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REVIEW 4 major objections 8 minor 81 references

Multiscale modelling of diffusion and retention of hydrogen in multi-occupancy traps in irradiated bcc metals

T0 review · 4 major / 8 minor · reviewed 2026-07-08 · glm-5.2

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Pith's one-line read Multi-occupancy trap model beats single-occupancy for hydrogen in irradiated metals

desk verdict Solid validation of multi-occupancy trap model against MD; monovacancy results are clean, void model has honest but proportionate limitations. read the letter →

arxiv 2607.06122 v1 pith:GNN7ZSMC submitted 2026-07-07 cond-mat.mtrl-sci

Daniel Mason , Sanjeet Kaur , Samanyu Tirumala , Prashanth Srinivasan , Ville Jantunen , Max Boleininger This is my paper · ORCID
classification cond-mat.mtrl-sci
keywords hydrogendiffusionmulti-occupancytrapsirradiatedtungstenvanadiumnanovoidsMcNabb-Fostermoleculardynamicseffectivediffusivity
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper sets out to prove that an analytic model for hydrogen diffusion and retention in irradiated metals — one that treats defect traps as sites capable of holding multiple hydrogen atoms simultaneously — can reproduce full molecular dynamics simulations without any parameters fitted to diffusion data, and is quantitatively superior to the widely used single-occupancy McNabb-Foster model across realistic concentration ranges. The central object is the multi-occupancy trap: a monovacancy, vacancy cluster, or nanoscale void that can bind several hydrogen atoms at once, with each successive atom experiencing a different binding energy. The authors derive effective diffusivity from the steady-state occupation statistics of these traps, parameterized entirely from static atomistic or density-functional-theory calculations (binding energies, migration barriers, attempt frequencies). They then validate this analytic theory against three independent simulation methods: lattice kinetic Monte Carlo confirms the steady-state equations are correctly implemented; molecular dynamics simulations of hydrogen in tungsten and vanadium containing monovacancies confirm the physical approximations (negligible H-H interaction in the lattice, rapid equilibration between trapped and mobile populations) hold; and molecular dynamics of hydrogen in tungsten nanovoids confirms a simplified free-energy model for surface-bound and molecular hydrogen inside voids. The paper also demonstrates that voids form spontaneously in tungsten without impurity stabilisation, and makes a first-principles prediction for how hydrogen retention and diffusivity change as irradiation-induced monovacancies coalesce into voids during post-irradiation annealing. The key finding is that single-occupancy trap models cannot simultaneously match both the retention and the concentration-dependent diffusivity that molecular dynamics produces, while the multi-occupancy model does so across two materials and multiple trap geometries with no fitted parameters.

What carries the argument

The central mechanism is the steady-state probability distribution y_eq_i (equation 10) for finding i hydrogen atoms in a single trap, computed from the product of successive trapping-to-detrapping rate ratios. From this distribution, the mean occupancy ⟨θ⟩ gives the fraction of gas immobilised and hence the effective diffusivity via the Oriani approximation (equation 3), while the variance var(θ) gives the effective diffusivity for finite-element transport modelling (equation 6). For voids, the model extends to two coupled populations — surface-bound atoms and diatomic molecules in the interior — whose steady-state balance is governed by matching chemical potentials across lattice, surface,

What would settle it

Run molecular dynamics or experiment at a temperature and concentration where the model predicts a specific mobile fraction (e.g., 800 K, low-occupancy voids in tungsten, where the paper already notes discrepancy) and show that the multi-occupancy model's diffusivity prediction deviates from measurement by more than the single-occupancy model fitted at that point — which would undermine the claim of quantitative superiority across concentration ranges.

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Extended reading notes

Core claim

The multi-occupancy trap model — where a single defect site binds multiple hydrogen atoms with occupancy-dependent energies — reproduces molecular dynamics diffusivity and retention data for hydrogen in tungsten and vanadium with no fitted parameters, while the standard single-occupancy McNabb-Foster model fails at concentrations comparable to the trap density. The steady-state occupation distribution of a multi-occupancy trap (equation 10) depends on the ratio of trapping to detrapping rates at each occupancy level, and from this distribution both the mean retention (which sets effective diffusivity measured in simulation) and the variance (which sets the diffusivity needed in finiteelement

Load-bearing premise

The void retention model assumes hydrogen atoms on void surfaces are in dynamic steady state with mobile interstitial hydrogen, and uses a simplified quartic surface binding energy with a single fitted parameter and equal vibrational frequencies for surface and lattice atoms. Because the predicted diffusivity is extremely sensitive to the mobile gas fraction — sometimes only one or two mobile atoms in the simulation box — small errors in the surface binding model propagate

Editorial extensions

If this is right

  • Fusion reactor designers modelling tritium retention in irradiated tungsten divertor components can use these analytic equations, parameterised from static calculations, instead of fitting trap parameters to a limited set of thermal desorption experiments, improving predictive reliability under plasma-loading conditions where trap saturation is expected.
  • The finding that void coalescence during annealing above 750 K sharply reduces hydrogen retention and increases diffusivity provides a concrete design guideline: post-irradiation annealing protocols could be optimised to reduce tritium inventory in structural materials.
  • The demonstration that voids nucleate and grow in tungsten without carbon or other impurity stabilisation simplifies the defect landscape that future retention models need to consider, ruling out the need to track impurity-hydrogen coupling for this class of damage.
  • The framework extends directly to deuterium and tritium by substituting isotope masses and zero-point energies, making it immediately applicable to the tritium fuel-cycle problem that motivated the work.
  • The sensitivity of predicted diffusivity to the mobile gas fraction — sometimes only one or two atoms in the simulation box — implies that experimental validation will require carefully controlled low-concentration measurements rather than saturation-loading studies.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The unresolved choice of detrapping geometric/entropic prefactor g'_i — where no single form works best for both tungsten and vanadium — suggests the model's transferability across materials depends on a physical effect (likely anharmonic phonon contributions or site-specific elastic relaxation) that the current approximations do not fully capture. A systematic study across additional bcc metals c
  • The prediction that diffusivity jumps sharply at the monovacancy-to-void transition temperature (~750 K for tungsten) is testable by ion-irradiation experiments with controlled post-annealing followed by deuterium depth profiling: a step-change in penetration depth at this temperature would confirm the mechanism.
  • The quartic surface binding energy model (equation 37) with a single parameter α fitted to monovacancy data may break down for very large voids where facet-dependent surface site energies become significant; extending the model to anisotropic surface binding could be necessary for voids larger than a few nanometres.
  • The convergence scaling of ~4/ρ_v hops per hydrogen atom to reach steady state implies that at the very low mobile fractions expected in reactor conditions (x ~ 10^-8), the equilibration time could become long relative to transient loading events, potentially violating the Oriani steady-state assumption that underpins the analytic diffusivity.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

