Atomic displacements, replacements, and radiation damage of structural materials

[Astronuc]

An important aspect of nuclear materials, and components of which they are made, is their ability to perform over the design life. The components include the 'cladding', the encapsulating feature that surrounds the fuel and forms a hermetic barrier to the release of fission products and transuranic elements, the core support structures and reactor internals, the reactor vessel and the rest of the heavy components (e.g., piping and heat exchangers) that maintain a second barrier to fission products and TU elements to the environment.

The fuel systems generally serves several cycles in the core, which could mean 2 x 24-month cycles (4 years), 3 x 18-month cycles (4.5 years), 4 or 5 annual (12-month) cycles (4 or 5 years), and also longer operational times, of up to 5, 6, 7 and even 8 years. A cycle includes the period with the reactor shutdown for refueling (and fuel shuffling (core design/management). With less than 100% capacity factor (CF), the actual service time is less than the cumulative cycle lengths; for example, with a 90% CF, an 8-year service time would be 7.2 effective fuel power years. Capacity factor is based on the effective operating time at full (or rated) power, which accounts for reduced power and shutdowns. Some plants may achieve CFs of 95% or better, but that means running at full power with short refueling outages.

Reactor internals and core support structure remain in service much longer than the fuel, and in some cases, may be replaced after 15, 20, or more years. The reactor vessel (or reactor pressure vessel, RPV) and associated piping and heat exchangers would ideally last the service life of the plant; however, due to material degradation (corrosion, erosion, and/or cracking over time), some components may be replaced before the initial design life (as has been the case of many PWR steam generators).

In the core and on the core periphery, the structural materials are subject to a harsh irradiation environment from neutrons, gammas and electrons (assciated with gammas: photoelectrons, Compton scattering, pair-production). Neutrons not absorbed in the fuel (and fission products) and coolant are absorbed by the internal and external structual material. Neutrons diplace atoms in the structural materials, and they my also be aborbed by atoms in the structural materials, leading to activiation ( A + n => A+1 ) with the emission of a prompt gamma, but then also later a beta particle and subsequent decay gamma.

We attempt to determine the radiation damage in materials by calculating the displacements per atom (dpa), which has been somewhat correlated with fast neutron fluence, and the microstructural changes associated with those atomic displacements. There has been considerable development of radiation damage modeling during the past decade; the understanding of radiation damage has been going on for 70+ years.

A fairly recent paper from 2018, K. Norldund et al. provides a good background on the discipliine.
Improving atomic displacement and replacement calculations with physically realistic damage models

Abstract:
Atomic collision processes are fundamental to numerous advanced materials technologies
such as electron microscopy, semiconductor processing and nuclear power generation.
Extensive experimental and computer simulation studies over the past several decades
provide the physical basis for understanding the atomic-scale processes occurring during
primary displacement events. The current international standard for quantifying this energetic
particle damage, the Norgett−Robinson−Torrens displacements per atom (NRT-dpa) model,
has nowadays several well-known limitations. In particular, the number of radiation defects
produced in energetic cascades in metals is only ~1/3 the NRT-dpa prediction, while the
number of atoms involved in atomic mixing is about a factor of 30 larger than the dpa value.
Here we propose two new complementary displacement production estimators (athermal
recombination corrected dpa, arc-dpa) and atomic mixing (replacements per atom, rpa)
functions that extend the NRT-dpa by providing more physically realistic descriptions of
primary defect creation in materials and may become additional standard measures for
radiation damage quantification.

Nordlund, K., Zinkle, S.J., Sand, A.E. et al. Improving atomic displacement and replacement calculations with physically realistic damage models. Nat Commun 9, 1084 (2018). https://doi.org/10.1038/s41467-018-03415-5

Apparently, the same work is reported in Journal of Nuclear Materials, and it appears to be open access.
https://www.sciencedirect.com/science/article/pii/S002231151831016X

The introduction in the JNM article gives a nice overview of the scope of radiation applications and the consequent interest in understanding the 'radiation effects'.

Particles with kinetic energies clearly above conventional thermal energies, i.e. with E > 1 eV, exist in nature due to cosmic radiation and radiation decay, but are nowadays produced in a wide range of man-made devices for basic research and practical applications. For instance, the great accelerators at CERN and other particle physics laboratories in the world attempt to unravel the fundamental nature of the universe [1,2], and numerous smaller devices are widely used for equally exciting research in physics [3], chemistry [4], medicine [5] and nanoscience [6]. On the application side, ion implantation is one of the key technologies in silicon chip manufacturing [7], and electron accelerators are one of the key ways to treat cancer [8]. All of these activities make it interesting and important to understand what are the fundamental effects of high-energy particles on matter. Moreover, in nuclear fission reactors, which currently provide about 13% of the world's electricity, materials degradation associated with neutron irradiation damage is a key factor [9].

I would add gamma radiation to the neutron irradiation, which is important to understand; the effects of gamma radiation are probably less understood and appreciated compared to that of neutrons, electrons and ions. Of course, gammas produce electrons through photoelectron effect, Compton scattering and pair (e⁺e^-) production.

Edit/update: Paper from 2023
S.J. Zinkle, R.E. Stoller, "Quantifying defect production in solids at finite temperatures: Thermally-activated correlated defect recombination corrections to DPA (CRC-DPA)," Journal of Nuclear Materials, Volume 577, 15 April 2023, 154292
See the Open Manuscript if one cannot access the pdf from ScienceDirect.

 

[Astronuc]

A related paper by Jean-Paul Crocombette and Christian Van Wambek,
Quick calculation of damage for ion irradiation: implementation in Iradina and comparisons to SRIM
https://www.epj-n.org/articles/epjn/pdf/2019/01/epjn190004.pdf

Abstract. Binary collision approximation (BCA) calculation allows for two types of damage calculation: full
cascade and quick calculations. Full cascade mode describes fully the cascades while in quick calculations, only
the trajectory of the ion is followed and effective formulas give an estimation of the damage resulting from each
collision of the ion. We implement quick calculation of damage in the Iradina code both for elemental and multi-
component solids. Good agreement is obtained with SRIM. We show that quick calculations are unphysical in
multi-component systems. The choice between full cascade and quick calculations is discussed. We advise to
favour full cascade over quick calculation because it is more grounded physically and applicable to all materials.
Quick calculations remain a good option for pure solids in the case of actual quantitative comparisons with
neutron irradiations simulations in which damage levels are estimated with the NRT (Norgett-Robinson and
Torrens) formulas.

An important piece of information:

The limitations of such BCA approaches are well-known. For instance, thanks to molecular dynamics (MD) simulations [6,7] and experiments [8], it has been known for decades that BCA codes overestimate the
number of created defects by primary damage. Moreover, they cannot give information about the detailed structure of the clusters of defects formed directly after the collisions cascades. Nevertheless, BCA simulations remain extremely useful because they are simple and fast. The principles of BCA have been described many times in previous works [3–5] and we just recall that BCA uses generic pair-wise interaction potentials and rely intensively on scattering theory. While some rare codes use energy integrals in the BCA framework to calculate average number of collisions and atomic displacements (e.g. the DART code [9]), most of the BCA codes deal with real space trajectories and describe explicitly the sequence of collisions sustained by the
incoming ion.

Apparently, there is an error in one line of code in SRIM, which when using the Full Cascade mode results in an over-prediction of the radiation damage. There is an adjustment/correction that one can make however, which I will post about later.