references.bib

@article{dark_festim_2026,
    title = {{FESTIM} v2.0: {Upgraded} framework for multi-species hydrogen transport and enhanced performance},
    volume = {220},
    issn = {0360-3199},
    shorttitle = {{FESTIM} v2.0},
    url = {https://www.sciencedirect.com/science/article/pii/S0360319926006245},
    doi = {10.1016/j.ijhydene.2026.153987},
    abstract = {FESTIM is an open-source finite element framework for modelling the transport of hydrogen isotopes in materials. This paper presents FESTIM v2.0, a major release that broadens the framework’s physical scope and software infrastructure. The new formulation supports fully coupled multi-species transport, advanced trapping and reaction networks, isotope exchange, decay, advection, and generalised treatments of interfaces and boundaries. FESTIM v2.0 is built on DOLFINx, providing improved scalability, interoperability, and long-term sustainability. Performance benchmarks on representative multi-material diffusion problems show speedups of up to approximately 15× relative to FESTIM v1, enabling more efficient engineering-scale, multiphysics simulations. The framework is designed for applications ranging from laboratory-scale permeation experiments to component-level analyses relevant to fusion fuel-cycle technologies. Together, these advances establish FESTIM v2.0 as a versatile and efficient platform for hydrogen transport modelling in complex materials systems.},
    urldate = {2026-02-23},
    journal = {International Journal of Hydrogen Energy},
    author = {Dark, James and Delaporte-Mathurin, Rémi and Dokken, Jørgen S. and Yang, Huihua and Khurana, Chirag and Dunnell, Kaelyn and Ferrero, Gabriele and Kulagin, Vladimir and Meschini, Samuele and Dufour, Jonathan and Hodille, Etienne A.},
    month = mar,
    year = {2026},
    keywords = {FESTIM, FEniCSx, Finite element, Hydrogen transport, Modelling},
    pages = {153987},
}
@article{hodille_macroscopic_2015,
    title = {Macroscopic rate equation modeling of trapping/detrapping of hydrogen isotopes in tungsten materials},
    volume = {467},
    issn = {0022-3115},
    url = {http://www.sciencedirect.com/science/article/pii/S0022311515300660},
    doi = {10.1016/j.jnucmat.2015.06.041},
    abstract = {Relevant parameters for trapping of Hydrogen Isotopes (HIs) in polycrystalline tungsten are determined with the MHIMS code (Migration of Hydrogen Isotopes in MaterialS) which is used to reproduce Thermal Desorption Spectrometry experiments. Three types of traps are found: two intrinsic traps (detrapping energy of 0.87 eV and 1.00 eV) and one extrinsic trap created by ion irradiation (detrapping energy of 1.50 eV). Then MHIMS is used to simulate HIs retention at different fluences and different implantation temperatures. Simulation results agree well with experimental data. It is shown that at 300 K the retention is limited by diffusion in the bulk. For implantation temperatures above 500 K, the retention is limited by trap creation processes. Above 600 K, the retention drops by two orders of magnitude as compared to the retention at 300 K. With the determined detrapping energies, HIs outgassing at room temperature is predicted. After ions implantation at 300 K, 45\% of the initial retention is lost to vacuum in 300 000 s while during this time the remaining trapped HIs diffuse twice as deep into the bulk.},
    urldate = {2019-10-07},
    journal = {Journal of Nuclear Materials},
    author = {Hodille, E. A. and Bonnin, X. and Bisson, R. and Angot, T. and Becquart, C. S. and Layet, J. M. and Grisolia, C.},
    month = dec,
    year = {2015},
    keywords = {Macroscopic rate equations},
    pages = {424--431},
}
@article{simon_moose-based_2025,
    title = {{MOOSE}-based {Tritium} {Migration} {Analysis} {Program}, {Version} 8 ({TMAP8}) for advanced open-source tritium transport and fuel cycle modeling},
    volume = {214},
    issn = {0920-3796},
    url = {https://www.sciencedirect.com/science/article/pii/S0920379625000766},
    doi = {10.1016/j.fusengdes.2025.114874},
    abstract = {Tritium management is critical for the safety, sustainability, and economics of fusion energy systems, and advanced and reliable modeling tools help accelerate the development of tritium technologies. This paper presents the Tritium Migration Analysis Program, Version 8 (TMAP8), an open-source, MOOSE-based application developed to provide state-of-the-art tritium transport and fuel cycle modeling capabilities. TMAP8 aims to expand the capabilities of previous versions (i.e., TMAP4 and TMAP7) by leveraging modern computational techniques, ensuring high software quality assurance standards (key to building trust), and enabling multispecies, multiscale, and multiphysics simulations for integrated tritium transport modeling in complex geometries. This paper outlines TMAP8’s scope and rigorous development practices, emphasizing its transparency, accessibility, modularity, and reliability. We present the current suite of verification and validation cases based on those from TMAP4, demonstrating TMAP8’s accuracy and reliability against analytical solutions and experimental data. Additionally, the paper showcases TMAP8’s integrated fuel cycle modeling capabilities, highlighting its applicability at various scales and levels. The TMAP8 code and documentation are openly available, promoting collaborative development and widespread adoption within the fusion community. Future work will soon expand TMAP8’s verification and validation suite to include those from TMAP7 and other recent experimental studies for validation.},
    urldate = {2026-01-07},
    journal = {Fusion Engineering and Design},
    author = {Simon, Pierre-Clément A. and Icenhour, Casey T. and Singh, Gyanender and Lindsay, Alexander D. and Bhave, Chaitanya and Yang, Lin and Riet, Adriaan and Che, Yifeng and Humrickhouse, Paul and Calderoni, Pattrick and Shimada, Masashi},
    month = may,
    year = {2025},
    keywords = {Computational fusion, MOOSE, Software quality assurance, TMAP, Tritium transport and fuel cycle, Verification and validation},
    pages = {114874},
}
@article{hodille_molecular_2022,
    title = {Molecular dynamics study of hydrogen isotopes at the {Be}/{BeO} interface},
    volume = {34},
    issn = {0953-8984, 1361-648X},
    url = {https://iopscience.iop.org/article/10.1088/1361-648X/ac8328},
    doi = {10.1088/1361-648X/ac8328},
    abstract = {Molecular dynamics simulations are used to investigate the behaviour of D atoms at two interfaces between beryllium (Be) and beryllium oxide (BeO). After relaxation of the simulation cell, there are (a) localised defects at the interface and (b) a hexagonal misfit dislocation network creating a succession of compressed and expanded area from each side of the interface. The simulations between 750 K and 1500 K for tens to hundreds of nanoseconds show that both interfaces act as trapping sites for D atoms. The simulations also show that D atoms tend to migrate in the material where the hydrogen isotope solubility is the highest as predicted by thermodynamics. However, the simulations also shows that there are additional kinetic barriers (D trapping sites, D2 formation/dissociation in BeO) that slow down the path to equilibrium. These additional kinetic barriers may influence the fuel retention and permeation in Be materials.},
    language = {en},
    number = {40},
    urldate = {2026-06-26},
    journal = {Journal of Physics: Condensed Matter},
    author = {Hodille, E A and Byggmästar, J and Ferro, Y and Nordlund, K},
    month = oct,
    year = {2022},
    pages = {405001},
}
@article{silva-solis_hydrogen_2026,
    title = {Hydrogen transport at metallic interfaces: {Modeling} the tungsten-copper system},
    volume = {10},
    issn = {2475-9953},
    shorttitle = {Hydrogen transport at metallic interfaces},
    url = {https://link.aps.org/doi/10.1103/lnnc-h1yy},
    doi = {10.1103/lnnc-h1yy},
    language = {en},
    number = {4},
    urldate = {2026-06-26},
    journal = {Physical Review Materials},
    author = {Silva-Solís, Yosvany and Denis, Julien and Hodille, Etienne A. and Ferro, Yves},
    month = apr,
    year = {2026},
    pages = {045404},
}

Added for the metal / molten-salt revamp.

VERIFICATION NOTICE: the five entries below were assembled from web
search results, not exported from a reference manager. Author lists,
volumes and page ranges are UNCONFIRMED. Re-import each from Zotero or
the publisher before submission. Placeholder entries are marked TODO in
their author field so they fail loudly rather than silently.
(BibTeX has no inline comment character -- text outside entry blocks,
like this, is ignored by BibTeX and is the correct place for notes.)



