Equation of state for He bubbles in W and model of He bubble growth and bursting near W{100} surfaces derived from molecular dynamics simulations.

Molecular dynamics (MD) simulations are performed to derive an equation of state (EOS) for helium (He) bubbles in tungsten (W) and to study the growth of He bubbles under a W(100) surface until they burst. We study the growth as a function of the initial nucleation depth of the bubbles. During growth, successive loop-punching events are observed, accompanied by shifts in the depth of the bubble towards the surface. Subsequently, the MD data are used to derive models that describe the conditions that cause the loop punching and bursting events. Simulations have been performed at 500, 933, 1500, 2000, and 2500 K to fit the parameters in the models. To compute the pressure in the bubble at the loop punching and bursting events from the models, we derive an EOS for He bubbles in tungsten with an accompanying volume model to compute the bubble volume for a given number of vacancies ([Formula: see text]), He atoms ([Formula: see text]), and temperature (T). To derive the bubble EOS, we firstly derive the EOS for a free He gas. The derived free-gas EOS can accurately predict all MD data included in the analysis (which span up to 54 GPa at 2500 K). Subsequently, the bubble EOS is derived based on the free-gas EOS by correcting the gas density to account for the interaction between He and W atoms. The EOS for the bubbles is fitted to data from MD simulations of He bubbles in bulk W that span a wide range of gas density and sizes up to about 3 nm in diameter. The pressure of subsurface bubbles at the loop punching events as calculated using the bubble-EOS and the volume model agrees well with the pressure obtained directly from the MD simulations. In the loop punching model, for bubbles consisting of [Formula: see text] vacancies and [Formula: see text] helium atoms, the [Formula: see text] ratio that causes the event, the resulting increase in [Formula: see text], and the associated shift of the bubble depth are formulated as a function of [Formula: see text] and T. In the bursting model, a bubble must simultaneously reach a certain depth and [Formula: see text] ratio in order to burst. The burst depth and [Formula: see text] are also modeled as a function of [Formula: see text] and T. The majority of the loop punching events occur at bubble pressures between 20 and 60 GPa, depending on the bubble size and temperature. The larger the bubble and the higher the temperature, the lower the bubble pressure. Furthermore, our results indicate that at a higher temperature, a bubble can burst from a deeper region.

Effect of helium flux on near-surface helium accumulation in plasma-exposed tungsten.

We report results of object kinetic Monte Carlo (OKMC) simulations to understand the effect of helium flux on the near-surface helium accumulation in plasma-facing tungsten, which is initially pristine, defect-free, and has a (100) surface orientation. These OKMC simulations are performed at 933 K for fluxes ranging from 1022to 4 × 1025He/m2 s with 100 eV helium atoms impinging on a (100) surface up to a maximum fluence of 4 × 1019He/m2. In the near-surface region, helium clusters interact elastically with the free surface. The interaction is attractive and results in the drift of mobile helium clusters towards the surface as well as increased trap mutation rates. The associated kinetics and energetics of the above-mentioned processes obtained from molecular dynamics simulations are also considered. The OKMC simulations indicate that in pristine tungsten, as the flux decreases, the retention of implanted helium decreases, and its depth distribution shifts to deeper below the surface. Furthermore, the fraction of retained helium diffusing into the bulk increases as well, so much so that for the flux of 1022He/m2 s, almost all of the retained helium diffused into the bulk with minimal/negligible near-surface helium accumulation. At a given flux, with increasing fluence, the fraction of retained helium initially decreases and then starts to increase after reaching a minimum. The occurrence of the retention minimum shifts to higher fluences as the flux decreases. Although the near-surface helium accumulation spreads deeper into the material with decreasing flux and increasing fluence, the spread appears to saturate at depths between 80 and 100 nm. We present a detailed analysis of the influence of helium flux on the size and depth distribution of total helium and helium bubbles.

Theoretical Model of Helium Bubble Growth and Density in Plasma-Facing Metals.

We present a theoretically-motivated model of helium bubble density as a function of volume for high-pressure helium bubbles in plasma-facing tungsten. The model is a good match to the empirical correlation we published previously [Hammond et al., Acta Mater. 144, 561-578 (2018)] for small bubbles, but the current model uses no adjustable parameters. The model is likely applicable to significantly larger bubbles than the ones examined here, and its assumptions can be extended trivially to other metals and gases. We expect the model to be broadly applicable and useful in coarse-grained models of gas transport in metals.

Thermal neutron scattering cross sections of 238U and 235U in the γ phase.

