This thesis entails a detailed microstructure analysis of directionally solidified (DS) Al-7Si alloys processed in microgravity aboard the International Space Station and similar duplicate ground based experiments at Cleveland State University. In recent years, the European Space Agency (ESA) has conducted experiments on alloy solidification in microgravity. NASA and ESA have collaborated for three DS experiments with Al- 7 wt. % Si alloy, aboard the International Space Station (ISS) denoted as MICAST6, MICAST7 and MICAST12. The first two experiments were processed on the ISS in 2009 and 2010. MICAST12 was processed aboard the ISS in the spring of 2014; the resulting experimental results of MICAST12 are not discussed in this thesis. The primary goal of the thesis was to understand the effect of convection in primary dendrite arm spacings (PDAS) and radial macrosegregation within DS aluminum alloys. The MICAST experiments were processed with various solidification speeds and thermal gradients to produce alloy with differences in microstructure features. PDAS and radial macrosegregation were measured in the solidified ingot that developed during the transition from one solidification speed to another. To represent PDAS in DS alloy in the presence of no convection, the Hunt-Lu model was used to represent diffusion-controlled growth. By sectioning cross-sections throughout the entire length of solidified samples, PDAS was measured and calculated. The ground-based (1-g) experiments done at Cleveland State University CSU were also analyzed for comparison to the ISS experiments (0-g). During steady state in the microgravity environment, there was a reasonable agreement between the measured and calculated PDAS. In ground-based experiments, transverse sections exhibited obvious radial macrosegregation caused by thermosolutal convection resulting in a non-agreement with the Hunt- Lu model. Using a combination of image processing techniques and Electron Microprobe Analysis, the extent of radial macrosegregation was found to be a function of processing conditions and PDAS.

Thesis (PhD) -- Stellenbosch University, 2014. / ENGLISH ABSTRACT: The process route for the production of base and platinum-group metals from natural sulfide ores commonly requires the conversion of high-iron furnace matte into an iron-lean converter matte. This is followed by pre-treatment through cooling of the iron-lean molten matte, physical processing of the solidified matte and hydrometallurgical metal extraction. Lonmin is the third largest producer of platinum-group metals in the world and utilizes Peirce-Smith converters for blowing high-iron furnace matte with air to a final iron concentration or endpoint. The molten matte is water granulated and solidification occurs via fast-cooling. The solidified matte is ground in a closed circuit ball mill with hydrocyclone classification and subjected to first stage atmospheric leaching. The specification of an ideal or desirable converter iron endpoint requires careful consideration. Most importantly, it must ensure the crystallization of converter matte with mineralogical qualities that are within the setpoints of the downstream unit processes and techniques. An additional consideration is for the final blown converter matte to achieve an optimum bulk concentration of the base metals Ni and Cu and platinum-group metals Pt, Pd, Rh, Ru and Ir. Mattes characteristic of variable iron endpoints were regularly produced at the Lonmin converter plant section. Uncertainty by plant metallurgists in knowing the desirable iron endpoint, particularly within the context of the Lonmin base metal refinery, and poor control has had detrimental effects on the mineralogical quality of the final matte and hence on the processing characteristics of the solidified matte particles downstream. A desirable iron endpoint required investigation, selection and implementation at Lonmin. The primary focus of this study was therefore to quantify the effect of a specific iron endpoint on the mineralogy and mineral chemistry of solidified converter matte. A fundamental examination of the solidification process upon cooling was regarded as critical