Added 2026-08-06, from the interface literature review (lit_review_interfaces.md).

PROVENANCE: metadata for the entries below was pulled from Crossref by DOI,
not exported from Zotero. DOIs, titles, journals, volumes and pages are
therefore machine-sourced and internally consistent, but author name
spellings and diacritics have NOT been checked against the published
articles. Two known issues are flagged in note fields below
(ida_hydrogen_1992, kulagin_kinetic_2024). Re-export from Zotero before
submission if any of these carry a load-bearing claim.

% ---- gas/solid surface kinetics: the direct ancestry of Eq. (3) ----

@article{ali-khan_rate_1978,
    title = {The rate of hydrogen release out of clean metallic surfaces},
    volume = {76-77},
    issn = {0022-3115},
    url = {http://dx.doi.org/10.1016/0022-3115(78)90167-8},
    doi = {10.1016/0022-3115(78)90167-8},
    journal = {Journal of Nuclear Materials},
    publisher = {Elsevier BV},
    author = {Ali-Khan, I. and Dietz, K. J. and Waelbroeck, F. G. and Wienhold, P.},
    month = sep,
    year = {1978},
    pages = {337--343},
}

@article{baskes_calculation_1980,
    title = {A calculation of the surface recombination rate constant for hydrogen isotopes on metals},
    volume = {92},
    issn = {0022-3115},
    url = {http://dx.doi.org/10.1016/0022-3115(80)90117-8},
    doi = {10.1016/0022-3115(80)90117-8},
    number = {2-3},
    journal = {Journal of Nuclear Materials},
    publisher = {Elsevier BV},
    author = {Baskes, M. I.},
    month = sep,
    year = {1980},
    pages = {318--324},
}

@article{pick_model_1985,
    title = {A model for atomic hydrogen-metal interactions: application to recycling, recombination and permeation},
    volume = {131},
    issn = {0022-3115},
    url = {http://dx.doi.org/10.1016/0022-3115(85)90459-3},
    doi = {10.1016/0022-3115(85)90459-3},
    number = {2-3},
    journal = {Journal of Nuclear Materials},
    publisher = {Elsevier BV},
    author = {Pick, M. A. and Sonnenberg, K.},
    month = apr,
    year = {1985},
    pages = {208--220},
}

@article{pisarev_gas-driven_2003,
    title = {Gas-driven hydrogen permeation in the surface-limited regime},
    volume = {320},
    issn = {0022-3115},
    url = {http://dx.doi.org/10.1016/S0022-3115(03)00110-7},
    doi = {10.1016/s0022-3115(03)00110-7},
    number = {3},
    journal = {Journal of Nuclear Materials},
    publisher = {Elsevier BV},
    author = {Pisarev, A. and Shestakov, V. and Hayakawa, R. and Hatano, Y. and Watanabe, K.},
    month = aug,
    year = {2003},
    pages = {214--222},
}

@article{denisov_surface-limited_2018,
    title = {Surface-limited permeation regime in the study of hydrogen interactions with metals},
    volume = {117},
    issn = {0263-2241},
    url = {http://dx.doi.org/10.1016/j.measurement.2017.12.018},
    doi = {10.1016/j.measurement.2017.12.018},
    journal = {Measurement},
    publisher = {Elsevier BV},
    author = {Denisov, E. A. and Kompaniets, M. V. and Kompaniets, T. N. and Spitsyn, V. I.},
    month = mar,
    year = {2018},
    pages = {258--265},
}

@article{hodille_kinetic_2020,
    title = {Kinetic model for hydrogen absorption in tungsten with coverage dependent surface mechanisms},
    volume = {60},
    issn = {1741-4326},
    url = {http://dx.doi.org/10.1088/1741-4326/aba454},
    doi = {10.1088/1741-4326/aba454},
    number = {10},
    journal = {Nuclear Fusion},
    publisher = {IOP Publishing},
    author = {Hodille, E. A. and Markelj, S. and Pecovnik, M. and Ajmalghan, M. and Piazza, Z. A. and Ferro, Y. and Schwarz-Selinger, T. and Grisolia, C.},
    month = sep,
    year = {2020},
    pages = {106011},
}

% ---- multi-isotope exchange equilibria ----

@article{san_marchi_solubility_2008,
    title = {Solubility of hydrogen and its isotopes in metals from mixed gases},
    volume = {372},
    issn = {0022-3115},
    url = {http://dx.doi.org/10.1016/j.jnucmat.2007.02.016},
    doi = {10.1016/j.jnucmat.2007.02.016},
    number = {2-3},
    journal = {Journal of Nuclear Materials},
    publisher = {Elsevier BV},
    author = {San Marchi, C. and Somerday, B. P. and Larson, R. S. and Rice, S. F.},
    month = jan,
    year = {2008},
    pages = {421--425},
}

% ---- detailed balance and thermodynamic consistency ----

@article{mhadeshwar_thermodynamic_2003,
    title = {Thermodynamic consistency in microkinetic development of surface reaction mechanisms},
    volume = {107},
    issn = {1520-5207},
    url = {http://dx.doi.org/10.1021/jp034954y},
    doi = {10.1021/jp034954y},
    number = {46},
    journal = {The Journal of Physical Chemistry B},
    publisher = {American Chemical Society (ACS)},
    author = {Mhadeshwar, A. B. and Wang, H. and Vlachos, D. G.},
    month = oct,
    year = {2003},
    pages = {12721--12733},
}

@article{mhadeshwar_thermodynamically_2005,
    title = {A thermodynamically consistent surface reaction mechanism for {CO} oxidation on {Pt}},
    volume = {142},
    issn = {0010-2180},
    url = {http://dx.doi.org/10.1016/j.combustflame.2005.01.019},
    doi = {10.1016/j.combustflame.2005.01.019},
    number = {3},
    journal = {Combustion and Flame},
    publisher = {Elsevier BV},
    author = {Mhadeshwar, A. B. and Vlachos, D. G.},
    month = aug,
    year = {2005},
    pages = {289--298},
}

@article{gorban_extended_2011,
    title = {Extended detailed balance for systems with irreversible reactions},
    volume = {66},
    issn = {0009-2509},
    url = {http://dx.doi.org/10.1016/j.ces.2011.07.054},
    doi = {10.1016/j.ces.2011.07.054},
    number = {21},
    journal = {Chemical Engineering Science},
    publisher = {Elsevier BV},
    author = {Gorban, A. N. and Yablonsky, G. S.},
    month = nov,
    year = {2011},
    pages = {5388--5399},
}

@book{kjelstrup_non-equilibrium_2019,
    title = {Non-equilibrium thermodynamics of heterogeneous systems},
    edition = {2},
    isbn = {9789811216770},
    issn = {2010-1996},
    url = {http://dx.doi.org/10.1142/11729},
    doi = {10.1142/11729},
    series = {Series on Advances in Statistical Mechanics},
    publisher = {World Scientific},
    author = {Kjelstrup, Signe and Bedeaux, Dick},
    month = dec,
    year = {2019},
}

% ---- reactive transport: the same argument, already settled elsewhere ----

@article{knapp_spatial_1989,
    title = {Spatial and temporal scales of local equilibrium in dynamic fluid-rock systems},
    volume = {53},
    issn = {0016-7037},
    url = {http://dx.doi.org/10.1016/0016-7037(89)90316-5},
    doi = {10.1016/0016-7037(89)90316-5},
    number = {8},
    journal = {Geochimica et Cosmochimica Acta},
    publisher = {Elsevier BV},
    author = {Knapp, Richard B.},
    month = aug,
    year = {1989},
    pages = {1955--1964},
}

@article{steefel_coupled_1994,
    title = {A coupled model for transport of multiple chemical species and kinetic precipitation/dissolution reactions with application to reactive flow in single phase hydrothermal systems},
    volume = {294},
    issn = {0002-9599},
    url = {http://dx.doi.org/10.2475/ajs.294.5.529},
    doi = {10.2475/ajs.294.5.529},
    number = {5},
    journal = {American Journal of Science},
    publisher = {American Journal of Science (AJS)},
    author = {Steefel, C. I. and Lasaga, A. C.},
    month = may,
    year = {1994},
    pages = {529--592},
}

