Zone recrystallization modeling and optimization based on the concept of average impurity concentration in the ingot portion being refined

Abstract

We present a mathematical model and results of computational experiments aimed at investigating multipass zone refining kinetics based on the concept of average impurity concentration in the ingot portion being refined and demonstrate that ultrapurification of an ingot at a small molten zone length has an induction period. Using stepwise optimization of zone recrystallization with a molten zone length varying from pass to pass, we find a zone length control function that minimizes the number of zone passes needed to ensure a given purity level.