to an in-depth understanding of the attained mineralogy and mineral chemistry as a function of a specific iron endpoint. It became equally important to quantify the effect of the resultant mineralogy, and hence iron endpoint, on the physical property of mineral structures in relation to downstream grinding, liberation and leaching characteristics. Despite considerable industry context, limited in-depth and coherent studies on the effect of a specific iron endpoint on fast-cooled converter matte systems were found in both industrial and scholarly literature. Previous findings in literature offered a limited quantitative understanding of the effect on mineralogy and mineral chemistry. Phase and cooling equilibria of multi-component, iron endpoint specific Ni-Cu-S matte systems were also not fully available. These would have been particularly useful in understanding the complexities of converter matte solidification as a function of iron endpoint. Physical property knowledge of converter matte mineral structures was hardly available and even less so in relation to grinding, liberation and leaching processes. A comprehensive investigation was therefore required to address these extensive knowledge gaps with respect to fastcooled converter matte systems in an industrial framework. Three Peirce-Smith converter production samples, representative of the extent in variability of iron endpoints attained at the converter plant, were used in a systematic investigation coupled to a novel combination of modern analytical techniques, computational thermochemistry and metallurgical testwork. The modern analytical techniques included the application of high resolution transmission electron microscopy and focused ion beam scanning electron microscopy tomography. Computational thermochemistry was applied through the use of MTDATA phase diagram software. Metallurgical testwork involved laboratory batch grinding at various specific energies. Closely associated leach experiments were also considered relevant to this wide-ranging investigation. The Peirce-Smith converter samples investigated were indicative of mattes that attained specific endpoints of 5.17%, 0.99% and 0.15 weight% Fe. The highest combined bulk concentration of the important base and platinum-group metals was achieved in the matte which attained a specific iron endpoint of 0.99%. The mineralogy of all three converter mattes was dominated by nickel sulfide mineral structures matched to the natural mineral of heazlewoodite. Mineral structures of copper sulfide, NiCu-alloy, spinel and OsRu-alloy were also constituents of the different converter mattes. The attainment of a specific iron endpoint was found to result in measurable mineralogical differences with respect to relative mineral abundances, external morphological characteristics and mineral chemistry. The mineralogical differences were particularly distinct between mineral structures of the high (5.17%) and low (0.99% and 0.15%) iron mattes. Subtle mineralogical differences were evident between mineral structures of the low iron mattes. The 0.99% Fe matte was characteristic of a significantly higher NiCu-alloy relative abundance, compared to the 5.17% Fe matte. The NiCu-alloy structures were found to act as the primary collectors of the economically significant platinum-group metals. Mineralogical observations were used to develop an understanding of the underlying mineralization mechanism of NiCu-alloy structures. High-fidelity color and grayscale 3D reconstructions were produced of the resultant mineralized structures. It was shown theoretically that variations in iron endpoint specific starting compositions of oxygen-free liquid matte systems alter the solidification pathway towards the eutectic. Moreover, a quantitative understanding of liquid phase solidification of the high and low iron matte systems, including oxygen, was developed to within ±2.5 oC. Most of the specific energy available for grinding was expended breaking the nickel sulfide matrix, particularly of the high iron matte. The breakage rates of copper sulfide mineral structures in the 5.17% Fe matte were calculated to be higher than in the 0.15% Fe