Rates of diffusion controlled reactions for one-dimensionally-moving species in 3D space

ABSTRACT

The asymmetry in diffusion dimensionality between self-interstitial atom (SIA) clusters and vacancies is a fundamental feature of irradiation damage in crystals, leading to a defect buildup imbalance that manifests itself as measurable dimensional and mechanical property changes. It is well known that, while vacancies and mobile vacancy clusters diffuse in a three-dimensional (3D) fashion, SIA clusters perform one-dimensional motion along mostly rectilinear trajectories. Despite this, a complete set of kinetic coefficients, including coagulation reaction rates and sink strengths, does not exist for 1D-moving objects. In this paper, we derive analytical expressions for these coefficients from continuum diffusion theory particularised to 1D motion. Moreover, we carry out kinetic Monte Carlo simulations of numerical replicas of the geometry of diffusing particles and sinks to validate the proposed solutions. Our simulations, which are conducted entirely independently from the analytical derivations, reveal excellent agreement with the proposed expressions, adding confidence to their validity. We compare the 1D and 3D cases and discuss their relevance for kinetic codes for damage accumulation calculations.

KEYWORDS:

• Diffusion reaction
• irradiation damage
• one-dimensional diffusion
• reaction rate
• sink strength
• self-interstitial clusters

Acknowledgments

Computer time allocations at UCLA's IDRE Hoffman2 supercomputer are acknowledged. Useful discussions with Sergei Dudarev and Alexander Barashev are acknowledged.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 We will show later that this is not necessarily the case in certain particle concentration regimes.

2 This is easy to show by considering the motion of one particle relative to the motion of the other, as proved in (see proof in Appendix).

Additional information

Funding

This work has been supported by the US Department of Energy's Office of Fusion Energy Sciences, project DE-SC0012774:0001.