The sink strengths of other defects can be obtained in a similar way. For dislocation loops of a toroidal shape97

 

kL(v, i) = 2pRlZL4

 

[62]

 

where Rl and r^e are the loop radius and the effec­tive core radii for absorption of vacancies and SIAs, respectively. Similar to dislocations, the capture effi­ciency for SIAs is larger than that of vacancies, ZL > ZL, for loops. For a spherical GB of radius Rg (see, e. g., Singh et a/.98)

 

m is the shear modulus, n the Poisson ratio and DO the dilatation volume of the PD under consideration. The solution of eqn [35] in this case was obtained by Ham95 but is not reproduced here because of its complexity. It has been shown that a reasonably accurate approximation is obtained by treating the dislocation as an absorbing cylinder with radius R, = Aeg/4kBT, where g = 0.5772 is Euler’s con — stant.95 The solution is then given by

 

K (kr) Ko(kRd)

 

G Dk2

 

C (r)

 

[57]

 

where K0(x) is the modified Bessel function of zero order. Using eqns [47] and [57], one obtains the total flux of PDs to a dislocation and the dislocation sink strength as I = -2nRdPdDJ (Rd) = k1iD(C1 — Ceq) [58]

 

k2 kL/2coth(kL/2) — 1

 

k2 kfoil

 

[65]

 

In the limiting case of kL ^ 1, that is, when the foil surfaces are the main sinks,

 

k2 = ra Z Zd 2p ln(l/kRa)

 

12 L2

 

[59]

 

kf2oil

 

[66]