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Radiation creep and swelling are irreversible deformation phenomena occurring in materials irradiated even at low temperatures. On the microscopic scale, energetic particles initiate collision cascades, generating and eliminating defects that then interact and coalesce in the presence of internal and external stress. We investigate how copper and tungsten swell and deform under various applied stress states in the low- and high-energy irradiation limits. Simulations show that the two metals respond in a qualitatively similar manner, in a remarkable deviation from the fundamentally different low-temperature plastic behaviour of bcc and fcc. The deviatoric part of plastic strain is particularly sensitive to applied stress, leading to anisotropic dimensional changes. At the same time, the volume change, vacancy content and dislocation density are almost insensitive to the applied stress. Low- as opposed to high-energy irradiation gives rise to greater swelling, faster creep, and higher defect content for the same dose. Simulations show that even at low temperatures, where thermal creep is absent, irradiation results in a stress-dependent irreversible anisotropic deformation of considerable magnitude, with the orientation aligned with the orientation of applied stress. To model the high dose microstructures, we develop an algorithm that at the cost of about 25% overestimation of the defect content is up to ten times faster than collision cascade simulations. The direct time integration of equations of motion of atoms in cascades is replaced by the minimisation of energy of molten spherical regions; multiple insertion of molten zones and the subsequent relaxation steps simulate the increasing radiation exposure.

The occurrence of high stress concentrations in reactor components is a still intractable phenomenon encountered in fusion reactor design. We observe and quantitatively model a non-linear high-dose radiation mediated microstructure evolution effect that facilitates fast stress relaxation in the most challenging low-temperature limit. In situ observations of a tensioned tungsten wire exposed to a high-energy ion beam show that internal stress of up to 2 GPa relaxes within minutes, with the extent and time-scale of relaxation accurately predicted by a parameter-free multiscale model informed by atomistic simulations. As opposed to conventional notions of radiation creep, the effect arises from the self-organisation of nanoscale crystal defects, athermally coalescing into extended polarized dislocation networks that compensate and alleviate the external stress., Comment: 10 pages, 5 figures

We demonstrate a practical way to perform decomposition of the elasto-plastic deformation directly from atomistic simulation snapshots. Through molecular dynamics simulations on a large single crystal, we elucidate the intricate process of converting plastic strain, atomic strain, and rigid rotation during irradiation. Our study highlights how prismatic dislocation loops act as initiators of plastic strain effects in heavily irradiated metals, resulting in experimentally measurable alterations in lattice strain. We show the onset of plastic strain starts to emerge at high dose, leading to the spontaneous emergence of dislocation creep and irradiation-induced lattice swelling. This phenomenon arises from the agglomeration of dislocation loops into a dislocation network. Furthermore, our numerical framework enables us to categorize the plastic transformation into two distinct types: pure slip events and slip events accompanied by lattice swelling. The latter type is particularly responsible for the observed divergence in interstitial and vacancy counts, and also impacts the behavior of dislocations, potentially activating non-conventional slip systems.

High-shear methods have long been used in experiments to refine grain structures in metals, yet the underlying mechanisms remain elusive. We demonstrate a refinement process using molecular dynamic simulations of iron, wherein nanocrystalline structures are generated from initially perfect lattices under high-shear strain. The simulation cells undergo a highly disordered state, followed by an atomic reordering and grain coarsening, resulting in nanograins. We explore the dependence on parameters such as temperature, heat dissipation rate, shear strain rate, and carbon impurity concentration. Higher temperatures lead to the formation of larger and longer grains. The faster heat dissipation sample initially yields more small grains, but their number subsequently reduces, and is lower than the slower heat dissipation sample at approximately {\gamma} = 1.5. Slower strain rates do not promote nanograin formation. The presence of carbon impurities appears to have little effect on grain formation. This detailed analysis affords insight into the mechanisms that control the formation of nanograins under high-shear conditions.

We describe the parameterization of a tungsten-hydrogen empirical potential designed for use with large-scale molecular dynamics simulations of highly irradiated tungsten containing hydrogen isotope atoms, and report test results. Particular attention has been paid to getting good elastic properties, including the relaxation volumes of small defect clusters, and to the interaction energy between hydrogen isotopes and typical irradiation-induced defects in tungsten. We conclude that the energy ordering of defects changes with the ratio of H atoms to point defects, indicating that this potential is suitable for exploring mechanisms of trap mutation, including vacancy loop to plate-like void transformations.

