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
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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
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where m and v are the shear modulus and Poisson ratio, respectively. Hence, the growth rates of vacancy and SIA loops are
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Eb(x)=Ev — [gsf + Eel(R)]b2 [90]
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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.
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