matte at 25kWh/t specific energy. The degree of copper sulfide liberation was shown to be higher for the 5.17% Fe matte than for the 0.15% Fe matte at the same specific energy of grinding. A higher degree of Ni extraction and Cu cementation could be achieved when leaching low iron matte particles. The production of converter matte attaining a specific iron endpoint of 0.99% was found to be the most suitable with respect to endpoint selection criteria. A practical iron endpoint range of 1.6% to 1.0% was recommended for the production of converter matte with a resultant mineralogical quality within the constraints of the Lonmin base metal refinery. This study offers an integrated understanding of base and platinum-group metals production as a function of a desirable iron endpoint at Lonmin. This was not previously available in metal production literature. New technology for the monitoring and consistent control of such a practical iron endpoint range can subsequently be implemented. / AFRIKAANSE OPSOMMING: Die prosesroete vir die produksie van onedel en platinumgroepmetale uit natuurlike swawelertse vereis gewoonlik die omsetting van ’n ysterryke hoogoondmat in ’n ysterarm omsettermat. Hierna volg voorbehandeling deur die afkoeling van die ysterarm gesmelte mat, fisiese verwerking van die soliede mat, en hidrometallurgiese metaalekstraksie. Lonmin is die derde grootste produsent van platinumgroepmetale ter wêreld en gebruik Peirce-Smith-omsetters om ysterryke hoogoondmat met lug te blaas totdat dit ’n finale ysterkonsentrasie- of ystereindpunt bereik. Die gesmelte mat word met water granuleer, en solidifikasie vind deur middel van snelafkoeling plaas. Die soliede mat word in ’n geslotekringbalmeul met hidrosikloonklassifikasie gemaal en aan eerstestadium- atmosferiese loging onderwerp. Die spesifikasie van ’n ideale of gewenste ystereindpunt verg deeglike oorweging. Bowenal moet dit verseker dat die omsettermat kristalliseer met mineralogiese eienskappe wat binne die setpunte van die eenheidsprosesse en - tegnieke verder af in die prosesstroom val. ’n Bykomende oorweging is dat die uiteindelike geblaasde omsettermat ’n optimale massakonsentrasie van die onedel metale Ni en Cu en die platinumgroepmetale Pt, Pd, Rh, Ru en Ir moet bevat. Matte met die kenmerke van wisselende ystereindpunte is gereeld by die Lonminomsetteraanleg geproduseer. Die onsekerheid van metallurge by die aanleg oor die gewenste ystereindpunt – veral binne die konteks van die Lonmin-raffinadery vir onedel metale – sowel as swak beheer het ’n nadelige uitwerking gehad op die mineralogiese gehalte van die uiteindelike mat, en dus ook op die verwerkingskenmerke van die soliede matdeeltjies verder af in die prosesstroom. Die bepaling van die gewenste ystereindpunt het sorgvuldige ondersoek, seleksie en toepassing deur Lonmin vereis. Hierdie studie is dus hoofsaaklik uitgevoer om die uitwerking van ’n spesifieke ystereindpunt op die mineralogie en minerale chemie van soliede omsettermat te kwantifiseer. ’n Grondliggende ondersoek na die solidifikasieproses by afkoeling is as noodsaaklik beskou vir ’n diepgaande begrip van die verworwe mineralogie en minerale chemie as ’n funksie van ’n spesifieke ystereindpunt. Mettertyd het dit egter ewe belangrik geword om die uitwerking van die gevolglike mineralogie, en dus die ystereindpunt, op die fisiese eienskappe van minerale strukture met betrekking tot maling-, vrystellings- en loogprosesse verder af in die prosesstroom te kwantifiseer. Ondanks heelwat bedryfskonteks, het nóg bedryfs- nóg vakkundige literatuur veel diepte- en samehangende studies oor die uitwerking van ’n spesifieke ystereindpunt op snelafgekoelde omsettermatstelsels opgelewer. Vorige bevindinge in die literatuur het boonop ’n beperkte kwantitatiewe begrip van die uitwerking op mineralogie en minerale chemie getoon. Die fase- en afkoelingsekwilibriums van ystereindpuntspesifieke Ni-Cu-S-matstelsels met veelvuldige komponente was ook nie ten volle beskikbaar nie. Dít sou veral goed te pas gekom het om die kompleksiteite van omsettermatsolidifikasie as ’n funksie van ystereindpunt te verstaan. Kennis van die fisiese eienskappe van die minerale strukture