A técnica da Distribuição do Tamanho de Cristais - DTC (Crystal Size Distribution - CSD), que relaciona a densidade de cristais com a distribuição do tamanho, foi aplicada à população de plagioclásio de diques máficos do Enxame de Cabo Frio - Búzios (RJ). Os diques possuem larguras variáveis, de alguns centímetros a 20 metros, e orientação em torno de N45E. A textura dos diques é geralmente fina, localmente microporfirítica e intergranular no centro dos diques mais largos. Bordas resfriadas de alguns centímetros de largura são frequentes nos contatos com as rochas metamórficas encaixantes. Foram estudados dois diques na Praia das Conchas com espessura de 0,8m e 8,2m e, um outro na Praia da Lagoinha, com 2m de largura. As amostras foram coletadas junto às margens (~10 cm do contato) e no centro dos diques. O tamanho médio dos cristais de plagioclásio varia de 0,07 a 0,13 mm na borda dos diques mais finos (<= 2 m de largura) e de 0,09 a 0,20 mm na borda do dique mais largo. No centro do dique de Lagoinha e no dique largo de Praia das Conchas o tamanho de plagioclásio é da ordem de 0,19 ± 0,02 mm e 0,60 ± 0,07 mm, respectivamente. As DTCs nas bordas dos diques, independentemente de sua largura, mostraram um padrão tipicamente encurvado, e que tem sido atribuído na literatura como evidência para misturas de magmas com populações de cristais de tamanhos distintos. No entanto, no centro do dique largo (8,2m) de Praia das Conchas, a DTC é log-linear consistente com uma cristalização magmática simples. A química mineral mostrou que os cristais maiores (precoces) de plagioclásio apresentam um teor mais elevado em An (bytownita-labradorita) que os cristais menores (tardios) da matriz (labradorita-andesina). Além disso, a olivina é mais rica em Fo na borda que no centro do dique e, respectivamente, o piroxênio mais enriquecido em Ca. Esses resultados indicam que as margens resfriadas são mais máficas que o centro sugerindo uma evolução química normal com o resfriamento do magma. Portanto, as DTCs encurvadas provavelmente refletem taxas de cristalização heterogêneas possivelmente induzidas pela despressurização durante a ascensão do magma basáltico seguida de rápido resfriamento. O padrão da DTC log-linear no centro do dique de 8,2m de largura é atribuído ao maior tempo de residência do magma que favoreceria os processos de difusão química e re-equilíbrio textural. Os cálculos da taxa de resfriamento utilizando a inclinação da DTC permitiram estimar que o centro do dique largo da Praia das Conchas estaria completamente cristalizado (~ 900 °C) em torno de 73 dias. O estudo da Orientação Preferencial de Forma (OPF) de plagioclásio mostrou que a petrotrama tende a isotrópica nas margens dos diques com largura menor que 2 metros, o que poderia refletir uma rápida cristalização de plagioclásio por despressurização. Quando a trama é localmente definida, como no dique largo da Praia das Conchas, a lineação de plagioclásio é subhorizontal sugerindo que o fluxo magmático moveu-se predominantemente na lateral do dique. / The method of Crystal Size Distribution (CSD), which relates crystal density with size distribution, has been applied on the plagioclase population of the Mafic Dyke Swarm of Cabo Frio-Búzios (RJ). The dykes are NE-trending with widths from a few centimetres to 20m. The texture is generally fine grained and locally microporphyritic and intergranular at the center of the larger dykes. Chilled margins of a few centimetres in width are common at contacts with the metamorphic basement. Two dykes of 0.8m and 8.2m in width of the Conchas Beach and another of 2m in width at the Lagoinha Beach have been studied. Samples were collected at the margins (~10cm from the contact) and at the center of the dykes. The average characteristic size of the plagioclase crystals varies from 0.07 to 0.13mm at the margins of the narrow dykes (<=2m of width) and from 0.09 to 0.20mm at the margins of the large dyke. At the center of the Lagoinha and Conchas dykes the plagioclase size varies from 0.19 ±0.02mm and 0.60±0.07mm respectively. The CSDs at the dyke margins, irrespective of the dyke width, are typically concave-up, and in literature such patterns have been attributed as evidence of magma mixing with distinct crystal populations. However, at the center of the largest dyke (8.2m) of Conchas Beach, the CSD is log-linear, consistent with simple steady-state crystallization pattern. The mineral chemistry shows that the plagioclase phenocrysts