Growth restriction factor in Al-Si-Mg-Cu alloys

The Growth Restriction Factor, Q, proved to be useful to analyse and control grain refinement during solidification of alloys [1-3]. It is known that in multicomponent alloys a simple summation of the Q_i values of the individual constituents taken from the binary phase diagrams can lead to grossly wrong results and that the ternary or higher-level phase diagram needs to be evaluated. This work demonstrates that the actual evaluation of Q using the liquidus gradient and partition coefficients of the multicomponent phase diagram requires some precautions and may be cumbersome. More importantly, this approach entirely fails if an intermetallic phase turns out to be the primary solidifying phase even in tiny amount. A very simple and general solution of this problem is illustrated for Al-Si-Mg-Cu alloys.