We developed and successfully tested a differential scanning calorimetry (DSC) method to estimate the liquidus temperature (TL) of good glass‐forming systems, i.e., that are reluctant to crystallize. The method was first tested for several Li2O–B2O3 glasses. The onset, peak, and endpoint temperatures of DSC melting peaks were measured and compared with the liquidus in the phase equilibrium diagram. DSC runs were carried out at different heating rates and TL at equilibrium was estimated by extrapolation to 0°C/min. For glasses that do not crystallize during a typical DSC run, a previous heat treatment was necessary to induce crystallization. The liquidus of three multicomponent glasses were then obtained by DSC and compared with the TL obtained by a direct technique using optical microscopy. The endpoint of the DSC melting peaks measured at different rates and extrapolated to 0°C/min was the best estimate for the liquidus of such glasses. Most results differ by not more than 10°C. Because of the small amount of glass needed, the possibility of instrumental detection, simultaneous crystallization pretreatment of many different compositions, and the speed of the DSC analysis, the proposed technique may be a valuable option to estimate the liquidus of simple or complex multicomponent glasses.

Metallurgical grade silicon was melted and directionally solidified in transient conditions by extracting heat from the base of a cylindrical ingot and inserting heat at the ingot top. A heat-transfer mathematical model was implemented to predict the solidification velocity and temperature gradient using cooling curves measured directly in the silicon melt. Nearly 70% of the resulting ingot displays a region of columnar grains aligned with the ingot axis. In this region, the concentration of metallic impurities is usually below the quantification limit of the analytical technique and intermetallic particles are absent, strongly indicating significant purification. The transition from the purified region of the ingot to the ingot top, where impurity concentrations increase and intermetallic particles are seen, is consistent with a change of the solid-liquid interface morphology from planar to cellular/dendritic, as similarly reported in the literature and as indicated by a preliminary analysis with the constitutional undercooling criterion.

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ResumoUm modelo para prever a formação da macrossegregação em ligas metálicas binárias foi proposto e implantado a partir das equações macroscópicas de conservação de massa e espécies químicas, resolvidas numericamente em forma adimensionalizada através do Método dos Volumes Finitos para a realização de uma análise paramétrica, na qual se verificou o efeito de parâmetros de processo como o gradiente e a velocidade de solidificação, além de parâmetros do material como o coeficiente de partição de soluto. A análise paramétrica indicou condições nas quais a macrossegregação induzida pela macrodifusão se torna considerável, convergindo para sistemas com interface plana, enquanto altas velocidades de solidificação tornam esse efeito desprezível, aproximando o sistema do perfil de solidificação de Scheil para a fração de sólido. O efeito da reação eutética também foi avaliado, indicando sua influência na formação da segregação de soluto e na estabilidade da interface sólido-líquido planar. Palavras-chave: Macrossegregação; Solidificação direcional; Estabilidade interfacial. UNIFIED MATHEMATICAL MODEL OF MICRO AND MACROSEGREGATION FOR PLANAR/CELLULAR UNIDIRECTIONAL SOLIDIFICATION AbstractA model to predict the formation of macrosegregation in binary metallic alloys was proposed and implemented using macroscopic conservation equations for mass and chemical species. The equations were solved with the Finite Volume Method using a scaled format prepared for a parametrical analysis, in which the effect of process parameters, such as the thermal gradient or solidification velocity, and material properties, like the solute partition coefficient, was evaluated. The analysis pointed conditions where diffusion-induced macrosegregation becomes important until converging to a planar-interface system, while high solidification velocities rendered it negligible, moving it towards the Scheil model. The eutectic reaction's effect was also checked, showing its influence in solute segregation and in the planar interface stability.

RESUMO-Esse trabalho teve como objetivo avaliar o módulo de solidificação do software comercial FLUENT para simulação de macrossegregação durante a solidificação de ligas metálicas. A avaliação foi feita por comparação a um algoritmo próprio desenvolvido e validado com dados experimentais e de literatura. Os resultados mostram que o módulo de solidificação do software comercial é falho para boa representatividade do fenômeno de macrossegregação e se limita a condições específicas de solidificação como, por exemplo, homogeneidade da fração de soluto no líquido.

Directional solidification is an essential refining step to obtain solar grade silicon from metallurgical silicon. This step can be carried out in a Bridgman furnace, where nearly constant temperature gradients and solidification velocities are imposed on the solid-liquid interface. In the present work, this directional solidification was conducted in a static furnace, in which large temperature gradients and low solidification velocities were enforced to increase macrosegregation. The resulting ingots were analyzed regarding their macrostructures, microstructures and chemical composition. Using measured cooling curves in the ingot as boundary conditions, a mathematical model based on the concept of a stagnant liquid layer at the solid-liquid interface was implemented to predict the macrosegregation profiles. The chemical analyses of the ingots show macrosegregation of several impurities to the ingots top. The mathematical model indicates that liquid convection plays an important role in stabilizing the planar solid-liquid interface, increasing the macrosegregation of impurities.

Resumo O efeito da convecção forçada foi estudado na micro e macroestrutura de lingotes de silício grau metalúrgico obtidos pela solidificação unidirecional a partir da extração de calor por uma base refrigerada em contato com o fundo do cadinho com o banho líquido. Um disco sob rotação foi imerso no silício líquido para promover a convecção forçada. Em lingotes de 100 mm, esta convecção aumenta de 8 para 80 mm o comprimento de uma região de grãos colunares claramente alinhados e livre de intermetálicos, indicando um aumento da macrossegregação. Um modelo de transferência de calor e massa indica que o aumento de transporte de soluto causado pela convecção forçada diminui o super-resfriamento constitucional e, consequentemente, aumenta a estabilidade da interface sólido-líquido plana, sem células ou dendritas. A ausência de células e dendritas pode ter contribuído para a maior macrossegregação de impurezas observada sob efeito de convecção forçada.

New process routes are under development to obtain solar grade silicon from metallurgical grade one, and the directional solidification is an essential step in all proposed process routes. The silicon refining by directional solidification is based on the impurities macrosegregation phenomena. Transient solidification experiments were conducted under a static condition in a furnace projected for this work. From a reference experiment it was analyzed the effects of the changing the material of the crucible base, the ingot height and the cooling condition of the furnace. A mathematical model was proposed and implemented in order to study the solidification conditions and the main mechanisms regarding the macrosegregation phenomena. The mathematical model considers the conservation equations in one direction and the transport of chemical species occurs by diffusion and convection. The convection was treated using the diffusion layer theory. The velocity of solidliquid interface, temperature gradient and profiles of solute concentration and solid fraction were obtained using the temperatures on silicon during the solidification experiments as boundaries conditions of the model. The experimental results showed that under some conditions it was obtained ingots with typical unidirectional macrostructure and, besides, showed in the microstructure evidences of macrosegregation. The mathematical model results showed that the solidification took place under different conditions of solid-liquid interface velocities and temperature gradient in the experiments. The results from the mathematical model showed that convection plays an essential role in the macrosegregation phenomena.