Criteria for Observing Hydrogen Tunneling in Metals

V. B.Vykhodets; T. E. Kurennykh

doi:10.17804/2410-9908.2024.4.024-034

V. B.Vykhodets, T. E. Kurennykh

CRITERIA FOR OBSERVING HYDROGEN TUNNELING IN METALS

DOI: 10.17804/2410-9908.2024.4.024-034

Based on the analysis of the results of theoretical and experimental research, this study develops criteria that metals must meet for it to be possible to observe hydrogen tunneling in metals, as well as methods for measuring quantum diffusion coefficients. Firstly, the distance between the nearest equilibrium positions of hydrogen atoms in the metal lattice must be small enough, about 0.15 nm. Secondly, the Debye temperature of the metal must be low enough, below 350 K. Thirdly, the necessary condition for observing hydrogen tunneling is a correct choice of methods for measuring hydrogen diffusion coefficients. If the hydrogen diffusion coefficient according to the classical migration mechanism is about 10–11 m2/s or higher in the Debye temperature range, it is expedient to use indirect methods based on the Gorsky effect or on measuring the spin lattice relaxation rate via nuclear magnetic resonance (NMR). At lower values of the classical diffusion coefficient in the Debye temperature range of metals, to observe quantum diffusion, it is necessary to use the technique of direct online nuclear reaction analysis (NRAOL) alone or in combination with nuclear reaction analysis (NRA).

Acknowledgement: The research was carried out under the state assignment from the Ministry of Science and Higher Education of the Russian Federation (theme Function, No. 122021000035-6).

Keywords: hydrogen, metals, tunneling, observation criteria, equilibrium positions, Debye temperature, quantum diffusion, experimental techniques

References:

Fang, W., Richardson, J.O., Chen, J., Li, X.-Z., and Michaelides, A. Simultaneous deep tunneling and classical hopping for hydrogen diffusion on metals. Phys. Rev. Lett., 2017, 119, 126001. DOI: 10.1103/PhysRevLett.119.126001.
Emin, D., Baskes, M.I., and Wilson, W.D. Small-polaronic diffusion of light interstitials in bcc metals. Phys. Rev. Lett., 1979, 42, 791–794. DOI: 10.1103/PhysRevLett.42.791.
Schober, H.R. and Stoneham, A.M. Diffusion of hydrogen in niobium. Phys. Rev. Lett., 1988, 60, 2307–2310. DOI: 10.1103/PhysRevLett.60.2307.
Sundell, P.G. and Wahnström, G. Activation energies for quantum diffusion of hydrogen in metals and on metal surfaces using delocalized nuclei within the density-functional theory. Phys. Rev. Lett., 2004, 92 (15), 155901. DOI: 10.1103/PhysRevLett.92.155901.
Di Stefano, D., Mrovec, M., and Elsässer, C. First-principles investigation of quantum mechanical effects on the diffusion of hydrogen in iron and nickel. Phys. Rev. B, 2015, 92 (22), 224301. DOI: 10.1103/PhysRevB.92.224301.
Kimizuka, H., Ogata, S., and Shiga, M. Mechanism of fast lattice diffusion of hydrogen in palladium: interplay of quantum fluctuations and lattice strain. Phys. Rev. B, 2018, 97, 014102. DOI: 10.1103/PhysRevB.97.014102.
Schober, H.R. and Stoneham, A.M. Diffusion of hydrogen in transition metals. J. Less-Common Metals, 1991, 172–174, 538–547. DOI: 10.1016/0022-5088(91)90174-3.
Stoneham, A.M. Non-classical diffusion procession. J. Nucl. Mater., 1978, 69–70, 109–116. DOI:
Kimizuka, H., Ogata, S., and Shiga, M. Unraveling anomalous isotope effect on hydrogen diffusivities in fcc metals from first principles including nuclear quantum effects. Phys. Rev. B, 2019, 100, 024104. DOI: 10.1103/PhysRevB.100.024104.
Kimizuka, H., Mori, H., and Ogata, S. Effect of temperature on fast hydrogen diffusion in iron: a path-integral quantum dynamics approach. Phys. Rev. B, 2011, 83. DOI: 094110. 10.1103/PhysRevB.83.094110.
Yoshikawa, T., Takayanagi, T., Kimizuka, H., and Shiga, M. Quantum–thermal crossover of hydrogen and tritium diffusion in α-iron. J. Phys. Chem. C, 2012, 116, 23113–23119. DOI: 10.1021/jp307660e.
Kashlev, Yu.A. Three regimes of diffusion migration of hydrogen atoms in metals. Theor. Math. Phys., 2005, 145, 1590–1603. DOI: 10.1007/s11232-005-0185-8.
Qi, Z., Volkl, J., Lasser, R., and Wenzl, H. Tritium diffusion in V, Nb and Ta. J. Phys. F: Met. Phys., 1983, 13, 2053–2062. DOI: 10.1088/0305-4608/13/10/015.
Flynn, C.P. and Stoneham, A.M. Quantum theory of diffusion with application to light interstitials in metals. Phys. Rev. B, 1970, 1, 3966–3978. DOI: 10.1103/PhysRevB.1.3966.
Johnson, D.F. and Carter, E.A. Hydrogen in tungsten: absorption, diffusion, vacancy trapping, and decohesion. J. Mater. Res., 2010, 25, 315–327. DOI: 10.1557/jmr.2010.0036.
Jiang, D.E. and Carter, E.A. Diffusion of interstitial hydrogen into and through bcc Fe from first principles. Phys. Rev. B, 2004, 70, 064102. DOI: 10.1103/PhysRevB.70.064102.
Vykhodets, V., Nefedova, O., Kurennykh, T., Obukhov, S., and Vykhodets, Ye. Quantum diffusion of deuterium in sodium. J. Phys. Chem. A, 2019, 123, 7536–7539. DOI: 10.1021/acs.jpca.9b06231.
Vykhodets, V., Nefedova, O., Kurennykh, T., Obukhov, S., and Vykhodets, E. Debye temperature and quantum diffusion of hydrogen in body-centered cubic metals. ACS Omega, 2022, 7 (10), 8385–8390. DOI: 10.1021/acsomega.1c05902.
Vykhodets, V., Nefedova, O., Kurennykh, T., and Vykhodets, E. First observation of quantum diffusion in non‐cubic metal: deuterium diffusion in In. Metals, 2023, 13, 394–405. DOI: 10.3390/met13020394.
Vykhodets, V., Nefedova, O., Kurennykh, T., and Danilov, S. Strong increase of tunneling rate of hydrogen in Indium in the presence of vacancies. J. Phys. Chem. C, 2024, 128 (6), 2730–2736. DOI: 10.1021/acs.jpcc.3c08044.
Hagi, H. Diffusion coefficient of hydrogen in iron without trapping by dislocations and impurities. Mater. Trans. JIM, 1994, 35, 112–117. DOI: 10.2320/matertrans1989.35.112.
Bryan, W.L. and Dodge, B.F. Diffusivity of hydrogen in pure iron. AIChE J., 1963, 9, 223–228. DOI: 10.1002/aic.690090217.
Nagano, M., Hayashi, Y., Ohtani, N., Isshiki, M., and Igaki, K. Hydrogen diffusivity in high purity alpha iron. Scripta Metallurgica, 1982, 16, 973–976. DOI: 10.1016/0036-9748(82)90136-3.
Messer, R., Blessing, A., Dais, S., Höpfel, D., Majer, G., Schmidt, C., Seeger, A., Zag, W., and Lässer, R. Nuclear magnetic resonance studies of hydrogen diffusion, trapping, and site occupation in metals. Zeitschrift für Physikalische Chemie, 1986, 1986 (s2), 61–119. DOI: 10.1524/zpch.1986.1986.Suppl_2.061.
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В. Б.Выходец, Т. Е. Куренных

