We explore how the thermodynamic properties and dynamics of a self-interstitial prismatic dislocation loop are affected by microscopic-scale variations in its geometric configuration, an aspect that rarely received attention in literature. First, we develop a machine-learning (ML) model to predict the formation energy of an arbitrary geometrically complex configuration of a self-interstitial atom dislocation loop. Trained on atomistic simulation data, the ML model achieves high predictive accuracy across a broad range of configurations, with a typical error in the 1

Materials used in commercial D-T fusion reactors will be exposed to irradiation and a mixture of helium and hydrogen plasma. Modeling the microstructural evolution of such materials requires the use of large-scale molecular dynamics simulations. The focus of this study is to develop a fast embedded atom method potential for the interactions among the three elements (W, H, and He), fitted to accurately reproduce both theab initioformation energies and relaxation volumes of small defect clusters containing light gases within tungsten. The potential enables the study of tungsten under irradiation and in the presence of light gases. To demonstrate the utility of the potential, we construct a thermodynamically motivated model for predicting the energetics of light-gas-filled voids. The W-He-H system energy is represented by analytical expressions that describe the energetics of hydrogen occupying distinct configurations. The model is validated using molecular dynamics simulations with the new interatomic potential and results in a simple expression that quantifies the difference in hydrogen trapping between a mono-vacancy and a large void.

We use molecular dynamics simulations to directly compute the effective diffusivity of hydrogen gas atoms in homogeneous distributions of monovacancies in tungsten and vanadium, and voids in tungsten. Rather than fitting the results to an Arrhenius law, we compare to an analytic approximation for the effective diffusivity recently derived for multi-occupancy traps [Kaur et al (2025), Phys. Rev. Mater. 9:125404]. We find good agreement between full atomistic simulation and our theory, validating the analytic model for diffusivity for materials containing nanoscale defects characteristic of radiation damage. There are no parameters fitted, only physically motivated quantities that can be computed with static density functional or atomistic potential calculations. In this study we prove rapid convergence of hydrogen trap occupation to the steady state using lattice kinetic Monte Carlo, the spontaneous emergence of voids in tungsten using atomistic simulation with empirical potentials, and molecular hydrogen formation in voids using molecular dynamics. We conclude with a prediction for diffusion and retention of hydrogen in voids in tungsten starting from first principles. This work shows that not only is the analytic form for diffusivity and retention in multi-occupancy traps a practical scheme for making predictive simulations of hydrogen isotope diffusion and retention in irradiated microstructures, derived and parameterized from first principles, it is superior to existing single-occupancy trap formalisms.

Materials used in commercial D-T fusion reactors will be exposed to irradiation and a mixture of helium and hydrogen plasma. Modeling the microstructural evolution of such materials requires the use of large-scale molecular dynamics simulations. The focus of this study is to develop a fast EAM potential for the interactions among the three elements (W, H, and He), fitted to accurately reproduce both the ab initio formation energies and relaxation volumes of small defect clusters containing light gases within tungsten. The potential enables the study of tungsten under irradiation and in the presence of light gases. To demonstrate the utility of the potential, we construct a thermodynamically motivated model for predicting the energetics of light-gas-filled voids. The model is then validated through molecular dynamics simulations with our new potential.

Radiation creep and swelling are irreversible deformation phenomena occurring in irradiated materials. With thermal activation, deformations can reach several percent; at low temperature, fundamentally different and saturating mechanisms are active and are the topic of this work. Collision cascades generate and eliminate defects that interact and coalesce under 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. 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 strain is particularly sensitive to applied stress, leading to anisotropic dimensional changes, contrary to the total volume change, vacancy content and dislocation density. 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, with no thermal creep, irradiation results in a swelling of about 0.1%-1% and stress-dependent irreversible anisotropic deformations of up to a few percent aligned with the orientation of applied stress. To simulate 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 is replaced by the energy minimisation of molten spherical regions during their solidification; multiple insertion of molten zones and subsequent relaxation steps simulate the accumulation of radiation exposure.

Nanocrystalline materials are promising candidates for future fusion reactor applications, due to their high density of grain boundaries which may serve as sinks for irradiation induced defects. We use molecular dynamics to simulate collision cascades in nanocrystalline iron and compare these to collision cascades in initially defect free single crystals. We create nanocrystalline samples via Voronoi tessellation of initially randomly placed grain seeds and via severe plastic shearing. An irradiation induced annealing is observed whereby after 2 displacements per atom (dpa), irradiation drives all simulation cells to a single crystalline state. Irradiation-induced defects that distort the lattice generate elastic strain, so we use excess potential energy as a measure of defect content. At low doses, the Voronoi samples feature a few large, low energy grains, whereas the sheared samples show many small, high energy grains due to the high defect and grain boundary content caused by severe deformation. As dose increases beyond 1 dpa however, all nanocrystalline samples converge to a similar behaviour. Excess potential energy mirrors this trend, plateauing above 4 dpa. We hypothesise that the initially pristine cells will also reach a similar plateau after 5 dpa, which is seemingly confirmed by running a single instance of each cell type to 10 dpa. A model is developed to explain the energy evolution.