@article{aziz_model_1982,
    title = {Model for solute redistribution during rapid solidification},
    volume = {53},
    issn = {1089-7550},
    url = {http://dx.doi.org/10.1063/1.329867},
    doi = {10.1063/1.329867},
    number = {2},
    journal = {Journal of Applied Physics},
    publisher = {AIP Publishing},
    author = {Aziz, M. J.},
    month = feb,
    year = {1982},
    pages = {1158--1168},
}

% ---- interfacial reaction control in series with diffusion, solid state ----

@article{deal_general_1965,
    title = {General relationship for the thermal oxidation of silicon},
    volume = {36},
    issn = {1089-7550},
    url = {http://dx.doi.org/10.1063/1.1713945},
    doi = {10.1063/1.1713945},
    number = {12},
    journal = {Journal of Applied Physics},
    publisher = {AIP Publishing},
    author = {Deal, B. E. and Grove, A. S.},
    month = dec,
    year = {1965},
    pages = {3770--3778},
}

@article{gosele_growth_1982,
    title = {Growth kinetics of planar binary diffusion couples: thin-film case versus bulk cases},
    volume = {53},
    issn = {1089-7550},
    url = {http://dx.doi.org/10.1063/1.331028},
    doi = {10.1063/1.331028},
    number = {4},
    journal = {Journal of Applied Physics},
    publisher = {AIP Publishing},
    author = {G{\"o}sele, U. and Tu, K. N.},
    month = apr,
    year = {1982},
    pages = {3252--3260},
}

@article{cui_interface-reaction_2013,
    title = {Interface-reaction controlled diffusion in binary solids with applications to lithiation of silicon in lithium-ion batteries},
    volume = {61},
    issn = {0022-5096},
    url = {http://dx.doi.org/10.1016/j.jmps.2012.11.001},
    doi = {10.1016/j.jmps.2012.11.001},
    number = {2},
    journal = {Journal of the Mechanics and Physics of Solids},
    publisher = {Elsevier BV},
    author = {Cui, Zhiwei and Gao, Feng and Qu, Jianmin},
    month = feb,
    year = {2013},
    pages = {293--310},
}

@article{swartz_thermal_1989,
    title = {Thermal boundary resistance},
    volume = {61},
    issn = {0034-6861},
    url = {http://dx.doi.org/10.1103/RevModPhys.61.605},
    doi = {10.1103/revmodphys.61.605},
    number = {3},
    journal = {Reviews of Modern Physics},
    publisher = {American Physical Society (APS)},
    author = {Swartz, E. T. and Pohl, R. O.},
    month = jul,
    year = {1989},
    pages = {605--668},
}

% ---- hydrogen at metal/metal interfaces ----

@article{delaporte-mathurin_influence_2021,
    title = {Influence of interface conditions on hydrogen transport studies},
    volume = {61},
    issn = {1741-4326},
    url = {http://dx.doi.org/10.1088/1741-4326/abd95f},
    doi = {10.1088/1741-4326/abd95f},
    number = {3},
    journal = {Nuclear Fusion},
    publisher = {IOP Publishing},
    author = {Delaporte-Mathurin, R{\'e}mi and Hodille, Etienne A. and Mougenot, Jonathan and Charles, Yann and De Temmerman, Gregory and Leblond, Floriane and Grisolia, Christian},
    month = feb,
    year = {2021},
    pages = {036038},
}

@article{silva-solis_solution_2024,
    title = {Solution and solubility of {H} atoms at the {W}/{Cu} interface},
    volume = {36},
    issn = {1361-648X},
    url = {http://dx.doi.org/10.1088/1361-648X/ad6f62},
    doi = {10.1088/1361-648x/ad6f62},
    number = {46},
    journal = {Journal of Physics: Condensed Matter},
    publisher = {IOP Publishing},
    author = {Silva-Sol{\'i}s, Y. and Denis, J. and Hodille, E. A. and Ferro, Y.},
    month = aug,
    year = {2024},
    pages = {465001},
    note = {Has a 2025 corrigendum, see silva-solis\_corrigendum\_2025. Source of
            the interfacial site solution energies used to fix the reverse
            barriers in Table V of silva-solis\_hydrogen\_2026.},
}


@incollection{ogorodnikova_model_2002,
    title = {A model for the steady state plasma- and gas-driven hydrogen isotope permeation through multi-layer metal},
    isbn = {9789401004442},
    url = {http://dx.doi.org/10.1007/978-94-010-0444-2_10},
    doi = {10.1007/978-94-010-0444-2_10},
    booktitle = {Hydrogen and Helium Recycling at Plasma Facing Materials},
    publisher = {Springer Netherlands},
    author = {Ogorodnikova, O. V.},
    year = {2002},
    pages = {95--103},
}

% ---- hydrogen speciation in molten fluorides ----

@article{lam_impact_2021,
    title = {The impact of hydrogen valence on its bonding and transport in molten fluoride salts},
    volume = {9},
    issn = {2050-7496},
    url = {http://dx.doi.org/10.1039/d0ta10576g},
    doi = {10.1039/d0ta10576g},
    number = {3},
    journal = {Journal of Materials Chemistry A},
    publisher = {Royal Society of Chemistry (RSC)},
    author = {Lam, Stephen T. and Li, Qing-Jie and Mailoa, Jonathan and Forsberg, Charles and Ballinger, Ronald and Li, Ju},
    year = {2021},
    pages = {1784--1794},
}

@article{carotti_electrochemical_2021,
    title = {An electrochemical study of hydrogen in molten 2{LiF}-{BeF}2 ({FLiBe}) with addition of {LiH}},
    volume = {367},
    issn = {0013-4686},
    url = {http://dx.doi.org/10.1016/j.electacta.2020.137114},
    doi = {10.1016/j.electacta.2020.137114},
    journal = {Electrochimica Acta},
    publisher = {Elsevier BV},
    author = {Carotti, Francesco and Liu, Ertai and Macdonald, Digby D. and Scarlat, Raluca O.},
    month = jan,
    year = {2021},
    pages = {137114},
}

@article{chan_deciphering_2023,
    title = {Deciphering when metal corrosion is spontaneous in molten fluorides using potential-activity diagrams},
    volume = {79},
    issn = {1938-159X},
    url = {http://dx.doi.org/10.5006/4401},
    doi = {10.5006/4401},
    number = {11},
    journal = {Corrosion},
    publisher = {Association for Materials Protection and Performance (AMPP)},
    author = {Chan, Ho Lun and Scully, John R.},
    month = sep,
    year = {2023},
    pages = {1236--1240},
}

