Dislocation loop growth rate1ё

The concentration of vacancies, (Cvq)vHl, in equilib­rium with the dislocation loop of radius R of vacancy (subscript ‘vl’) and SIA (subscript ‘il’) type can be obtained in the same way as in the previous subsec­tion (e. g., Bullough et at29)

(c:q)vl, il = cfexp ±- where gsf, Eel, and b are the stacking-fault energy, the interaction energy of PDs with dislocation and the dislocation Burgers vector, respectively. The ‘+’ and ‘—’ in the exponent correspond to the cases of vacancy and SIA loops, respectively. In the case

image078

image808

where

 

Eb (x) = EV + (gsf + Eel(x))b2 [88]

For vacancy loops, the rates Pvl(x) and Qvl(x) are given by

Pvl(x) = WlX1=2ZL DvCv

 

where m and v are the shear modulus and Poisson ratio, respectively. Hence, the growth rates of vacancy and SIA loops are

 

dRvl

dt

 

image809

-Eb! (x) . квТ

 

Qvl(x) = щх1!1

 

ZL DiCi + ZL Dv exp

 

[89]

 

dRil

dt

 

ZL DiCi — ZLDvCv

 

where

 

image810

[82]

 

Eb(x)=Ev — [gsf + Eel(R)]b2 [90]

 

The equations given above have been obtained by neglecting mutual recombination between vacancies and SIAs. Accounting for recombination makes the diffusion equations for the concentrations of PDs nonlinear, an approximate solution for which has been obtained using a linearization procedure.1 The correction is, however, insignificant for condi­tions of practical importance.