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Irradiation-induced ductility loss is a major concern facing structural steels in next-generation nuclear reactors. Currently, the mechanisms for this are unclear but crucial to address for the design of reactor components. Here, the deformation characteristics around nanoindents in Fe and Fe10Cr irradiated with Fe ions to $\sim$1 displacement-per-atom at 313 K are non-destructively studied. Deformation localisation in the irradiated materials is evident from the increased pile-up height and slip step formation, measured by atomic force microscopy. From 3D X-ray Laue diffraction, measurements of lattice rotation and strain fields near the indent site show a large confinement, over 85%, of plasticity in the irradiated material. We find that despite causing increased irradiation hardening, Cr content has little effect on the irradiation-induced changes in pile-up topography and deformation fields. The results demonstrate that varying Cr content in steels has limited impact on retaining strain hardening capacity and reducing irradiation-induced embrittlement., Comment: 23 pages, 9 figures (1 graphical abstract, 4 figures in main text, 4 figures in supplementary file)

We investigate the dynamics of chemical reaction networks (CRNs) with the goal of deriving an upper bound on their reaction rates. This task is challenging due to the nonlinear nature and discrete structure inherent in CRNs. To address this, we employ an information geometric approach, using the natural gradient, to develop a nonlinear system that yields an upper bound for CRN dynamics. We validate our approach through numerical simulations, demonstrating faster convergence in a specific class of CRNs. This class is characterized by the number of chemicals, the maximum value of stoichiometric coefficients of the chemical reactions, and the number of reactions. We also compare our method to a conventional approach, showing that the latter cannot provide an upper bound on reaction rates of CRNs. While our study focuses on CRNs, the ubiquity of hypergraphs in fields from natural sciences to engineering suggests that our method may find broader applications, including in information science., Comment: 11 pages

Severe plastic deformation changes the microstructure and properties of steels, which may be favourable for their use in structural components of nuclear reactors. In this study, high-pressure torsion (HPT) was used to refine the grain structure of Eurofer-97, a ferritic/ martensitic steel. Electron microscopy and X-ray diffraction were used to characterise the microstructural changes. Following HPT, the average grain size reduced by a factor of $\sim$ 30, with a marked increase in high-angle grain boundaries. Dislocation density also increased by more than one order of magnitude. The thermal stability of the deformed material was investigated via in-situ annealing during synchrotron X-ray diffraction. This revealed substantial recovery between 450 K - 800 K. Irradiation with 20 MeV Fe-ions to $\sim$ 0.1 dpa caused a 20% reduction in dislocation density compared to the as-deformed material. However, HPT deformation prior to irradiation did not have a significant effect in mitigating the irradiation-induced reductions in thermal diffusivity and surface acoustic wave velocity of the material. These results provide a multi-faceted understanding of the changes in ferritic/martensitic steels due to severe plastic deformation, and how these changes can be used to alter material properties., Comment: 59 pages, 19 figures

Ferritic/martensitic steels will be used as structural components in next generation nuclear reactors. Their successful operation relies on an understanding of irradiation-induced defect behaviour in the material. In this study, Fe and FeCr alloys (3-12%Cr) were irradiated with 20 MeV Fe-ions at 313 K to doses ranging between 0.00008 dpa to 6.0 dpa. This dose range covers six orders of magnitude, spanning low, transition and high dose regimes. Lattice strain and hardness in the irradiated material were characterised with micro-beam Laue X-ray diffraction and nanoindentation, respectively. Irradiation hardening was observed even at very low doses (0.00008 dpa) and showed a monotonic increase with dose up to 6.0 dpa. Lattice strain measurements of samples at 0.0008 dpa allow the calculation of equivalent Frenkel pair densities and corrections to the Norgett-Robinson-Torrens (NRT) model for Fe and FeCr alloys at low dose. NRT efficiency for FeCr is 0.2, which agrees with literature values for high irradiation energy. Lattice strain increases up to 0.8 dpa and then decreases when the damage dose is further increased. The strains measured in this study are lower and peak at a larger dose than predicted by atomistic simulations. This difference can be explained by taking temperature and impurities into account., Comment: 49 pages, 9 figures, 3 tables

