640 



THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956 



gation coefficients (usually antimony, whose k = 0.003 as donor, and 

 indium whose k = 0.001 as acceptor). However, the principles of zone 

 leveling are broad and capable of application to any solvent-solute sys- 

 tem within the range of solubilities of its solid and liquid phases. The 

 general method of attack' is first to find that composition of the liquid 

 zone which will deposit the desired solid solution. Secondly, if one or 

 more of the segregation coefficients involved is not small, the liquid zone 

 must be maintained at its proper composition by admixing to the solid 

 charge the same solutes that the zone will deposit in its product. Thus 

 the solutes that are removed from the liquid zone at the freezing end 

 will be replenished at the melting end. 



The above mathematical treatment leads one to expect an essentially 

 uniform solute distribution throughout a zone leveled crystal for the case 

 under discussion in which k is small and the zone moves through a charge 

 of pure solvent as indicated in Fig. 2. Irregular variations of Cs along 

 the length or over the cross-section of the ingot are not predicted. The 



CO 



= 1.0 

 m 0.8 



!< 0.6 

 _J 



UJ 



°' 0.4 



z 



in 

 O 



z" 



o 



^ 



cr 



(- 

 z 



UJ 



o 



z 

 o 

 u 



0.2 



o.to 



0.08 

 0.06 



0.04 

 0.02 

 0.01 



ZONE -LENGTHS SOLIDIFIED, X/£ 



10 



Fig. 2 — Solute concentration curves predicted for zone leveling with a start- 

 ing charge of solute into pure solvent. 