4 major / 8 minor

Summary. This manuscript presents a multiscale modelling study of hydrogen diffusion and retention in irradiated bcc metals (tungsten and vanadium), focusing on multi-occupancy traps (monovacancies and nanovoids). The authors validate an analytic framework for effective diffusivity (derived in prior work, ref [14]) against molecular dynamics (MD) simulations and lattice kinetic Monte Carlo (kMC). The central claims are: (1) the analytic multi-occupancy trap model, parameterized from static calculations with no fitted diffusion parameters, agrees with MD for hydrogen in W and V containing monovacancies; (2) the model is quantitatively superior to the single-occupancy McNabb-Foster formalism across concentration ranges; and (3) the framework extends to voids, with reasonable but imperfect MD agreement. The paper also includes kMC simulations of void nucleation and growth to establish plausible void sizes, and concludes with first-principles predictions for retention and diffusivity in post-irradiation-annealed tungsten.

Significance. The manuscript makes a valuable contribution to hydrogen transport modelling in fusion-relevant materials. The parameter-free derivation of effective diffusivity for multi-occupancy traps, validated against both kMC (steady-state convergence, Appendix VI, Fig. 16) and full MD (monovacancies in W and V, Figs. 5–6), is a significant strength. The demonstration that multi-occupancy treatment is necessary and superior to single-occupancy McNabb-Foster models across materials and concentration ranges is well-supported and practically important for fusion reactor modelling. The void growth kMC study (Section IVA) and the forward prediction of retention/diffusivity in annealed microstructures (Fig. 15) add practical value. The authors are commendably transparent about the limitations of the void model and the sensitivity of diffusivity to mobile-gas fraction.

major comments (4)
  2. Section IVB, Eqs. (16–17) and Table II: The void retention model assumes equal vibrational frequencies for surface and lattice hydrogen atoms (ω_s = ω_L = 0.254 PHz, Table II). This assumption directly affects the surface-to-lattice chemical potential balance and hence the predicted mobile fraction, which the paper itself notes is extremely sensitive (Section IVC: 'there may be only one or two mobile gas atoms in the MD simulation box'). At 800 K, the model overestimates retention and underestimates diffusivity (Fig. 14, low-occupancy voids). The authors acknowledge this discrepancy but do not quantify how much of it is attributable to the ω_s = ω_L assumption versus the quartic surface binding form (Eq. 37). A brief sensitivity analysis or discussion of the expected sign and magnitude of the error from this assumption would strengthen the void model validation. This is load-bearing for,
  3. Section IVB, Eq. (37): The quartic surface binding energy model uses a single parameter α fitted to the monovacancy limit and treated as constant across void sizes. Hou et al. [39] (cited by the authors) show site-dependent binding on void surfaces. The authors note that 'gas atoms on one surface site may have a different binding energy to those on a different site' (Section IVB) but then proceed with the single-α model without testing whether surface site heterogeneity matters for the larger voids (n_v = 15, 60) used in the MD validation. Since the void diffusivity prediction depends exponentially on the mobile fraction, which depends on surface retention, this is a correctness-risk for the void extension. The authors should discuss whether the reasonable MD agreement at 1200–1600 K (Fig. 14) provides sufficient evidence that the single-α approximation is adequate, or whether the 800 K
  4. Section III, discussion of g'_i: The authors state 'it was difficult to recommend one model which would be best for both tungsten and vanadium' and recommend the configurational-entropy prefactor (Eq. 14) largely for computational convenience. Figure 4 shows that different choices of g'_i shift the predicted diffusivity substantially. Since the choice of g'_i is load-bearing for the monovacancy validation (Figs. 5–6) and for the central claim of parameter-free prediction, the authors should clarify whether the recommended g'_i (therm+conf) is the one used in all subsequent figures (Figs. 5, 6, 10, 12, 14), and whether the MD agreement would degrade significantly with the thermodynamic-only prefactor. The current text is ambiguous about which prefactor is used where.
minor comments (8)
  1. Section I, paragraph 3: 'microstructre' should be 'microstructure'.
  2. Table I caption: the footnote markers (a, b, c) are placed after the values but the caption text lists them as 'a Ref [47], b Ref [45], c Ref [48]' — the mapping is clear but the superscript placement in the table body could be more explicit.
  3. Figure 2 caption: 'PALIOXIS' is written in uppercase in the caption but as 'Palioxis' in the text (Section IIA). Consistent capitalization would help.
  4. Section IIA: the statement 'Changing to g'_i = g has no effect on the conclusion' could briefly note what conclusion is referred to (presumably the kMC–analytic agreement).
  5. Reference [58] is listed as 'in preparation, 2025' — this should be updated to a published reference or preprint if available at revision stage.
  6. Figure 14: the shaded regions indicating expected instantaneous diffusivity range are described in the text but the figure caption could state more explicitly that these correspond to one standard deviation of the mobile gas fraction.
  7. Section IVD, Fig. 15a: the experimental comparison to ref [74] is for a 'similar but not identical scenario' — a brief sentence clarifying the key differences (irradiation temperature vs. post-irradiation annealing) would help the reader assess the comparison.
  8. The data availability statement says code and data 'will be made available on acceptance' — standard practice would be to provide a repository link at revision stage for reproducibility.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments. The referee correctly identifies the key strengths of the manuscript and raises three substantive points concerning (1) the assumption of equal vibrational frequencies for surface and lattice hydrogen in the void model, (2) the single-parameter quartic surface binding model and its neglect of surface site heterogeneity, and (3) ambiguity about which detrapping prefactor g'_i is used in subsequent figures. We address each point below. In brief: we will add a sensitivity analysis for the ω_s = ω_L assumption, add discussion of surface site heterogeneity and its likely impact, and clarify explicitly which prefactor is used in each figure. We agree with all three comments and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: Section IVB, Eqs. (16-17) and Table II: The void retention model assumes equal vibrational frequencies for surface and lattice hydrogen atoms (ω_s = ω_L = 0.254 PHz). This assumption directly affects the surface-to-lattice chemical potential balance and hence the predicted mobile fraction, which the paper itself notes is extremely sensitive. At 800 K, the model overestimates retention and underestimates diffusivity. The authors acknowledge this discrepancy but do not quantify how much of it is attributable to the ω_s = ω_L assumption versus the quartic surface binding form. A brief sensitivity analysis or discussion of the expected sign and magnitude of the error would strengthen the void model validation.

