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REVIEW 3 major objections 5 minor 49 references

Kinetic surface model in FESTIM: Verification and Validation

T0 review · 3 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read FESTIM's new kinetic surface model is verified by manufactured solutions and validated against four hydrogen-retention experiments in Ti, W, and EUROFER.

desk verdict A useful open-source V&V contribution with a genuine internal inconsistency in the key flux for one validation case; fixable but needs to be corrected before publication. read the letter →

arxiv 2411.16474 v1 pith:OTQXKLML submitted 2024-11-25 cond-mat.mtrl-sci physics.comp-ph

Vladimir Kulagin , Rémi Delaporte-Mathurin , Etienne A. Hodille , Mikhail Zibrov This is my paper · ORCID
classification cond-mat.mtrl-sciphysics.comp-ph
keywords kineticsurfacemodelFESTIMhydrogentransportmethodofmanufacturedsolutionsvalidationisotoperetentionthermaldesorptionspectroscopyfiniteelement
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 reports that FESTIM v1.3's newly added kinetic surface model is correctly implemented and usable for hydrogen transport simulations. It verifies the numerical implementation with the method of manufactured solutions on a coupled bulk-surface diffusion problem, obtaining small L2 errors that decrease with refinement. It then claims reliability by reproducing four published experiments on hydrogen isotope uptake and release in titanium, tungsten, and EUROFER, using surface flux expressions taken from earlier models. Cross-code comparisons with MHIMS and TESSIM-X match essentially curve-for-curve, which the authors present as evidence that the new model solves the same physics as established packages.

What carries the argument

The load-bearing object is the kinetic surface model itself: a surface concentration $c_s$ (particles per area) evolved by balancing the subsurface-to-surface flux $J_{bs}$, the surface-to-subsurface flux $J_{sb}$, and an arbitrary user-supplied net vacuum-to-surface flux $J_{vs}$, with the bulk connected through the Robin condition $\mathbf{J}\cdot\mathbf{n} = \lambda_{IS}\,\partial c_m/\partial t + J_{bs} - J_{sb}$. The model generalizes the earlier concentration-only surface treatment, which assumed adsorbed and absorbed populations are in equilibrium; the new variable allows surface kinetics to be rate-limiting, as in low-energy atom exposure or low-temperature sorption. The machinery is completed by Arrhenius frequency factors and site-blocking factors $(1 - c_s/n_{surf})$.

What would settle it

Run the same four cases with a manufactured solution whose L2 errors do not decrease as the mesh and time step are refined, or reproduce one of the experiments using independently measured sticking and desorption parameters not fitted to that experiment; either failure would show that the model or its validation is not conclusive.

Watch

Extended reading notes

Core claim

The central claim is that the kinetic surface model — which tracks an explicit adsorbed surface concentration $c_s$ governed by $dc_s/dt = J_{bs} - J_{sb} + J_{vs}$, coupled to the bulk McNabb–Foster diffusion-trapping equations through a Robin condition — is a correct and reliable extension of FESTIM. Correctness is established by manufactured-solution convergence; reliability is established by agreement with four experiments spanning different materials (Ti absorption at 473–923 K, D desorption from oxygen-covered W(110), NRA-measured D retention in self-damaged W, and TDS from damaged EUROFER) and with two independent codes.

Load-bearing premise

The validation assumes that the surface flux expressions and parameter values taken from earlier models are the correct physics for these experiments, even though several of those parameters were fitted to the same or closely related data.

Editorial extensions

If this is right

  • FESTIM users can model surface-limited uptake and release processes, such as low-energy atom exposure, sorption experiments, and transient plasma events, with an explicit adsorbed hydrogen concentration.
  • The manufactured-solution test provides a benchmark problem for the kinetic surface model that other hydrogen transport codes can reproduce.
  • Because FESTIM matches MHIMS and TESSIM-X on the same inputs, the four validation cases can serve as a shared reference set for cross-code comparisons.
  • The near-instant surface equilibration seen in the self-damaged tungsten case justifies a steady-state approximation of surface kinetics for long-time simulations.
  • The validation cases will be added to FESTIM's verification and validation book, giving users documented confidence in the new feature.