van omsettermat was kwalik beskikbaar, terwyl selfs minder inligting oor maling-, vrystellings- en loogprosesse opgespoor kon word. Daarom was ’n omvattende ondersoek nodig om hierdie beduidende kennisleemtes met betrekking tot snelafgekoelde omsettermatstelsels in ’n nywerheidsraamwerk aan te vul. Drie Peirce-Smith-omsetterproduksiemonsters wat die wisselende bestek van ystereindpunte by die omsetteraanleg verteenwoordig, is in ’n stelselmatige ondersoek gebruik, tesame met ’n vernuwende kombinasie van moderne ontledingstegnieke, gerekenariseerde termochemiese bewerkings en metallurgiese toetswerk. Die moderne ontledingstegnieke sluit onder andere in hoëresolusie-transmissie-elektronmikroskopie (HRTEM) en gefokusdeioonstraalskandering-elektron-mikroskopie (FIB SEM) tomografie. Die gerekenariseerde termochemiese bewerkings is met behulp van MTDATAfasediagramsagteware uitgevoer. Metallurgiese toetswerk het die maling van laboratoriumlotte teen verskillende spesifieke energieë behels. Nou verwante loogproefnemings is ook as relevant vir hierdie omvattende studie beskou. Die bestudeerde Peirce-Smith-omsettermonsters het op matte met spesifieke eindpunte van 5.17%, 0.99% en 0.15 gewig% Fe gedui. Die hoogste gekombineerde massakonsentrasie van die belangrike onedel en platinumgroepmetale is in die mat met ’n spesifieke ystereindpunt van 0.99% gevind. Die mineralogie van ál drie omsettermatte is oorheers deur die minerale strukture van nikkelsulfied, wat met die natuurlike mineraal heazlewoodiet ooreenstem. Die verskillende omsettermatte het ook die minerale strukture van kopersulfied, NiCu-allooi, spinel en OsRu-allooi bevat. Daar is bevind dat die verkryging van ’n spesifieke ystereindpunt tot meetbare mineralogiese verskille in die relatiewe volopheid van minerale, die eksterne morfologiese kenmerke sowel as minerale chemie lei. Die mineralogiese verskille was veral duidelik te sien tussen die minerale strukture van die ysterryke (5.17% Fe) en ysterarm (0.99% en 0.15% Fe) matte. Fyn mineralogiese verskille is ook tussen die minerale strukture van die ysterarm matte bespeur. Die 0.99% Fe-mat het tipies beduidend meer NiCu-allooi as die 5.17% Fe-mat bevat. Die NiCu-allooistrukture tree oënskynlik op as die hoofversamelaars van die ekonomies belangrike platinumgroepmetale. Mineralogiese waarnemings is gebruik om ’n begrip te ontwikkel van die onderliggende mineralisasiemeganisme van NiCuallooistrukture. Die gevolglike gemineraliseerde strukture is met behulp van driedimensionele rekonstruksies met hoë kleurgetrouheid sowel as in grysskaal voorgestel. Daar is teoreties aangetoon dat variasies in ystereindpuntspesifieke beginsamestellings van suurstofvrye vloeibare matstelsels die solidifikasieroete na die eutetikum wysig. Daarbenewens is die vloeifasesolidifikasie van die ysterryke en ysterarm matstelsels, wat suurstof insluit, op sowat ±2.5 oC gekwantifiseer. Die meeste van die spesifieke energie wat vir maling beskikbaar was, is gebruik om die nikkelsulfiedmatriks te breek, veral vir die ysterryke mat. Berekeninge toon dat die breektempo’s van die minerale strukture van kopersulfied by die 5.17% Fe-mat hoër was as by die 0.15% Fe-mat teen ’n spesifieke energie van 25 kWh/t. Die mate van kopersulfiedvrystelling was hoër by die 5.17% Fe-mat as by die 0.15% Fe-mat by dieselfde spesifieke energie vir maling. ’n Hoër mate van Ni-ekstraksie en Cu-sementasie is verkry toe ysterarm matdeeltjies geloog is. Wat eindpuntseleksiemaatstawwe betref, is die produksie van ’n omsettermat met ’n spesifieke ystereindpunt van 0,99% as die mees geskikte aangewys. ’n Praktiese ystereindpuntbestek van 1.6% tot 1.0% word aanbeveel vir die produksie van ’n omsettermat met ’n gevolglike mineralogiese gehalte wat binne die perke van die Lonmin-raffinadery vir onedel metale val. Hierdie studie bied ’n geïntegreerde begrip van die produksie van onedel en platinumgroepmetale as ’n funksie van ’n gewenste ystereindpunt by Lonmin. Hierdie inligting was nie voorheen in literatuur oor metaalproduksie beskikbaar nie. Nuwe tegnologie vir die monitering en konsekwente beheer van so ’n praktiese ystereindpuntbestek kan dus op grond hiervan in werking gestel word.