have a high An content (bytownite-labradorite) than the groundmass grains (labradorite-andesine). At the margins olivine is richer in Fo than at the center, and respectively, pyroxene is richer in Ca. These results indicate that the chilled margin is more mafic than the center suggesting a normal chemical evolution in a cooling magma. Nevertheless, the concave-up CSDs probably depict heterogeneous crystallization rates possibly induced by depressurization during the ascent of the basaltic magma followed by rapid cooling. The log-linear CSD pattern at the center of the Conchas dyke (8.2m width) is attributed to a higher residence time of the magma which favors the processes of chemical diffusion and textural re-equilibration. The calculated cooling rates using the CSD slope enables us to estimate that the larger dyke of Conchas would be completely crystallized (at ~900oC) in 73 days. The study of the Shape Preferred Orientation (SPO) in plagioclase shows an isotropic petrofabric at the margins of the dykes <=2m, which could reflect a rapid crystallization of plagioclase by depressurization. When the fabric is defined, as in the larger Conchas Beach dyke, the plagioclase lineation is subhorizontal, suggesting that the magma flow was predominantly lateral to the dyke plane.

Magmatic processes are major agents responsible for the formation and differentiation of the Earth's crust. In contrast to extensive efforts to improve understanding and utility of igneous geochemistry, physical processes of magma differentiation and solidification remain largely unclear. Large variability of igneous textures provides record of these processes and intensive parameters governing the crystallization. In this thesis, we develop quantitative methods, which allow us to better interpret igneous textures in the framework of physics of solidification. We have developed a new three-dimensional model of crystallization from one- component melt driven by homogeneous and heterogeneous nucleation and crystal growth. The predicted textures are quantitatively characterized by crystal size distributions, spatial distribution functions and parameters representing grain contact relationships. The model employs high resolution in a large volume simulation domain in order to produce statistically stable results. Our simulations, performed for various functional forms of nucleation and growth rates with respect to time, imply that (i) crystals are ordered (anti-clustered) on short length scales. This reflects that other crystals already have a finite size at the time of nucleation of younger crystal,...

L'objectif principal de ce travail de recherche est de contrôler l'évolution de la distribution des tailles de cristaux (DTC) dans un procédé de cristallisation en batch. Nous avons été amenés à chercher une résolution numérique du bilan de population et à proposer un algorithme rapide et précis. La méthode numérique a été étendue au cas de la taille des cristaux multidimensionnels en utilisant un maillage mouvant. Nous avons étudié le problème de la commandabilité du système à partir de son modèle discrétisé et puis à partir du modèle continu. Nous avons conçu une loi de commande en boucle fermée pour atteindre la DTC désirée à partir de la condition initiale. Pour compenser l'incertitude des paramètres du modèle, nous avons ajouté un second contrôle par retour d'état afin d'assurer la poursuite de la DTC désirée en présence de l'incertitude des paramètres. Nous avons construit un observateur qui nous permet d'avoir en ligne l'estimation des variables d'états. Ces variables d'état estimées sont utilisées dans la synthèse de la loi du contrôle / The main objective of this research is to control the evolution of the Crystal Size Distribution (CSD) in a batch crystallization process. We are led to study a numerical resolution of the population balance and propose an algorithm for fast and accurate simulation. This method was extended to the case of the two-dimensional crystal by using a moving mesh. We studied the problem of controllability of the system from its discretized model and then from the continuous model. To compensate the uncertainty of the model parameters, we added the second state feedback control to ensure the tracking of the desired CSD in presence of parameter uncertainty. We constructed an observer who provides us with on-line estimation of state variables. These state variables estimated are used in the control law synthesis