Reading between the lines

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

  • A consequence the paper leaves implicit: the experiments constrain only a few surface parameters; many come from fits to the same or closely related measurements, so the validation primarily shows that FESTIM reproduces the equations of prior codes rather than independently confirming the surface physics.
  • A stricter test would use the kinetic surface model with parameters measured from independent surface-science experiments (for example, desorption energies from density functional theory and sticking coefficients from beam experiments) and predict a retention experiment without refitting.
  • The steady-state reduction the authors mention could be formalized by taking $dc_s/dt \approx 0$ and eliminating $c_s$, yielding an effective surface boundary condition; a useful extension would be to quantify when this approximation breaks down, such as during fast transients or large $J_{vs}$.
  • Extending the model beyond 1D would let surface diffusion couple adjacent faces; the current 1D restriction means predictions for geometrically complex components still rely on the equilibrium surface assumption.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper describes the implementation of a kinetic surface model in the open-source hydrogen transport code FESTIM v1.3, in which the surface concentration of adsorbed hydrogen is treated as an independent field evolved by a flux balance equation coupled to bulk diffusion-trapping transport. The implementation is checked with a method-of-manufactured-solutions (MMS) test, and then applied to reproduce four experimental datasets on hydrogen isotope retention in Ti, oxidized W, self-damaged W, and EUROFER, including comparisons with the MHIMS and TESSIM-X codes. The authors claim that the MMS test proves correctness of the implementation and that the four validation cases demonstrate reliability of the model.

Significance. If the implementation and validation are sound, the paper is valuable: FESTIM is a widely used open-source package, and a documented, flexible kinetic surface model with a public validation script repository [27] would be a useful community resource. The MMS test is a standard and appropriate verification tool, and the cross-code comparisons with MHIMS and TESSIM-X provide a meaningful consistency check. However, the validation strength is limited by the reuse of parameters fitted to the same or closely related experiments in earlier work, by the absence of quantitative error measures and experimental uncertainty bars, and by an internal inconsistency in the key flux input of Case 4 that must be resolved before the central claim can be accepted.

major comments (3)
  1. [Section 4.4, Table 4 and Fig. 8] The text states that EUROFER samples were irradiated with a low-energy D flux of ≈9×10^19 m^-2 s^-1, and Fig. 8 shows flux values around 9 on an axis labeled in units of 10^19 m^-2 s^-1, but Table 4 lists ΓD = 5.8×10^18 m^-2 s^-1, a factor of about 15 lower. Since the surface fluxes Jads (∝ ΓD), Jloss (∝ ΓD(1-r)θ), and the implantation source S all scale with this flux, the two values lead to quantitatively different predicted retention and TDS spectra. The reader cannot determine from the paper which value was actually used in the FESTIM simulations. This is a load-bearing inconsistency for the fourth validation case and for the paper's overall claim of reproducing the experimental cases; it must be corrected and clarified.
  2. [Section 3, MMS verification] The paper claims that 'these errors decrease with decreasing stepsizes' but reports only single L2 error values (Ebulk = 2.33×10^-5, Esurf = 4.29×10^-5) for one mesh size and one time step, with no convergence table or convergence-rate analysis. A verification claim of 'correctness' in a V&V paper should include a systematic refinement study showing the expected order of accuracy. Please add a grid/time-step convergence table or at least a log-log plot of error versus step size.
  3. [Section 4.2, Section 4.3, Section 4.4] The validation cases inherit many parameters that were fitted to the same or closely related experimental data in prior studies: the coverage-dependent desorption parameters in Table 2 are from Hodille et al. [5], the trap concentrations and detrapping energies in Table 3 are from [45], and Case 4 relies on parameters from [46] plus additional values from private communication. Consequently, the agreement with experiment is largely a consistency check that FESTIM solves the same equations as the earlier codes, not an independent confirmation of the underlying physics. The paper should state this limitation explicitly and temper the claim that the model's 'reliability' is demonstrated by these cases.
minor comments (5)
  1. [Section 4.4, text after Eq. (24)] The sentence 'The front surface (at x = 0) is assumed...' and the following paragraph contain 'ad hocloss' which should be 'ad hoc loss channel'.
  2. [Section 4.1, Eq. (12)] The symbol for the sample cross-section area appears to be missing in the text; it is denoted only by '= 1.3 × 10^-4 m^2' after Eq. (12). Please define the symbol explicitly.
  3. [Figure 9] In the sentence before Fig. 9, '(see Fig. 9.' is missing a closing parenthesis; it should read '(see Fig. 9).'
  4. [Section 4.3, Table 3] The table and text state that the D flux is 5.8×10^18 m^-2 s^-1, which is consistent with the cited experiment, but no experimental uncertainty is quoted for the NRA data or the flux; adding error bars or a stated uncertainty would strengthen the comparison.
  5. [General] The paper would benefit from a reproducibility statement explicitly listing the version of FESTIM, the FESTIM V&V book reference, and the exact contents of the Zenodo repository [27], since the repository link is central to the verification and validation claims.