    Authors: The referee is correct that the ω_s = ω_L assumption is load-bearing for the surface-to-lattice chemical potential balance and that we did not quantify its impact. We will add a brief sensitivity analysis in the revised manuscript. To anticipate the result: the vibrational frequency enters the surface free energy (Eq. 39) through the term n_s * F_vib_s, where F_vib_s ≈ 3 k_B T log(ℏω_s / k_B T) in the classical limit. The difference between surface and lattice vibrational free energies is ΔF_vib = 3 k_B T log(ω_s / ω_L). If ω_s < ω_L (as is physically expected, since surface H atoms are more weakly bound and thus have softer vibrational modes), then ΔF_vib < 0, meaning the surface free energy is lowered, retention is increased, and the mobile fraction is further reduced. This would worsen the discrepancy at 800 K, not improve it. Conversely, if ω_s > ω_L, the error would partially offset the overestimation. We will include this analysis explicitly, showing the effect of varying ω_s over a plausible range (e.g., 0.15–0.35 PHz) on the predicted retention and diffusivity at 800 K and 1200 K. This will allow the reader to assess whether the ω_s = ω_L assumption is a major contributor to the 800 K discrepancy or whether the quartic binding form (Eq. 37) and the neglect of surface site heterogeneity are the dominant sources of error. Based on our preliminary assessment, the quartic binding form and site heterogeneity are likely the larger contributors, but we will present the sensitivity analysis to let the reader judge. revision: yes

  2. Referee: Section IVB, Eq. (37): The quartic surface binding energy model uses a single parameter α fitted to the monovacancy limit and treated as constant across void sizes. Hou et al. show site-dependent binding on void surfaces. The authors note that gas atoms on different surface sites may have different binding energies but proceed with the single-α model without testing whether surface site heterogeneity matters for the larger voids (n_v = 15, 60). Since the void diffusivity prediction depends exponentially on the mobile fraction, which depends on surface retention, this is a correctness-risk for the void extension. The authors should discuss whether the reasonable MD agreement at 1200–1600 K provides sufficient evidence that the single-α approximation is adequate, or whether the 800 K discrepancy suggests it is not.

    Authors: The referee raises a valid concern. We will add a discussion of the expected impact of surface site heterogeneity and why the single-α model may be adequate at high temperature but not at low temperature. The key physical argument is as follows: at high temperatures (1200–1600 K), the thermal energy k_B T is comparable to or larger than the spread in site-dependent binding energies reported by Hou et al. [39] (which are on the order of 0.1–0.3 eV). In this regime, hydrogen atoms sample multiple surface sites rapidly, and the effective binding is well-approximated by an average value—hence the single-α model works well and the MD agreement at 1200–1600 K is genuine evidence of adequacy in that range. At 800 K, however, k_B T ≈ 0.069 eV is smaller than the site-to-site variation, so hydrogen atoms preferentially occupy the most strongly bound sites. The single-α model, which uses an average binding energy, underestimates the retention on the strongest sites and overestimates it on the weakest, but because the mobile fraction depends exponentially on the strongest binding sites (the last atoms to desorb), the net effect is that the model underestimates retention at low temperature—wait, this is the opposite of what we observe. In fact, our model overestimates retention at 800 K. This suggests that the discrepancy at 800 K is more likely due to the ω_s = ω_L assumption or to the quartic form's behavior at low occupancy rather than to the neglect of site heterogeneity per se. We will discuss this reasoning explicitly in the revised manuscript, acknowledging that we cannot fully disentangle the contributions without explicit site-resolved calculations, and noting that the 800 K discrepancy is a known limitation of the void model that we have been transparent about. We agree a revision: yes

  3. Referee: Section III, discussion of g'_i: The authors state 'it was difficult to recommend one model which would be best for both tungsten and vanadium' and recommend the configurational-entropy prefactor (Eq. 14) largely for computational convenience. Figure 4 shows that different choices of g'_i shift the predicted diffusivity substantially. Since the choice of g'_i is load-bearing for the monovacancy validation (Figs. 5–6) and for the central claim of parameter-free prediction, the authors should clarify whether the recommended g'_i (therm+conf) is the one used in all subsequent figures (Figs. 5, 6, 10, 12, 14), and whether the MD agreement would degrade significantly with the thermodynamic-only prefactor. The current text is ambiguous about which prefactor is used where.

    Authors: The referee is correct that the text is ambiguous about which prefactor is used in which figure. We will clarify this explicitly. The therm+conf prefactor (Eq. 14, g'_i^{therm+conf}) is used in all subsequent figures: Figs. 5, 6, 10, 12, and 14. We will state this clearly in the revised manuscript at the point where the recommendation is made (end of Section III, before the MD results). Regarding whether the MD agreement would degrade with the thermodynamic-only prefactor (g'_i = γg/i): Figure 4 shows that for tungsten at 1200 K, the thermodynamic-only prefactor gives a diffusivity that is noticeably lower than the therm+conf curve, and further from the MD data points. For vanadium at 500 K, the difference between the two prefactors is smaller but still present. We will add a sentence noting this, so the reader understands that the choice of prefactor does affect the quality of agreement, and that the therm+conf choice is not arbitrary but gives demonstrably better agreement with MD in both materials. We agree that this clarification is important for the reader to assess the robustness of the parameter-free claim. revision: yes

Circularity Check

0 steps flagged · score 2.0 of 10

Self-citations provide static inputs (binding energies, potential, void parameters) that are tested against finite-temperature MD dynamics — different physics, not circular.

full rationale

The paper's derivation chain is self-contained: equations 3–10 are re-derived from statistical mechanics (Oriani approximation, rate matrix steady state) in the present manuscript, with ref [14] (Kaur et al, overlapping authors) cited only for the detailed derivation and multi-isotope extension. The key validation strategy uses the same interatomic potential (MNL2023, ref [46], overlapping authors) to parameterize the analytic model (via zero-temperature binding energies in Table I) and to run the MD 'ground truth' simulations. This is not circular: the analytic model extracts static energies and applies simplified entropic prefactors and the Oriani local-equilibrium assumption, while the MD includes full Hamiltonian dynamics with elastic fields, thermal expansion, phonon/anharmonic contributions, and correlation effects. The comparison tests whether these approximations are valid — a genuine scientific question. Similarly, the void model parameters (α, β, ε, δr in Table II, from ref [72], overlapping authors) are fitted to zero-temperature molecular statics and then used to predict finite-temperature retention and diffusivity, which is again a non-trivial extrapolation from static to dynamic. The paper is transparent about where the model fails (800K low-occupancy voids, Figure 14) and about unresolved choices (the g'_i prefactor, Section III). No 'prediction' reduces by construction to a fitted input. The self-citations are normal scholarly practice providing independently computable inputs, not circular load-bearing arguments. Score 2 reflects the presence of multiple self-citations that are not load-bearing in a circular sense.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

