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THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956 



DISTANCE, X 



DISTANCE, X 



Fig. 7 — Schematic solute concentration and temperature curves in liquid, . 

 near freezing interface, illustrating constitutional supercooling. The left edge 

 of each diagram represents the solid-liquid interface. 



on the single crystal germanium seed. In order to achieve this situation, 

 it is essential that no stable nuclei form. Thus, not only must the tem- 

 perature of the liquid zone be above its freezing point everywhere except 

 at the interface, but the liquid must also be free of foreign bodies that can 

 ct as nuclei. Furthermore, temperature fluctuations are to be avoided. 



The requirement that the liquid temperature be above its freezing 

 point necessitates a slow growth rate because of what has been termed 

 "constitutional supercooling."^^ This phenomenon can best be described 

 with the aid of Fig. 7. The freezing point of a liquid is depressed by in- 

 creasing concentration of solutes having /c's less than unity. Because 

 of the rise in Cl near the solidifying interface, the freezing point is more 

 depressed in this region than that in the bulk of the liquid zone as shown 

 in Fig. 7. 



It has also been shown^^ for crystals growing in one dimension that the 

 temperature gradient in the liquid decreases for increasing growth rates. 

 The temperature gradients for two growth rates are plotted on Fig. 7. 

 It can be seen that where the growth rate is slow and the temperatin-e 





" Chalmers, B., J. Metals, 6, No. 5, Section 1, May, 1954. 

 " Burton, J. A., and Slichter, W. P., private communication. 