Circularity Check

0 steps flagged · score 2.0 of 10

No material circularity: the implementation-correctness claim is backed by a self-contained MMS test and independent cross-code benchmarks; the experimental 'reproductions' reuse earlier published parameters and are not framed as predictions.

full rationale

The central verification claim is the MMS test (Section 3): an exact manufactured solution is inserted into the governing equations, the source and boundary terms are derived from it, and the computed solution is compared with that exact solution. This is self-contained and does not reduce to the model's own inputs. The cross-code comparisons with MHIMS and TESSIM-X (Figs. 5, 6, 9) are consistency checks of the implementation against independent codes, and the paper is explicit that the same smooth temperature/flux histories were used for the TESSIM-X comparison (Section 4.4), which is the correct benchmarking procedure. The four experimental cases are called 'reproductions', not predictions; parameters are taken from prior publications (Tables 1-4), including some co-authored works (Hodille et al. [5,31,45]). This is a minor self-citation, but it is not load-bearing because the MMS test and the external experimental datasets (Hirooka et al. [35], Dunand et al. [38], Markelj et al. [44], Schmid et al. [48]) provide the independent content. The paper also flags its own limitations: Case 4 notes 'Certain required parameters not specified in [46] were obtained through private communication' and 'some parameters differ between the published paper and the input files of TESSIM-X', and Case 4 diffusivity parameters 'were determined for a limited temperature range (623-722 K)'. These weaken reproducibility but are not circularity. Separately, not counted as circularity: Table 4 lists ΓD = 5.8×10^18 m^-2 s^-1 while Section 4.4 and Fig. 8 state ≈9×10^19 m^-2 s^-1 for Case 4; this is an internal consistency/reproducibility bug, not a circular derivation. Overall, the derivation chain does not reduce to its inputs; score 2 reflects the minor self-citation and calibrated-parameter caveat only.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central claim is about implementation correctness. The MMS test is self-contained. The validation relies on many inherited fitted parameters, increasing the circularity burden for the reliability claim. No new physical entities are introduced.

free parameters (4)
  • Coverage-dependent desorption parameters (E0, ΔE, θ0, δθ, α, β) = Clean and two O-coverages; values in Table 2
    Fitted to W TDS data in Hodille et al. [5] and reused here, so experimental agreement in Section 4.2 is not an independent prediction.
  • Trap concentrations and detrapping energies for Case 3 = n1=n2=1e-4 nW, n3=1.9e-3 nW, n4=1.6e-3 nW, n5=2e-4 nW; Ep=0.85, 1.00, 1.65, 1.85, 2.06 eV
    Taken from Hodille et al. [45], originally tuned to reproduce D retention in damaged W; using them here is a consistency check.
  • Ωloss effective yield for ion-impact loss in Case 4 = 8e4
    Ad hoc loss channel from Schmid et al. [46], fitted to EUROFER ion-exposure data; no independent measurement cited.
  • Extrinsic trap concentration n2 in Case 4 = 2.5e-4 nEFe or 5.0e-4 nEFe
    Selected depending on D presence during damaging; parameter inherited from prior work, Section 4.4.
assumptions (6)
  • domain assumption Fickian diffusion and McNabb-Foster trapping model govern bulk hydrogen transport
    Invoked in Section 2.1 as the bulk physics basis.
  • domain assumption Surface flux balance equations (3)-(5) and the Robin boundary condition (4) describe surface-bulk coupling
    Section 2.2, based on Pick & Sonnenberg and Hodille et al.
  • domain assumption No surface diffusion and 1D geometry are sufficient for the test cases
    Stated limitation in Section 2.2.
  • domain assumption Coverage-dependent desorption energy expressions (16)-(17) are valid for the W surface
    Case 2, from DFT calculations and prior fitting in Hodille et al.
  • domain assumption Sieverts' law is enforced by setting ksb via equation (23)
    Case 4, used to relate surface-to-subsurface transition to solubility.
  • ad hoc to paper Parameters from private communication are correct for the EUROFER samples
    Section 4.4 states certain required parameters were obtained through private communication.