Nanocrystalline materials have been proposed for use in future fusion reactors due to their high grain boundary density that may act as a sink for irradiation-induced defects. We use molecular dynamics to model collision cascades in nanocrystalline iron and compare the damage evolution to that observed in initially perfect, single crystalline iron. The nanocrystalline material is generated either by Voronoi tessellation or severe plastic shearing. Upon irradiation, the grains in nanocrystalline simulations coarsen, with all ultimately becoming single crystalline above 2 dpa. Above a damage dose of 1 dpa, nanocrystalline cells show a lower dislocation density and lower lattice swelling than their initially pristine counterparts. Experimental X-ray diffraction data is collected on nanocrystalline iron samples subjected to self-ion irradiation. Line profile analysis data agrees with the trends observed in the atomistic simulations, revealing the presence of an irradiation induced annealing process, with a clear reduction in micro-strain with increasing dose. We attempt to determine why some grains in our atomistic simulations grow, while others shrink, by creating a Toy Model that simulates volume exchange between grains based on different hypothesised exchange mechanisms. This suggests that irradiation-induced grain growth is consistent with random growth.

The change in materials properties subjected to irradiation by highly energetic particles strongly depends on the irradiation dose rate. Atomistic simulations can in principle be used to predict microstructural evolution where experimental data is sparse or unavailable, however, fundamental limitations of the method make it infeasible to replicate the experimental timescale spanning from seconds to hours. Here, we present an atomistic simulation method where the motion of vacancies is accelerated, while the fast degrees of freedom are propagated with standard molecular dynamics. The resulting method is free of adjustable parameters and can predict microstructural evolution under irradiation at elevated temperatures. Simulating the microstructural evolution of tungsten under irradiation at dose rates of $10^{-5}$, $10^{-4}$, and $10^{-3}$ dpa/second, we find that increasing the temperature or reducing the dose rate primarily results in a reduction of the steady-state defect concentration, in qualitative agreement with deuterium retention and post-irradiation resistivity recovery experiments. The formation of a nanoscale void is observed if a system initially containing a large dislocation loop is irradiated. We present a minimally simple rate theory model which reproduces the time-dependent defect concentration and volume swelling behaviour obtained from the simulations.

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.

We recast the Howie-Whelan equations for generating simulated transmission electron microscope (TEM) images, replacing the dependence on local atomic displacements with atomic positions only. This allows very rapid computation of simulated TEM images for arbitrarily complex atomistic configurations of lattice defects and dislocations in the dynamical two beam approximation. Large scale massively-overlapping cascade simulations performed with molecular dynamics, are used to generate representative high-dose nanoscale irradiation damage in tungsten at room temperature, and we compare the simulated TEM images to experimental TEM images with similar irradiation and imaging conditions. The simulated TEM shows 'white-dot' damage in weak-beam dark-field imaging conditions, in line with our experimental observations and as expected from previous studies, and in bright-field conditions a dislocation network is observed. In this work we can also compare the images to the nanoscale lattice defects in the original atomic structures, and find that at high dose the white spots are not only created by small dislocation loops, but rather arise from nanoscale fluctuations in strains around curved sections of dislocation lines.

A finite-element method (FEM) model for the Mega-Ampere Spherical Tokamak - Upgrade (MAST-U) fusion tokamak has been developed to evaluate stress and deformations in the full device structure and to assess the stability of the whole tokamak with respect to its simulated exposure to an artificial level of neutron irradiation. Here, we use MAST-U as a proxy for a fusion power plant to explore the level of fidelity made possible by modern supercomputing systems. Gravity and atmospheric pressure were used to test the high-resolution FEM model, involving in excess of 122 million elements. Taking the MASTU fusion plasma as a neutron source, we perform full-scale neutron transport calculations to quantify spatial variations in the neutron flux and assess the neutron radiation exposure across the structure. This is a first step towards applying recently developed multiscale computational tools to evaluate the spectrum of stress in the tokamak, identifying the location of stress concentrations as well as their magnitude. This study provides an example of full fusion device neutronics and FEM simulations which are enabling UKAEA to define computational requirements for modelling a whole fusion power plant as well as for specifying operating conditions for the relevant materials.

Neutrons interacting with atomic nuclei in most of the materials included in the current fusion reactor designs—notably tungsten, ferritic and stainless steels, copper alloys—generate a γ-photon flux that is comparable in magnitude and energy with that of the neutrons, and which in turn generates an intense flux of high-energy electrons in the materials themselves. The occurrence of these γ- and electron fluxes has implications, among others, for the mobility of crystal defects in the materials, for the stability of the plasma, and for the internal heating of reactor components. While a highly spatially resolved numerical calculation of neutron, photon, and electron fluxes on the reactor scale is computationally unfeasible, it is possible to provide estimates based on solutions of Boltzmann's transport equation in a stationary and homogeneous material. Within their limits of validity, these estimates are robust and straightforward and they enable studying photon and electron generation in various materials, under different fission and fusion irradiation conditions and at various locations inside a reactor. We show that the irradiation environment provided by the IFMIF irradiation facility is similar to the expected fusion power plant conditions both in terms of the energy and intensity of photons and electrons generated by the neutrons in tungsten and steels.