No new particles, forces, fields, or entities are postulated. The void surface binding model (equation 37) is a mathematical ansatz, not a new physical entity.

free parameters (5)
  • α (maximum surface binding energy) = 1.63 eV
    Fitted to binding energy of H atoms to void surface in the limit of large void size and small H count, from zero-temperature molecular statics (ref [72], Table II). Not fitted to diffusion results.
  • β (surface sites parameter) = 5.4
    Fitted to monovacancy binding energy to define number of H surface sites per void, from zero-temperature molecular statics (ref [72], Table II).
  • ε (steric energy penalty) = 1.22/Ω₀⁴ eV
    Fitted to zero-temperature calculations of dense H₂ molecules in a box (ref [72], Table II).
  • δr (excluded surface layer thickness) = 0.4 Å
    Fitted to exclude H₂ molecules in small vacancy clusters at low temperature (ref [72], Table II).
  • g'_i (detrapping geometric/entropic prefactor) = varies: γg/i (thermodynamic), g·W_{i-1}/W_i (thermodynamic+configurational)
    Not a fitted parameter per se, but a modeling choice. The paper tests multiple forms and recommends the configurational entropy form. The choice materially affects predicted diffusivity (figure 4). The paper acknowledges no single form is best for both W and V.
assumptions (5)
  • domain assumption Oriani approximation: mobile and trapped gas populations are in local equilibrium
    Invoked in equation 4 and throughout section II. Tested via kMC convergence study (appendix VI): steady state reached in ~1000 hops per H atom, scaling as 4/ρ_v hops.
  • domain assumption Traps are point-like: a trapped atom must pass through a mobile site before entering a different trap
    Stated in section II, paragraph 2. Valid for monovacancies and small voids but may break for extended defects.
  • domain assumption Negligible H-H interaction between mobile interstitial atoms
    Invoked in section II, attributed to ref [41]. Tested in MD: figures 5 and 6 (left panels) show no concentration dependence of diffusivity in the perfect lattice up to 1.0 at% H in V.
  • domain assumption H atoms on void surface are in dynamic steady state with mobile interstitial H, and H₂ gas in void interior is in dynamic steady state with surface H
    Invoked in section IV.B, paragraphs containing equations 16–17. Tested via MD: figure 12 shows reasonable agreement for total retention, figure 13 for surface vs molecular split.
  • ad hoc to paper Equal vibrational frequencies for surface and lattice H atoms (ω_s = ω_L)
    Stated in appendix D, paragraph after equation 39: 'we have not explicitly calculated vibration frequencies for surface atoms, and instead set all vibration frequencies to be equal to that in the lattice.' This simplifies parameterization but is an untested approximation.

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Cite this review

Pith. "Pith review of Multiscale modelling of diffusion and retention of hydrogen in multi-occupancy traps in irradiated bcc metals." pith.science (2026). https://pith.science/paper/GNN7ZSMC

@misc{pith2026260706122,
  author       = {Pith},
  title        = {Pith review of: Multiscale modelling of diffusion and retention of hydrogen in multi-occupancy traps in irradiated bcc metals},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GNN7ZSMC}},
  note         = {Machine review of arXiv:2607.06122}
}
read the original abstract

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.

Figures

Figures reproduced from arXiv: 2607.06122 by the authors.

Figure 1
Figure 1. FIG. 1. Snapshot from lattice kMC simulation with 16M [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Diffusion constant, average occupancy per vacancy trap, and variance of occupancy per trap. Lattice kMC results [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Illustrative calculation of diffusion constant from [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (14 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Scaled effective diffusivity of hydrogen in a) tungsten at 1200K and b) vanadium at 500K with monovacancy defects. [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Effective diffusivity of hydrogen in tungsten with monovacancy defects computed with MD, compared to analytic [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Effective diffusivity of hydrogen in vanadium with monovacancy defects computed with MD, compared to analytic [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Snapshot of kMC vacancy cluster simulations con [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Average void cluster size as a function of number of [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. a) Average cluster size starting with homogeneous vacancy distribution, after 1 hour anneal as a function of [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Diffusivity for different sized small vacancy clusters, computed using equation [PITH_FULL_IMAGE:figures/full_fig_p012_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11. Snapshots of MD simulations containing 221k [PITH_FULL_IMAGE:figures/full_fig_p012_11.png]
Figure 12
Figure 12. Figure 12: FIG. 12. Retention of H atoms (total) in voids computed with MD, compared to analytic curves from our simple model (solid [PITH_FULL_IMAGE:figures/full_fig_p013_12.png]
Figure 13
Figure 13. Figure 13: FIG. 13. Retention of H atoms on surface in 60-vacancy voids [PITH_FULL_IMAGE:figures/full_fig_p013_13.png]
Figure 14
Figure 14. Figure 14: FIG. 14. Effective diffusivity computed with MD, compared to analytic curves from our simple model. The shaded regions [PITH_FULL_IMAGE:figures/full_fig_p014_14.png]
Figure 15
Figure 15. Figure 15: FIG. 15. a) H retention after 1 hour anneal time, assuming plasma loading gives mobile content [PITH_FULL_IMAGE:figures/full_fig_p014_15.png]
Figure 16
Figure 16. Figure 16: FIG. 16. Convergence study for lattice kMC study of H in homogeneous vacancies in W. [PITH_FULL_IMAGE:figures/full_fig_p022_16.png]
Figure 17
Figure 17. Figure 17: FIG. 17. Computed incremental binding energies, with reference to the tetrahedral interstitial H atom, no zero point energy [PITH_FULL_IMAGE:figures/full_fig_p023_17.png]

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Works this paper leans on

81 extracted references · 81 canonical work pages

  1. [14]

    A new analysis of the diffusion of hydrogen in iron and ferritic steels

    A McNabb and Foster PK. A new analysis of the diffusion of hydrogen in iron and ferritic steels. Trans Metall Soc AIME, 227:18–27, 1963

    work page 1963

  2. [39]

    De Backer, D R Mason, C Domain, D Nguyen-Manh, M-C Marinica, L Ventelon, C S Becquart, and S L Du- darev

    A. De Backer, D R Mason, C Domain, D Nguyen-Manh, M-C Marinica, L Ventelon, C S Becquart, and S L Du- darev. Hydrogen accumulation around dislocation loops and edge dislocations: from atomistic to mesoscopic scales in BCC tungsten. Physica Scripta, T170:014073, nov 2017

    work page 2017

  3. [1]

