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  1. Assessment of the literature about Be-W mixed material layer formation in the fusion reactor environment

    Abstract All plasma facing surfaces in a fusion reactor, whether initially pure or an alloy, will rapidly evolve into a mixed material due to plasma-induced erosion, migration and redeposition. Beryllium (Be) erosion from the main chamber, and its transport and deposition on to a tungsten (W) divertor results in the growth of mixed Be-W layers, which can evolve to form beryllides. These Be-W mixed materials exhibit generally less desirable properties than pure tungsten or pure beryllium, such as lower melting points. In order to better understand the parameter space for growth of these alloys, this paper reviews the literature onmore » Be-W mixed material formation experiments – in magnetically confined fusion reactors, in linear plasma test stands, and during thin- film deposition – and on computational modeling of Be-W interactions, as well as briefly assesses the Be-W growth kinetics. We conclude that the following kinetic steps drive the material mixing: adsorption of the implanted/deposited ion on the metal surface; diffusion of the implanted/deposited ion from surface into the bulk, which is accelerated by defects; and loss of deposited material through erosion. Adsorption dominates (or prevents) material mixing in thin-film deposition experiments, whereas diffusion drives material mixing in plasma exposures due to the energetic ion implantation.« less
  2. Development of multi-scale computational frameworks to solve fusion materials science challenges

    Over the past two decades, the US-DOE has funded multiple projects that rely on high-performance computing and exascale computing platforms to accelerate scientific discoveries and address grand scientific challenges, such as harnessing fusion energy. In this article, we review in detail one of these efforts aimed at enhancing our capability to model plasma-facing materials subject to plasma and high-energy ion/neutron irradiation. The plasma surface interactions project has built a multi-scale modeling framework where many of the plasma- and high-energy ion/neutron irradiation-induced effects occurring in tungsten are explored. Here, this knowledge is used to develop atomistically-informed, high-fidelity continuum and meso-scale modelsmore » that can be validated against experiments. We review the developments within this project, with attention to experimental validation efforts, and specifically highlight activities associated with: helium bubble bursting and equation of state, and hydrogen-helium interactions in tungsten; atomistically-informed model development for beryllium-tungsten material mixing; coupling of scrape-of-layer plasma, sheath and material models; and coupling of stochastic cluster-dynamics and crystal plasticity models to address radiation effects in tungsten under stress. Finally, we present how the project is preparing for future computational architectures, for instance through efforts to adapt atomistic methods to exascale computing.« less
  3. Helium bubble size effects on the surface morphological response of plasma-facing tungsten

    Abstract We report a simulation study on the effects of helium (He) bubble size on the morphological evolution and pattern formation on the surface of tungsten used as a plasma-facing component (PFC) in nuclear fusion devices. We have carried out a systematic investigation based on self-consistent dynamical simulations of surface morphological evolution according to an atomistically-informed, 3D continuum-scale model that captures well the relevant length and time scales of surface nanostructure formation in PFC tungsten. The model accounts for PFC surface diffusion, driven by the biaxial compressive stress originating from the over-pressurized He bubbles in the near-surface region of PFCmore » tungsten as a result of He plasma exposure, combined with the formation of self-interstitial atoms in tungsten that diffuse toward the PFC surface and the flux of surface adatoms generated as a result of surface vacancy-adatom pair formation upon He implantation; this transport of surface adatoms contributes to the anisotropic growth of surface nanostructural features due to the different rates of adatom diffusion along and across step edges of islands on the tungsten surface. Our detailed analysis reveals that varying the average He bubble size plays an important role in the PFC surface growth kinetics as well as the resulting surface topography. Specifically, we find that an increase in the He bubble size leads to a deceleration in the growth rate of the tungsten nanotendrils that emanate from the PFC surface. We also find that the separation distance between the resulting surface features increases with increasing He bubble size, as well as over time. This coarsening effect is a thermally activated process resulting in an accurate description of the temperature dependence of the average surface feature separation by an Arrhenius relation.« less
  4. Impact of Soret effect on hydrogen and helium retention in PFC tungsten under ELM-like conditions

