A statistical prediction of undercooling level in the solidification Sn-57%Bi eutectic alloy using factorial design

Various methods appropriate to achieving deep undercooling are applied in laboratory investigations such as containerless processing by levitation techniques, drop tube processing, droplet emulsion technique or the method of embedding the sample in a matrix of molten flux (melt-fluxing technique). In this technique, the alloy is molten while covered by a flux that isolates it from contact withcrucible walls and atmosphere, and absorbs impurities or changes their structure to make them less active, thus avoiding sites that favor heterogeneous nucleation. According to the literature, some variables of this technique influence the level of undercooling such as: cooling rate, flux, number of cycles of melting/solidifying, and overheating. The aim of the present work was to study the application of the factorial design to evaluate the influence of these variables of the Sn‐57%Bi eutectic alloy on the undercooling level. Initially, we used a fractional factorial design (2^4-1 + 3 = 11 experiments) to select among the four (4) variables that influence the undercooling level. It was observed that only the variable cooling rate and flux had an influence on the undercooling level. From this selection, a complete factorial design with central points (2² + 3 = 7 experiments) was carried to evaluate the influence of the two variables and their interaction with the undercooling level. It was observed that the two variables, type flux and cooling rate, as well as their interaction, influenced the undercooling level, with a dependability level of 95%.