A model of grain refinement incorporating alloy constitution and potency of heterogeneous nucleant particles

A model for the determination of relative grain size is developed based on the assumption that nucleant substrates are activated by constitutional undercooling generated by growth of an adjacent grain. The initial rate of development of constitutional undercooling is shown to be equivalent to the growth restriction factor and is a useful approximation for the effect of solute on grain size when potent nucleant substrates are present. However, when the nucleants are of a poor potency then a calculation of the fraction solid necessary to develop the constitutional undercooling required for nucleation needs to be performed. Using the model, trends in grain size observed experimentally by the addition of titanium to pure aluminium and to a typical casting alloy, AlSi7Mg0.3, can be predicted. It was also found that summing the individual growth restriction factors of each solute element in a multi-component alloy can grossly overestimate the actual value of the growth restriction factor for the alloy.