    Abstract In our previous work, we have demonstrated using nonequilibrium molecular-dynamics simulations that the fluxes of helium and self-interstitial atoms in the presence of a thermal gradient in tungsten are directed opposite to the heat flux, indicating that species transport is governed by a Soret effect, namely, thermal-gradient-driven diffusion, characterized by a negative heat of transport that drives species transport uphill, i.e., from the cooler to the hot regions of the tungsten sample. In this work, the findings of our thermal and species transport analysis have been implemented in our cluster-dynamics code, Xolotl, which has been used to compute temperaturemore » and species profiles over spatiotemporal scales representative of plasma-facing component (PFC) tungsten under typical reactor operating conditions, including extreme heat loads at the plasma-facing surface characteristic of plasma instabilities that induce edge localized modes (ELMs). We demonstrate that the steady-state species profiles, when properly accounting for the Soret effect, vary significantly from those where temperature-gradient-driven transport is not accounted for and discuss the implications of such a Soret effect on the response to plasma exposure of plasma-facing tungsten. Although our cluster dynamics simulations do not yet include self-clustering of helium or hydrogen blister formation, our simulation results show that the Soret effect substantially reduces helium and hydrogenic species retention inside PFC tungsten.« less
  5. Effects of surface vacancy-adatom pair formation on PFC tungsten surface morphological response

    We report a simulation study of the effect of He-irradiation-induced surface vacancy-adatom pair formation on the surface morphological evolution of plasma-facing component (PFC) tungsten and examine a number of factors that impact such evolution. Our analysis is based on self-consistent dynamical simulations according to an atomistically-informed, continuum-scale surface evolution model that has been developed following a hierarchical multiscale modeling strategy and can access the spatiotemporal scales of relevance to fuzz formation. The model accounts for the flux of surface adatoms generated as a result of the surface vacancy-adatom pair formation effect upon He implantation, which contributes to the anisotropic growthmore » of surface nanostructural features due to the different rates of adatom diffusion along and across step edges of islands on the tungsten surface. We have carried out atomic-scale computations of optimal diffusion pathways along and across island step edges on the W(110) surface and calculated Ehrlich-Schwoebel (ES) barriers in adatom diffusion along and across such step edges. This aspect of surface adatom diffusion contributes to anisotropic surface atomic fluxes, terrace and step diffusive currents, and has been incorporated into our PFC surface evolution model, which predicts the formation of preferentially aligned nanoridge stripe patterns on the PFC surface. We establish that these anisotropic diffusive currents accelerate nanotendril growth on the PFC surface and the onset of surface nanostructure pattern formation. We also explore systematically the dependence of the PFC surface morphological response on the surface temperature and He ion incident flux, characterize in detail the resulting surface topographies and growth kinetics, and compare the predicted surface morphologies with experimental observations. Our simulation predictions for the emerging surface nanostructure patterns under certain plasma exposure conditions are consistent with experimental findings in the literature.« less
  6. Hole formation effect on surface morphological response of plasma-facing tungsten

    We report simulation results on the effect of helium (He) bubble bursting-mediated surface hole formation on the surface morphological response of tungsten plasma-facing components (PFCs) in nuclear fusion devices. Our analysis is based on an atomistically informed, continuum-scale model, which is capable of accessing the spatiotemporal scales relevant to the fuzz nanostructure formation process on the surface of PFC tungsten. Our simulations account, in an empirical fashion, for two types of subsurface bubble dynamical phenomena in the nanobubble region of PFC tungsten during He plasma irradiation, involving bubble bursting and surface crater formation. We demonstrate that the hole formation effectmore » on the PFC tungsten surface accelerates the growth rate of nanotendrils and the onset of fuzz formation. As a result, the predicted incubation time for surface nanotendril growth is shortened, in agreement with experimental data of incubation fluence at comparable plasma exposure conditions. We also explore systematically the dependence of the PFC surface morphological response on the areal density of holes introduced at regular time intervals onto the He-implanted tungsten surface, a parameter in our analysis that serves as a proxy for the rate of He bubble bursting. More importantly, our simulations capture fine surface features in the PFC tungsten surface morphology and predict that the average spacing between nanotendrils is on the order of 100  nm, consistent with the experimental findings.« less
  7. Thermal gradient effect on helium and self-interstitial transport in tungsten