The development of metallic, low-enrichment uranium fuels requires accurate prediction of their neutron transport properties and reactivity parameters, which in turn require thermal neutron scattering data. Accurate prediction of thermal neutron scattering data, including thermal cross sections, requires knowledge of the phonon scattering properties of the medium, but such matrix binding effects in next-generation fuels such as U-Mo, U-Zr, and U-Si are typically neglected because these effects are often difficult to measure or calculate. Using molecular dynamics simulations with previously published interatomic potentials, we calculate the phonon dispersion relations and phonon densities of states for 235U and 238U in the α and γ phases. The performance of these potentials was evaluated using published ab initio simulation data and inelastic neutron scattering data. The phonon densities of states obtained by each potential were then utilized to calculate the thermal neutron scattering cross sections of 235U and 238U at 1113 K using the NJOY program. The resulting thermal neutron scattering cross sections are assessed by comparison to data obtained from available experimental densities of states. The cross sections generated show how the addition of binding effects decreases the cross section by up to a factor of six over the free-atom model. A definite effect on reactivity is also demonstrated by the use of these thermal libraries on a simple core model. As a consequence, the cross sections generated in this work provide a better description of the true cross section than the free-atom data currently available. We also discuss the sensitivity of the thermal scattering cross sections to the phonon density of states.

Helium in-plane migration behavior on 〈1 0 0〉 symmetric tilt grain boundaries in tungsten.

We present the results of an atomistic modeling study of small helium cluster migration in the plane of symmetric tilt grain boundaries. The relevant migration pathways and energies were determined by way of temperature accelerated dynamics and the nudged elastic band method. We find that small helium clusters show much higher migration energies when bound to the grain boundary than in the bulk for all types of grain boundaries, indicating strongly-impeded helium transport behavior. Larger helium clusters (up to three helium atoms) tend to have higher migration energies compared with smaller clusters. Longer-distance migrations also tend to have higher migration energies, but helium cluster migration is highly affected by the structure of the grain boundary. The binding energy of the grain boundaries studied is high enough that helium clusters would be unlikely to leave the grain boundary plane. However, vacancy migration energies are relatively low compared to the bulk, and are also much lower than helium cluster migration energies on the grain boundary plane. This suggests that helium cluster migration on the grain boundary is actually governed by the rate of vacancy migration: in the bulk, helium clusters are mobile, but they become bound to and immobilized by grain boundaries, forming bubbles. Bubbles, however, are likely more mobile on the grain boundary than they are in the bulk due to the increased rate of vacancy migration on the grain boundary. We expect similar migration behavior for other types of grain boundaries because of the increased excess volume found near all grain boundaries.

Helium segregation on surfaces of plasma-exposed tungsten.

We report a hierarchical multi-scale modeling study of implanted helium segregation on surfaces of tungsten, considered as a plasma facing component in nuclear fusion reactors. We employ a hierarchy of atomic-scale simulations based on a reliable interatomic interaction potential, including molecular-statics simulations to understand the origin of helium surface segregation, targeted molecular-dynamics (MD) simulations of near-surface cluster reactions, and large-scale MD simulations of implanted helium evolution in plasma-exposed tungsten. We find that small, mobile He n (1⩽ n ⩽ 7) clusters in the near-surface region are attracted to the surface due to an elastic interaction force that provides the thermodynamic driving force for surface segregation. This elastic interaction force induces drift fluxes of these mobile He n clusters, which increase substantially as the migrating clusters approach the surface, facilitating helium segregation on the surface. Moreover, the clusters' drift toward the surface enables cluster reactions, most importantly trap mutation, in the near-surface region at rates much higher than in the bulk material. These near-surface cluster dynamics have significant effects on the surface morphology, near-surface defect structures, and the amount of helium retained in the material upon plasma exposure. We integrate the findings of such atomic-scale simulations into a properly parameterized and validated spatially dependent, continuum-scale reaction-diffusion cluster dynamics model, capable of predicting implanted helium evolution, surface segregation, and its near-surface effects in tungsten. This cluster-dynamics model sets the stage for development of fully atomistically informed coarse-grained models for computationally efficient simulation predictions of helium surface segregation, as well as helium retention and surface morphological evolution, toward optimal design of plasma facing components.

Simple pair-wise interactions for hybrid Monte Carlo-molecular dynamics simulations of titania/yttria-doped iron.

