Atomistic calculation of point-defect diffusion anisotropy and irradiation growth inα-zirconium

Abstract

The configuration and energetics of the mono-vacancy and self-interstitial of hcp zirconium, both in the ground state and the saddle-point configurations, are computed atomistically using the conjugate gradient method, from which the diffusion anisotropy difference (DAD) between the two types of defects is obtained. Based on this information, the growth rates of interstitial loops of different Burgers vectors in a zirconium foil irradiated in a high-voltage electron microscope and the stress-free in-reactor deformation rates in hcp zirconium are directly calculated. Experimental observations in both cases are shown to be well accounted for. The significance of the DAD effect is thus directly confirmed.

Cluster Dynamics modelling of irradiation growth of zirconium single crystals

“…Influence of the SIA diffusion coefficient Di on the calculated size distribution of prismatic interstitial loops at a fluence of 0.2 dpa. calculations by Osetsky [11], Woo [12,13] are respectively 5.8 Â 10 À5 , 1.7 Â 10 À4 and 8.2 Â 10 À4 cm 2 s À1 , which is higher than the SIA diffusion coefficient we used. Nevertheless, it must be noticed that the effect of the D i value on the growth curves is not so strong (see Fig.…”

“…It has been shown that D a i > D c i [9][10][11][12][13], so that p < 1 and Z a i > z i . Thus, the SIA diffusion anisotropy leads to a better SIA absorption efficiency by prismatic loops.…”

“…[17]). In that 'extended' model, only SIA diffusion is assumed to be anisotropic, whereas vacancy diffusion is supposed isotropic [9][10][11][12][13]. It should be emphasized that in this model, only point defects are supposed mobile.…”

“…Vacancy diffusion coefficient at 553 K Dv 3.0 Â 10 À17 cm 2 .s À1 Adjusted input SIA diffusion coefficient at 553 K b D i 10 À6 cm 2 s À1 Adjusted input SIA diffusion anisotropy factor at 553 K p 0.765 [11][12][13] Recombination radius r iv 10 À7 cm [33] Vacancy/dislocation elastic interaction zv 1.0 SIA/dislocation elastic interaction z i 1.1 [15,34] Bürgers vector (prismatic loops) b 3.23 Â 10 À8 cm [22] a The di-vacancy and di-interstitial binding energy is needed to calculate the binding energy of the loops as a function of their size (see [17] for a detailed explanation). b D i is the SIA mean diffusion coefficient:…”

“…2. Second, some of these models [2][3][4][5] do not take the DAD (Diffusion Anisotropy Difference) effect: it has been demonstrated that in zirconium diffusion of self-interstitial atoms (SIA) is anisotropic [9][10][11][12][13] (whereas vacancy diffusion can reasonably be considered isotropic). This Diffusion Anisotropy Difference (DAD) can induce a large bias that can 'completely dominate the conventional dislocation bias caused by first order elastic interaction between the point defects and the sink' (cited from [7]).…”