At temperatures below the onset of vacancy migration, metals exposed to energetic ions develop dynamically fluctuating steady-state microstructures. Statistical properties of these microstructures in the asymptotic high exposure limit are not universal and vary depending on the energy and mass of the incident ions. We develop a model for the microstructure of an ion-irradiated metal under athermal conditions, where internal stress fluctuations dominate the kinetics of structural evolution. The balance between defect production and recombination depends sensitively not only on the total exposure to irradiation, defined by the dose, but also on the energy of the incident particles. The model predicts the defect content in the high dose limit as an integral of the spectrum of primary knock-on atom energies, with the finding that low energy ions produce a significantly higher amount of damage than high energy ions., Comment: 9 pages, 5 figures, plus supplemental material

We derive a simple analytical line integral expression for the relaxation volume tensor of an arbitrary interconnected dislocation network. This quantity determines the magnitude of dislocation contribution to the dimensional changes and volumetric swelling of a material, and highlights the fundamental dual role of dislocations as sources of internal strain as well as carriers of plastic deformation. To illustrate applications of the method, we compute the relaxation volume of a stacking fault tetrahedron, a defect commonly occurring in fcc metals; the volume of an unusual tetrahedral configuration formed by the (a/2)<111> and a<001> dislocations in a bcc metal; and estimate the relative contribution of extended dislocations to the volume relaxation of heavily irradiated tungsten., Comment: 15 pages, 6 figures

The changing thermal conductivity of an irradiated material is among the principal design considerations for any nuclear reactor, but at present few models are capable of predicting these changes starting from an arbitrary atomistic model. Here we present a simple model for computing the thermal diffusivity of tungsten, based on the conductivity of the perfect crystal and resistivity per Frenkel pair, and dividing a simulation into perfect and athermal regions statistically. This is applied to highly irradiated microstructures simulated with Molecular Dynamics. A comparison to experiment shows that simulations closely track observed thermal diffusivity over a range of doses from the dilute limit of a few Frenkel pairs to the high dose saturation limit at 3 displacements per atom (dpa)., Comment: preprint submitted to journal

Hydrogen isotopes are retained in materials for fusion power applications, changing both hydrogen embrittlement and tritium inventory as the microstructure undergoes irradiation damage. But modelling of highly damaged materials - exposed to over 0.1 displacements per atom (dpa) - where asymptotic saturation is observed, for example tungsten facing the plasma in a fusion tokamak reactor, is difficult because a highly damaged microstructure cannot be treated as weakly interacting isolated defect traps. In this paper we develop computational techniques to find the defect content in highly irradiated materials without adjustable parameters. First we show how to generate converged high dose (>1 dpa) microstructures using a combination of the creation-relaxation algorithm and molecular dynamics simulations of collision cascades. Then we make robust estimates of point defects and void regions with simple developments of the Wigner-Seitz decomposition of lattice sites. We use our estimates of the void surface area to predict the deuterium retention capacity of tungsten as a function of dose. This is then compared to 3He nuclear reaction analysis (NRA) measurements of tungsten samples self-irradiated at 290 K to different damage doses and exposed to deuterium plasma at low energy at 370 K. We show that our simulated microstructures give an excellent match to the experimental data, with both model and experiment showing 1.5-2.0 at.% deuterium retained in tungsten in the limit of high dose., Comment: preprint for submission to journal

Combining spatially resolved X-ray Laue diffraction with atomic-scale simulations, we observe how ion-irradiated tungsten undergoes a series of non-linear structural transformations with increasing irradiation exposure. Nanoscale defect-induced deformations accumulating above 0.02 displacements per atom (dpa) lead to highly fluctuating strains at ~0.1 dpa, collapsing into a driven quasi-steady structural state above ~1 dpa. The driven asymptotic state is characterized by finely dispersed vacancy defects coexisting with an extended dislocation network, and exhibits positive volumetric swelling due to the creation of new crystallographic planes through self-interstitial coalescence, but negative lattice strain., Comment: 9 pages, 9 figures, in print with PRL

