Quantifying defect production in solids at finite temperatures: Thermally-activated correlated defect recombination corrections to DPA (CRC-DPA)

Abstract

It has long been recognized from low-temperature defect production experiments and molecular dynamics (MD) simulations of displacement events in metals that the surviving defect fraction relative to the calculated Norgett-Robinson Torrens (NRT) displacements per atom (dpa) ranges from ∼1 for near-threshold displacements (representative of electron irradiation) to ∼0.3 for energetic displacement cascades (relevant for fast neutrons or energetic heavy ion irradiations). This correlated point defect recombination that occurs within a few picoseconds following the creation of a primary knock-on atom (PKA) has recently been formalized in the athermal recombination corrected dpa (ARC-DPA) parameter. However, at elevated temperatures additional thermally-stimulated correlated defect recombination processes need to be considered. For example, at irradiation temperatures above defect recovery Stage I (typically ∼40–100 K for most metals), mobile self-interstitial atoms induce additional thermally-activated correlated defect recombination that can amount to 70–80% reduction in the surviving defect fraction for low PKA energies and ∼20 to 30% reduction for high PKA energies. Since most nuclear material applications involve operation above room temperature, it is generally important to include this additional correlated defect recombination in radiation effects models. Published experimental defect recovery and defect production studies on 26 metals are analyzed to extract the surviving defect fraction following thermally-activated correlated recombination as a function of PKA energy. These experimental estimates of the athermal- plus thermal-activated correlated recombination-corrected DPA (CRC-DPA) are compared with new long-term MD simulation results on Cu and Fe. The analysis indicates the CRC-DPA fraction of surviving defects in most elements for irradiation at temperatures where interstitials are mobile is ∼25% of the NRT DPA over a wide range of PKA energies relevant for electron, ion and fast neutron irradiation conditions. Limited experimental and kinetic Monte Carlo studies suggest a further reduction to ∼10% of the NRT DPA over a wide range of PKA energies when correlated recombination due to thermally activated vacancy migration is considered. This temperature-dependent CRC-DPA should be used as the defect production parameter (rather than NRT DPA or ARC-DPA) for materials irradiated at all temperatures where defects are mobile.