In the case where 1D migrating SIA clusters are generated during irradiation in addition to PDs, the ME has to account for their interaction with the immobile defects. In the simplest case where the mean-size approximation is used for the clusters, Ggl(x) = Gg8(x — xg), the ME for the defects such as voids or vacancy and SIA loops takes a form22

dfs (x, t) /dt = Gs (x)+ J(x — 1, t)

— J (x, t) — P1D (x)fs (x)

± P1d(x T xg)f s(x T xg), x > 2 [126]

where P1d(x) is the rate of glissile loop absorption by the defects. The ± and T in eqn [126] are used to distinguish between vacancy-type defects (voids and vacancy loops/SFT) and SIA type because capture of SIA glissile clusters leads to a decrease in the size in the former case and an increase in the latter one.

The rate P1d (x) depends on the type of immobile defects. In the case of voids, their interaction with the SIA clusters is weak and therefore the cross-sections may be approximated by the corresponding geomet­rical factor equal to nR2vNY. The rate P1d (x) in this case is given by (see eqn [11c] in Singh eta/.22) 3PPY/3ADgCg 2/3

4 O1/3 x where A = J kg/2. Note that the factor 2 in eqn

[127] was missing in Singh eta/.22

In the case of dislocation loops, the situation is more complicated as the cross-section is defined by long-range elastic interaction. A fully quantitative evaluation is rather difficult because of the compli­cated spatial dependence of elastic interactions, in particular, for elastically anisotropic media. For loops of small size, the effective trapping radii turn out to be large compared with the geometrical radii of the loops and hence the ‘infinitesimal loop approx­imation’ may be applied. It is shown (see Trinkaus et a/.20) that in this case the cross-section is propor­tional to (xxg)1/3 thus the rate P1d (x) is equal to 2=3

ADg Cgx2/3

where T and Tm are temperature and melting tem­perature, the multiplier q is a correction factor which is introduced because eqn [4] in Trinkaus et a/.20 was obtained using some approximations ofthe elastically isotropic effective medium and, consequently, it can be considered as a qualitative estimate of the cross­section rather than a quantitative description. The factor q is of order unity and was introduced as a fitting parameter. Since sessile SIA and vacancy clus­ters have different structures (loops in the case of the SIA clusters and frequently SFTs in the case of vacancy clusters), the multiplier q and, consequently, the appropriate cross-sections may be slightly differ­ent. Also note that qO = Tm has been used in

Trinkaus eta/.20 as an estimate on a homologous basis.

In the case of large size dislocation loops, the cross-section of their interaction with the SIA glissile clusters can be calculated in a way similar to that of edge dislocations. Namely, it is proportional to the product of the length of dislocation line, that is, 2kRi, and the capture radius, by The rate P1d(x) in that case is given by

P1D(x)= Vopbb1ADgCgx1/2 [129]

Note that in the more general case where differ­ent sizes of the SIA glissile clusters are taken into account, the last term on the right side of eqn [126] has to be replaced with the sum

p=*“x

prn(x T y)f (x T y).

j=xm"