CHEMICAL INTERACTIONS AMONG DEFECTS IN Gg AND Si 619 



In the other extreme with No « Na (B6) becomes 



-f 



1 + 



«-^^ 



4/laWJ 



Do 



1 + ^Na 



(B15) 



Since Q Na can exceed unity by a large amount it is evident that the re- 

 lation in (B15) predicts a large reduction in diffusivity towards the 

 front end of a diffusion curve where Nd « A^^ , and (B14) a smaller re- 

 duction in Do where Np may be close to Na . That part of the medium 

 near the front of the diffusion curve acts therefore like a region of high 

 resistance, confining the diffusant to the back end where the resistance 

 is low. 



Appendix C 



solution of boundary value problem for relaxation 



In Section X equations (10.23), (10.21), (10.20), and (10.19) defined 

 a boundary value problem which we reproduce here, except that (10.20) 

 and (10.19) have been written more completely with the aid of (10.16). 

 Thus 



r^ dr \ dr . 



Do dt 



dp , R n T 



r- + ^P=0, r = L, 

 dr r^ 



r = a 



p = N\ t == 0, 



a <r < L 



(CI) 



(C2) 

 (C3) 



In principle this problem is soluble by separation of variables.^^ Thus we 

 define 



pir, t) = Gir) S(t) (C4) 



which upon substitution into (CI), yields the two ordinary differential 

 equations 



d 



dr 



2 dG , r,^ 



r -T- + RG 

 dr 



+ 77'(? = 



d (n S 2r, A 

 -^ + ^Z)o = 



(C5) 

 (C6) 



where 77 is an arbitrary positive parameter. 

 The allowable values of -q are determined by (C2) which can now be 