Magnesium alloys have been extensively used for structural and functional applications due to their low densities. In order to improve the mechanical properties, grain refinement of the microstructures of magnesium alloys has been studied for many years. However, an effective and efficient grain refiner or refinement technique hasn’t been achieved yet, especially for those with aluminium contained. In this study, solution for this problem has been discovered through further understanding of the solidification process, including the potency and the efficiency of nucleation particles, the role of solute, and the role of casting conditions. First of all, the study suggested that MgO particles can act as nuclei in magnesium alloys by measuring and analyzing the differences in cooling curves with various amount of endogenous MgO particles. The differences indicated that the number density of MgO particles has a huge influence on the microstructure. This idea has been fatherly proved by the inoculation of MgO particles in magnesium alloys because the microstructures have been significantly refined after the inoculation. A new kind of refiner (AZ91D-5wt%MgO) has been developed based on such understandings. Secondly, the study discovered that the role of solute has much smaller effect on the grain size than it was suggested in traditional understandings. The inverse-proportional relationship between the grain size and the solute is highly suspected and the major role of solute is to cause columnar- equiaxed transition. The role of casting conditions has also been studied in order to provide experimental evidence for the existence of melt quenching effect in magnesium alloys. It is shown that various casting conditions, such as pouring temperatures and mould temperatures, have large influence on the critical heat balance temperature after rapid pouring. In this study, a theoretical model based on the analysis of cooling curves is presented for grain size prediction. An analytical model of the advance of equiaxed solidification front is developed based on the understanding of the role of casting conditions. Eventually, all these understandings have been applied to magnesium direct-chill (DC) casting. The refined microstructure of DC cast ingots can further assist in understanding the mechanism of advanced shearing achieved by MCAST unit. The comparison of the ingots with and without melt shearing indicated that the advance shearing device can disperse MgO film into individual particles.

La rupture à chaud, ou crique à chaud est un défaut majeur en solidification, qui conduit au rebut de nombreuses pièces ou demi-produits. Elle correspond à l'ouverture de criques en fond de zone pâteuse, c'est-à-dire dans les régions à haute fraction de solide (typiquement 0.9 et au-delà), lorsque ces régions sont soumises à des déformations favorisant la mise en traction des films liquides résiduels. Différents critères peuvent être trouvés dans la littérature pour diagnostiquer la fissuration à chaud. L'objectif de cette étude est d'évaluer leur capacité à prédire correctement l'apparition de ce type de défauts, et ce pour différents domaines d'application tels que la solidification en lingotière et la coulée continue de billettes et de brames. Pour cela, deux types d'essais différents ont été analysés avec le modèle thermomécanique par éléments finis THERCAST® dans lequel nous avons implanté une sélection de critères. Un nouveau dispositif expérimental de solidification sous contrainte (le dispositif Crickacier) a alors été développé et mis en œuvre au CEMEF pour les besoins de cette étude. Ce dispositif s'est révélé capable de faire apparaître des défauts similaires à ceux observés dans les procédés industriels, et ce dans des conditions identifiables et discriminantes. Sa modélisation thermomécanique a permis de mettre en valeur le critère le plus pertinent. L'application de cette méthodologie à un autre type d'essai, le cintrage de lingot en cours de solidification, pour lequel nous avons accès à des résultats existants à Arcelor Research sur plusieurs nuances d'acier, nous a permis de suggérer des améliorations à apporter à l'écriture du critère. Au final, nous avons proposé un nouveau critère directement adapté à une utilisation dans un code de simulation comme THERCAST.