    First-wall materials in a fusion reactor are expected to withstand harsh conditions, with high heat and particle fluxes that modify the materials microstructure. These fluxes will create strong gradients of temperature and concentration of diverse species. Besides the He ash and the hydrogenic species, neutron particles generated in the fusion reaction will collide with the material creating intrinsic defects, such as vacancies, self-interstitials atoms (SIAs), and clusters of such point defects. These defects and the He atoms will then migrate in the presence of the aforementioned gradients. In this study, we use nonequilibrium molecular dynamics to analyze the transport ofmore » He and SIAs in the presence of a thermal gradient in tungsten. We observe that, in all cases, the defects and impurity atoms tend to migrate toward the hot regions of the tungsten sample. The resulting species concentration profiles are exponential distributions, rising toward the hot regions of the sample, in agreement with irreversible thermodynamics analysis. For both He atoms and SIAs, we find that the resulting species flux is directed opposite to the heat flux, indicating that species transport is governed by a Soret effect (thermal-gradient-driven diffusion) characterized by a negative heat of transport that drives species diffusion uphill (from the cooler to the hot regions of the sample). We demonstrate that the steady-state species profiles obtained accounting for the Soret effect vary significantly from those where temperature-gradient-driven transport is not considered and discuss the implications of such a Soret effect on the response to plasma exposure of plasma-facing tungsten.« less
  8. Effects of elastic softening and helium accumulation kinetics on surface morphological evolution of plasma-facing tungsten

    Based on a continuous-domain model, capable of accessing the spatiotemporal scales relevant to fuzz formation on the surface of plasma-facing component (PFC) tungsten, we report self-consistent simulation results that elucidate the effects of elastic softening and helium (He) accumulation kinetics on the surface morphological response of PFC tungsten. The model accounts for the softening of the elastic moduli in the near-surface region of PFC tungsten, including both thermal softening at high temperature and softening due to He accumulation upon He implantation. The dependence of the elastic moduli on the He content follows an exponential scaling relation predicted by molecular-dynamics simulations,more » while the He content in the near-surface region of PFC tungsten evolves according to a first-order saturation kinetics, consistent with experimental and simulation results reported in the literature. We establish that this elastic softening accelerates both nanotendril growth on the PFC surface and the onset of fuzz formation. We also explore the role of the rate of He accumulation to a saturation level in the near-surface region of irradiated tungsten in the onset of fuzz formation. For PFC tungsten surfaces such as W(110) where, under typical irradiation conditions, the characteristic time scale for stress-driven surface diffusion is comparable to the characteristic time scale for He accumulation, we find that accelerating the rate of He accumulation accelerates the growth rate of nanotendrils emanating from the surface. Additionally, we present a systematic parametric study of the PFC surface morphological response to explore its dependence on the He accumulation kinetics that is controlled by the irradiation conditions for low-energy implantation. Finally, we introduce an incubation time for nanotendril growth on the PFC surface, a concept equivalent to that of incubation fluence discussed in the literature, to predict and explain the minimum exposure time required to observe fuzz formation on PFC tungsten surfaces.« less
  9. On the origin of ‘fuzz’ formation in plasma-facing materials

    Tungsten, the material used in the plasma-facing components (PFCs) of nuclear fusion reactors, develops a fuzz-like surface morphology under typical reactor operating conditions. This fragile 'fuzz' surface nanostructure adversely affects reactor performance and operation. Developing predictive models, capable of simulating the spatiotemporal scales relevant to the fuzz formation process is essential for understanding the growth of such extremely complex surface features and improving PFC and reactor performance. Here, we report the development of an atomistically-informed, continuous-domain model for the onset of fuzz formation in helium plasma-irradiated tungsten and validate the model by comparing its predictions with measurements from carefully designedmore » experiments. Our study demonstrates that fuzz forms in response to stress induced in the near-surface region of PFCs as a result of plasma exposure and helium gas implantation. In conclusion, our model sets the stage for detailed descriptions of this complex fuzz formation phenomenon and similar phenomena observed in other materials.« less
  10. Surface nanopattern formation due to current-induced homoepitaxial nanowire edge instability

    Physical nanopatterning based on a precise control of macroscopic forcing is an essential tool of nanoscale science and technology. Using an externally applied electric field as the macroscopic force, we report here a computational study on the formation of surface nanopatterns consisting of single-layer homoepitaxial islands as a result of a morphological instability that can occur under edge electromigration conditions on the straight edge of a single-layer nanowire grown epitaxially on a crystalline substrate. Direct dynamical simulations based on a model that has been validated experimentally for the Ag/Ag system show that the current-induced nanowire edge instability causes the breakupmore » of the nanowire and leads to the formation of uniformly distributed islands, arranged in linear or V-shaped arrays, which are uniformly sized with nanoscale dimensions. The simulation results are supported by linear stability theory and demonstrate that the geometrical features of the island patterns and the island sizes can be controlled precisely by controlling the electric field direction with respect to the nanowire axis and the electric field strength. Our findings have important implications for developing physical nanopatterning approaches toward enabling future nanofabrication technologies.« less
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