@article{fuerst_molten_2025,
    title = {The molten salt tritium transport experiment: a pumped fluoride salt loop for hydrogen isotope experimentation},
    volume = {223},
    issn = {0306-4549},
    url = {http://dx.doi.org/10.1016/j.anucene.2025.111659},
    doi = {10.1016/j.anucene.2025.111659},
    journal = {Annals of Nuclear Energy},
    publisher = {Elsevier BV},
    author = {Fuerst, Thomas F. and Bowers, Anthony G. and Gietl, Hanns A. and France, Nicole L. and Loftus, L. Shayne and Riet, Adriaan A. and Eklund, Matthew D. and Taylor, Chase N. and Shimada, Masashi},
    month = dec,
    year = {2025},
    pages = {111659},
}
@article{louthan_hydrogen_1975,
    title = {Hydrogen diffusion and trapping in nickel},
    volume = {23},
    issn = {0001-6160},
    url = {https://www.sciencedirect.com/science/article/pii/0001616075900577},
    doi = {10.1016/0001-6160(75)90057-7},
    abstract = {Analysis of hydrogen transport in nickel has shown that both trapping and short-circuit diffusion occur and both have small but significant effects on permeation, evolution and absorption. Both effects appear to be associated primarily with the dislocation substructure of nickel. The data from this study of deuterium permeation and tritium absorption and outgassing in pure polycrystalline nickel, both annealed and heavily cold-rolled, were evaluated and combined with earlier measurements of diffusivity and solubility of hydrogen isotopes to yield the following relations for describing hydrogen transport in nickel: Diffusivity (D) = 7.0 × 10−7√Mexp(−39,500RT), m2/sec Solubility (C) = 1.1 × 103exp (−15,800RT), mole (H)/m3 Permeability (φ) = 7.9 × 10−4√M̄exp (−55,300RT), mole (H)/sec/√Mpa).
Résumé
L'analyse du transport de l'hydrogène dans le nickel montre qu'il se produit piègeage et diffusion par court-circuit, et que ces deux phénomènes ont un effet faible, mais significatif sur la pénétration, l'évolution et l'absorption. Ces deux effets semblent être associés principalement à la sous-structure de dislocations du nickel. On a évalué dans cette étude la pénétration du deuterium et l'absorption et la désorption du tritium dans le nickel pur polycristallin. recuit ou sévèrement laminé, et on les a combinées à des résultats de mesures antérieures du coefficient de diffusion et de la solubilité des isotopes de l'hydrogène: on a obtenu ainsi les relations suivantes pour décrire le transport de l'hydrogène dans le nickel: Coefficient de diffusion: (D) = 7.0 × 10−7√Mexp(−39,500RT), m2/sec Solubilité (C) = 1.1 × 103exp (−15,800RT), mole (H)/m3 Perméabilité (φ) = 7.9 × 10−4√M̄exp (−55,300RT), mole (H)/sec/√Mpa).
Zusammenfassung
Die Analyse des Wasserstofftransports in Nickel hat gezeigt, daβ sowohl Trapping als auch Kurzschluβdiffusion stattfinden und beide haben einen kleinen, jedoch sehr wichtigen Einfluβ auf die Durchdringung. Evolution und Absorption. Beide Effekte hängen primär mit der Versetzungssubstruktvr in Nickel zusammen. Die Daten dieser Untersuchung der Deuteriumdurchdringung und Tritiumabsorption und der Entgasung in reinem polykristallinem Nickel (sowohl in angelassenem als auch in stark kałtverformtem) wurden ausgewertet und mit früheren Messungen der Diffusivität und Löslichkeit von Wasserstoffisotopen verglichen. Es ergeben sich die folgenden Beziehungen zur Beschreibung des Wasserstofftransports in Nickel: Diffusivity (D) = 7.0 × 10−7√Mexp(−39,500RT), m2/sec Solubility (C) = 1.1 × 103exp (−15,800RT), mole (H)/m3 Permeability (φ) = 7.9 × 10−4√M̄exp (−55,300RT), mole (H)/sec/√Mpa).},
    language = {en},
    number = {6},
    urldate = {2022-09-29},
    journal = {Acta Metallurgica},
    author = {Louthan, M. R. and Donovan, J. A. and Caskey, G. R.},
    month = jun,
    year = {1975},
    pages = {745--749},
}
@article{satoshi_fukada_hydrogen_2006,
    title = {Hydrogen permeability through a mixed molten salt of {LiF}, {NaF} and {KF} ({Flinak}) as a heat-transfer fluid},
    volume = {358},
    doi = {10.1016/j.jnucmat.2006.07.011},
    abstract = {Abstract   Permeability, diffusivity and solubility of hydrogen in Flinak, a mixed molten salt of LiF (46.5\%), NaF (11.5\%) and KF (42\%), were determined using a vessel supported by a Ni plate. Diffusion-limiting permeation was confirmed by experimental data where hydrogen permeation rates were in reverse proportion to the thickness of Flinak. Diffusivities determined in the range of 500–750°C were correlated to an Arrhenius equation with the activation energy of 50kJ/mol. Since the dependence of hydrogen solubility in Flinak on pressure was almost linear, hydrogen was dissolved as H 2  in Flinak. The H 2  solubility in Flinak was correlated to a Henry law, and its solubility constant was discussed in terms of macroscopic surface tension and unspecified interaction energy between the molten salt and dissolved gaseous molecules.},
    number = {2},
    journal = {Journal of Nuclear Materials},
    author = {{Satoshi Fukada} and Fukada, Satoshi and {Akio Morisaki} and Morisaki, Akio},
    month = nov,
    year = {2006},
    pages = {235--242},
}
@misc{yang_quantifying_2026,
    title = {Quantifying {Multidimensional} {Transport} {Effects} on {Permeability} {Inference} in {FLiBe} {Systems} {Using} a {Validation}-{Informed} {Modeling} {Framework}},
    url = {http://arxiv.org/abs/2605.12750},
    doi = {10.48550/arXiv.2605.12750},
    abstract = {Permeability of hydrogen isotopes in molten salts is commonly inferred from permeation experiments using simplified one-dimensional interpretations, which may not capture the coupled transport pathways present in realistic systems. In this work, a multi-dimensional, multi-material hydrogen isotope transport modeling framework implemented in FESTIM is benchmarked against permeation measurements from the HYPERION experiment conducted at the MIT Plasma Science and Fusion Center.The model explicitly resolves transport across molten salt and nickel structures, as well as external boundary conditions, enabling system-level interpretation of the measured permeation fluxes over the temperature range 773-973K. Rather than relying on idealized one-dimensional formulations for permeability estimation, this study employs a validation-informed inverse framework to assess how multidomain transport and external boundary assumptions influence the permeability inferred from experimental fluxes.Two limiting external boundary conditions, representing ideal coating and uncoated vessel behavior, are used to define a physically motivated envelope for hydrogen isotope exchange with the environment.The model captures the observed magnitude and temperature dependence of permeation fluxes under both conditions, while revealing significant lateral transport and sidewall leakage pathways that are not represented in one-dimensional interpretations.The inferred FLiBe permeability exhibits consistent Arrhenius behavior but spans a range that depends strongly on the assumed boundary conditions, demonstrating that using one-dimensional formulations to describe a permeation experiment may not be adequate to extract accurate permeability.These results provide a physically grounded framework for interpreting permeation measurements in coupled liquid-metal systems and highlight the importance of multidomain transport modeli},
    urldate = {2026-05-20},
    publisher = {arXiv},
    author = {Yang, Huihua and Saraswat, Abhishek and Zhou, Weiyue and Woller, Kevin and Dark, James and Khurana, Chirag and Dunnell, Kaelyn and Peterson, Ethan and Delaporte-Mathurin, Remi},
    month = may,
    year = {2026},
    keywords = {Physics - Computational Physics, Physics - Plasma Physics},
}
@article{ferry_libra_2022,
    title = {The {LIBRA} {Experiment}: {Investigating} {Robust} {Tritium} {Accountancy} in {Molten} {FLiBe} {Exposed} to a {D}-{T} {Fusion} {Neutron} {Spectrum}},
    volume = {0},
    issn = {1536-1055},
    shorttitle = {The {LIBRA} {Experiment}},
    url = {https://doi.org/10.1080/15361055.2022.2078136},
    doi = {10.1080/15361055.2022.2078136},
    abstract = {The Liquid Immersion Blanket: Robust Accountancy (LIBRA) experiment will be a first-of-a-kind experiment to explore and develop the liquid immersion blanket (LIB) concept. The LIB is a radically simple molten–LiF-BeF2 (FLiBe)–salt tritium breeding blanket for deuterium-tritium (D-T)–fueled fusion power plants (FPPs) achieving a high tritium breeding ratio (TBR) in neutronics models. However, tritium breeding in FLiBe is inherently difficult to study experimentally. As a result, the coupled issues of FLiBe radiochemistry and tritium (T) transport are poorly understood. LIBRA approaches this challenge by simulating an FPP blanket environment using a D-T neutron generator and ≈1000 kg of FLiBe. LIBRA will investigate T breeding, containment, and extraction, coupled with FLiBe redox control and radiochemistry. The primary goal of LIBRA is to demonstrate robust T accountancy in blanket prototypical conditions. Here, T accountancy encompasses accurate predictions of T breeding in the FLiBe; detection and measurement of all T bred in LIBRA; and speciation of the T extracted from the FLiBe. Initial neutronics simulations of LIBRA indicate that a global TBR of ∼1 is possible, where the TBR is defined as the number of tritons bred and extracted from FLiBe relative to the number of neutrons produced by D-T fusion reactions in the neutron generator. In this paper, we present the LIBRA concept and its scientific goals in the context of T breeding experiments. We also consider the potential impact of the LIB on the future fusion power industry, motivating further development of FLiBe-based T breeding research activities such as LIBRA.},
    number = {0},
    urldate = {2022-07-05},
    journal = {Fusion Science and Technology},
    publisher = {Taylor \& Francis},
    author = {Ferry, Sara E. and Woller, Kevin B. and Peterson, Ethan E. and Sorensen, Caroline and Whyte, Dennis G.},
    month = jun,
    year = {2022},
    note = {\_eprint: https://doi.org/10.1080/15361055.2022.2078136},
    keywords = {FLiBe, fusion power, liquid immersion blanket, tritium accountancy, tritium breeding},
    pages = {1--23},
}
@article{calderoni_measurement_2008,
    title = {Measurement of tritium permeation in flibe ({2LiF}–{BeF2})},
    volume = {83},
    doi = {10.1016/j.fusengdes.2008.05.016},
    abstract = {Abstract   This paper reports on the experimental investigation of tritium permeation in flibe (2LiF–BeF2) at the Safety and Tritium Applied Research facility of the Idaho National Laboratory. A stainless steel cell formed by two independent volumes separated by a 2-mm thick nickel membrane is maintained at temperatures between 500 and 700°C. A controlled amount of T2 gas is flown in excess of argon in the source volume in contact with the bottom side of the nickel membrane, while a layer of molten salt is in contact with the top side. The tritium permeating above the liquid surface is carried by an argon flow to a diagnostic system comprised of a quadrupole mass spectrometer, a gas chromatographer and a proportional counter. Tritium permeability in flibe as a function of temperature is determined by the measured permeation flow rates reached in steady-state conditions, while the diffusivity is determined by fitting the transient process with the analytical solution for the diffusion process. As a result, the solubility of tritium in flibe as a function of temperature is also determined.},
    number = {7},
    journal = {Fusion Engineering and Design},
    author = {{P. Calderoni} and Calderoni, Pattrick and {Phil Sharpe} and Sharpe, P. and {Masanori Hara} and Hara, Masanori and {Yasuhisa Oya} and Oya, Yasuhisa},
    month = dec,
    year = {2008},
    note = {MAG ID: 2010928666},
    pages = {1331--1334},
}