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Cite this review

Pith. "Pith review of Kinetic surface model in FESTIM: Verification and Validation." pith.science (2026). https://pith.science/paper/OTQXKLML

@misc{pith2026241116474,
  author       = {Pith},
  title        = {Pith review of: Kinetic surface model in FESTIM: Verification and Validation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OTQXKLML}},
  note         = {Machine review of arXiv:2411.16474}
}
read the original abstract

The open-source code FESTIM (Finite Element Simulation of Tritium In Materials) is a powerful user-friendly software for hydrogen transport simulations. Up to now, it was capable of addressing various hydrogen transport problems with surface processes dependent on the concentration of solute species. However, the kinetics of surface hydrogen concentration should be considered under certain conditions. The recent 1.3 release of FESTIM introduced a new kinetic surface model, implemented in a flexible way for various applications. The correctness of the implementation is first proven using the method of manufactured solutions. Then, reliability of the model is demonstrated by reproducing four experimental cases on dynamics of hydrogen isotope retention in different materials. An additional cross-code comparison with two other simulation packages, MHIMS and TESSIM-X, shows an excellent agreement and strengthens the validity of the model.

Figures

Figures reproduced from arXiv: 2411.16474 by the authors.

Figure 1
Figure 1. Near surface energy landscape of a hydrogen-metal system. Energy levels are measured from the H2 state (EH2 ). Arrows indicate H transition paths near the surface. Dissociation Langmuir-Hinshelwood recombination Atomic adsorption (desorption) Sputtering Hot-atom recombination Eley-Rideal recombination [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Possible surface processes taking place on a surface of a metal. Blue circles represent incident particles (atoms or molecules) from a near-surface environment and green circles - initially adsorbed atoms. coming from the vacuum onto the surface and Jout is the sum of all fluxes coming from the surface to the vacuum. Jin can be used to set up adsorption fluxes from different processes, for example, molecular dissoci… view at source ↗
Figure 3
Figure 3. Evolution of the mobile concentration profile cm (top) and temporal evolution of the surface concentration cs (bottom). 4. Validation This section presents four cases used to validate the implemented surface model. They reproduce experiments on the retention of hydrogen isotopes in Ti/W/EUROFER under exposure with low-energy atoms/molecules. In addi￾tion, three cases include a cross-code comparison between the resul… view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Temporal dependencies of the H content in Ti at different temperatures. simulated. At each time step, the amount of H in Ti is evaluated and the chamber pressure is updated explicitly. Temperature-dependent frequency factors for transi￾tions between surface and subsurf…
Figure 5
Figure 5. Figure 5: TDS spectra of D from W with different O coverages. Comparison with the experimental data (left) and MHIMS simulations (right). Temperature-dependent (eqs. (13)) frequency factors of D transitions between surface and subsurface are used. Ac￾tivation energy for re-absor…
Figure 6
Figure 6. Figure 6: Temporal evolution of the D retention in W (bottom). Comparison between FESTIM and NRA measurements (middle) and FESTIM and MHIMS simulations (top). 8 [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: Temporal evolution of the D surface concentra￾tion. energy for detrapping. The results produced by FESTIM are in good agreement with the experimental data and correlate perfectly with MHIMS. An interesting finding in [45] is that the surface concen￾tration of D evolves…
Figure 8
Figure 8. Figure 8: Temporal evolutions of material temperature (top) and D flux (bottom) used in ”143 h plasma” sim￾ulation case. implanted D atoms, r is the reflection coefficient. The flux of molecules (ΓD2 ) is calculated using eqs. (10). The subsurface-to-surface transition is assume…
Figure 9
Figure 9. Figure 9: TDS spectra of D from different EUROFER samples. Comparison with the experimental data (top) and TESSIM-X simulations (bottom). The front surface (at x = 0) is assumed to be irra￾diated with the flux of energetic D ions. Therefore, the full kinetic surface model is imp…

