Contribution to Mathematics of Zone Melting

Numerical study and experimental investigation of zone refining in ultra-high purification of gallium and its use in the growth of GaAs epitaxial layers

“…Spim proposed an efficient purification approach with a normalized zone length of 0.2 for first three passes, followed by 0.1 up to 6th pass and 0.05 for passes greater than six [19]. This concept is also in agreement with Burris's suggestion of having longer zone length for early passes followed by a shorter zone length for later passes [23]. Ho et al theoretically calculated the optimum zone length and optimum variation of zone length in each refining passes in multi-pass zone refining operation [24,25].…”

Determination of Distribution Coefficients in 1‐Ethyl‐3‐Methyl Imidazolium Chloride‐Methylimidazole Mixtures by Zone Melting

“…The basic zone melting equation, as given by Reiss [12] and Lord [13], relates the solute concentration c s,n (x) in the solid formed from the molten zone at coordinate x during the n-th pass to the concentration during the (n-1) pass. A similar mathematical approach consisting of the partitioning of the ingot into cells of arbitrarily selected length and zone moving in one-cell increments was proposed by Hamming and taken with some modifications by Burris, Stockman, and Dillon [14]. As in our algorithm approach, their treatment assumes constant zone length and k diff , negligible diffusion in the solid, and homogeneous composition in the liquid.…”

Zone Refining Applied to a Bismuth--Tin System.

“…The s o l i d curves i n t h e s e f i g u r e s were pl..otted from experimental d a t a while the dashed curves represent values computed by Harming (7) and Burris, e t a l . ( 2 ) . The parameters of t h e curves a r e the d i s t r i b u .…”