“…In other alloy systems, it is well understood that, in addition to potent nucleant particles, effective grain refinement also requires solute to provide constitutional undercooling and restrict growth. [17][18][19][20][21] The grain-refining effectiveness of a solute can be predicted by a parameter a) known as the growth restriction factor (Q), given by Q 5 mC 0 (k À 1), where m is the liquidus gradient (from the alloy phase diagram), C 0 is the composition of the alloy in wt%, and k is the partition coefficient. The growth restriction factor was first derived by Maxwell and Hellawell 22 and was shown to have an inverse relationship with grain size.…”