Van der Waals atomic solids of noble gases on metals at cryogenic temperatures were the first experimental examples of two-dimensional systems. Recently such structures have also been created on surfaces under encapsulation by graphene, allowing studies at elevated temperatures through scanning tunneling microscopy. However, for this technique, the encapsulation layer often obscures the actual arrangement of the noble gas atoms. Here, we create Kr and Xe clusters in between two suspended graphene layers, and uncover their atomic structure through direct imaging with transmission electron microscopy. We show that small crystals (N<9) arrange as expected based on the simple non-directional van der Waals interaction. Crystals larger than this show some deviations for the outermost atoms, possibly enabled by deformations in the encapsulating graphene lattice. We further discuss the dynamics of the clusters within the graphene sandwich, and show that while all Xe clusters with up to N~100 remain solid, Kr clusters with already N~16 turn occasionally fluid under our experimental conditions with an estimated pressure of ca. 0.3 GPa. This study opens a way for the so-far unexplored frontier of encapsulated two-dimensional van der Waals solids with exciting possibilities for fundamental condensed matter physics research and possible applications in quantum information technology., Comment: 31 pages, 14 figures, including the supplement

We investigated the effect of nano-structuring by high-pressure torsion (HPT) on the irradiation performance of Eurofer-97. Material was deformed to shear strains from 0 to ~230, and then exposed to Fe$^{3+}$ irradiation doses of 0.01 and 0.1 displacements-per-atom (dpa). Nanoindentation hardness increases monotonically with deformation, and with irradiation for the undeformed material. For both damage levels, less irradiation hardening is observed in severely deformed material. This effect is most prominent in the strain range ~60 to ~160, suggesting that nano-structuring may provide an approach for reducing irradiation hardening., Comment: 11 pages, 4 figures, Credit author statement included

One of the main complications for the interpretation of reflectance spectra of airless planetary bodies is surface alteration by space weathering caused by irradiation by solar wind and micrometeoroid particles. We aim to evaluate the damage to the samples from H and laser irradiation and relate it to the observed alteration in the spectra. We used olivine (OL) and pyroxene (OPX) pellets irradiated by 5 keV H ions and individual fs laser pulses and measured their visible (VIS) and near-infrared (NIR) spectra. We observed the pellets with scanning and transmission electron microscopy. We studied structural, mineralogical, and chemical modifications in the samples and connected them to changes in the reflectance spectra. In both minerals, H irradiation induces partially amorphous sub-surface layers containing small vesicles. In OL pellets, these vesicles are more tightly packed than in OPX ones. Related spectral change is mainly in the VIS spectral slope. Changes due to laser irradiation are mostly dependent on material's melting temperature. Only the laser-irradiated OL contains nanophase Fe particles, which induce detectable spectral slope change throughout the measured spectral range. Our results suggest that spectral changes at VIS-NIR wavelengths are mainly dependent on thickness of (partially) amorphous sub-surface layers. Amorphisation smooths microroughness, increasing the contribution of volume scattering and absorption over surface scattering. Soon after exposure to the space environment, the appearance of partially amorphous sub-surface layers results in rapid changes in the VIS spectral slope. In later stages (onset of micrometeoroid bombardment), we expect an emergence of nanoparticles to also mildly affect the NIR spectral slope. An increase in dimensions of amorphous layers and vesicles in the more space-weathered material will only cause band-depth variation and darkening., Comment: 9 pages, 8 figures, 1 table. Abstract was modified to comply with the required maximum number of characters of arXiv abstracts