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Works this paper leans on

49 extracted references · 35 canonical work pages

  1. [27]

    Kulagin, R

    V. Kulagin, R. Delaporte-Mathurin, KulaginVladimir/FESTIM-SurfaceKinetics-Validation: Sub- mission release (Nov. 2024). doi:10.5281/zenodo.14217067. URL https://doi.org/10.5281/zenodo.14217067

    work page doi:10.5281/zenodo.14217067 2024

  2. [5]

    Hodille, B

    E. Hodille, B. Pavec, J. Denis, A. Dunand, Y. Ferro, M. Minissale, T. Angot, C. Grisolia, R. Bisson, Deuterium uptake, desorption and sputtering from W(110) surface cov- ered with oxygen, Nuclear Fusion 64 (2024) 046022. doi: 10.1088/1741-4326/AD2A29

    doi:10.1088/1741-4326/ad2a29 2024

  3. [45]

    Hodille, X

    E. Hodille, X. Bonnin, R. Bisson, T. Angot, C. Becquart, J. Layet, C. Grisolia, Macroscopic rate equation modeling of trapping/detrapping of hydrogen isotopes in tungsten materi- als, Journal of Nuclear Materials 467 (2015) 424–431. doi: 10.1016/j.jnucmat.2015.06.041

    doi:10.1016/j.jnucmat.2015.06.041 2015

  4. [46]

    Schmid, T

    K. Schmid, T. Schwarz-Selinger, A. Theodorou, Modeling intrinsic- and displacement-damage-driven retention in EURO- FER, Nuclear Materials and Energy 36 (2023) 101494. doi: 10.1016/J.NME.2023.101494

    arXiv 2023

  5. [1]

    G. H. Lu, H. B. Zhou, C. S. Becquart, A review of modelling and simulation of hydrogen behaviour in tungsten at different scales, Nuclear Fusion 54 (2014) 086001. doi:10.1088/0029-5 515/54/8/086001

    doi:10.1088/0029-5 2014

  6. [2]

    S. Guo, L. Xu, S. Dong, Y. F. Cheng, Finite element modeling of hydrogen atom diffusion and distribution at corrosion defect on aged pipelines transporting hydrogen, International Journal of Hydrogen Energy 48 (2023) 13566–13577. doi:10.1016/J. IJHYDENE.2022.12.287

    doi:10.1016/j 2023

  7. [3]

    Kobayashi, K

    C. Kobayashi, K. Tanabe, Electromagnetic–thermal–mass transport triple hybrid model for energy-efficient hydrogen re- lease from metal particles by induction heating, International Journal of Hydrogen Energy 69 (2024) 918–926. doi:10.1016/ J.IJHYDENE.2024.05.005

    work page 2024

  8. [4]

    X. Li, X. Ma, J. Zhang, E. Akiyama, Y. Wang, X. Song, Review of Hydrogen Embrittlement in Metals: Hydrogen Diffusion, Hy- drogen Characterization, Hydrogen Embrittlement Mechanism and Prevention, Acta Metallurgica Sinica (English Letters) 33 (2020) 759–773. doi:10.1007/S40195-020-01039-7/METRICS

    work page doi:10.1007/s40195-020-01039-7/metrics 2020

Show all 49 references
  1. [6]

    Schmid, Diffusion-trapping modelling of hydrogen recycling in tungsten under ELM-like heat loads, Physica Scripta 2016 (2016) 014025

    K. Schmid, Diffusion-trapping modelling of hydrogen recycling in tungsten under ELM-like heat loads, Physica Scripta 2016 (2016) 014025. doi:10.1088/0031-8949/T167/1/014025. URL https://iopscience.iop.org/article/10.1088/0031-8 949/T167/1/014025https://iopscience.iop.org/artic...