Les poudres d'alliages aluminium-nickel produites par atomisation peuvent être traitées pour préparer du nickel de Raney, un catalyseur utilisé dans de nombreux procédés industriels. L'activité du catalyseur dépend fortement du déroulement des multiples réactions de solidification pendant l'atomisation. Un modèle de microségrégation pour la solidification d'alliages métalliques est alors développé. En considérant des flux de diffusion finis, des cinétiques de réactions dendritique, péritectique et eutectique et des surfusions de germination, une alternative plus évoluée est proposée aux modèles de Gulliver-Scheil ou de la loi des leviers. Le couplage avec des calculs d'équilibre thermodynamique est effectué pour évaluer les compositions des interfaces et les termes d'enthalpie dans le bilan d'énergie. Le modèle est appliqué à un alliage binaire, avec des densités de phases constantes, pour simuler le procédé d'atomisation de gouttes d'alliage Al-Ni. Un modèle dédié est choisi pour les conditions aux limites d'échange de chaleur. Les résultats sont comparés à des mesures expérimentales obtenues par diffraction de neutron. Des interprétations sont alors établies sur les comportements non triviaux des alliages Al-Ni solidifiés rapidement. Le modèle proposé permet ainsi d'appréhender les effets concurrents des différentes cinétiques (diffusion chimique, bilan d'énergie, vitesse croissance des microstructures, etc.) lors de la solidification hors équilibre. Les principaux développements envisageables autour de ce travail incluent : l'extension aux alliages multicomposés, l'inclusion de densités variables, le couplage avec des calculs macroscopiques.

<p>Aluminum alloys are widely used in many manufacturing areas due to good castability, lightness and mechanical properties. The purpose of this research is to investigate copper’s influence on an Al-Si-Mg alloy (A356). Copper in the range of 0.6 – 1.6 wt. % has been used in an A356 aluminum based alloy. In this work a simulation of three different casting processes, sand-, die- and high pressure die-casting has been employed with the help of gradient solidification equipment. The microstructure of the samples has been studied by optical and scanning electron microscopy. Materials in both as-cast and heat treated states have been investigated through tensile test bars  to get the mechanical properties of the different conditions.</p><p> </p><p>Questions that have been subjected to answer are what influence does copper have on the plastic deformation and on fracture behavior and whether there is a relationship between the content of copper and increased porosity or not; and in that case explore this relationship  between the amount of copper and the mechanical behaviour.</p><p> </p><p>It has been analyzed that a peak of mechanical properties is obtained with a content about 1.6 wt. % copper. The increment of copper seems to have a remarkable impact on the mechanical properties and especially after the aging process showing a large raise on the ultimate tensile strength and yield strength.</p><p>Relationship between the copper content and increased porosity could not be found.</p>

There is growing interest in using additive manufacturing for various alloy systems and industrial applications. However, existing process development and part qualification techniques, both involve extensive experimentation-based procedures which are expensive and time-consuming. Recent developments in understanding the process control show promise toward the efforts to address these challenges. The current research uses the process mapping approach to achieve control of melt pool geometry and microstructure in different alloy systems, in addition to location specific control of microstructure in an additively manufactured part. Specifically, results demonstrate three levels of microstructure control, starting with the prior beta grain size control in Ti-6Al-4V, followed by cell (solidification structure) spacing control in AlSi10Mg, and ending with texture control in Inconel 718. Additionally, a prediction framework has been presented, that can be used to enable a preliminary understanding of melt pool geometry for different materials and process conditions with minimal experimentation. Overall, the work presented in this thesis has the potential to reduce the process development and part qualification time, enabling the wider adoption and use of additive manufacturing in industry.

