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THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956 



of this effect based on a dielectric cavity model show it to be of the order 

 of some 10 or 15 percent of the energy computed on the assumption of 

 the dielectric continuum, the increased binding energy showing up as a 

 reduced value of a. This may account for the fact that the observed a, 



at 1.7 X 10" cm is less than the theoretical value, 1.86 X 10" cm. 



The above example shows the ion pairing phenomenon in action as a 

 structural tool, useful in investigating isolated impurities. In particular 

 the demonstration that lithium is interstitial is interesting. The values 

 of a have much more meaning as independent parameters in solids than 

 they have in liquids, where a given ion may be surrounded by a sheath of 

 solvating solvent molecules. Under the latter conditions the value of (i 

 can only be determined through application of the ion pairing theor}- 

 itself. 



Of course, certain unusual situations arise in solids also, and values of 

 a (determined from ion pairing) are valuable indications of structural 

 peculiarities. 



Similar experiments have been performed on specimens doped with 

 indium and boron. The results of all our investigations on the cross-over 

 phenomenon are tabulated in Table V. In the table the first column 

 lists the acceptor involved, and the second and third the appropriate 

 concentrations of impurities. The fourth column contains the cross-over 

 temperature, while the fifth, the measured value of a determined from 

 it. The last column lists the values of a to be expected on the basis of the 

 addition of tetrahedral covalent radii to the ionic radius of lithium — all 

 of which appear in Pauling. 



The reliability of the measurements are in the order gallium, alumi- 

 num, boron, and indium. The principal reason for this is that the indium 

 crystal was not grown specially for this work and was somewhat non- 

 uniform. Of the two values obtained for a we tend to place more confi- 



Table V 



