A Simplistic Analytical Model for Hydrogen Surface Coverage Under the Influence of Various Surface-Related Processes and Ion Bombardment

Keywords: Secondary ion mass spectrometry, Hydrogen storage, Sputtering, Adsorption, Desorption, Ion bombardment, Kinetics


The paper describes a simple analytical model that allows the calculation of hydrogen surface coverage under the influence of several processes that can co-occur during the ion-beam bombardment/sputter analysis of a sample surface, in particular during analysis by secondary ion mass spectrometry (SIMS). The model considers processes of dissociative adsorption, desorption, absorption from the surface into the sample volume, and removal by ion bombardment. After describing the model, we provide some examples of its practical applications for interpretation of the experimental results obtained during in situ SIMS studies of hydrogen interaction with the hydrogen-storage alloys TiFe, Zr2Fe, and with nickel. In the examples, some quantitative characteristics of surface-related processes involving hydrogen, such as hydrogen sputtering rate, activation energy of hydrogen desorption and absorption, have been successfully determined using various model approaches.


Download data is not yet available.


Z. Zhu, V. Shutthanandan, and M. Engelhard, “An investigation of hydrogen depth profiling using ToF-SIMS”, Surface and Interface Analysis, 44(2), 232–237 (2012). https://doi.org/10.1002/sia.3826

F.A. Stevie, “Analysis of hydrogen in materials with and without high hydrogen mobility”, Surface and Interface Analysis, 48(5), 310–314 (2016). https://doi.org/10.1002/sia.5930

S. Pal, J. Barrirero, M. Lehmann, Q. Jeangros, N. Valle, F.-J. Haug, A. Hessler-Wyser, C.N. Shyam Kumar, F. Mücklich, T. Wirtz, and S. Eswara, “Quantification of hydrogen in nanostructured hydrogenated passivating contacts for silicon photovoltaics combining SIMS-APT-TEM: A multiscale correlative approach”, Applied Surface Science, 555, 149650 (2021). https://doi.org/10.1016/j.apsusc.2021.149650

M. Riedel, and H. Düsterhöft, “Hydrogen outgassing of ZrNiCu(H) amorphous alloy studied by secondary ion mass spectrometry”, Rapid Communications in Mass Spectrometry, 12(20), 1510–1514 (1998). https://doi.org/10.1002/(SICI)1097-0231(19981030)12:20<1510::AID-RCM334>3.0.CO;2-2

A. Nishimoto, M. Koyama, S. Yamato, Y. Oda, T. Awane, and H. Noguchi, “Detection of Charged Hydrogen in Ferritic Steel through Cryogenic Secondary Ion Mass Spectrometry”, ISIJ International, 55(1), 335–337 (2015). https://doi.org/10.2355/isijinternational.55.335

T. Asakawa, D. Nagano, S. Denda, and K. Miyairi, “Influence of primary ion beam irradiation conditions on the depth profile of hydrogen in tantalum film”, Applied Surface Science, 255(4), 1387–1390 (2008). https://doi.org/10.1016/j.apsusc.2008.05.042

X. Lin, A. Fucsko, K. Noehring, E. Gabriel, A. Regner, S. York, and D. Palsulich, “New SIMS method to characterize hydrogen in polysilicon films”, Journal of Vacuum Science & Technology B, 40(1), (2022). https://doi.org/10.1116/6.0001472

J. Sameshima, and S. Numao, “Behavior and process of background signal formation of hydrogen, carbon, nitrogen, and oxygen in silicon wafers during depth profiling using dual‐beam TOF‐SIMS”, Surface and Interface Analysis, 54(2), 165–173 (2022). https://doi.org/10.1002/sia.7035

D. Andersen, H. Chen, S. Pal, L. Cressa, O. De Castro, T. Wirtz, G. Schmitz, and S. Eswara, “Correlative high-resolution imaging of hydrogen in Mg2Ni hydrogen storage thin films”, International Journal of Hydrogen Energy, 48(37), 13943–13954 (2023). https://doi.org/10.1016/j.ijhydene.2022.12.216