Durante a solidificação de ligas metálicas, a decantação de grãos equiaxiais pode causar: macrossegregação, mudança na posição da transição colunar-equiaxial e alteração no tamanho de grão equiaxial. O objetivo do presente trabalho é a implementação e análise de um modelo matemático para simular a solidificação sob efeito da decantação de grãos. Este modelo combina: (a) a técnica do autômato celular bi-dimensional em escala microscópica considerando a decantação de grãos, (b) um submodelo microscópico baseado em equações de conservação para simular os processos internos aos grãos e (c) um submodelo macroscópico também baseado em equações de conservação para simular os processos importantes da escala de tamanho macroscópica. Os submodelos macroscópico e microscópico compartilham informações correspondentes às suas escalas características de tamanho através de um método de acoplamento. O modelo matemático completo foi examinado inicialmente através da simulação de diversas situações idealizadas como: a decantação de uma esfera sólida, a decantação de um conjunto de esferas porosas e a decantação e solidificação simultânea de um grão dendrítico isolado e imerso em um líquido super-resfriado. Posteriormente, compararam-se os resultados do modelo para a solidificação isotérmica e para a solidificação unidirecional com resultados disponíveis na literatura obtidos por outros modelos numéricos e por técnicas experimentais. Os resultados do modelo mostraram que a decantação de grãos resulta nos seguintes efeitos no caso da solidificação unidirecional: variação de tamanho médio de grãos e macrossegregação ao longo do lingote e alteração ou até eliminação na posição da transição colunar-equiaxial. / During solidification of metallic alloys, the settling of equiaxed grains can cause macrosegregation, change the position of the columnar-to-equiaxed transition, and change the grain size of equiaxed grains. The objective of the present work is to implement and analyze a mathematical model to simulate the solidification under the effect of grain settling. The present model combines: (a) the cellular automaton technique in two dimensions applied in the microscopic lengthscale to account for the movement of grains; (b) a microscopic submodel based on conservation equations to simulate important phenomena occurring within the grains, and (c) a macroscopic submodel, also based on conservation equations, to simulate important phenomena of the macroscopic lengthscale. Using a strong coupling scheme, the macroscopic and microscopic submodels share important information specific to their typical lengthscales. The complete mathematical model was initially examined in several idealized conditions: the settling of a single solid sphere; the settling of a group of porous spheres; and the growth of a single dendritic grain settling in an undercooled liquid. The model was also used to simulate the isothermal solidification and the unidirectional solidification. For these cases, the outcome of the model was compared with experimental and calculated results available in the literature. For the unidirectional solidification, the model results showed that the settling of grains can cause a variation in the macrosegregation and grain size along the ingot and can change the position or even eliminate the columnar-to-equiaxed transition region.

Um modelo matemático multifásico para a solidificação equiaxial de ligas binárias capaz de prever o efeito de taxa de resfriamento e da concentração de soluto no tamanho médio final de grãos foi proposto no presente trabalho. O modelo matemático foi desenvolvido através do conceito de envelope envolvendo os grãos, utilizando as equações de conservação de energia, massa e espécies químicas. O modelo de nucleação utilizado possibilita que novos núcleos possam surgir durante todo o período de resfriamento. As equações diferenciais foram obtidas através de uma média volumétrica das equações de conservação em um volume elementar representativo contendo três \"pseudofases\": sólido, líquido interdendrítico e líquido extradendrítico. O efeito de algumas variáveis de processamento sobre o tamanho médio final de grão foi analisado. Os resultados do modelo proposto foram comparados com resultados de alguns modelos disponíveis na literatura. / A multiphase mathematical model for the equiaxed solidification of binary alloys was proposed in the present work to predict the effects of the cooling rate and the average solute concentration on the final average grain size. The mathematical model was based on the concept of the grain envelope and on the conservation of energy, mass and chemical species. A nucleation model was adopted to consider the nucleation of new grains during the whole solidification time. The differential equations were derived from the volume average of conservation equations within a representative elementary volume that consisted of three pseudophases: solid, interdendritic liquid, and extradendritic liquid. The effect of some processing variables on the final average grain size was studied. The results from the proposed model were compared with those available in the literature from other models.

