618 



THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956 



where D is the diffusivity. Comparison of (B5) with (B4) leads to the 

 relation 



D = 



Do 



1 + 



K^^- 



N^ + 



i/l(^«- 





(B6) 



so that D depends on the local concentration, No , of diffusant. 



It is interesting to explore the limiting forms of D when No « Na and 

 when Nd = Na . In the latter case (B6) reduces to 



1 + 



^ 



-f 



y 4fi2 ^ 12 _ 



(B7) 



while (B3) becomes 



N, 



^20 y 402 ^ j2 



(B8) 



Substituting the left side of (B8) for the denominator involving the 

 radical in (B7) leads to 



- = T° 



1 + 



2(Na - P)0 + IJ 

 But according to (B2), when Na = Nd , 



P 



(Na - P)0 = 



N, 



(B9) 



(BIO) 



so that (B9) becomes 



« = l" 



1 + 



2P 



N. 



+ 1 



(B12) 



Now in case the degree of pairing is high (which is, of course, the case 

 we are interested in) P will be almost equal to Na so that 



2P 



Na- P 



(B13) 



will be a very large number. If this is so the second term in brackets in 

 (B12) can be set equal to zero and we have 



D, 



D = 



(B14) 