@article{saraswat_permeation_2026,
    title = {Permeation behaviour of hydrogen isotopes in molten {FLiBe} ({2LiF}–{BeF2}): {Identifying} sources of uncertainty and associated measurement challenges},
    volume = {253},
    issn = {0360-3199},
    shorttitle = {Permeation behaviour of hydrogen isotopes in molten {FLiBe} ({2LiF}–{BeF2})},
    url = {https://www.sciencedirect.com/science/article/pii/S0360319926026546},
    doi = {10.1016/j.ijhydene.2026.156016},
    abstract = {This paper presents results from systematic investigations conducted in the HYPERION facility to quantify permeabilities of hydrogen isotopes in FLiBe over a temperature range of 773K – 973K. To address the knowledge gap resulting from widely scattered transport parameters reported in the earlier studies, HYPERION experiments incorporate specific provisions to probe unsubstantiated assumptions, including a one-dimensional permeation, membrane surface coverage by the salt, and ideal wettability of the salt-metal interface. Suppression of the isotopic transport behaviour for metal-side charging highlights the permeation barrier characteristics of a bubble-laden Ni–FLiBe interface, impacting permeability by up to 77\%. This work attempts to resolve this issue via salt-side charging and informs constraints on the permeant charging methodology for future studies. The initial insights from HYPERION experiments call into question the design choices and estimated transport properties in earlier works. This study provides a plausible explanation for the observed scatter in H/D/T transport in FLiBe.},
    urldate = {2026-08-11},
    journal = {International Journal of Hydrogen Energy},
    author = {Saraswat, Abhishek and Zhou, Weiyue and Kim, Nayoung and Cota, Jaron F. and Zheng, Guiqiu and Khechfe, Alexander A. and Barthel, Caroline S. and Short, Michael P. and Delaporte-Mathurin, Rémi and Woller, Kevin B.},
    month = jul,
    year = {2026},
    keywords = {Bubbles, FLiBe, Fusion blanket, Hydrogen, Molten salt, Permeability},
    pages = {156016},
}
@article{shimada_toward_2024,
    title = {Toward a high-fidelity tritium transport modeling for retention and permeation experiments},
    volume = {203},
    issn = {0920-3796},
    url = {https://www.sciencedirect.com/science/article/pii/S0920379624002916},
    doi = {10.1016/j.fusengdes.2024.114438},
    abstract = {Tritium Migration Analysis Program version 8 (TMAP8), the latest version of TMAP, was developed within the framework of the Multiphysics Object-Oriented Simulation Environment (MOOSE). Created at Idaho National Laboratory (INL), MOOSE is an open-source, dimension-agnostic, fully coupled, and fully implicit multiphysics platform featuring massively parallel computation capabilities. Using TMAP8, tritium transport in a divertor monoblock was analyzed to elucidate the effects of pulsed operation (up to fifty 1,600 s plasma discharge and cool-down cycles) on the tritium in-vessel inventory source term and ex-vessel release term (i.e., tritium retention and permeation) for safety analysis. With its built-in Message Passing Interface capability, TMAP8 can, in under 2 h, simulate tritium transport in three different layered materials (i.e., tungsten, copper, and copper-chromium-zirconium alloy) in 2D geometry, using a single device/computer with 10 cores. The MOOSE-based TMAP8 code can leverage other MOOSE tools developed under the Nuclear Energy Advanced Modeling and Simulation program to perform tritium and thermal transport in complex geometries and multiphysics environments. And via its massively parallel computation, MOOSE will enable the fusion pilot plant designers to conduct high-fidelity multiphysics modeling for the design of the divertor and blanket systems as well as for the safety analysis.},
    urldate = {2026-08-13},
    journal = {Fusion Engineering and Design},
    author = {Shimada, Masashi and Simon, Pierre-Clément A. and Icenhour, Casey T. and Singh, Gyanender},
    month = jun,
    year = {2024},
    keywords = {Fusion, MOOSE, Modeling, TMAP8, Tritium diffusion, Tritium permeation, Tritium retention, Tritium trapping},
    pages = {114438},
}
@article{arredondo_preliminary_2021,
    title = {Preliminary estimates of tritium permeation and retention in the first wall of {DEMO} due to ion bombardment},
    volume = {28},
    issn = {2352-1791},
    url = {https://www.sciencedirect.com/science/article/pii/S2352179121001125},
    doi = {10.1016/j.nme.2021.101039},
    abstract = {Tritium self-sufficiency presents a critical engineering challenge for DEMO, requiring efficient breeding and extraction systems, as well as minimizing tritium losses to the surrounding systems, such as plasma-facing components, vacuum vessel, cooling system, etc. Structural and plasma-facing components will act as a tritium sink, as tritium will be accumulated in the bulk of these components due to energetic particle bombardment and may permeate out of the vacuum system. The design of the plasma-facing components will consequently directly influence the plant lifetime, operational safety and cost of any future power plant. Therefore, modeling of tritium retention and permeation in these components is required for the engineering designs of the tritium breeding and safety systems. In this work, the diffusion-transport code TESSIM-X is benchmarked against the well-established TMAP7 code and a comparison with a simplified DEMO-relevant test case is performed. The use of either code for modeling of DEMO conditions is discussed. Following this, TESSIM-X is used to provide a preliminary assessment of tritium permeation and retention in the DEMO first wall, based on the current WCLL (Water Cooled Lithium Lead) and HCPB (Helium Cooled Pebble Bed) breeding blanket designs.},
    language = {en},
    urldate = {2021-11-10},
    journal = {Nuclear Materials and Energy},
    author = {Arredondo, R. and Schmid, K. and Subba, F. and Spagnuolo, G. A.},
    month = sep,
    year = {2021},
    keywords = {DEMO, First wall, Permeation, Retention, TESSIM, TMAP},
    pages = {101039},
}
@article{ferrero_preliminary_2022,
    title = {A {Preliminary} {CFD} and {Tritium} {Transport} {Analysis} for {ARC} {Blanket}},
    volume = {78},
    issn = {1536-1055},
    url = {https://doi.org/10.1080/15361055.2022.2096365},
    doi = {10.1080/15361055.2022.2096365},
    abstract = {The Affordable, Robust, Compact (ARC) fusion reactor is a preconceptual design proposed by the Plasma Science and Fusion Center at the Massachusetts Institute of Technology that will be developed by Commonwealth Fusion Systems. ARC features a Li2BeF4 (FLiBe) molten salt liquid blanket that provides reactor cooling, neutron shielding, and tritium breeding. This work aims to develop a preliminary coupled computational fluid dynamics (CFD) and tritium transport model to describe FLiBe flow inside the tank and to assess ARC tritium inventory in the vacuum vessel and blanket. Both models are built by taking advantage of COMSOL® Multiphysics. FLiBe velocity and temperature fields are evaluated by the CFD models, and they are passed as input to the tritium transport model. The tritium transport model computes tritium concentration inside solid materials and FLiBe. An auxiliary FLiBe inlet has been moved from the original position in the ARC preconceptual design to improve blanket cooling and to reduce the size of flow eddies. Results show that many recirculation zones generate inside the tank for the chosen tank geometry, size, and inlet-outlet conditions. Larger FLiBe temperature and tritium concentration are found in these zones. The high FLiBe temperature in recirculation areas may not allow for effective cooling, and Inconel 718 reaches critical temperatures. The largest tritium concentration for a steady-state model with continuity of tritium partial pressure at the interfaces is found in Inconel 718 while the second-highest concentration is reached in FLiBe. The total tritium inventory in the ARC blanket with the assumed model is quantified as 3.16 g.},
    number = {8},
    urldate = {2022-10-27},
    journal = {Fusion Science and Technology},
    publisher = {Taylor \& Francis},
    author = {Ferrero, Gabriele and Meschini, Samuele and Testoni, Raffaella},
    month = nov,
    year = {2022},
    note = {\_eprint: https://doi.org/10.1080/15361055.2022.2096365},
    keywords = {ARC fusion reactor, blanket, computational fluid dynamics, tokamak, tritium transport},
    pages = {617--630},
}
@article{dark_influence_2021,
    title = {Influence of hydrogen trapping on {WCLL} breeding blanket performances},
    volume = {61},
    copyright = {All rights reserved},
    issn = {0029-5515},
    url = {https://doi.org/10.1088/1741-4326/ac28b0},
    doi = {10.1088/1741-4326/ac28b0},
    abstract = {Tritium transport simulations in water-cooled lithium lead (WCLL) breeding blankets have been performed with FESTIM. Fluid dynamics and heat transfer were coupled to evaluate how temperature and LiPb velocity fields affect tritium transport. The 2D WCLL model consisted of tungsten, EUROFER and liquid LiPb. Tritium inventories and permeation fluxes have been computed and the influence of trapping effects in solid domains was highlighted. It was evaluated that inclusion of trapping mechanisms increases inventory values by 15\% and delays permeation to the cooling channels. A parametric study was conducted to investigate the impact of the uncertainty in the literature (2 orders of magnitude) regarding hydrogen solubility in LiPb on these quantities. Varying the lithium lead solubility over the range found in the literature was found to vary the EUROFER inventory by a factor of 25. Permeation fluxes to the coolant channels was found to vary over a factor of 3.},
    language = {en},
    number = {11},
    urldate = {2021-12-08},
    journal = {Nuclear Fusion},
    publisher = {IOP Publishing},
    author = {Dark, James and Delaporte-Mathurin, Remi and Charles, Yann and Hodille, Etienne A. and Grisolia, Christian and Mougenot, Jonathan},
    month = oct,
    year = {2021},
    pages = {116076},
}
@article{hodille_tritium_2026,
    title = {Tritium retention in the {ITER}/{DEMO} actively cooled tungsten monoblock in the presence of neutron-induced defects},
    volume = {205},
    issn = {0360-3199},
    url = {https://www.sciencedirect.com/science/article/pii/S0360319925062482},
    doi = {10.1016/j.ijhydene.2025.153245},
    abstract = {Tritium retention in ITER like divertor monoblock is simulated with FESTIM adding trapping induced by neutron damage in the tungsten armor. The simulated scenario is a 10 MWm−2 heat flux representing an exposure near the strike line during an ITER attached plasma. The tungsten armor is damaged with rate from 5 dpa/fpy to 100 dpa/fpy in the range of expected DEMO damaging rates. It is observed that the temperature field affects the distribution of the neutron-induced traps with a significant annealing of them in the hottest part of the monoblock, which affects the resulting tritium distribution. The tritium retention is 28 times higher in the damaged monoblock compared to undamaged monoblock after a dpa level of 0.64 dpa with a high dpa rate of 100 dpa/fpy, which is an extreme damage rate for ITER or DEMO. The damaged layer slows down the tritium permeation toward the coolant, acting as a temporary permeation barrier until all the damaged-induced traps are filled. This effect is more effective with higher dpa rates as two extreme regimes exists for the growth of the tritium inventory: (i) limited by the tritium migration (low dpa rates) (ii) limited by the neutron-induced trap creation (high dpa rates).},
    urldate = {2026-01-07},
    journal = {International Journal of Hydrogen Energy},
    author = {Hodille, E. A. and Dark, J. and Delaporte-Mathurin, R. and Grisolia, C. and Charles, Y. and Mougenot, J.},
    month = jan,
    year = {2026},
    keywords = {Modeling, Neutron damage, Plasma material interactions, Tritium},
    pages = {153245},
}
@article{meschini_impact_2025,
    title = {Impact of trapping on tritium self-sufficiency and tritium inventories in fusion power plant fuel cycles},
    volume = {65},
    issn = {0029-5515},
    url = {https://dx.doi.org/10.1088/1741-4326/adacfa},
    doi = {10.1088/1741-4326/adacfa},
    abstract = {The dynamic analysis of fusion power plant (FPP) fuel cycles highlights the challenge of achieving tritium self-sufficiency in future FPPs. While state-of-the-art fuel cycle models offer valuable insights into the necessary design parameters for attaining tritium self-sufficiency, none of these models currently consider the impact of tritium trapping within fuel cycle components. However, detailed analysis of individual components reveals that substantial amounts of tritium can be trapped within the first wall, divertors, and breeding blanket systems, suggesting that tritium trapping may significantly influence the FPP ability to achieve self-sufficiency. The compounded effects of additional tritium traps generated by irradiation effects and component replacements further exacerbate this challenge. The novelty of this work is the integration of an explicit, physics-based model for tritium trapping, evolution of damage-induced traps, and component replacements into a dynamic, system-level model of a fuel cycle. The results show an increase of a factor of tritium inventory in the first wall and vacuum vessel of an ARC-class FPP when accounting for the aforementioned phenomena. This, coupled with the replacement of components subject to significant tritium trapping, slows down fuel cycle dynamics, resulting in an extended tritium doubling time (50\% increase), higher start-up inventory (30\% increase), and higher required tritium breeding ratio (2\%–5\%) compared to a scenario without tritium trapping.},
    language = {en},
    number = {3},
    urldate = {2025-08-13},
    journal = {Nuclear Fusion},
    author = {Meschini, Samuele and Delaporte-Mathurin, Rémi and Tynan, George R. and Ferry, Sara E.},
    month = feb,
    year = {2025},
    pages = {036010},
}
@article{meschini_modeling_2023,