Tungsten is a promising candidate material for plasma-facing armour components in future fusion reactors. A key concern is irradiation-induced degradation of its normally excellent thermal transport properties. In this comprehensive study, thermal diffusivity degradation in ion-implanted tungsten and its evolution from room temperature (RT) to 1073 K is considered. Five samples were exposed to 20 MeV self-ions at RT to achieve damage levels ranging from 3.2 x 10-4 to 3.2 displacements per atom (dpa). Transient grating spectroscopy with insitu heating was then used to study thermal diffusivity evolution as a function of temperature. Using a kinetic theory model, an equivalent point defect density is estimated from the measured thermal diffusivity. The results showed a prominent recovery of thermal diffusivity between 450 K and 650 K, which coincides with the onset of mono-vacancy mobility. After 1073 K annealing samples with initial damage of 3.2 x 10-3 dpa or less recover close to the pristine value of thermal diffusivity. For doses of 3.2 x 10-2 dpa or higher, on the other hand, a residual reduction in thermal diffusivity remains even after 1073 K annealing. Transmission electron microscopy reveals that this is associated with extended, irradiation-induced dislocation structures that are retained after annealing. A sensitivity analysis shows that thermal diffusivity provides an efficient tool for assessing total defect content in tungsten up to 1000 K.

Space weathering is a process that changes the surface of airless planetary bodies. Prime space weathering agents are solar wind irradiation and micrometeoroid bombardment. These processes alter planetary reflectance spectra and often modify their compositional diagnostic features. In this work we focused on simulating and comparing the spectral changes caused by solar wind irradiation and by micrometeoroid bombardment to gain a better understanding of these individual space weathering processes. We used olivine and pyroxene pellets as proxies for planetary materials. To simulate solar wind irradiation we used hydrogen, helium, and argon ions with energies from 5 to 40 keV and fluences of up to $10^{18}$ particles/cm$^2$. To simulate micrometeoroid bombardment we used individual femtosecond laser pulses. We analysed the corresponding evolution of different spectral parameters, which we determined by applying the Modified Gaussian Model, and we also conducted principal component analysis. The original mineralogy of the surface influences the spectral evolution more than the weathering agent, as seen from the diverse evolution of the spectral slope of olivine and pyroxene upon irradiation. The spectral slope changes seen in olivine are consistent with observations of A-type asteroids, while the moderate to no slope changes observed in pyroxene are consistent with asteroid (4) Vesta. We also observed some differences in the spectral effects induced by the two weathering agents. Ions simulating solar wind have a smaller influence on longer wavelengths of the spectra than laser irradiation simulating micrometeoroid impacts. This is most likely due to the different penetration depths of ions and laser pulses. Our results suggest that in some instances it might be possible to distinguish between the contributions of the two agents on a weathered surface., Comment: Astronomy and Astrophysics

Understanding the mechanisms of plasticity in structural steels is essential for the operation of next-generation fusion reactors. Elemental composition, particularly the amount of Cr present, and irradiation can have separate and synergistic effects on the mechanical properties of ferritic/martensitic steels. The study of ion-irradiated FeCr alloys is useful for gaining a mechanistic understanding of irradiation damage in steels. Previous studies of ion-irradiated FeCr did not clearly distinguish between the nucleation of dislocations to initiate plasticity, and their propagation through the material as plasticity progresses. In this study, Fe3Cr, Fe5Cr, and Fe10Cr were irradiated with 20 MeV Fe$^{3+}$ ions at room temperature to nominal doses of 0.01 dpa and 0.1 dpa. Nanoindentation was carried out with Berkovich and spherical indenter tips to study the nucleation of dislocations and their subsequent propagation. The presence of irradiation-induced defects reduced the theoretical shear stress and barrier for dislocation nucleation. The presence of Cr further enhanced this effect due to increased retention of irradiation defects. However, this combined effect is still small compared to dislocation nucleation from pre-existing sources such as Frank-Read sources and grain boundaries. The yield strength, an indicator of dislocation mobility, of FeCr increased with irradiation damage and Cr. The increased retention of irradiation defects due to the presence of Cr also further increased the yield strength. Reduced work hardening capacity was also observed following irradiation. The synergistic effects of Cr and irradiation damage in FeCr appear to be more important for the propagation of dislocations, rather than their nucleation., Comment: 32 pages, 10 figures