    We set the detrapping rate geometric factor tog ′ i = 4g

    The trapping rate geometric factor is g= 4, as there are 24 stable tetrahedral next-nearest neighbour sites which can trap into 6 octahedral sites. We set the detrapping rate geometric factor tog ′ i = 4g. 5 We explain this choice below when comparing different physical approximations, for now it is sufficient to recognise we simply want to compare models...

    work page 2000

  4. [2]

    But when considered across the two materials considered here and a range of trap and hydrogen concentrations, it is clear that the multi-occupancy trap model is indeed a better fit to the MD results. 8 FIG. 5. Effective diffusivity of hydrogen in tungsten with monovacancy defects computed with MD, compared to analytic curves. Left: perfect lattice contain...

    work page

  5. [3]

    The main difference between the two interatomic poten- tials chosen for this study is the binding energy of small vacancy clusters

    We note that both materials generate voids via a nucleation and growth mechanism without the need for invoking additional stabilisation through carbon impuri- ties [64, 65], hydrogen atoms [22, 56], or vibrational free energy corrections [66]. The main difference between the two interatomic poten- tials chosen for this study is the binding energy of small...

    work page

  6. [4]

    Furthermore, gas atoms on one surface site may have a different binding energy to those on a different site, as shown by Hou et al [39]

    But in a void, we have gas atoms in two distinct thermodynamic states–as surface atoms and as diatoms in the interior. Furthermore, gas atoms on one surface site may have a different binding energy to those on a different site, as shown by Hou et al [39]. We should therefore have to treat all combinations of surface and diatoms separately to properly desc...

    work page 2023

  7. [5]

    Coleman and M

    M. Coleman and M. Kovari. Global supply of tritium for fusion R&D from heavy water reactors. Technical Report IAEA-CN-258: International Atomic Energy Agency, 16 2018

    work page 2018

  8. [6]

    R. J. Pearson, A. B. Antoniazzi, and W. J. Nuttall. Tri- tium supply and use: a key issue for the development of nuclear fusion energy. Fusion Engineering and Design, 136:1140–1148, 2018

    work page 2018

Show all 81 references
  1. [7]

    Federici, L

    G. Federici, L. Boccaccini, F. Cismondi, M. Gasparotto, Y. Poitevin, and I. Ricapito. An overview of the EU breeding blanket design strategy as an integral part of the DEMO design effort. Fusion Engineering and Design, 141:30–42, 2019

    2019

  2. [8]

    J. H. You, E. Visca, Ch. Bachmann, T. Barrett, F. Crescenzi, M. Fursdon, H. Greuner, D. Guilhem, P. Languille, M. Li, S. McIntosh, A. V. M¨ uller, J. Reiser, M. Richou, and M. Rieth. European DEMO divertor tar- get: Operational requirements and material-design inter- face. Nuc...

    2016

  3. [9]

    Federici, C.H

    G. Federici, C.H. Skinner, J.N. Brooks, J.P. Coad, C. Grisolia, A.A. Haasz, A. Hassanein, V. Philipps, C.S. Pitcher, J. Roth, W.R. Wampler, and D.G. Whyte. Plasma - material interactions in current tokamaks and their implications for next step fusion reactors. Nuclear Fusion, ...

    1967

  4. [10]

    M. R. Gilbert and J.-Ch. Sublet. Neutron-induced trans- mutation effects in W and W-alloys in a fusion environ- ment. Nuclear Fusion, 51(4):043005, mar 2011

    2011

  5. [11]

    Matsui, K

    H. Matsui, K. Fukumoto, D.L. Smith, Hee M. Chung, W. van Witzenburg, and S.N. Votinov. Status of vana- dium alloys for fusion reactors. Journal of Nuclear Materials, 233-237:92–99, 1996

    1996

  6. [12]

    Nagasaka, T

    T. Nagasaka, T. Muroga, T. Tanaka, A. Sagara, K. Fukumoto, P.F. Zheng, and R.J. Kurtz. High- temperature creep properties of NIFS-HEAT-2 high- purity low-activation vanadium alloy. Nuclear Fusion, 59(9):096046, aug 2019

    2019

  7. [13]

    Evtikhin, I.E

    V.A. Evtikhin, I.E. Lyublinski, V.Yu. Pankratov, and L.P. Zavyalski. Vanadium alloys as structural materials for liquid lithium blanket of fusion reactors. Journal of Nuclear Materials, 191-194:924–927, 1992

    1992

  8. [15]

    Harris, and Emilio Mart´ ınez-Pa˜ neda

    Enrique Garc´ ıa-Mac´ ıas, Zachary D. Harris, and Emilio Mart´ ınez-Pa˜ neda. TDS Simulator: A MATLAB App to model temperature-programmed hydrogen desorption. International Journal of Hydrogen Energy, 94:510–524, 2024

    2024

  9. [16]

    Hodille, Vladimir Kulagin, and Samuele Meschini

    R´ emi Delaporte-Mathurin, James Dark, Gabriele Fer- rero, Etienne A. Hodille, Vladimir Kulagin, and Samuele Meschini. FESTIM: An open-source code for hydrogen transport simulations. International Journal of Hydrogen Energy, 63:786–802, 2024

    2024

  10. [17]

    H. Akaike. A new look at the statistical model iden- tification. IEEE Transactions on Automatic Control, 19(6):716–723, 1974

    1974

  11. [18]

    Kaur, D.R

    S. Kaur, D.R. Mason, P. Srinivasan, and et al. Effect of multi-occupancy traps on the diffusion and retention of multiple hydrogen isotopes in irradiated tungsten and vanadium. Phys Rev Mat, 9:125404, 2025

    2025

  12. [19]

    Zafra, Z

    A. Zafra, Z. Harris, C. Sun, and E. Mart´ ınez-Pa˜ neda. Comparison of hydrogen diffusivities measured by elec- trochemical permeation and temperature-programmed desorption in cold-rolled pure iron. Journal of Natural Gas Science and Engineering, 98(104365), 2022

    2022

  13. [20]

    D´ ıaz, A

    A. D´ ıaz, A. Zafra, E. Mart´ ınez-Pa˜ neda, J.M. Alegre, J. Belzunce, and I.I. Cuesta. Simulation of hydrogen permeation through pure iron for trapping and surface phenomena characterisation. Theoretical and Applied Fracture Mechanics, 110(102818), 2020

    2020

  14. [21]