We present pair-wise, charge-neutral model potentials for an iron-titanium-yttrium-oxygen system. These simple models are designed to provide a tractable method of simulating nanostructured ferritic alloys (NFAs) using off-lattice Monte Carlo and molecular dynamics techniques without deviating significantly from the formalism employed in existing Monte Carlo simulations. The model is fitted to diamagnetic density functional theory (DFT) calculations of the various species over a range of densities and concentrations. The resulting model potentials provide reasonable and in some cases even excellent mechanical and thermodynamic properties for the pure metals. The model replicates the qualitative trends in formation energy predicted by DFT, though the energies of formation do not agree as well for dilute systems as they do for more concentrated systems. We find that on-lattice models will consistently favor tetrahedral oxygen interstitial sites over octahedral interstitial sites, while relaxed systems typically favor octahedral sites. This emphasizes the need for the off-lattice simulations for which this potential was designed.

Searching for microporous, strongly basic catalysts: experimental and calculated 29Si NMR spectra of heavily nitrogen-doped Y zeolites.

Nitrogen substituted zeolites with high crystallinity and microporosity are obtained by nitrogen substitution for oxygen in zeolite Y. The substitution reaction is performed under ammonia flow by varying the temperature and reaction time. We examine the effect of aluminum content and charge-compensating cation (H(+)/Na(+)/NH(4)(+)) on the degree of nitrogen substitution and on the preference for substitution of Si-O-Al vs Si-O-Si linkages in the FAU zeolite structure. Silicon-29 magic angle spinning (MAS) nuclear magnetic resonance (NMR) and (1)H/(29)Si cross-polarization MAS NMR spectroscopy have been used to probe the different local environments of the nitrogen-substituted zeolites. Experimental data are compared to simulated NMR spectra obtained by constructing a compendium (>100) of zeolite clusters with and without nitrogen, and by performing quantum calculations of chemical shifts for the NMR-active nuclei in each cluster. The simulated NMR spectra, which assume peak intensities predicted by statistical analysis, agree remarkably well with the experimental data. The results show that high levels of nitrogen substitution can be achieved while maintaining porosity, particularly for NaY and low-aluminum HY materials, without significant loss in crystallinity. Experiments performed at lower temperatures (750-800 degrees C) show a preference for substitution at Si-OH-Al sites. No preference is seen for reactions performed at higher temperatures and longer reaction times (e.g., 850 degrees C and 48 h).

Spectroscopic signatures of nitrogen-substituted zeolites.

Nanoporous acid catalysts such as zeolites form the backbone of catalytic technologies for refining petroleum. With the promise of a biomass economy, new catalyst systems will have to be discovered, making shape-selective base catalysts especially important because of the high oxygen content in biomass-derived feedstocks. Strongly basic zeolites are attractive candidates, but such materials are notoriously difficult to make due to the strong inherent acidity of aluminosilicates. Several research groups have endeavored to produce strongly basic zeolites by treating zeolites with amines, but to date there is no compelling evidence that nitrogen is incorporated into zeolite frameworks. In this communication, we detail synthesis, NMR spectroscopy, and quantum mechanical calculations showing that nitrogen adds onto both surface and interior sites while preserving the framework structure of zeolites. This finding is crucial for the rational design of new biomass-refinement catalysts, allowing 50 years of zeolite science to be brought to bear on the catalytic synthesis of biofuels.

Physical adsorption analysis of intact supported MFI zeolite membranes.

We compare the adsorption properties of intact supported silicalite membranes with those of silicalite powder and of alumina supports using nitrogen and argon as adsorbates at 77 K. We disentangle contributions from the membrane and support and find that the support contributes significantly to the total quantity adsorbed due to its relative thickness. The micropore-filling regions of the adsorption isotherms of the powder and the supported membrane are nearly identical for the membranes studied, but the isotherms differ at higher pressures--the supported membranes exhibit a much higher quantity adsorbed than the powders. Despite this difference, no hysteresis is observed in the membrane isotherms, indicating a lack of mesoporosity (pores in the 2-50 nm range) in either membrane or support for this preparation. We estimate argon transport fluxes at steady state by assuming surface diffusion with both a constant and concentration-dependent Maxwell-Stefan diffusion coefficient in the zeolite and the support. Further, we use the respective adsorption isotherms to determine the thermodynamic correction factors--that is, the ratios of the Fick and Maxwell-Stefan diffusion coefficients--required to solve the diffusion equation. The estimated argon flux is virtually the same using adsorption data from powders and membranes. For the relatively thick supports used in our study (approximately 2 mm), we find that the support exerts a much greater influence on the predicted fluxes for a wide range of values of the ratio of the support to zeolite diffusion coefficients. We emphasize that the results are specific to the architecture of the supported membranes studied, and thus, the results should be interpreted accordingly.