Stress−induced diffusion of point defects to spherical sinks

Abstract

Radiation damage in metals at elevated temperatures produces small dislocation loops and voids. The growth of these sinks is determined by the steady−state diffusion of point defects migrating in the stress field of these sinks. To obtain the steady−state current of point defects to these spherical sinks a perturbation method is developed to deal with the drift term of the diffusion equation. It is shown that the contribution of the drift term to the current can be expressed by a bias factor which differs from unity if the point defects interact with the spherical sink. Explicit expressions of the bias factors for voids and infinitesimal dislocation loops are given. If the metal is subject to external loads the bias factors of voids depend on the elastic dilatation, whereas the bias factors for dislocation loops depend on the deviatoric elastic strain. These results then provide the basis for stress−induced swelling and irradiation creep of metals. Both of these phenomena are briefly discussed.

A study of xenon aggregates in uranium dioxide using X-ray absorption spectroscopy

“…(4) is only a variation on a theme developed by other authors relative to stress induced diffusion of point defects around dislocations (see [16,17] for instance). It shows that the stress gradient around the bubble is a thermodynamic force in the same way as the concentration gradient.…”

Calculation of radiation-induced deformation of SUS 316 in the ITER-relevant condition

“…Important parameter values used in the numerical calculation are listed in Table 1. Z i (interstitial bias) and DZ i (stress-induced bias) for loops and network dislocations were calculated using the equations given by Wolfer and Ashkin [6] and Heald and Speight [7], respectively. At each numerical iteration step the loop size was re-averaged, and Z i;v and DZ i;v were re-evaluated.…”

A multi-scale model for stresses, strains and swelling of reactor components under irradiation

“…This does not agree with ab initio calculations, showing that vacancies have negative relaxation volumes whereas self-interstitial atom defects have positive relaxation volumes. Swelling results from the agglomeration of self-interstitial defects into dislocation loops and extended dislocation network; vacancies aggregate into voids, the relaxation volume of which in the macroscopic limit is negative and small [39].…”

“…For example, the volume of a dislocation loop in the macroscopic limit equals the scalar product of its Burgers vector and its vector area (b · A), and can be positive or negative, depending on the interstitial or vacancy character of the loop [7,31]. The relaxation volume of a void, which is a large cluster of vacancies, vanishes in the macroscopic limit [39]. The relaxation volume of a vacancy-helium cluster depends on the relative number of vacancies and helium atoms in a cluster [8].…”

“…Assuming that pressure at R 1 and R 2 is negligible in comparison with the stresses developing in the material due to the accumulation of defects, we adopt the traction free boundary conditions [25] σ ij (r)n j = 0 at r = R 1 and r = R 2 . Strains can be found by differentiating (39). They have the form…”