We present a morphological analysis of atom probe data of nanoscale microstructural features, using methods developed by the astrophysics community to describe the shape of superclusters of galaxies. We describe second-phase regions using Minkowski functionals, representing the regions' volume, surface area, mean curvature and Euler characteristic. The alloy data in this work show microstructures that can be described as sponge-like, filament-like, plate-like, and sphere-like at different concentration levels, and we find quantitative measurements of these features. To reduce user decision-making in constructing isosurfaces and to enhance the accuracy of the analysis a maximum likelihood based denoising filter was developed. We show that this filter performs significantly better than a simple Gaussian smoothing filter. We also interpolate the data using natural cubic splines, to refine voxel sizes and to refine the surface. We demonstrate that it is possible to find a mathematically well-defined, quantitative description of microstructure from atomistic datasets, to sub-voxel resolution, without user-tuneable parameters., Comment: Author Accepted Manuscript Paper Accepted for publication in Ultramicroscopy

We describe the development of a new object kinetic Monte Carlo code where the elementary defect objects are off-lattice atomistic configurations. Atomic-level transitions are used to transform and translate objects, to split objects and to merge them together. This gradually constructs a database of atomic configurations -- a set of relevant defect objects and their possible events generated on-the-fly. Elastic interactions are handled within objects with empirical potentials at short distances, and between spatially distinct objects using the dipole tensor formalism. The model is shown to evolve mobile interstitial clusters in tungsten faster than an equivalent molecular dynamics simulation, even at elevated temperatures. We apply the model to the evolution of complex defects generated using molecular dynamics simulations of primary radiation damage in tungsten. We show that we can evolve defect structures formed in cascade simulations to experimentally observable timescales of seconds while retaining atomistic detail. We conclude that the first few nanoseconds of simulation following cascade initiation would be better performed using molecular dynamics, as this will capture some of the near-temperature-independent evolution of small highly-mobile interstitial clusters. We also conclude that, for the 20keV PKA cascades annealing simulations considered here, internal relaxations of sessile objects difficult to capture using conventional object KMC with idealised object geometries establish the conditions for long timescale evolution.

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.

Unique electrodynamic response of graphene implies a manifestation of an unusual propagating and localised transverse-electric (TE) mode near the spectral onset of interband transitions. However, excitation and further detection of the TE mode supported by graphene is considered to be a challenge for it is extremely sensitive to excitation environment and phase matching condition adherence. Here for the first time, we experimentally prove an existence of the TE mode by its direct optical probing, demonstrating significant coupling to an incident wave in electrically doped multilayer graphene sheet at room temperature. We believe that proposed technique of careful phase matching and obtained access to graphene TE excitation would stimulate further studies of this unique phenomenon, and enable its potential employing in various fields of photonics as well as for characterization of graphene.

Knowledge of mechanical and physical property evolution due to irradiation damage is essential for the development of future fission and fusion reactors. Ion-irradiation provides an excellent proxy for studying irradiation damage, allowing high damage doses without sample activation. Limited ion-penetration-depth means that only few-micron-thick damaged layers are produced. Substantial effort has been devoted to probing the mechanical properties of these thin implanted layers. Yet, whilst key to reactor design, their thermal transport properties remain largely unexplored due to a lack of suitable measurement techniques. Here we demonstrate non-contact thermal diffusivity measurements in ion-implanted tungsten for nuclear fusion armour. Alloying with transmutation elements and the interaction of retained gas with implantation-induced defects both lead to dramatic reductions in thermal diffusivity. These changes are well captured by our modelling approaches. Our observations have important implications for the design of future fusion power plants., Comment: 15 pages, 3 figures

In radiation damage cascade displacement spikes ions and electrons can reach very high temperatures and be out of thermal equilibrium. Correct modelling of cascades with molecular dynamics should allow for the non-adiabatic exchange of energy between ions and electrons using a consistent model for the electronic stopping, electronic temperature rise, and thermal conduction by the electrons. We present a scheme for correcting embedded atom potentials for these non-adiabatic properties at the level of the second-moment approximation, and parameterize for the bcc transition metals above the Debye temperature. We use here the Finnis-Sinclair and Derlet-Nguyen-Manh-Dudarev potentials as models for the bonding, but the corrections derived from them can be applied to any suitable empirical potential., Comment: 31 pages, 6 figures. This is an author-created, un-copyedited version of an article submitted for publication in : J. Phys.: Condens. Matter. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it