    2016 doi

  2. [7]

    Schmid, M

    K. Schmid, M. Zibrov, On the use of recombination rate coef- ficients in hydrogen transport calculations, Nuclear Fusion 61 (2021) 086008. doi:10.1088/1741-4326/ac07b2

    2021 doi

  3. [8]

    G. R. Longhurst, TMAP7 User Manual (12 2008). doi:10.217 2/952013

    2008

  4. [9]

    A. D. Lindsay, TMAP8 (2021). URL https://mooseframework.inl.gov/TMAP8/index.html

    2021

  5. [10]

    R. D. Smirnov, J. Guterl, S. I. Krasheninnikov, Modeling of Multispecies Dynamics in Fusion-Related Materials with F ACE, Fusion Science and Technology 71 (2017) 75–83. doi:10.13182 /FST16-125

    2017

  6. [11]

    Matveev, M

    D. Matveev, M. Wensing, L. Ferry, F. Virot, M. Barrachin, Y. Ferro, C. Linsmeier, [reaction-diffusion modeling of hydrogen transport and surface effects in application to single-crystalline be], Nuclear Instruments and Methods in Physics Research Sec- tion B: Beam Interactions...

    2018 doi

  7. [12]

    Delaporte-Mathurin, J

    R. Delaporte-Mathurin, J. Dark, G. Ferrero, E. A. Hodille, V. Kulagin, S. Meschini, Festim: An open-source code for hy- drogen transport simulations, International Journal of Hydro- gen Energy 63 (2024) 786–802. doi:10.1016/J.IJHYDENE.202 4.03.184

    2024 doi

  8. [13]

    Delaporte-Mathurin, H

    R. Delaporte-Mathurin, H. Yang, J. Denis, J. Dark, E. A. Hodille, G. D. Temmerman, X. Bonnin, J. Mougenot, Y. Charles, H. Bufferand, G. Ciraolo, C. Grisolia, Fuel retention in west and iter divertors based on festim monoblock simula- tions, Nuclear Fusion 61 (12 2021). doi:10....

    2021 doi

  9. [14]

    E. A. Hodille, R. Delaporte-Mathurin, J. Denis, M. Pecovnik, E. Bernard, Y. Ferro, R. Sakamoto, Y. Charles, J. Mougenot, A. D. Backer, C. S. Becquart, S. Markelj, C. Grisolia, Modelling of hydrogen isotopes trapping, diffusion and permeation in di- vertor monoblocks under ITER...

    2021 doi

  10. [15]

    J. Dark, R. Delaporte-Mathurin, Y. Charles, E. A. Hodille, C. Grisolia, J. Mougenot, Influence of hydrogen trapping on WCLL breeding blanket performances, Nuclear Fusion 61 (11 2021). doi:10.1088/1741-4326/AC28B0

    2021 doi

  11. [16]

    Dunnell, R

    K. Dunnell, R. Delaporte-Mathurin, Simulating tritium trans- port for nuclear fusion extractors (04 2024). doi:10.13140/RG. 2.2.13923.16164

    2024

  12. [17]

    J. Dark, R. Delaporte-Mathurin, T. Schwarz-Selinger, E. A. Hodille, J. Mougenot, Y. Charles, C. Grisolia, Modelling neu- tron damage effects on tritium transport in tungsten, Nuclear Fusion 64 (8 2024). doi:10.1088/1741-4326/AD56A0

    2024 doi

  13. [18]

    Kulagin, Y

    V. Kulagin, Y. Gasparyan, Numerical simulation of deuterium retention in tungsten under ELM-like conditions, Journal of Nu- clear Materials 603 (1 2025). doi:10.1016/J.JNUCMAT.2024.1 55370

    2025 doi

  14. [19]

    Guterl, R

    J. Guterl, R. Smirnov, P. Snyder, Effects of surface processes on hydrogen outgassing from metal in desorption experiments, Nuclear Fusion 59 (2019) 096042. doi:10.1088/1741-4326/ab 280a