    title = {Modeling and analysis of the tritium fuel cycle for {ARC}- and {STEP}-class {D}-{T} fusion power plants},
    volume = {63},
    copyright = {All rights reserved},
    issn = {0029-5515},
    url = {https://dx.doi.org/10.1088/1741-4326/acf3fc},
    doi = {10.1088/1741-4326/acf3fc},
    abstract = {The limited tritium resources available for the first fusion power plants (FPPs) make fuel self-sufficiency and tritium inventory minimization leading issues in FPP design. This work builds on the model proposed by Abdou et al (2020 Nucl. Fusion 61 013001), which analyzed the fuel cycle (FC) of a DEMOnstration nuclear FPP-class FPP with a time-dependent system-level model. Here, we use a modified version of their model to analyze the FC of an Affordable, Robust, Compact (ARC)-class tokamak and two versions of a Spherical Tokamak for Energy Production (STEP)-class tokamak. The ARC-class tokamak breeds tritium in a 2LiF + BeF2 liquid immersion blanket, while the STEP-class tokamak breeds tritium utilizing either a liquid-lithium blanket design or an encapsulated breeding blanket. A time-dependent system-level model is developed in Matlab Simulink® to simulate the evolution of tritium flows and tritium inventories in the FC. The main goals of this work are to assess tritium self-sufficiency of the ARC- and STEP-class designs and to determine quantitative design requirements that can be used to analyze the adequacy of a proposed FC system. These design requirements are aimed at achieving a low tritium inventory doubling time () and a low start-up inventory () while keeping the required tritium breeding ratio (TBR) as low as possible. We also consider how improvements in FC technology and POs affect TBR and . The model results show that TBR for ARC- and STEP-class FPPs should be achievable if the tritium burn efficiency (TBE) reaches 0.5\%–1\% (TBR1.2). This assumes significant, but attainable, improvements over current abilities. However, the model results indicate that an FPP must achieve ambitious performance targets, including FPP availability 70\%, tritium processing time 4 h, and the implementation of direct internal recycling (DIR). If future research yields major improvements to achievable TBE, it may be possible to achieve tritium self-sufficiency while operating at lower availability and without implementing DIR.},
    language = {en},
    number = {12},
    urldate = {2023-12-22},
    journal = {Nuclear Fusion},
    publisher = {IOP Publishing},
    author = {Meschini, Samuele and Ferry, Sara E. and Delaporte-Mathurin, Rémi and Whyte, Dennis G.},
    month = sep,
    year = {2023},
    pages = {126005},
}
@misc{delaporte-mathurin_baby_2025,
    title = {{BABY} {1L}: {First} {Tritium} {Breeding} {Campaign} {Results}},
    shorttitle = {{BABY} {1L}},
    url = {http://arxiv.org/abs/2509.26174},
    doi = {10.48550/arXiv.2509.26174},
    abstract = {Achieving tritium self-sufficiency is a critical challenge for future fusion power plants. The BABY 1L experiment, part of the LIBRA project at MIT, aims to benchmark tritium breeding and release in molten salt breeder systems under deuterium-tritium (DT) neutron irradiation. Building on the initial {\textbackslash}SI\{100\}\{mL\} campaign, BABY 1L introduces a tenfold increase in breeder volume, improved thermal and gas handling systems, and enhanced neutron diagnostics, including a proton recoil telescope. We report on results from four irradiation experiments using sealed-tube DT neutron generators, with tritium collected by water bubblers measured via liquid scintillation counting. Experimentally determined Tritium Breeding Ratios (TBRs) were compared to OpenMC neutronics simulations, showing very good agreement. The measured TBR values demonstrate a six-fold improvement over the {\textbackslash}SI\{100\}\{mL\} experiments, largely attributed to the increased solid angle and improved measurement fidelity. We also investigate tritium release dynamics and identify diffusion-limited transport as the dominant regime in the salt volume in the temperature range 630-750 {\textbackslash}si\{{\textbackslash}celsius\}. Additionally, we observe that the introduction of hydrogen in the helium carrier gas significantly accelerates tritium release, consistent with an isotopic exchange mechanism. All analysis is conducted through the open-source {\textbackslash}texttt\{libra-toolbox\} {\textbackslash}cite\{libra-toolbox\}, which streamlines simulation, data processing, and validation across experimental campaigns. These results provide critical insights into the design and operation of future liquid breeder systems and demonstrate the maturity of the BABY platform as a testbed for tritium breeding studies.},
    urldate = {2025-12-12},
    publisher = {arXiv},
    author = {Delaporte-Mathurin, Rémi and Goles, Nikola and Dunn, Collin and Edwards, Emily and Ferry, Sara and MacDonald, Ross and Peterson, Ethan and Pettinari, Davide and Segantin, Stefano and Zhou, Weiyue and Woller, Kevin B.},
    month = sep,
    year = {2025},
    note = {arXiv:2509.26174 [physics]},
    keywords = {Physics - Instrumentation and Detectors, Physics - Plasma Physics},
}
@article{delaporte-mathurin_advancing_2024,
    title = {Advancing {Tritium} {Self}-{Sufficiency} in {Fusion} {Power} {Plants}: {Insights} from the {BABY} {Experiment}},
    issn = {0029-5515},
    shorttitle = {Advancing {Tritium} {Self}-{Sufficiency} in {Fusion} {Power} {Plants}},
    url = {http://iopscience.iop.org/article/10.1088/1741-4326/ada2ab},
    doi = {10.1088/1741-4326/ada2ab},
    abstract = {In the pursuit of fusion power, achieving tritium self-sufficiency stands as a pivotal challenge. Tritium breeding within molten salts is a critical aspect of next-generation fusion reactors, yet experimental measurements of {\textbackslash}glstbr have remained elusive. Here we present the results of the {\textbackslash}glsbaby experiment, which represents a pioneering effort in tritium research by utilizing high-energy ({\textbackslash}SI14{\textbackslash}mega{\textbackslash}electronvolt) neutron irradiation of molten salts, a departure from conventional low-energy neutron approaches.  Using a small-scale ({\textbackslash}SI100{\textbackslash}milliłitre) molten salt tritium breeding setup, we not only simulated, but also directly measured a {\textbackslash}glstbr {\textbackslash}textcolorred({\textbackslash}num3.57e-4).  This innovative approach provides crucial experimental validation, offering insights unattainable through simulation alone. Moreover, our findings reveal a surprising outcome: tritium was predominantly collected as HT, contrary to the expected TF.  This underscores the complexity of tritium behavior in molten salts, highlighting the need for further investigation. This work lays the foundation for a more sophisticated experimental setup, including increasing the volume of the breeder, enhancing neutron detection, and refining tritium collection systems. Such improvements are crucial for advancing our understanding of fusion reactor feasibility and paving the way for future experiments.},
    language = {en},
    urldate = {2025-01-08},
    journal = {Nuclear Fusion},
    author = {Delaporte-Mathurin, Rémi and Goles, Nikola and Ball, John Leland and Dunn, Collin and Edwards, Emily and Ferry, Sara and Lamere, Edward and Lanzrath, Andrew and Leccacorvi, Rick and Meschini, Samuele and Peterson, Ethan and Segatin, Stefano and Vieira, Rui and Whyte, Dennis and Zhou, Weiyue and Woller, Kevin Benjamin},
    year = {2024},
}
@article{schmid_implications_2024,
    title = {Implications of {T} loss in first wall armor and structural materials on {T}-self-sufficiency in future burning fusion devices},
    volume = {64},
    issn = {0029-5515},
    url = {https://doi.org/10.1088/1741-4326/ad52a7},
    doi = {10.1088/1741-4326/ad52a7},
    abstract = {Future fusion reactors will have to breed enough tritium (T) to sustain continuous operation and to produce excess T to power up other fusion reactors. Therefore, T is a scarce resource that must not be lost inside the fusion power plants systems. The factor that describes the T production is the ‘tritium breeding ratio’ (TBR) which is the ratio of the breading rate in atoms per second to the burn rate in atoms per second. Its value is calculated from neutronics analyses of the breeding process in the blanket and coupled dynamics of the T processing plant. However, these calculations generally ignore the T transport and loss in the first wall by assuming essentially instantaneous recycling of the impinging T in-flux. In this paper the transport and retention of T in the main chamber first wall of a future EU-DEMO reactor is investigated based on the available material data and expected particle loads onto the wall. Two breeding blanket concepts are compared WCLL (water cooled lithium lead) and HCPB (helium cooled pebble bed) and the resulting wall-loss probabilities are compared with a simple balance model that describes the maximum allowable wall loss given a TBR to achieve T-self-sufficiency.},
    language = {en},
    number = {7},
    urldate = {2026-08-14},
    journal = {Nuclear Fusion},
    publisher = {IOP Publishing},
    author = {Schmid, K. and Schwarz-Selinger, T. and Arredondo, R. and Theodorou, A. and Pomella Lobo, T.},
    month = jun,
    year = {2024},
    pages = {076056},
}
@article{forsberg_fusion_2020,
    title = {Fusion {Blankets} and {Fluoride}-{Salt}-{Cooled} {High}-{Temperature} {Reactors} with {Flibe} {Salt} {Coolant}: {Common} {Challenges}, {Tritium} {Control}, and {Opportunities} for {Synergistic} {Development} {Strategies} {Between} {Fission}, {Fusion}, and {Solar} {Salt} {Technologies}},
    volume = {206},
    issn = {0029-5450},
    shorttitle = {Fusion {Blankets} and {Fluoride}-{Salt}-{Cooled} {High}-{Temperature} {Reactors} with {Flibe} {Salt} {Coolant}},
    url = {https://doi.org/10.1080/00295450.2019.1691400},
    doi = {10.1080/00295450.2019.1691400},
    abstract = {Recent developments in high-magnetic-field fusion systems have created large incentives to develop flibe (Li2BeF4) salt fusion blankets that have four functions: (1) convert the high energy of fusion neutrons into heat for the power system, (2) convert lithium into tritium—the fusion fuel, (3) shield the magnets against radiation, and (4) cool the first wall that separates the plasma from the salt blanket. Flibe is the same coolant proposed for fluoride-salt-cooled high-temperature reactors that use clean flibe coolant and graphite-matrix coated-particle fuel. Flibe is also the coolant proposed for some molten salt reactors (MSRs) where the fuel is dissolved in the coolant. The multiple applications for flibe as a coolant create large incentives for cooperative fusion-fission programs for development of the underlying science, design tools, technology (pumps, instrumentation, salt purification, materials, tritium removal, etc.), and supply chains. Other high-temperature molten salts are being developed for alternative MSR systems and for advanced Gen-III concentrated solar power (CSP) systems. The overlapping characteristics of flibe salt with these other salt systems create significant incentives for cooperative fusion-fission-solar programs in multiple areas. We describe the fission and fusion flibe-cooled systems, what has created this synergism, what is different and the same between fission and fusion in terms of using flibe, and the common challenges. We review (1) the characteristics of flibe salts, (2) the status of the technology, (3) the options for tritium capture and control in the salt, heat exchangers, and secondary heat transfer loops, and (4) the coupling to power cycles with heat storage. The technology overlap between flibe systems and other high-temperature MSR and CSP salt systems is described. This defines where there are opportunities for cooperative programs across fission, fusion, and CSP salt programs.},
    number = {11},
    urldate = {2026-08-20},
    journal = {Nuclear Technology},
    author = {Forsberg, Charles and Zheng, Guiqiu (Tony) and Ballinger, Ronald G. and Lam, Stephen T.},
    month = nov,
    year = {2020},
    keywords = {Salt-cooled reactors, flibe salt, fluoride-salt-cooled high-temperature reactor, fusion, molten salt reactor},
    pages = {1778--1801},
}
@article{zhu_modeling_2024,
    title = {Modeling the {Co}-permeation of hydrogen isotopes through metals in all rate-limited regimes},
    volume = {601},
    issn = {0022-3115},
    url = {https://www.sciencedirect.com/science/article/pii/S0022311524003921},
    doi = {10.1016/j.jnucmat.2024.155290},
    abstract = {Tritium safety plays a crucial role in D-T fusion engineering. During normal operations, tritium(T) is typically dissolved with protium(H) or deuterium(D) in structural materials. However, there are still controversial issues related to the synergistic isotopic effects when considering T permeation through metals with H/D. In this work, a numerical model is built to describe the co-permeation behavior of multi-component hydrogen isotopes through metals in all rate-limited regimes. This model involves isotope exchange reactions in the gas phase, molecular dissolution, and atomic recombination at the gas-solid interface, as well as the diffusion process in the bulk. By simulating the mixed hydrogen gas permeation through various metals, different results are observed. In surface limited regime, the effective permeation flux of D is slightly enhanced by the presence of H due to isotopic effect. In diffusion-limited regime, the recombination of heteronuclear hydrogen molecules (HD) will deviate the equilibrium concentration of D on the upstream side from Sievert's Law, thereafter suppressing the D permeation flux on the downstream side.},
    urldate = {2026-08-20},
    journal = {Journal of Nuclear Materials},
    author = {Zhu, Jipeng and Ye, Xiaoqiu and Chen, Chang'an and Sun, Fei and Jin, Wei and Liu, Xuxu},
    month = dec,
    year = {2024},
    keywords = {Co-permeation, Deuterium, Hydrogen, Isotopic effects, Tritium},
    pages = {155290},
}