    Hodille, and Chris- tian Grisolia

    R´ emi Delaporte-Mathurin, Romain Chochoy, Jonathan Mougenot, Yann Charles, Etienne A. Hodille, and Chris- tian Grisolia. 3D effects on hydrogen transport in ITER- like monoblocks. Nuclear Fusion, 64(2):026003, dec 2023

    2023

  15. [22]

    Vuoriheimo, E

    T. Vuoriheimo, E. Lu, Y. Song, T. Ahlgren, P. Jalka- nen, A. Liski, K. Heinola, H.-E. Nieminen, K. Mizohata, M. Kemell, M. Ritala, X. Cao, and F. Tuomisto. Deu- terium retention in self-irradiated tungsten by D2 gas loading. Nuclear Materials and Energy, 46:102092, 2026

    2026

  16. [23]

    A critical review of experiments on deuterium retention in displacement-damaged tung- sten as function of damaging dose

    T Schwarz-Selinger. A critical review of experiments on deuterium retention in displacement-damaged tung- sten as function of damaging dose. Materials Research Express, 10(10):102002, oct 2023

    2023

  17. [24]

    Dwaipayan Dasgupta, Sophie Blondel, Enrique Mart´ ınez, Dimitrios Maroudas, and Brian D. Wirth. Impact of Soret effect on hydrogen and helium retention in PFC tungsten under ELM-like conditions. Nuclear Fusion, 63(7):076029, jun 2023

    2023

  18. [25]

    D. Kato, H. Iwakiri, Y. Watanabe, K. Morishita, and T. Muroga. Super-saturated hydrogen effects on radia- tion damages in tungsten under the high-flux divertor plasma irradiation. Nuclear Fusion, 55(8):083019, jul 2015

    2015

  19. [26]

    Lindblad, D.R

    V. Lindblad, D.R. Mason, and F. Granberg. The effect of deuterium on defect production in irradiated tungsten. Journal of Nuclear Materials, 603:155422, 2025

    2025

  20. [27]

    Piaggi, E.M

    P.M. Piaggi, E.M. Bringa, R.C. Pasianot, N. Gordillo, M. Panizo-Laiz, J. del R´ ıo, C. G´ omez de Castro, and R. Gonzalez-Arrabal. Hydrogen diffusion and trapping in nanocrystalline tungsten. Journal of Nuclear Materials, 458:233–239, 2015

    2015

  21. [28]

    Hydrogen diffusion in tung- sten: A molecular dynamics study

    Yi-Nan Liu, Tiefeng Wu, Yi Yu, Xiao-Chun Li, Xiaolin Shu, and Guang-Hong Lu. Hydrogen diffusion in tung- sten: A molecular dynamics study. Journal of Nuclear Materials, 455(1):676–680, 2014. Proceedings of the 16th International Conference on Fusion Reactor Materials (ICFRM-16)

    2014

  22. [29]

    Molecular dynamics studies of hydro- gen diffusion in tungsten at elevated temperature: Con- centration dependence and defect effects

    Li-Fang Wang, Xiaolin Shu, De-Ye Lin, Guang-Hong Lu, and Hai-Feng Song. Molecular dynamics studies of hydro- gen diffusion in tungsten at elevated temperature: Con- centration dependence and defect effects. International Journal of Hydrogen Energy, 45(1):822–834, 2020

    2020

  23. [30]

    Damage dose dependence of deuterium retention in high-temperature self-ion irradi- ated tungsten, 2026

    Mikhail Zibrov, Thomas Schwarz-Selinger, Michael Kli- menkov, and Ute J¨ antsch. Damage dose dependence of deuterium retention in high-temperature self-ion irradi- ated tungsten, 2026

    2026

  24. [31]

    Granberg, K

    F. Granberg, K. Nordlund, M. W. Ullah, K. Jin, C. Lu, H. Bei, L. M. Wang, F. Djurabekova, W. J. Weber, and Y. Zhang. Mechanism of radiation damage reduction in equiatomic multicomponent single phase alloys. Phys. Rev. Lett., 116(13):135504, 2016

    2016

  25. [32]

    Granberg, J

    F. Granberg, J. Byggm¨ astar, and K. Nordlund. Defect accumulation and evolution during prolonged irradiation of Fe and FeCr alloys. J. Nucl. Mater., 528:151843, 2020

    2020

  26. [33]

    Granberg, J

    F. Granberg, J. Byggm¨ astar, and K. Nordlund. Molec- ular dynamics simulations of high-dose damage produc- tion and defect evolution in tungsten. Journal of Nuclear Materials, 556:153158, 2021. 17

    2021

  27. [34]

    Mason, Suchandrima Das, Peter M

    Daniel R. Mason, Suchandrima Das, Peter M. Derlet, Sergei L. Dudarev, Andrew J. London, Hongbing Yu, Nicholas W. Phillips, David Yang, Kenichiro Mizohata, Ruqing Xu, and Felix Hofmann. Observation of transient and asymptotic driven structural states of tungsten ex- posed to ra...

    2020

  28. [35]

    Mason, Abdallah Reza, Fredric Granberg, and Felix Hofmann

    Daniel R. Mason, Abdallah Reza, Fredric Granberg, and Felix Hofmann. Estimate for thermal diffusivity in highly irradiated tungsten using molecular dynamics simulation. Phys. Rev. Mater., 5:125407, Dec 2021

    2021

  29. [36]

    Mason, Max Boleininger, Jack Haley, Eric Pre- stat, Guanze He, Felix Hofmann, and Sergei L

    Daniel R. Mason, Max Boleininger, Jack Haley, Eric Pre- stat, Guanze He, Felix Hofmann, and Sergei L. Dudarev. Simulated TEM imaging of a heavily irradiated metal. Acta Materialia, 277:120162, 2024

    2024

  30. [37]

    Mason, Fredric Granberg, Max Boleininger, Thomas Schwarz-Selinger, Kai Nordlund, and Sergei L

    Daniel R. Mason, Fredric Granberg, Max Boleininger, Thomas Schwarz-Selinger, Kai Nordlund, and Sergei L. Dudarev. Parameter-free quantitative simulation of high-dose microstructure and hydrogen retention in ion- irradiated tungsten. Phys. Rev. Mater., 5:095403, Sep 2021

    2021

  31. [38]

    Boleininger, D.R

    M. Boleininger, D.R. Mason, A.E. Sand, and et al. Mi- crostructure of a heavily irradiated metal exposed to a spectrum of atomic recoils. Sci Rep, 13:1684, 2023

    2023

  32. [40]