    2019 doi

  15. [20]

    A. A. Pisarev, O. V. Ogorodnikova, M. O. Titkov, Plasma driven tritium uptake and leakage through plasma facing mate- rials, Fusion Engineering and Design 41 (1998) 103–109. doi: 10.1016/S0920-3796(98)00223-3

    1998 doi

  16. [21]

    M. H. Hoen, M. Mayer, A. W. Kleyn, P. A. Z. V. Emmichoven, Strongly reduced penetration of atomic deuterium in radiation- damaged tungsten, Physical Review Letters 111 (2013) 225001. doi:10.1103/PhysRevLett.111.225001

    2013 doi

  17. [22]

    P. N. Maya, Molecular dynamics studies of sticking and reflec- tion of low-energy deuterium on single crystal tungsten, Journal of Nuclear Materials 480 (2016) 411–419. doi:10.1016/J.JNUC MAT.2016.08.007

    2016 doi

  18. [23]

    O. V. Ogorodnikova, S. Markelj, U. V. Toussaint, Interaction of atomic and low-energy deuterium with tungsten pre-irradiated with self-ions, Journal of Applied Physics 119 (2016) 54901. doi:10.1063/1.4940678/142479

    2016 doi

  19. [24]

    N. Katz, I. Furman, O. Biham, V. Pirronello, G. Vidali, Molec- ular hydrogen formation on astrophysically relevant surfaces, The Astrophysical Journal 522 (1999) 305–312. doi:10.1086/ 307642/FULLTEXT/. URL https://iopscience.iop.org/article/10.1086/307642h ttps://iopscience.io...

    1999 doi

  20. [25]

    T. Hama, N. Watanabe, Surface processes on interstellar amor- phous solid water: Adsorption, diffusion, tunneling reactions, and nuclear-spin conversion, Chemical Reviews 113 (2013) 8783–8839. doi:10.1021/CR4000978/ASSET/IMAGES/CR- 201 3-000978_M050.GIF. URL https://pubs.acs.o...

    2013 doi

  21. [26]

    Delaporte-Mathurin, J

    R. Delaporte-Mathurin, J. Santana, Festim v&v book (2024). URL https://dspace.mit.edu/handle/1721.1/156690

    2024

  22. [28]

    McNabb, P

    A. McNabb, P. K. Foster, A New Analysis of the Diffusion of Hydrogen in Iron and Ferritic Steels, Transactions of the Met- allurgical Society of AIME 227 (1963) 618

    1963

  23. [29]

    M. A. Pick, K. Sonnenberg, A model for atomic hydrogen- metal interactions — application to recycling, recombination and permeation, Journal of Nuclear Materials 131 (1985) 208–

    1985

  24. [30]

    A. A. Pisarev, O. V. Ogorodnikova, Elementary processes near the interface between hydrogen gas and solid, Journal of Nuclear Materials 248 (1997) 52–59. doi:10.1016/S0022-3115(97)002 01-8

    1997 doi

  25. [31]

    E. A. Hodille, A. Zaloˇ znik, S. Markelj, T. Schwarz-Selinger, C. S. Becquart, R. Bisson, C. Grisolia, Simulations of atomic deuterium exposure in self-damaged tungsten, Nuclear Fusion 57 (2017) 056002. doi:10.1088/1741-4326/AA5AA5

    2017 doi

  26. [32]

    P. J. Roache, Code verification by the method of manufactured 12 solutions, Journal of Fluids Engineering 124 (2002) 4–10. doi: 10.1115/1.1436090

    2002 doi

  27. [33]

    W. L. Oberkampf, C. J. Roy, Verification and Validation in Scientific Computing, Cambridge University Press, 2010

    2010

  28. [34]

    Delaporte-Mathurin, J

    R. Delaporte-Mathurin, J. Dark, natethegreatINL, T. Fuerst, paulbrrn, V. Kulagin, C. Hill, RemDelaporteMathurin/h- transport-materials: Release 0.17 (Oct. 2024). doi:10.5281/ze nodo.13912922. URL https://doi.org/10.5281/zenodo.13912922

    2024 doi

  29. [35]

