Corrigendum to “Energy spectra of primary knock-on atoms under neutron irradiation” [J. Nucl. Mater. 467 (Part 1) (2015) 121–134

Abstract

Journal of Nuclear Materials 467 (2015) 121e134 Contents lists available at ScienceDirect Journal of Nuclear Materials journal homepage: www.elsevier.com/locate/jnucmat Energy spectra of primary knock-on atoms under neutron irradiation M.R. Gilbert a, * , J. Marian b , J.-Ch. Sublet a a b Culham Centre of Fusion Energy, Culham Science Centre, Abingdon, OX14 3DB, UK Department of Materials Science and Engineering, University of California Los Angeles, Los Angeles, CA, 90095, USA a r t i c l e i n f o a b s t r a c t Article history: Received 2 July 2015 Received in revised form 11 September 2015 Accepted 14 September 2015 Available online 16 September 2015 Materials subjected to neutron irradiation will suffer from a build-up of damage caused by the displacement cascades initiated by nuclear reactions. Previously, the main “measure” of this damage accumulation has been through the displacements per atom (dpa) index, which has known limitations. This paper describes a rigorous methodology to calculate the primary atomic recoil events (often called the primary knock-on atoms or PKAs) that lead to cascade damage events as a function of energy and recoiling species. A new processing code SPECTRA-PKA combines a neutron irradiation spectrum with nuclear recoil data obtained from the latest nuclear data libraries to produce PKA spectra for any material composition. Via examples of fusion relevant materials, it is shown that these PKA spectra can be complex, involving many different recoiling species, potentially differing in both proton and neutron number from the original target nuclei, including high energy recoils of light emitted particles such as a - particles and protons. The variations in PKA spectra as a function of time, neutron field, and material are explored. The application of PKA spectra to the quantification of radiation damage is exemplified using two approaches: the binary collision approximation and stochastic cluster dynamics, and the results from these different models are discussed and compared. © 2015 EURATOM. Published by Elsevier B.V. All rights reserved. Keywords: Radiation damage quantification Primary knock-on atoms (PKAs) Nuclear data processing Neutron irradiation Recoil energy spectrum 1. Introduction Understanding through modelling of the damage accumulated in materials irradiated by neutrons remains a primary goal for computational simulation of materials for advanced nuclear energy systems. Several different approaches exist for predicting the for- mation, evolution and behaviour of this damage, including: computationally demanding molecular dynamics simulations of damage cascades with full atomic interactions; rate theory models, where defects are described as objects with defined behaviour; and kinetic Monte-Carlo (kMC) simulations. However, without excep- tion, all of these techniques need, as input at some level, informa- tion about the initial primary disruptions, in the form of the type, energy and spatial distribution of the primary knock-on atoms (PKAs). In particular, this kind of data goes far beyond the limited information provided by the traditional and ubiquitous defect in- dex of initial damage formation known as “displacements per atom” (dpa). The so-called Norgett, Robinson and Torrens NRT-dpa [1] reduces the predicted irradiation environment, perhaps * Corresponding author. E-mail address: mark.gilbert@ccfe.ac.uk (M.R. Gilbert). http://dx.doi.org/10.1016/j.jnucmat.2015.09.023 0022-3115/© 2015 EURATOM. Published by Elsevier B.V. All rights reserved. obtained from a Monte-Carlo neutron transport simulation on a reactor geometry, to a single number that converts the energy deposited into a material by the irradiation into an estimate of the number of atomic displacements that could be generated. The dpa measure has proven to correlate well with various radiation dam- age phenomena, but is not well suited to distinguishing between different types of irradiation, and, more importantly, it does not provide information about damage evolution. It is also the case that it should not be used as a basis for comparing irradiation behaviour in different materials [2]. A more complete picture of radiation damage evolution, that may be afforded by modern computational techniques, requires the spatial and energy distribution of all the initial displacement events, including both emitted and residual nuclei from nuclear interactions. In modern nuclear data evaluations, for a single target species, such as the major 56 Fe isotope in Fe, there are many nuclear reac- tion channels that produce recoiling species, including elastic, in- elastic, and nonelastic nuclear reactions. In nuclear fusion, in particular, the generally higher energy of the incident neutrons, when compared to fission, leads to many more channels becoming relevant, which in turn produces a more complex distribution of PKAs in both energy and type. These PKAs lead to cascades of atomic displacements, which can subsequently evolve and collapse