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

Ion-irradiated FeCr alloys are useful for understanding and predicting neutron-damage in the structural steels of future nuclear reactors. Previous studies have largely focused on the structure of irradiation-induced defects, probed by transmission electron microscopy (TEM), as well as changes in mechanical properties. Across these studies, a wide range of irradiation conditions has been employed on samples with different processing histories, which complicates the analysis of the relationship between defect structures and material properties. Furthermore, key properties, such as irradiation-induced changes in thermal transport and lattice strain, are little explored. Here we present a systematic study of Fe3Cr, Fe5Cr and Fe10Cr binary alloys implanted with 20 MeV Fe$^{3+}$ ions to nominal doses of 0.01 dpa and 0.1 dpa at room temperature. Nanoindentation, transient grating spectroscopy (TGS) and X-ray micro-beam Laue diffraction were used to study the changes in hardness, thermal diffusivity and strain in the material as a function of damage and Cr content. Our results suggest that Cr leads to an increased retention of irradiation-induced defects, causing substantial changes in hardness and lattice strain. However, thermal diffusivity varies little with increasing damage and instead degrades significantly with increasing Cr content in the material. We find significant lattice strains even in samples exposed to a nominal displacement damage of 0.01 dpa. The defect density predicted from the lattice strain measurements is significantly higher than that observed in previous TEM studies, suggesting that TEM may not fully capture the irradiation-induced defect population.

Developing a comprehensive understanding of the modification of material properties by neutron irradiation is important for the design of future fission and fusion power reactors. Self-ion implantation is commonly used to mimic neutron irradiation damage, however an interesting question concerns the effect of ion energy on the resulting damage structures. The reduction in the thickness of the implanted layer as the implantation energy is reduced results in the significant quandary: Does one attempt to match the primary knock-on atom energy produced during neutron irradiation or implant at a much higher energy, such that a thicker damage layer is produced? Here we address this question by measuring the full strain tensor for two ion implantation energies, 2 MeV and 20 MeV in self-ion implanted tungsten, a critical material for the first wall and divertor of fusion reactors. A comparison of 2 MeV and 20 MeV implanted samples is shown to result in similar lattice swelling. Multi-reflection Bragg coherent diffractive imaging (MBCDI) shows that implantation induced strain is in fact heterogeneous at the nanoscale, suggesting that there is a non-uniform distribution of defects, an observation that is not fully captured by micro-beam Laue diffraction. At the surface, MBCDI and high-resolution electron back-scattered diffraction (HR-EBSD) strain measurements agree quite well in terms of this clustering/non-uniformity of the strain distribution. However, MBCDI reveals that the heterogeneity at greater depths in the sample is much larger than at the surface. This combination of techniques provides a powerful method for detailed investigation of the microstructural damage caused by ion bombardment, and more generally of strain related phenomena in microvolumes that are inaccessible via any other technique., Comment: Please refer to the supplementary information and movies SM1-3 for data visualisation

