Engineering topics

Hammond, Karl D.

Publications and source records attributed to Hammond, Karl D..

8 records

DOE OSTI2023

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

Abstract 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 ( $$N_\text {V}$$ N V ), He atoms ( $$N_\text {He}$$ N He ), 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 $$N_\text {V}$$ N V vacancies and $$N_\text {He}$$ N He helium atoms, the $$N_\text {He}/N_\text {V}$$ N He / N V ratio that causes the event, the resulting increase in $$N_\text {V}$$ N V , and the associated shift of the bubble depth are formulated as a function of $$N_\text {V}$$ N V and T . In the bursting model, a bubble must simultaneously reach a certain depth and $$N_\text {He}/N_\text {V}$$ N He / N V ratio in order to burst. The burst depth and $$N_\text {He}/N_\text {V}$$ N He / N V are also modeled as a function of $$N_\text {V}$$ N V 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.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Helium impurities and interactions in lithium

Here we investigate helium interactions with lithium using density functional theory. Like other body-centered cubic (bcc) metals, the lowest-energy site for interstitial helium is a tetrahedral site. However, helium in lithium shows a higher substitutional formation energy than either the tetrahedral or octahedral interstitial formation energies, which is unique. The calculated migration energies of helium in lithium are also very low ( ~ 1 meV), an order of magnitude lower than those in other bcc metals. We find an increase in the binding energy to a vacancy as the number of helium atoms bound to it increases. The extremely low migration energies suggest that helium transport in lithium will be very fast.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Xenon mobility in γ-uranium and uranium–molybdenum alloys

Diffusion in bcc uranium and U–Mo alloys is of great interest because fission gas and other fission products impact the performance of nuclear fuels. We investigate the mobility of xenon and molybdenum in bcc uranium (⁠$γ$-U) and metallic U–Mo alloys by calculating the migration energies of xenon and molybdenum for various local compositions using density functional theory. We also calculate the solute–vacancy binding energies of different solutes to vacancies in bcc uranium. We find that the solute–vacancy binding energy in bcc uranium is significantly higher than it is in other bcc metals (e.g., Fe and W). We also find that the migration energy of molybdenum is substantially higher than the migration energy of xenon, indicating that xenon is much more mobile than molybdenum in bcc uranium. The presence of molybdenum in the nearest-neighbor shell around a xenon atom typically increases the migration energy of xenon, which indicates a reduction of xenon mobility in U–Mo alloys compared to pure bcc uranium.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Effect of Helium Flux on Near-surface Helium Accumulation in Plasma-Exposed Tungsten

We report results of object kinetic Monte Carlo (OKMC) simulations aimed at understanding the effect of helium flux on the near-surface helium accumulation in plasma-facing tungsten, which is initially defect-free and has a W(100) surface orientation. These OKMC simulations are performed at 933 K for fluxes ranging from 10 22 to 4 × 10 25 He/m 2 s, with 100 eV helium atoms impinging on a W(100) surface up to a maximum fluence of 4×10 19 He/m 2 . 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 as the flux decreases, the retention of implanted helium decreases, and its depth distribution shifts to deeper below the surface in initially pristine tungsten. Furthermore, the fraction of retained helium diffusing into the bulk increases as well, so much so that for 10 22 He/m 2 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. Finally, we present a detailed analysis of the influence of helium flux on the size and depth distribution of total helium and helium bubbles.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Temperature-dependent model of helium bubble expansion and bursting in tungsten

Continuum-scale models that can reliably predict the behavior of helium in tungsten are of interest to the fusion community due to the projected impact of these materials on fusion reactor operation. In this work, we perform molecular dynamics simulations of spherical helium bubbles of various sizes in tungsten at different temperatures and depths with the goal of determining a mathematical model of the pressure and density at which the bubbles initially expand or burst as a function of depth, size, temperature, and surface orientation. The bubbles are small enough that their loop-punching pressures cannot be accurately predicted with continuum mechanics, and their expansion behavior is important, as it appears to cause many of the features observed on helium-irradiated tungsten surfaces. We vary the temperature, bubble size, bubble depth, and surface orientation in each case, recording the bubble pressure and density that result in bubble expansion. An exponential function with three adjustable parameters is found to fit the results well; the parameters that best fit our results are provided.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Non-dilute helium-related defect interactions in the near-surface region of plasma-exposed tungsten

We report a systematic energetic analysis of helium-related defect interactions that mediate helium (He) segregation on surfaces of plasma-exposed tungsten at different levels of He ion implantation. We focus on high He fluences that increase the He content in the plasma-exposed material well beyond the dilute limit of He concentration and employ atomic configurations generated by large-scale molecular dynamics simulations of He-implanted tungsten. We perform systematic molecular statics computations of cluster– defect interaction energetics in the highly defect-rich near-surface region of plasma-exposed tungsten for small mobile helium clusters as a function of the cluster distance from the surface. In this region, mobile clusters are also subjected to the stress fields generated by defects such as helium bubbles and other clusters, which govern cluster–defect interactions in addition to the cluster–surface interaction. Based on systematic investigation of individual cluster–defect interactions, we develop a mathematical framework to describe the interaction energy landscapes consisting of elastic interaction potential perturbations to finite-width square-well potentials, where the potential well accounts for cluster trapping by the defect at close range and subsequent coalescence and the perturbation potential is parameterized according to elastic inclusion theory. Superposition of all the relevant interaction potentials provides a comprehensive description of the interaction energy landscape that would be experienced by a small mobile cluster along its migration path toward the plasma-exposed surface at high He fluence. Such descriptions are particularly important for developing atomistically-informed, hierarchical multi-scale models of helium cluster dynamics in plasma-facing materials.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Corrigendum and Addendum: Helium flux effects on bubble growth and surface morphology in plasma-facing tungsten from large-scale molecular dynamics simulations (2019 Nucl. Fusion 59 066035)

Two of the simulations discussed in a prior article (Hammond et al 2019 Nucl. Fusion 59 066035) were affected by a simulation glitch. We repeated the affected calculations and discuss them here. Here, the overall conclusions are essentially unchanged, though the details are different. In particular, observations that we referred to as ‘concerted bursting’ were caused primarily by non-physical heating and cooling applied by the thermostat after most atoms’ velocities were deleted (for reasons that are not known for certain). The phenomenon of one bubble bursting and causing another nearby bubble to burst does exist, though its effects are much less spectacular in the absence of non-physical driving forces. The observation of an interconnected network of sub-surface cavities formed by burst bubbles is real, and the observation of holes on the surface 1–2 nm in diameter is also confirmed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

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.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