Interaction mechanisms of glissile loops in FCC systems by the elastic theory

doi:10.1016/j.jnucmat.2008.12.310

Journal of Nuclear Materials

Volumes 386–388, 30 April 2009, Pages 188-190

https://doi.org/10.1016/j.jnucmat.2008.12.310 Get rights and content

Abstract

The elastic theory calculations are conducted to clarify the interaction between a large dislocation loop and a small glissile loop in face-centered-cubic systems. In the parallel Burgers vector case, the interaction force changes from repulsive to attractive when the small loop moves along its glide cylinder. In the perpendicular Burgers vector cases, the interaction strongly depends on the spatial position of the glide cylinder of the small loop from the center of the large loop. There are attractive regions in any combinations of the Burgers vectors and spatial positions calculated in this study, which may induce the loop decoration.

Introduction

The production and formation of irradiation-induced defects under high energetic particle injections are quite different from that under the electron and light ion irradiation [1], as recent MD simulations demonstrate that high damage energy irradiation directly produces defect clusters as well as Frenkel pairs [2], [3]. These clusters, when no longer subject to the rapid Brownian motion, are synonymous with dislocation loops [4]. They are still highly mobile because of their low activation energies, or low Peierls potentials [5], [6], and interact with other loops or line dislocations [7], [8], [9], [10]. As a result, the growth of larger loops as well as the evolution of network dislocations depends also on the capture rate of these small glissile loops rather than of individual self-interstitials only. Since the mobile directions of the small loops are constraint to specific directions, the growth kinetics of the larger loops under collision cascades are strongly different from that by three-dimensional defect migrations. Therefore, the loop–loop interaction is a mechanism which we should clarify in order to build up models for the microstructural evolution, and resultant macroscopic changes such as void swelling or irradiation hardening, especially under 14 MeV fusion neutrons [3].

In this study, the elastic theory is used to elucidate the loop behavior under the stress field of other loops in face-centered-cubic (FCC) systems. We incorporate the glide motion and rotation of the loop into the model.

Section snippets

Calculation methods

We use the equation derived by Wolfer et al. [4], which describes the interaction of a loop with any kinds of stress field. In their study, they remove the constraint of a fixed orientation of the loop, and allow the loop to rotate in order to minimize the energy under the stress field by assuming elastically isotropic solid, the detail of which is written in [4]. The equations used in this study are written as follow: $sgn (γ) \sqrt{k (1 - k)} Λ (k) = | \vec{t} | \cdot \sin γ$ where γ is the angle between the traction vector $\vec{t}$

Results and discussion

In this study, we choose the radius of the loop A (r_a) and loop B (r_b) to be 5.0 × 10⁻¹⁰ m and 2.0 × 10⁻⁹ m, respectively, while the closest distance between the centroids of the loops is set to be 3.0 × 10⁻⁹ m, which is shown as h in Fig. 1. The preliminary calculations confirm that the change in the energy is proportional to h⁻³, $r_{a}^{2}$ and $r_{b}^{2}$ , which is exactly agreed with the conventional dislocation theory [12]. Even when we include the loop rotation, although the stable position of the loop A is

Conclusions

We have evaluated the change in the energy by the glide motion of a loop exerted by the stress field originating from another loop, and incorporate the rotation of the loop under the stress field in FCC systems. When the Burgers vectors are parallel, the loop formed in the tensile region is attracted by the other loop, and they will be aligned nearby. When the Burgers vectors are perpendicular, the interaction depends on the angle between the position vector of the glide cylinder and the normal

Acknowledgements

The authors gratefully appreciate Dr. W.G. Wolfer in Lawrence Livermore National Laboratory and Prof. E. Kuramoto for their fruitful discussions and advices.

References (15)

B.N. Singh
J. Nucl. Mater.
(1998)
R.S. Averback et al.
R.E. Stoller et al.
J. Nucl. Mater.
(1997)
Y.N. Osetsky et al.
J. Nucl. Mater.
(2000)
N.M. Ghoniem et al.
J. Nucl. Mater.
(2000)
T. Okita et al.
J. Nucl. Mater.
(2007)
B.N. Singh et al.
J. Nucl. Mater.
(1997)

There are more references available in the full text version of this article.