@article{kulagin_kinetic_2024,
	title = {Kinetic surface model in {FESTIM}: {Verification} and validation},
	volume = {110},
	issn = {0360-3199},
	shorttitle = {Kinetic surface model in {FESTIM}},
	url = {https://www.sciencedirect.com/science/article/pii/S0360319925006937},
	doi = {10.1016/j.ijhydene.2025.02.128},
	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 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, the 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. The introduced model is therefore a valuable openly available extension making FESTIM even more versatile for the study of the H transport in materials.},
	urldate = {2025-04-22},
	journal = {International Journal of Hydrogen Energy},
	author = {Kulagin, Vladimir and Delaporte-Mathurin, Rémi and Hodille, Etienne A. and Zibrov, Mikhail},
	month = mar,
	year = {2024},
	keywords = {FESTIM, Finite element, Hydrogen transport, Kinetic surface model},
	pages = {90--100},
}


@unpublished{baratta_dolfinx_2023,
	title = {{DOLFINx}: {The} next generation {FEniCS} problem solving environment},
	shorttitle = {{DOLFINx}},
	doi = {10.5281/zenodo.10447665},
	abstract = {DOLFINx is the next generation problem solving environment from the FEniCS Project; it provides an expressive and performant environment for solving partial differential equations using the finite element method. We present the modern design principles that underpin the DOLFINx library, and describe approaches used in DOLFINx that preserve the high level of mathematical abstraction associated with FEniCS Project libraries, yet support extensibility and specialized customization. At the core of DOLFINx is a data- and function-oriented design, in contrast with the object-oriented design of more traditional libraries. We argue that this novel design approach leads to a compact and maintainable library, which is flexible in use and makes possible the creation of high performance programs in different languages.},
	author = {Baratta, Igor and Dean, Joseph and Dokken, Jørgen Schartum and Habera, Michal and Hale, Jack and Richardson, Chris and Rognes, Marie and Scroggs, Matthew and Sime, Nathan and Wells, Garth},
	month = dec,
    note = {preprint},
	year = {2023},
}

