multi-physiques et multi-échelles qui nécessite des modèles efficaces pour pouvoir traiter des configurations industrielles en 3D. La première partie de l’étude porte sur le développement de fonctions de paroi solutales dans le but d’estimer la ségrégation sans résoudre numériquement la couche limite solutale. Un modèle analytique est alors utilisé pour estimer le paramètre convecto-diffusif à partir de la contrainte de frottement à l’interface solide/liquide. L’approche proposée consiste à coupler une simulation hydrodynamique de la convection dans la phase liquide et un calcul analytique de la ségrégation. Cette démarche est validée sur un cas de référence en 2D. Le modèle développé fournit une estimation pertinente de la concentration dans un lingot solidifié avec une vitesse imposée, y compris sur un maillage ne résolvant pas la couche limite solutale. La deuxième partie de l’étude concerne l’utilisation d’un système de brassage mécanique dans le but de favoriser la ségrégation des impuretés. Des simulations transitoires de brassage sont réalisées avec le logiciel FLUENT. Les résultats sont comparés à des mesures de champ de vitesse par PIV effectuées sur une maquette en eau, afin de valider le modèle hydrodynamique. La simulation de brassage est ensuite couplée à un calcul de ségrégation en régime quasi-permanent qui permet d’analyser l’influence de l’écoulement sur la couche limite solutale. Dans la dernière partie de l’étude, une simulation de solidification dirigée 3D instationnaire en régime de convection forcée, intégrant la thermique du four, est réalisée. Un modèle empirique de forces volumiques est alors proposé pour décrire l’écoulement lié au brassage dans le silicium liquide. Une première tentative d’estimation des ségrégations par l’approche analytique est ensuite mise en œuvre. / The present study focuses on solute segregation during photovoltaic silicon directional solidification. This multi-physics problem involves various spatial and temporal scales. The numerical simulation of this process requires efficient models, especially for 3D industrial configurations. In the first part of the study, solute wall functions are derived from a scaling analysis in order to estimate the segregations without numerical resolution of the solute boundary layer. The method is based on the coupling of an hydrodynamic simulation of convection in the liquid phase and an analytical segregation computation. The developed analytical model provides an estimation of the convecto-diffusive parameter from the wall shear-stress at the solid/liquid interface. A reference case in 2D with imposed solidification rate is used for validation purposes. The developed model provides a meaningful estimation of concentration fields in the ingots. In a second part, we focus on segregation optimization by a mechanical stirrer. Transient stirring simulations, using a sliding mesh technique, are achieved with FLUENT commercial software. Results are compared to PIV velocity field measurements performed on an experimental setup using water. A segregation computation in a quasi-steady regime is then implemented in the stirring simulation. The effect of the stirring parameters are directly observed on the solute boundary layer at the solid/liquid interface. In a third part, a transient solidification simulation, including furnace thermal conditions, is performed in a 3D configuration with forced convection. The flow generated by the impeller is described thanks to an empirical model based on body forces. A first attempt is finally made to retrieve segregations in the ingot with the developed analytical method.

La radiographie X, synchrotron et avec une source de laboratoire, a été appliquée pour étudier des phénomènes en relation avec la solidification directionnelle d’alliages Al-Cu sous champs externes et dépendants du temps. La formation des microstructures de solidification a été analysée durant des campagnes des vols paraboliques dans le cadre du projet XRMON. Nous avons montré que les variations du niveau de gravité modifiait la couche solutale, et donc la surfusion du liquide devant l’interface solide/liquide. En particulier, l’accélération du niveau de gravité induit une transition Colonnaire-Equiaxe pour un alliage affiné. Pour un alliage non-affiné, la vitesse de croissance des dendrites varie suivant les variations du niveau de gravité durant chaque parabole. Le second volet de ma thèse concerne l'effet d'un champ magnétique permanent sur la solidification équiaxe dans un gradient de température. Nous avons établi que le couplage entre le champ magnétique et le gradient de température génère une force Thermo-Electro-Magnétique qui modifie la trajectoire des grains équiaxes au cours de leur sédimentation. L’action de cette force est bien décrite par le modèle analytique de Wang et al., moyennant des corrections associées au confinement et à la morphologie des grains. Certains effets du champ magnétique sur le liquide ont été également révélés. / X-ray radiography with synchrotron and laboratory source was applied to study phenomena related to the directional solidification of Al-Cu alloys under external fields and time-dependent. The solidification microstructures formation has been analyzed during parabolic flight campaigns in the framework of XRMON project. We have shown that the gravity level variations modified the solutal layer and then the liquid undercooling ahead of the solid/liquid interface. In particular, the acceleration of gravity level induces the Columnar-to-Equiaxed transition in a refined alloy. For a non-refined alloy, the dendrite growth velocity changes with respect to the gravity level variations during each parabola. The second part of this thesis relates to the effect of a permanent magnetic field on the equiaxed solidification in a temperature gradient. The coupling between the magnetic field and the temperature gradient generates a Thermo-Electro-Magnetic force that modifies the equiaxed grains trajectory during their sedimentation. The action of this force is well described by an analytical model proposed by Wang et al. with additional corrections associated to the wall confinement and the grain morphology. Effects of the magnetic field on the liquid have been also revealed.

Au cours de cette thèse, nous avons étudié in situ la solidification du silicium à l’aide de l'imagerie X-synchrotron. Les deux techniques utilisées lors de la solidification sont la radiographie et la diffraction de Bragg, elles permettent de caractériser: la dynamique des mécanismes de croissance, la cinétique de croissance, la nucléation et la compétition de grains, la déformation du réseau cristallin et les champs de contraintes liés aux dislocations. Ces observations sont combinées avec des caractérisations ex situ pour étudier l'orientation cristallographique, les déformations du réseau cristallin ainsi que les concentrations d'impuretés légères telles que le carbone et l'oxygène.La complémentarité de ces techniques permet d'étudier et de mieux comprendre : les phénomènes physiques liés à la formation de la structure de grain finale. Les résultats concernant la cinétique de croissance de l'interface solide-liquide et des facettes {111}, l'établissement de la structure de grain, l'importance du maclage, l'effet des impuretés légères, le champ de contrainte lié à la croissance et la compétition de grains et les dislocations sont discutés dans le manuscrit. / During this thesis, we studied in situ the solidification of silicon with X-synchrotron imaging. The two techniques used during solidification are radiography and Bragg diffraction and they allow characterizing: dynamic growth mechanisms, growth kinetics, grain nucleation and competition, lattice deformation and dislocation related strain fields. These observations are combined with ex situ characterizations to study the crystallographic orientation, the deformations of the crystal lattice as well as the concentrations of light impurities such as carbon and oxygen. The complementarity of these techniques makes it possible to study and to better understand: the physical phenomena related to the formation of the final grain structure. Results concerning the growth kinetics of the solid-liquid interface and of the {111} facets, the establishment of the grain structure, the importance of twinning, the effect of light impurities, the strain field related to growth and grain competition and dislocations are discussed in the manuscript.