    De Backer, D

    A. De Backer, D. R. Mason, C. Domain, D. Nguyen- Manh, M. C. Marinica, L. Ventelon, C. S. Becquart, and S. R. Dudarev. Multiscale modelling of the interaction of hydrogen with interstitial defects and dislocations in bcc tungsten. Nuclear Fusion, 58:016006, 2018

    2018

  33. [41]

    Dynamic equilibrium of displacement damage defects in heavy-ion irradiated tungsten

    Shiwei Wang, Wangguo Guo, Thomas Schwarz-Selinger, Yue Yuan, Lin Ge, Long Cheng, Xiaona Zhang, Xingzhong Cao, Engang Fu, and Guang-Hong Lu. Dynamic equilibrium of displacement damage defects in heavy-ion irradiated tungsten. Acta Materialia, 244:118578, 2023

    2023

  34. [42]

    G.S. Was. Fundamentals of Radiation Materials Science, 2nd ed, chapter 5, pages 207–252. Springer, New York, 2017

    2017

  35. [43]

    Hou, X.-S

    J. Hou, X.-S. Kong, X. Wu, J. Song, and C.S. Liu. Predictive model of hydrogen trapping and bubbling in nanovoids in bcc metals. Nature Materials, 18:833–839, 2019

    2019

  36. [44]

    Jenkins and M.A

    M.L. Jenkins and M.A. Kirk. Characterization of Radiation Damage by Transmission Electron Microscopy. Series in Microscopy in Materials Science. IOP, Bristol, 2001

    2001

  37. [45]

    Becquart and C

    C.S. Becquart and C. Domain. A density functional the- ory assessment of the clustering behaviour of He and H in tungsten. Journal of Nuclear Materials, 386-388:109–111,

  38. [46]

    Fusion Reactor Materials

  39. [47]

    Einstein

    A. Einstein. ¨Uber die von der molekularkinetischen the- orie der w¨ arme geforderte bewegung von in ruhenden fl¨ ussigkeiten suspendierten teilchen.Annalen der Physik, 322:549–560, 1905

    1905

  40. [48]

    R.A. Oriani. The diffusion and trapping of hydrogen in steel. Acta Met., 18:147–157, 1970

    1970

  41. [49]

    Dokken, Huihua Yang, Chirag Khurana, Kaelyn Dun- nell, Gabriele Ferrero, Vladimir Kulagin, Samuele Mes- chini, Jonathan Dufour, and Etienne A

    James Dark, R´ emi Delaporte-Mathurin, Jørgen S. Dokken, Huihua Yang, Chirag Khurana, Kaelyn Dun- nell, Gabriele Ferrero, Vladimir Kulagin, Samuele Mes- chini, Jonathan Dufour, and Etienne A. Hodille. FES- TIM v2.0: Upgraded framework for multi-species hydro- gen transport and...

    2026

  42. [50]

    Heinola, T

    K. Heinola, T. Ahlgren, K. Nordlund, and J. Keinonen. Hydrogen interaction with point defects in tungsten. Phys. Rev. B, 82:094102, Sep 2010

    2010

  43. [51]

    An em- pirical potential for simulating hydrogen isotope reten- tion in highly irradiated tungsten

    Daniel R Mason, Duc Nguyen-Manh, Victor W Lindblad, Fredric G Granberg, and Mikhail Yu Lavrentiev. An em- pirical potential for simulating hydrogen isotope reten- tion in highly irradiated tungsten. Journal of Physics: Condensed Matter, 35(49):495901, sep 2023

    2023

  44. [52]

    Heinola and T

    K. Heinola and T. Ahlgren. First-principles study of H on the reconstructed W(100) surface. Phys. Rev. B, 81:073409, Feb 2010

    2010

  45. [53]

    Heinola and T

    K. Heinola and T. Ahlgren. Diffusion of hydrogen in bcc tungsten studied with first principle calculations.Journal of Applied Physics, 107(11):113531, 2010

    2010

  46. [54]

    Bortz, M.H

    A.B. Bortz, M.H. Kalos, and J.L. Lebowitz. A new algo- rithm for Monte Carlo simulation of Ising spin systems. Journal of Computational Physics, 17(1):10 – 18, 1975

    1975

  47. [55]

    Visualization and analysis of atom- istic simulation data with OVITO–the open visualization tool

    Alexander Stukowski. Visualization and analysis of atom- istic simulation data with OVITO–the open visualization tool. Modelling and Simulation in Materials Science and Engineering, 18(1):015012, dec 2009

    2009

  48. [56]

    P. M. Derlet, M. R. Gilbert, and S. L. Dudarev. Simu- lating dislocation loop internal dynamics and collective diffusion using stochastic differential equations. Phys. Rev. B, 84:134109, Oct 2011

    2011

  49. [57]

    Published October 31, 2025, Version v1

    Palioxis code snapshot.https://doi.org/10.5281/ zenodo.17492671. Published October 31, 2025, Version v1

    2025

  50. [58]

    Fast parallel algorithms for short-range molecular dynamics

    Steve Plimpton. Fast parallel algorithms for short-range molecular dynamics. Journal of Computational Physics, 117(1):1 – 19, 1995

    1995

  51. [59]

    Study of hydrogen isotopes behavior in tungsten by a multi trap- ping macroscopic rate equation model

    E A Hodille, Y Ferro, N Fernandez, C S Becquart, T An- got, J M Layet, R Bisson, and C Grisolia. Study of hydrogen isotopes behavior in tungsten by a multi trap- ping macroscopic rate equation model. Physica Scripta, T167:014011, jan 2016

    2016

  52. [60]

    Schmid, U

    K. Schmid, U. von Toussaint, and T. Schwarz-Selinger. Transport of hydrogen in metals with occupancy de- pendent trap energies. Journal of Applied Physics, 116(13):134901, 10 2014

    2014

  53. [61]

    Hydrogen assisted vacancy formation in tungsten: A first-principles investigation

    Shi-Yao Qin, Shuo Jin, Lu Sun, Hong-Bo Zhou, Ying Zhang, and Guang-Hong Lu. Hydrogen assisted vacancy formation in tungsten: A first-principles investigation. Journal of Nuclear Materials, 465:135–141, 2015

    2015

  54. [62]

    Gao, and Guang-Hong Lu

    Xiao-Chun Li, Xiaolin Shu, Yi-Nan Liu, F. Gao, and Guang-Hong Lu. Modified analytical interatomic poten- tial for a W–H system with defects. Journal of Nuclear Materials, 408(1):12–17, 2011

    2011

  55. [63]

    Srinivasan, K

    P. Srinivasan, K. C. Pitike, W. Setyawan, M. R. Gilbert, and D. Nguyen-Manh. Performance of two machine- learning interatomic potentials for studying hydrogen dif- fusion in vanadium. in preparation, 2025