Cited by (4)

Complete characterization of sink-strengths for 1D to 3D mobilities of defect clusters: Bridging between limiting cases with effective sink-strengths calculations.
2022, Journal of Nuclear Materials
Citation Excerpt :
Even more problematically, the elastic interactions between the cluster and other sources from the medium should also play a role. Elastic models [39,40] show that, when exposed to the elastic field of a dislocation, the loops’ habit planes tend to rotate (which is different from the thermally activated rotation of the Burgers vector) to minimise elastic energy thus loosing their pure edge orientation [41]. This primarily plays a role in the decoration of dislocation lines by elastically trapped loops atmospheres [33], but it is also important at the loop’s scale since it results in a misalignment of the loops’ normal with the Burgers vector.
In a companion paper, new analytical expressions of the cluster sink-strength (CSS) for two one-dimensional diffusers were proposed. These expressions are indispensable to any complete parameterisation of rate-equations cluster dynamics intending to model mobile interstitial clusters such as dislocation loops. Indeed, simulating the long-term microstructural evolution in systems with fast diffusing species such as self-interstitial atom (SIA) clusters relies on establishing the CSS for rate-equation cluster dynamics which critically depends on the complex mobilities of clusters. In this second paper, we will estimate effective CSSs by object kinetic Monte-Carlo (OKMC) on wide ranges of radii, rotation energies, diffusion coefficients, and concentrations of both reaction partners. The symmetric roles of some parameters are used to infer a generic form of a semi-analytical expression of the CSS depending on all these interaction parameters. It is composed of, on one hand, the various analytical expressions established as limiting cases and, on the other hand, of fitted transition functions that allow a gradual switching between them. The analysis of the residuals shows that the overall agreement is reasonably good: it is only in the transition zones that some significant discrepancies are located. This semi-analytical expression answers our practical need for CSSs evaluation in our typical range of conditions, but further extending this range to much smaller diffusion coefficients ratios, it is quite striking to see that the domain for 1D-1D mobility is very extended. It is only when approaching a ratio of $10^{- 6}$ that the 1D-0 CSSs start becoming more relevant than the adapted 1D-1D CSSs which have completely different orders of magnitude and kinetic orders. Finally, the semi-analytical CSS expression is validated by comparing its implementation in rate-equation cluster dynamics to OKMC simulations of interstitial clusters aggregation. Companion paper: [1]
Complete characterization of sink-strengths for mutually 1D-mobile defect clusters: Extension to diffusion anisotropy analog cases
2022, Journal of Nuclear Materials
Simulating the long-term microstructural evolution in systems involving very fast diffusing species such as self-interstitial atom (SIA) clusters currently relies on mean-field or coarse-graining techniques. Rate-equation cluster dynamics (RECD) is one of the most popular of those when dealing with irradiated microstructure or second phase precipitation by thermal aging. Some of the most important input parameters of RECD are the absorption rates, also called cluster sink-strengths (CSS). These quantities crucially depend on the way clusters interact and diffuse and notably on the dimensionality of the involved random diffusion processes. As expected theoretically and experimentally confirmed, SIA clusters migrate in a one-dimensional fashion (possibly with random orientation changes, i.e. rotations of their Burgers vector). This complicates the calculation of the related CSS. When involving a 1D-mobile specie and an immobile reaction partner (a “1D-0” reaction) the expressions are quite well-known as well as the extension including random rotations (a “1DR-0” reaction). Expressions of CSS for absorptions between identical 1D-mobile species were proposed in the literature, but the general case of 1D-1D absorptions between different cluster classes is unknown. Here we propose a heuristic approach to such general expressions which turn out to depend on the respective capture radii of interacting clusters classes, concentrations and notably on the ratio of their respective diffusion coefficients through a power-law. In the companion paper [1], the same power-law formulation is found for 1D-3D absorptions but with different exponents, which thus appear as signatures of the dimensionality of the involved random motions. These limiting cases of CSS being established, they are finally implemented in an RECD calculation. The comparison with time-consuming kinetic Monte Carlo simulations completely validates their expression.
Complete characterization of sink-strengths for 1D to 3D mobilities of defect clusters: Bridging between limiting cases with effective sink-strengths calculations
2018, arXiv
Complete characterization of sink-strengths for mutually 1D-mobile defect clusters: Extension to diffusion anisotropy analog cases
2018, arXiv

View full text

Interaction mechanisms of glissile loops in FCC systems by the elastic theory

Abstract

Introduction

Section snippets

Calculation methods

Results and discussion

Conclusions

Acknowledgements

J. Nucl. Mater.

J. Nucl. Mater.

J. Nucl. Mater.

J. Nucl. Mater.

J. Nucl. Mater.

J. Nucl. Mater.