M.V. Lototskyy, B.P. Tarasov, and V.A. Yartys, “Gas-phase applications of metal hydrides”, Journal of Energy Storage, 72, 108165 (2023). https://doi.org/10.1016/j.est.2023.108165

V.A. Litvinov, I.I. Okseniuk, D.I. Shevchenko, and V.V. Bobkov, “Secondary-ion mass spectrometry study of LaNi5-hydrogen-oxygen system”, Ukrainian Journal of Physics, 66(8), 723–735 (2021). https://doi.org/10.15407/ujpe66.8.723

I. Okseniuk, and D. Shevchenko, “SIMS studies of hydrogen interaction with the TiFe alloy surface: hydrogen influence on secondary ion yields”, Surface Science, 716, 121963 (2022). https://doi.org/10.1016/j.susc.2021.121963

I.I. Okseniuk, V.O. Litvinov, D.I. Shevchenko, R.L. Vasilenko, S.I. Bogatyrenko, and V.V. Bobkov, “Hydrogen interaction with Zr-based getter alloys in high vacuum conditions: In situ SIMS-TPD studies”, Vacuum, 197, 110861 (2022). https://doi.org/10.1016/J.VACUUM.2021.110861

V.A. Litvinov, I.I. Okseniuk, D.I. Shevchenko, and V. V. Bobkov, “SIMS Study of Hydrogen Interaction with the LaNi5 Alloy Surface”, Journal of Surface Investigation, 12(3), 576–583 (2018). https://doi.org/10.1134/S1027451018030321

V.O. Litvinov, I.I. Okseniuk, D.I. Shevchenko, and V. V. Bobkov, “The Role of Surface in Hydride Formation Processes”, East European Journal of Physics, (3), 10–42 (2023). https://doi.org/10.26565/2312-4334-2023-3-01

C.S. Zhang, B. Li, and P.R. Norton, “The study of hydrogen segregation on Zr(0001) and Zr(1010) surfaces by static secondary ion mass spectroscopy, work function, Auger electron spectroscopy and nuclear reaction analysis”, Journal of Alloys and Compounds, 231(1–2), 354–363 (1995). https://doi.org/10.1016/0925-8388(95)01847-6

X.Y. Zhu, and J.M. White, “Hydrogen interaction with nickel(100): a static secondary ion mass spectroscopy study”, The Journal of Physical Chemistry, 92(13), 3970–3974 (1988). https://doi.org/10.1021/j100324a056

A. Benninghoven, P. Beckmann, D. Greifendorf, K.H. Müller, and M. Schemmer, “Hydrogen detection by secondary ion mass spectroscopy: Hydrogen on polycrystalline nickel”, Surface Science, 107(1), 148–164 (1981). https://doi.org/10.1016/0039-6028(81)90618-X

T. Asakawa, D. Nagano, H. Miyazawa, and I. Clark, “Absorption, discharge, and internal partitioning behavior of hydrogen in the tantalum and tantalum oxide system investigated by in situ oxidation SIMS and ab initio calculations”, Journal of Vacuum Science & Technology B, 38(3), 034008 (2020). https://doi.org/10.1116/6.0000100

A. Röhsler, O. Sobol, H. Hänninen, and T. Böllinghaus, “In-situ ToF-SIMS analyses of deuterium re-distribution in austenitic steel AISI 304L under mechanical load”, Scientific Reports, 10(1), 3611 (2020). https://doi.org/10.1038/s41598-020-60370-2

P. Kesten, A. Pundt, G. Schmitz, M. Weisheit, H.U. Krebs, and R. Kirchheim, “H- and D distribution in metallic multilayers studied by 3-dimensional atom probe analysis and secondary ion mass spectrometry,” Journal of Alloys and Compounds, (2002), pp. 225–228. https://doi.org/10.1016/S0925-8388(01)01596-1

C.S. Zhang, B. Li, and P.R. Norton, “The initial stages of interaction of hydrogen with the Zr(101̄0) surface”, Surface Science, 346(1–3), 206–221 (1996). https://doi.org/10.1016/0039-6028(95)00904-3

