# Relaxation volumes of microscopic and mesoscopic irradiation-induced defects in tungsten

## TL;DR

This study evaluates the relaxation volumes of irradiation-induced defects in tungsten using empirical potentials and compares them with density functional theory results, providing insights into defect behavior and elastic properties relevant for reactor materials.

## Contribution

It offers the first systematic analysis of relaxation volumes of defects in tungsten, highlighting potential-independent trends and empirical fits for defect size dependence.

## Key findings

- Relaxation volume of small defects can be predicted within 10% from defect count.
- Empirical potentials show varying results, but some trends are consistent.
- Relaxation volume of primary damage cascades can be estimated from PKA energy.

## Abstract

The low energy structures of irradiation-induced defects have been studied in detail, as these determine the available modes by which a defect can diffuse or relax. As a result, there are many studies concerning the relative energies of possible defect structures, and empirical potentials are commonly fitted to or evaluated with respect to these energies. But recently [Dudarev et al Nuclear Fusion 2018], we have shown how to determine the stresses, strains and swelling of reactor components under irradiation from the elastic properties of ensembles of irradiation-induced defects. These elastic properties have received comparatively little attention. Here we evaluate relaxation volumes of irradiation-induced defects in tungsten computed with empirical potentials, and compare to density functional theory results where available. Different empirical potentials give different results, but some potential-independent trends in relaxation volumes can be identified. We show that the relaxation volume of small defects can be predicted to within 10% from their point-defect count. For larger defects we provide empirical fits for the relaxation volume of as a function of size. We demonstrate that the relaxation volume associated with a single primary-damage cascade can be estimated from the primary knock-on atom (PKA) energy. We conclude that while annihilation of vacancy- and interstitial- character defects will invariably reduce the total relaxation volume of the cascade debris, empirical potentials disagree whether coalescence of defects will reduce or increase the total relaxation volume.