The effects of neutron irradiation on materials are often interpreted in terms of atomic recoils, initiated by neutron impacts and producing crystal lattice defects. In addition, there is a remarkable two-step process, strongly pronounced in the medium-weight and heavy elements. This process involves the generation of energetic {\gamma} photons in nonelastic collisions of neutrons with atomic nuclei, achieved via capture and inelastic reactions. Subsequently, high-energy electrons are excited through the scattering of {\gamma} photons by the atomic electrons. We derive and validate equations enabling a fast and robust evaluation of photon and electron fluxes produced by the neutrons in the bulk of materials. The two-step n-{\gamma}-e scattering creates a nonequilibrium dynamically fluctuating steady-state population of high-energy electrons, with the spectra of photon and electron energies extending well into the mega-electron-volt range. This stimulates vacancy diffusion through electron-triggered atomic recoils, primarily involving vacancy-impurity dissociation, even if thermal activation is ineffective. Tungsten converts the energy of fusion or fission neutrons into a flux of {\gamma} radiation at the conversion efficiency approaching 99%, with implications for structural materials, superconductors, and insulators, as well as phenomena like corrosion, and helium and hydrogen isotope retention.

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 fluence, 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 at comparable levels of exposure to radiation.

Undeformed tungsten suffers from a brittleness that makes it unsuitable for applications at low temperatures. Cold-worked tungsten materials such as drawn wires or rolled plates can however show considerable ductility even at low temperatures. The reason for this behaviour is so far not understood. We investigated a series of potassium-doped tungsten wires that were subsequently drawn from one sintered ingot, making them chemically identical. Hence, the properties of the wires could be studied without the influence of different impurity levels. Using transient mechanical tests, namely repeated stress relaxation experiments and strain-rate jump tests, the effective activation volumes V-eff and strain-rate sensitivities m of the wires were determined at room-temperature. Based on the obtained results, it is deduced that the motion of (a(0)/2)<1 1 1> screw dislocations by formation and dissociation of kink-pairs is controlling the rate of plastic deformation in all wires that show plasticity at room temperature. It is hence concluded that the ductility of drawn tungsten wires at low temperatures is not due to a change in the rate-controlling deformation mechanisms, but should be a consequence of the microstructural and textural changes during wire drawing.

The athermal irradiation-induced swelling and creep in iron under the influence of external uniaxial stress were investigated through atomic scale simulations using the creation-relaxation algorithm. The defect relaxation volume density tensors (or eigenstrains) were evaluated as a function of external uniaxial stress. When the dose exceeded the level at which isolated defects were formed, interstitial-type defect clusters were formed with polarization, resulting in crystal growth in the direction where tensile stress was applied, and growth in the other two perpendicular directions when compressive stress was applied. The concentration of vacancies, isolated self-interstitial atoms, Laves phases clusters, and dislocations in the microstructure were largely unaffected by external stress up to +/- 1 GPa. Biased crystal growth was primarily attributed to the anisotropic formation of new lattice planes through the coalescence of interstitial defect clusters, leading to plastic deformation depending on the direction and magnitude of the external stress.

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.

Effects of neutron irradiation on materials are often interpreted in terms of atomic recoils, initiated by neutron impacts and producing crystal lattice defects. We find that, in addition, there is a remarkable two-step process, strongly pronounced in heavy elements, involving the generation of energetic γ -photons in non-elastic collisions of neutrons with atomic nuclei followed by the production of high-energy electrons through the scattering of γ -photons by the atomic electrons. This two-step scattering creates a non-equilibrium steady-state population of high-energy electrons in the bulk of the material, which bombard atoms and stimulate vacancy diffusion, resulting in a variety of driven athermal microstructural reactions including the enhanced recombination of radiation defects. We find that tungsten converts the energy of fusion or fission neutrons into a flux of γ -radiation and subsequently high-energy electrons with the conversion efficiency approaching 99%, explaining the low defect content observed at moderate temperatures.

Using the notion of eigenstrain produced by the defects formed in a material exposed to high energy neutron irradiation, we develop a method for computing macroscopic elastic stress and strain arising in components of a fusion power plant during operation. In a microstructurally isotropic material, the primary cause of macroscopic elastic stress and strain fields is the spatial variation of neutron exposure. We show that under traction-free boundary conditions, the volume-average elastic stress always vanishes, signifying the formation of a spatially heterogeneous stress state, combining compressive and tensile elastic deformations at different locations in the same component, and resulting solely from the spatial variation of radiation exposure. Several case studies pertinent to the design of a fusion power plant are analysed analytically and numerically, showing that a spatially varying distribution of defects produces significant elastic stresses in ion-irradiated thin films, pressurised cylindrical tubes and breeding blanket modules.