КРИТЕРИИ ДЛЯ НАБЛЮДЕНИЯ ТУННЕЛИРОВАНИЯ ВОДОРОДА В МЕТАЛЛАХ

В работе на основе анализа результатов теоретических и экспериментальных исследований сформулированы критерии, которым должны удовлетворять металлы для наблюдения в них туннелирования водорода, и методики измерения коэффициентов квантовой диффузии. Во-первых, должно быть достаточно малым (на уровне 0,15 нм) расстояние между ближайшими равновесными позициями атомов водорода в кристаллической решетке металла. Во-вторых, должна быть достаточно низкой температура Дебая металла, ниже 350 К. В-третьих, необходимым условием наблюдения туннелирования водорода является корректный выбор методики измерения коэффициентов диффузии водорода. Если в районе температуры Дебая коэффициент диффузии водорода по классическому механизму миграции находится на уровне 10−11 м2/с и выше, то целесообразно применять непрямые методики, основанные на эффекте Горского или измерении скорости спин-решеточной релаксации с помощью ядерного магнитного резонанса. При более низких значениях коэффициента классической диффузии в районе температуры Дебая металла для наблюдения квантовой диффузии необходимо применять прямую методику ядерных реакций в режиме онлайн или ее же в сочетании с методом ядерных реакций.

Благодарность: Работа выполнена в рамках государственного задания Минобрнауки России (тема «Функция», № 122021000035-6).

Ключевые слова: водород, металлы, туннелирование, критерии наблюдения, равновесные позиции, температура Дебая, квантовая диффузия, экспериментальные методики

Библиография:

Simultaneous deep tunneling and classical hopping for hydrogen diffusion on metals / W. Fang, J. O. Richardson, J. Chen, X.-Z. Li, A. Michaelides // Phys. Rev. Lett. – 2017. – Vol. 119. – P. 126001. – DOI: 10.1103/PhysRevLett.119.126001.
Small-polaronic diffusion of light interstitials in bcc metals / D. Emin, M. I. Baskes, W. D. Wilson // Phys. Rev. Lett. – 1979. – Vol. 42. – P. 791–794. – DOI: 10.1103/PhysRevLett.42.791.
Schober H. R., Stoneham A. M. Diffusion of hydrogen in niobium // Phys. Rev. Lett. – 1988. – Vol. 60. – P. 2307–2310. – DOI: 10.1103/PhysRevLett.60.2307.
Sundell P. G., Wahnström G. Activation energies for quantum diffusion of hydrogen in metals and on metal surfaces using delocalized nuclei within the density-functional theory // Phys. Rev. Lett. – 2004. – Vol. 92 (15). – P. 155901. – DOI: 10.1103/PhysRevLett.92.155901.
Di Stefano D., Mrovec M., Elsässer C. First-principles investigation of quantum mechanical effects on the diffusion of hydrogen in iron and nickel // Phys. Rev. B. – 2015. – Vol. 92 (22). – P. 224301. – DOI: 10.1103/PhysRevB.92.224301.
Kimizuka H., Ogata S., Shiga M. Mechanism of fast lattice diffusion of hydrogen in palladium: Interplay of quantum fluctuations and lattice strain // Phys. Rev. B. – 2018. – Vol. 97. – P. 014102. – DOI: 10.1103/PhysRevB.97.014102.
Schober H. R., Stoneham A. M. Diffusion of hydrogen in transition metals // J. Less-Common Metals. – 1991. –Vol. 172–174. – P. 538–547. – DOI: 10.1016/0022-5088(91)90174-3.
Stoneham A. M. Non-classical diffusion procession // J. Nucl. Mater. – 1978. – Vols. 69–70. – P. 109–116. – DOI: 10.1016/0022-3115(78)90239-8.
Kimizuka H., Ogata S., Shiga M. Unraveling anomalous isotope effect on hydrogen diffusivities in fcc metals from first principles including nuclear quantum effects // Phys. Rev. B. – 2019. – Vol. 100. – P. 024104. – DOI: 10.1103/PhysRevB.100.024104.
Kimizuka H., Mori H., Ogata S. Effect of temperature on fast hydrogen diffusion in iron: A path-integral quantum dynamics approach // Phys. Rev. B. – 2011. – Vol. 83. – P. 094110. – DOI: 10.1103/PhysRevB.83.094110.
Quantum–thermal crossover of hydrogen and tritium diffusion in α-iron / T. Yoshikawa, T. Takayanagi, H. Kimizuka, M. Shiga // J. Phys. Chem. C. – 2012. – Vol. 116. – P. 23113–23119. – DOI: 10.1021/jp307660e.
Kashlev Ya. A. Three regimes of diffusion migration of hydrogen atoms in metals // Theor. Math. Phys. – 2005. – Vol. 145. – P. 1590−1603. – DOI: 10.1007/s11232-005-0185-8.
Tritium diffusion in V, Nb and Ta / Z. Qi, J. Volkl, R. Lasser, H. Wenzl // J. Phys. F: Met. Phys. – 1983. –Vol. 13. – P. 2053–2062. – DOI: 10.1088/0305-4608/13/10/015.
Flynn C. P., Stoneham A. M. Quantum theory of diffusion with application to light interstitials in metals // Phys. Rev. B. – 1970. – Vol. 1. – P. 3966–3978. – DOI: 10.1103/PhysRevB.1.3966.
Johnson D. F., Carter E. A. Hydrogen in tungsten: absorption, diffusion, vacancy trapping, and decohesion // J. Mater. Res. – 2010. – Vol. 25. – P. 315–327. – DOI: 10.1557/jmr.2010.0036.
Jiang D. E., Carter E. A. Diffusion of interstitial hydrogen into and through bcc Fe from first principles // Phys. Rev. B. – 2004. – Vol. 70. – P. 064102. – DOI: 10.1103/PhysRevB.70.064102.
Quantum diffusion of deuterium in sodium / V. Vykhodets, O. Nefedova, T. Kurennykh, S. Obukhov, Ye. Vykhodets // J. Phys. Chem. A. – 2019. – Vol. 123. – P. 7536–7539. – DOI: 10.1021/acs.jpca.9b06231.
Debye temperature and quantum diffusion of hydrogen in body-centered cubic metals / V. Vykhodets, O. Nefedova, T. Kurennykh, S. Obukhov, E. Vykhodets // ACS Omega. – 2022. – Vol. 7 (10). – P. 8385–8390. – DOI: 10.1021/acsomega.1c05902.
First observation of quantum diffusion in non‐cubic metal: deuterium diffusion in In / V. Vykhodets, O. Nefedova, T. Kurennykh, E. Vykhodets // Metals. – 2023. – Vol. 13. – P. 394–405. – DOI: 10.3390/met13020394.
Strong increase of tunneling rate of hydrogen in Indium in the presence of vacancies / V. Vykhodets, O. Nefedova, T. Kurennykh, S. Danilov // J. Phys. Chem. C. – 2024. – Vol. 128 (6). – P. 2730–2736. – DOI: 10.1021/acs.jpcc.3c08044.
Hagi H. Diffusion coefficient of hydrogen in iron without trapping by dislocations and impurities // Mater. Trans. JIM. – 1994. – Vol. 35. – P. 112–117. – DOI: 10.2320/matertrans1989.35.112.
Bryan W. L., Dodge B. F. Diffusivity of hydrogen in pure iron // AIChE J. – 1963. – Vol. 9. – P. 223–28. – DOI: 10.1002/aic.690090217.
Hydrogen diffusivity in high purity alpha iron / M. Nagano, Y. Hayashi, N. Ohtani, M. Isshiki, K. Igaki // Scripta Metallurgica. – 1982. – Vol. 16. – P. 973–976. – DOI: 10.1016/0036-9748(82)90136-3.
Nuclear magnetic resonance studies of hydrogen diffusion, trapping, and site occupation in metals / R. Messer, A. Blessing, S. Dais, D. Höpfel, G. Majer, C. Schmidt, A. Seeger, W. Zag, R. Lässer // Zeitschrift für Physikalische Chemie. – 1986. – 1986 (s2). – P. 61−119. – DOI: 10.1524/zpch.1986.1986.Suppl_2.061.
Peterson D. T., Hammerberg C. C. Diffusion of hydrogen in barium metal // J. Less. Com. Met. – 1968. – Vol. 16. – P. 457–460. – DOI: 10.1016/0022-5088(68)90144-6.

Библиографическая ссылка на статью

B.Vykhodets V., Kurennykh T. E. Criteria for Observing Hydrogen Tunneling in Metals // Diagnostics, Resource and Mechanics of materials and structures. - 2024. - Iss. 4. - P. 24-34. -
DOI: 10.17804/2410-9908.2024.4.024-034. -
URL: http://dream-journal.org/issues/content/article_469.html
(accessed: 21.12.2024).