    Hirooka, M

    Y. Hirooka, M. Miyake, T. Sano, A study of hydrogen absorp- tion and desorption by titanium, Journal of Nuclear Materials 96 (1981) 227–232. doi:10.1016/0022-3115(81)90566-3

    1981 doi

  30. [36]

    Shimohata, Y

    Y. Shimohata, Y. Hamamoto, K. Nishi, K. Tanabe, Improved kinetic model of hydrogen absorption and desorption in tita- nium with subsurface transport, Fusion Engineering and Design 173 (2021) 112833. doi:10.1016/J.FUSENGDES.2021.112833

    2021

  31. [37]

    G. W. Wille, J. W. Davis, Hydrogen in titanium alloys (4 1981). doi:10.2172/6420120

    1981 doi

  32. [38]

    Dunand, M

    A. Dunand, M. Minissale, J. B. Faure, L. Gallais, T. Angot, R. Bisson, Surface oxygen versus native oxide on tungsten: con- trasting effects on deuterium retention and release, Nuclear Fu- sion 62 (2022) 054002. doi:10.1088/1741-4326/AC583A

    2022 doi

  33. [39]

    Z. A. Piazza, M. Ajmalghan, Y. Ferro, R. D. Kolasinski, Sat- uration of tungsten surfaces with hydrogen: A density func- tional theory study complemented by low energy ion scattering and direct recoil spectroscopy data, Acta Materialia 145 (2018) 388–398. doi:10.1016/J.ACTAMAT...

    2018 doi

  34. [40]

    Ajmalghan, Z

    M. Ajmalghan, Z. A. Piazza, E. A. Hodille, Y. Ferro, Surface coverage dependent mechanisms for the absorption and desorp- tion of hydrogen from the W(110) and W(100) surfaces: a den- sity functional theory investigation, Nuclear Fusion 59 (2019) 106022. doi:10.1088/1741-4326/AB33E7

    2019 doi

  35. [41]

    Z. J. Bergstrom, C. Li, G. D. Samolyuk, B. P. Uberuaga, B. D. Wirth, Hydrogen interactions with low-index surface orienta- tions of tungsten, Journal of Physics: Condensed Matter 31 (2019) 255002. doi:10.1088/1361-648X/AB0F6B

    2019 doi

  36. [42]

    Ferro, E

    Y. Ferro, E. Hodille, J. Denis, Z. Piazza, M. Ajmalghan, Hydro- gen and oxygen on tungsten (110) surface: adsorption, absorp- tion and desorption investigated by density functional theory, Nuclear Fusion 63 (2023) 036017. doi:10.1088/1741-4326/ac b0e2

    2023 doi

  37. [43]

    Fernandez, Y

    N. Fernandez, Y. Ferro, D. Kato, Hydrogen diffusion and vacan- cies formation in tungsten: Density Functional Theory calcula- tions and statistical models, Acta Materialia 94 (2015) 307–318. doi:10.1016/J.ACTAMAT.2015.04.052

    2015 doi

  38. [44]

    Markelj, A

    S. Markelj, A. Zaloˇ znik, T. Schwarz-Selinger, O. V. Ogorod- nikova, P. Vavpetiˇ c, P. Pelicon, I. ˇCadeˇ z, In situ nra study of hydrogen isotope exchange in self-ion damaged tungsten ex- posed to neutral atoms, Journal of Nuclear Materials 469 (2016) 133–144. doi:10.1016/J....

    2016 doi

  39. [47]

    Aiello, I

    A. Aiello, I. Ricapito, G. Benamati, R. Valentini, Hydrogen iso- topes permeability in eurofer 97 martensitic steel, Fusion Sci- ence and Technology 41 (2002) 872–876. doi:10.13182/FST41 -872

    2002 doi

  40. [48]

    Schmid, T

    K. Schmid, T. Schwarz-Selinger, R. Arredondo, Influence of hy- drogen isotopes on displacement damage formation in EURO- FER, Nuclear Materials and Energy 34 (2023) 101341. doi: 10.1016/J.NME.2022.101341. 13

    2023

  41. [220]

    doi:10.1016/0022-3115(85)90459-3

    doi

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.