J. Ekar, P. Panjan, S. Drev, and J. Kovač, “ToF-SIMS Depth Profiling of Metal, Metal Oxide, and Alloy Multilayers in Atmospheres of H 2 , C 2 H 2 , CO, and O 2”, Journal of the American Society for Mass Spectrometry, 33(1), 31–44 (2022). https://doi.org/10.1021/jasms.1c00218

J. Ekar, and J. Kovač, “AFM Study of Roughness Development during ToF-SIMS Depth Profiling of Multilayers with a Cs + Ion Beam in a H 2 Atmosphere”, Langmuir, 38(42), 12871–12880 (2022). https://doi.org/10.1021/acs.langmuir.2c01837

J. Ekar, S. Kos, and J. Kovač, “Quantitative Aspects of ToF-SIMS Analysis of Metals and Alloys in a UHV, O2 and H2 Atmosphere”, Preprint (at https://www.ssrn.com), (2024). https://doi.org/10.2139/ssrn.4683611

O.B. Malyshev, Vacuum in Particle Accelerators (Wiley, 2019)

I. Sereda, Y. Hrechko, I. Babenko, and M. Azarenkov, “The emission of H− ions from Penning-type ion source with metal hydride cathode in pulsating regime”, Vacuum, 200, 111006 (2022). https://doi.org/10.1016/j.vacuum.2022.111006

I. Sereda, Y. Hrechko, I. Babenko, and M. Azarenkov, “The Features of Intense Electron Flow Impact on Metal Hydride Electrode”, East European Journal of Physics, (2), 99–102 (2022). https://doi.org/10.26565/2312-4334-2022-2-12

I. Sereda, Y. Hrechko, and I. Babenko, “The Plasma Parameters of Penning Discharge with Negatively Biased Metal Hydride Cathode at Longitudinal Emission of H– Ions”, East European Journal of Physics, (3), 81–86 (2021). https://doi.org/10.26565/2312-4334-2021-3-12

E.A. Hodille, S. Markelj, M. Pecovnik, M. Ajmalghan, Z.A. Piazza, Y. Ferro, T. Schwarz-Selinger, and C. Grisolia, “Kinetic model for hydrogen absorption in tungsten with coverage dependent surface mechanisms”, Nuclear Fusion, 60(10), 106011 (2020). https://doi.org/10.1088/1741-4326/aba454

K.E. Lu, and R.R. Rye, “Flash desorption and equilibration of H2 and D2 on single crystal surfaces of platinum”, Surface Science, 45(2), 677–695 (1974). https://doi.org/10.1016/0039-6028(74)90197-6

V.A. Litvinov, I.I. Okseniuk, D.I. Shevchenko, and V. V. Bobkov, “SIMS study of the surface of lanthanum-based alloys”, Ukrainian Journal of Physics, 62(10), 845–857 (2017). https://doi.org/10.15407/ujpe62.10.0845

V.T. Cherepin, M.O. Vasylyev, I.M. Makeeva, V.M. Kolesnik, and S.M. Voloshko, “Secondary Ion Emission during the Proton Bombardment of Metal Surfaces”, Uspehi Fiziki Metallov, 19(1), 49–69 (2018). https://doi.org/10.15407/ufm.19.01.049

A. Wucher, “Formation of atomic secondary ions in sputtering”, Applied Surface Science, 255(4), 1194–1200 (2008). https://doi.org/10.1016/j.apsusc.2008.05.252

K. Christmann, “Adsorption of Hydrogen,” in Surface and Interface Science, Volume 5 and 6: Volume 5 - Solid Gas Interfaces I; Volume 6 - Solid Gas Interfaces II, edited by K. Wandelt, (John Wiley & Sons, 2016), pp. 255–357

J. Sopka, and H. Oechsner, “Determination of hydrogen concentration depth profiles in a-Si:H by Secondary Neutral Mass Spectrometry (SNMS)”, Journal of Non-Crystalline Solids, 114, 208–210 (1989). https://doi.org/10.1016/0022-3093(89)90115-4

