648 



THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956 



DISTANCE, X 



k(x) = 



Cs 



(7L(ave) 



(3) 



In practice, however, the situation is complicated by the existence of 

 convection currents in the liquid zone. It is true that these currents tend 

 to stir the liciuid zone and thereby to minimize the concentration gradient 

 within it. However, the currents are not uniform over the growing inter- 

 face and they carry liquid of varying concentrations past the interface, 

 causing fluctuations in Cs • Since these convection currents cannot be 

 eliminated, one turns to the alternative of using forced stirring of the 

 liquid zone. Such a forced stirring is readily available when RF induc- 

 tion heating is used by allowing the RF field to couple directly with the 



Fig. 5 — Solute concentration in solid and liquid at equilibrium and at finite 

 growth rates. 



If the liquid were static, that is, without any currents, it should be I; 

 possible to obtain a uniform, controlled solute concentration in the solid 

 even at appreciable growth rates, merely by adjusting the average con- 

 centration in the liquid to arrange that the Cl obtained at the growing 

 interface will be the desired one. Instead of working with the equilibrium 

 distribution coefficient ko , one works with an effective distribution co- 

 efficient k(x) for the given growth rate, x: 