As ligas de cobre têm grande importância na fabricação de produtos metálicos que necessitam de boa resistência à corrosão e/ou alta condutividade térmica e elétrica. A sua estrutura de grãos bruta de solidificação define diversas propriedades requeridas em serviço/processamento e o refino desta estrutura pode ser realizado a partir da inoculação do banho metálico antes do início da solidificação, aumentando o número de núcleos sólidos formados. A inoculação e os mecanismos de refino de grão em ligas de cobre foram pouco investigados e não são entendidos suficientemente para permitir o projeto de inoculantes. O presente trabalho tem como principal objetivo identificar os mecanismos fundamentais de inoculação e refino de grão das ligas do sistema Cu-Sn a partir de adições de Zr aos banhos líquidos antes da solidificação. Amostras cilíndricas foram produzidas a partir da solidificação das ligas a uma taxa de resfriamento de ~ 0,8 ?C/s. Estas amostras foram analisadas por diferentes técnicas: (a) observação da macroestrutura de grãos; (b) análise térmica das curvas de resfriamento obtidas durante a solidificação; (c) análise química; (d) exame da microestrutura em microscopia óptica, microscopia eletrônica de varredura (MEV) com emissão de campo (FEG), microscopia eletrônica de transmissão (MET) com e sem o feixe de íons (FIB) e (e) microanálise por espectroscopia de energia dispersiva (EDS). Observa-se que adições de Zr na faixa de 0,04 a 0,4% a banhos da liga Cu-8%Sn com cobertura de pó de grafita reduzem o tamanho médio de grão em até 90%, mas não causam efeito significativo sem a cobertura de grafita. Este efeito da diminuição do tamanho de grão com a adição de Zr torna-se significativo somente para teores de Sn >=4%. Esta redução de tamanho médio de grão é acompanhada do aparecimento de partículas facetadas na microestrutura, identificadas como ZrC a partir de padrões de difração de elétrons e microanálises EDS. Uma análise teórica mostra desajustes entre os reticulados do ZrC e do Cu? tão pequenos quanto 1,9%, indicando que estas partículas podem funcionar como centros efetivos para a nucleação heterogênea e causar o refino de grão em ligas de Cu. Parâmetros extraídos da recalescência das curvas de resfriamento, como a diferença entre as temperaturas mínima e máxima da recalescência, apresentaram boa correlação com o tamanho médio de grão final, indicando a possibilidade do controle do tamanho de grão em ligas Cu-Sn com adições de Zr a partir da análise térmica. / Copper alloys are important to the production of metallic parts with good corrosion resistance and high thermal and electrical conductivity. The as-cast grain structures of these alloys are closely related to the properties required in service or during processing. The refining of the grain structure can be achieved by inoculation of the metallic melt, before the beginning of solidification, increasing the number of solid nuclei. The inoculantion and grain refining of copper alloys have been poorly investigated and are not sufficiently understood to enable the design of inoculants. The objective of the present work is to identify the fundamental mechanisms underlying the inoculation and grain refining of Cu-Sn alloys by additions of Zr to the melt prior to solidification. Cylindrical samples of these alloys were cast at a cooling rate of ~0,8 ?C/s. These samples were analyzed using different techniques: (a) observation of the grain macrostructure; (b) thermal analysis of the cooling curves collected during solidification; (c) chemical analysis; (d) observation of the microstructure in the optical microscope, scanning electron microscope (SEM) with field emission gun (FEG), trasmission electron microscope (TEM) with and without the focused ion beam (FIB) for sample preparation and (e) energy dispersive spectroscopy (EDS) microanalysis. The results show that additions of Zr in the range between 0,04 and 0,4% to melts of a Cu-8%Sn alloy with a graphite powder cover decrease the average grain size by up to 90%, but have no effect without the graphite cover. The decrease in grain size obtained with Zr additions become significant only for alloys with %Sn >==4 and is followed by the appearance of faceted particles in the microstructure, identified as ZrC after examining electron difraction patterns and EDS microanalyses of the particles.