    2025

  56. [64]

    H. C. Kang and W. H. Weinberg. Dynamic Monte Carlo with a proper energy barrier: Surface diffusion and two- dimensional domain ordering. The Journal of Chemical Physics, 90(5):2824–2830, 1989

    1989

  57. [65]

    An empirical potential for simulating vacancy clusters in tungsten

    D R Mason, D Nguyen-Manh, and C S Becquart. An empirical potential for simulating vacancy clusters in tungsten. Journal of Physics: Condensed Matter, 18 29(50):505501, 2017

    2017

  58. [66]

    Zepeda-Ruiz, Graeme J

    Seungwu Han, Luis A. Zepeda-Ruiz, Graeme J. Ackland, Roberto Car, and David J. Srolovitz. Interatomic poten- tial for vanadium suitable for radiation damage simula- tions. Journal of Applied Physics, 93(6):3328–3335, 03 2003

    2003

  59. [67]

    Predicting vacancy-mediated diffusion of interstitial solutes inα-fe

    Caroline Barouh, Thomas Schuler, Chu-Chun Fu, and Thomas Jourdan. Predicting vacancy-mediated diffusion of interstitial solutes inα-fe. Phys. Rev. B, 92:104102, Sep 2015

    2015

  60. [68]

    Resolving vacancy clustering mech- anisms in tungsten via machine-learning-potential-based simulations at experimental time scales

    Guo Wei, Zichen Song, Jie Hou, Jiaqi Wang, Akksay Singh, and Lei Li. Resolving vacancy clustering mech- anisms in tungsten via machine-learning-potential-based simulations at experimental time scales. Acta Materialia, page 121529, 2025

    2025

  61. [69]

    Influence of carbon on the evolution of irradiation defects in tungsten

    Yu-Ze Niu, Yu-Hao Li, Qing-Yuan Ren, Zhong-Zhu Li, Dmitry Terentyev, Hui-Zhi Ma, Hong-Bo Zhou, and Guang-Hong Lu. Influence of carbon on the evolution of irradiation defects in tungsten. Journal of Nuclear Materials, 579:154393, 2023

    2023

  62. [70]

    Chen, C.S

    Chi Song, Jie Hou, L. Chen, C.S. Liu, and Xiang-Shan Kong. Bridging the gap between theory and experiment in vacancy concentration, C/N/O diffusivity, and diva- cancy interaction in tungsten: Role of vacancy-C/N/O interaction. Acta Materialia, 263:119516, 2024

    2024

  63. [71]

    Anomalous self-diffusion in tungsten and molybdenum: Exonerating the di-vacancy contribution and the key role of interatomic interaction

    Clovis Lapointe, Anruo Zhong, Thomas D Swinburne, Fabien Bruneval, Manuel Ath` enes, and Mihai-Cosmin Marinica. Anomalous self-diffusion in tungsten and molybdenum: Exonerating the di-vacancy contribution and the key role of interatomic interaction. Physical Review Materials, ...

    2025

  64. [72]

    Muzyk, D

    M. Muzyk, D. Nguyen-Manh, K. J. Kurzyd lowski, N. L. Baluc, and S. L. Dudarev. Phase stability, point defects, and elastic properties of W-V and W-Ta alloys. Phys. Rev. B, 84:104115, Sep 2011

    2011

  65. [73]

    G. J. Ackland, D. J. Bacon, A. F. Calder, and T. Harry. Computer simulation of point defect properties in dilute fe—cu alloy using a many-body interatomic potential. Philosophical Magazine A, 75(3):713–732, 1997

    1997

  66. [74]

    Damage recovery stages revisited: Thermal evolution of non-saturated and saturated dis- placement damage in heavy-ion irradiated tungsten.Acta Materialia, 273:119942, 2024

    Shiwei Wang, Hanqing Wang, Xiaoou Yi, Wei Tan, Lin Ge, Yuhan Sun, Wangguo Guo, Qigui Yang, Long Cheng, Xiaona Zhang, Yue Yuan, Xingzhong Cao, Engang Fu, and Guang-Hong Lu. Damage recovery stages revisited: Thermal evolution of non-saturated and saturated dis- placement damage ...

    2024

  67. [75]

    Ishida, K

    S. Ishida, K. Ibano, Y. Ueda, and A.M. Ito. Kinetic monte carlo study on void behavior in high-temperature tungsten. Fusion Engineering and Design, 218:115111, 2025

    2025

  68. [76]

    A. E. Sand, M. J. Aliaga, M. J. Caturla, and K. Nord- lund. Surface effects and statistical laws of defects in primary radiation damage: Tungsten vs. iron. EPL (Europhysics Letters), 115(3):36001, 2016

    2016

  69. [77]

    An empirical potential to simulate helium and hydrogen in irradiated tungsten, applied to a mecha- nistic model for the energetics of gas-filled voids

    Samanyu Tirumala, Daniel R Mason, Oliver Shat- tock, Duc Nguyen-Manh, Felix Hofmann, and Max Boleininger. An empirical potential to simulate helium and hydrogen in irradiated tungsten, applied to a mecha- nistic model for the energetics of gas-filled voids. Journal of Physics:...

    2026

  70. [78]

    Zibrov and K

    M. Zibrov and K. Schmid. On the factors enhancing hydrogen trapping in spherical cavities in metals.Nuclear Materials and Energy, 38:101617, 2024

    2024

  71. [79]

    The synergies between displacement damage creation and hydrogen presence: the effect of D ion energy and flux

    Sabina Markelj, Matic Pecovnik, Thomas Schwarz- Selinger, and Mitja Kelemen. The synergies between displacement damage creation and hydrogen presence: the effect of D ion energy and flux. Physica Scripta, 97(2):024006, jan 2022

    2022

  72. [80]

    E. A. Hodille, N. Fernandez, Z. A. Piazza, M. Ajmal- ghan, and Y. Ferro. Hydrogen supersaturated layers in H/D plasma-loaded tungsten: A global model based on thermodynamics, kinetics and density functional theory data. Physical Review Materials, 2(9):093802, 2018

    2018

  73. [81]

    ARCHER2 Service Description

    George Beckett, Josephine Beech-Brandt, Kieran Leach, Z¨ oe Payne, Alan Simpson, Lorna Smith, Andy Turner, and Anne Whiting. ARCHER2 Service Description. De- cember 2024. APPENDIX In this appendix, we derive a simple model for the free energy of hydrogenic gases in a bubble. I...

    2024

Pith tools

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