@article{field_solubilities_1967,
    author = {Field, Paul E. and Shaffer, James H.},
    title = {The solubilities of hydrogen fluoride and deuterium fluoride in molten fluorides},
    journal = {The Journal of Physical Chemistry},
    volume = {71},
    number = {10},
    pages = {3218-3222},
    year = {2002},
    month = {05},
    issn = {0022-3654},
    doi = {10.1021/j100869a013},
    url = {https://doi.org/10.1021/j100869a013},
    eprint = {https://pubs.acs.org/jpchax/article-pdf/71/10/3218/10736042/j100869a013.pdf},
}

@software{remi_delaporte_mathurin_2026_22112697,
  author       = {Rémi Delaporte-Mathurin},
  title        = {festim-dev/interface-models: Release v0.1},
  month        = aug,
  year         = 2026,
  publisher    = {Zenodo},
  version      = {v0.1},
  doi          = {10.5281/zenodo.22112697},
  url          = {https://doi.org/10.5281/zenodo.22112697},
  swhid        = {swh:1:dir:46cc62255913e0fe08009c87aab312189dc09a7e
                   ;origin=https://doi.org/10.5281/zenodo.22112696;vi
                   sit=swh:1:snp:d416ce0df24a54d613e4c8e662547e6cc312
                   e49d;anchor=swh:1:rel:c7b434debc9ac22586df22dea9e5
                   f95cec7d90b7;path=festim-dev-interface-
                   models-146627c
                  },
}