Understanding defect production and evolution under irradiation is a long-standing multi-scale problem. Conventionally, experimental examination of irradiation-induced defects (IIDs) has mainly relied on transmission electron microscopy (TEM), which offers high spatial resolution but requires destructive sample preparation. Furthermore, limited field of view and low strain sensitivity make multi-scale characterisation and quantitative strain measurements difficult. Here we explore the potential of using advanced techniques in the scanning electron microscope (SEM) to non-destructively probe irradiation damage at the surface of bulk materials. Electron channelling contrast imaging (ECCI) is used to image nano-scale irradiation-induced defects in 20 MeV self-ion irradiated tungsten, the main candidate material for fusion reactor armour. The results show an evolution of the damage microstructure from uniformly and randomly distributed nano-scale defects at 0.01 dpa (displacement per atom) to string structures extending over hundreds of nanometres at 1 dpa. Cross-correlation based high-resolution EBSD (HR-EBSD) is used to probe the lattice strain fields associated with IIDs. While there is little strain fluctuation at 0.01 dpa, significant heterogeneity in the lattice strains is observed at 0.1 dpa, increasing with dose until saturation at 0.32 dpa. The characteristic length scale of strain fluctuations is ~500 nm. Together, ECCI and HR-EBSD reveal a transition from a structure where defects are disordered to a structure with long-range order driven by elastic interactions between pre-existing defects and new cascade damage. This study demonstrates that SEM provides an attractive tool for rapid throughput, non-destructive, multi-scale and multi-aspect characterisation of irradiation damage.

Predicting the dramatic changes in material properties caused by irradiation damage is key for the design of future nuclear fission and fusion reactors. Self-ion implantation is an attractive tool for mimicking the effects of neutron irradiation. However, the damaged layer of implanted samples is only few microns thick, making it difficult to estimate macroscopic properties. Here we address this challenge using a combination of experimental and modelling techniques. We concentrate on self-ion-implanted tungsten, the front-runner for fusion armour components and a prototypical bcc material. To capture dose-dependent evolution of properties, we experimentally characterise samples with damage levels from 0.01 to 1 dpa. Spherical nano-indentation of <001> grains shows hardness increasing up to a dose of 0.032 dpa, beyond which it saturates. AFM measurements show pile-up increasing up to the same dose, beyond which large pile-up and slip-steps are seen. Based on the observations we develop a crystal plasticity (CPFE) model for the irradiated material. It captures irradiation-induced hardening followed by strain-softening through interaction of irradiation-defects and gliding dislocations. Shear resistance of irradiation-defects is derived from TEM observations of similarly irradiated samples. Nano-indentation of pristine and implanted tungsten of doses 0.01, 0.1, 0.32 and 1 dpa is simulated. Two model parameters are fitted to the experimental results of the 0.01 dpa sample and are kept unchanged for all other doses. Peak load, indent surface profiles and damage saturation predicted by the CPFE model closely match experimental observations. Predicted lattice distortions and dislocation distributions around indents agree with corresponding measurements from HR-EBSD. Finally, the CPFE model is used to predict the macroscopic stress-strain response of similarly irradiated bulk tungsten material.

Using transient grating spectroscopy (TGS) we measure the thermal diffusivity of tungsten exposed to different levels of 20 MeV self-ion irradiation. Damage as low as 3.2 x 10^-4 displacements per atom (dpa) causes a measurable reduction in thermal diffusivity. Doses of 0.1 dpa and above, up to 10 dpa, give a degradation of around 55% from the pristine value at room temperature. Using a kinetic theory model, the density of irradiation-induced point defects is estimated based on the measured changes in thermal diffusivity as a function of dose. These predictions are compared with point defect and dislocation loop densities observed in transmission electron microscopy (TEM). Molecular dynamics (MD) predictions are combined with the TEM observations to estimate the density of point defects associated with defect clusters too small to be probed by TEM. When these "invisible" defects are accounted for, the total point defect density agrees well with that estimated from TGS for a range of doses spanning 3 orders of magnitude. Kinetic theory modelling is also used to estimate the thermal diffusivity degradation expected due to TEM-visible and invisible defects. Finely distributed invisible defects appear to play a much more important role in the thermal diffusivity reduction than larger TEM-visible dislocation loops. This work demonstrates the capability of TGS, in conjunction with kinetic theory models, to provide rapid, quantitative insight into defect densities and property evolution in irradiated materials., Comment: The following article has been revised and submitted to Acta Materialia. After it is published, it will be found at https://www.journals.elsevier.com/acta-materialia