“…The purification takes place by redistributing the impurities at the freezing interface when one or a series of molten zone(s) move through a solid bar. Many experimental and theoretical investigations have been conducted in recent decades with focus on improving refining and/or production efficiencies [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 ]. Two general categories, as characterized by different emphases, can be summarized from these investigations.…”