J. Scholz, H. Züchner, H. Paulus, and K.-H. Müller, “Ion bombardment induced segregation effects in VDx studied by SIMS and SNMS”, Journal of Alloys and Compounds, 253–254, 459–462 (1997). https://doi.org/10.1016/S0925-8388(96)03000-9

D.N. Denzler, C. Frischkorn, C. Hess, M. Wolf, and G. Ertl, “Electronic Excitation and Dynamic Promotion of a Surface Reaction”, Physical Review Letters, 91(22), 226102 (2003). https://doi.org/10.1103/PhysRevLett.91.226102

F. Le Pimpec, O. Gröbner, and J.M. Laurent, “Electron stimulated molecular desorption of a non-evaporable Zr–V–Fe alloy getter at room temperature”, Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 194(4), 434–442 (2002). https://doi.org/10.1016/S0168-583X(02)01034-0

Y. Kudriavtsev, R. Asomoza, A. Hernandez, D.Y. Kazantsev, B.Y. Ber, and A.N. Gorokhov, “Nonlinear effects in low-energy ion sputtering of solids”, Journal of Vacuum Science & Technology A, 38(5), 053203 (2020). https://doi.org/10.1116/6.0000262

V. V Ovchinnikov, F.F. Makhin’ko, and V.I. Solomonov, “Thermal-spikes temperature measurement in pure metals under argon ion irradiation (E = 5-15 keV)”, Journal of Physics: Conference Series, 652, 012070 (2015). https://doi.org/10.1088/1742-6596/652/1/012070

L.O. Williams, Hydrogen Power: An Introduction to Hydrogen Energy and Its Applications (Pergamon press, 2013)

K. Christmann, “Interaction of hydrogen with solid surfaces”, Surface Science Reports, 9(1–3), 1–163 (1988). https://doi.org/10.1016/0167-5729(88)90009-X

G. Ross, “Analysis of hydrogen isotopes in materials by secondary ion mass spectrometry and nuclear microanalysis”, Vacuum, 45(4), 375–387 (1994). https://doi.org/10.1016/0042-207X(94)90306-9

M. Wilde, M. Matsumoto, L. Gao, T. Schwarz-Selinger, A. Manhard, and W. Jacob, “Cross section of 15N-2D nuclear reactions from 3.3 to 7.0 MeV for simultaneous hydrogen and deuterium quantitation in surface layers with 15N ion beams”, Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 478, 56–61 (2020). https://doi.org/10.1016/j.nimb.2020.05.020

M. Wilde, S. Ohno, S. Ogura, K. Fukutani, and H. Matsuzaki, “Quantification of Hydrogen Concentrations in Surface and Interface Layers and Bulk Materials through Depth Profiling with Nuclear Reaction Analysis”, Journal of Visualized Experiments, (109), (2016). https://doi.org/10.3791/53452

V.P. Zhdanov, “Arrhenius parameters for rate processes on solid surfaces”, Surface Science Reports, 12(5), 185–242 (1991). https://doi.org/10.1016/0167-5729(91)90011-L

H.J. Kreuzer, S.H. Payne, and Y.K. Tovbin, “Equilibria and Dynamics of Gas Adsorption on Heterogeneous Solid Surfaces,” in Studies in Surface Science and Catalysis, edited by G.Z. Edited by W. Rudziński, W.A. Steele, (Elsevier, 1997), pp. 153–284

K. Christmann, “Kinetics, energetics and structure of hydrogen adsorbed on transition metal single crystal surfaces”, Bulletin Des Sociétés Chimiques Belges, 88(7–8), 519–539 (2010). https://doi.org/10.1002/bscb.19790880706

D.L.S. Nieskens, A.P. van Bavel, and J.W. Niemantsverdriet, “The analysis of temperature programmed desorption experiments of systems with lateral interactions; implications of the compensation effect”, Surface Science, 546(2–3), 159–169 (2003). https://doi.org/10.1016/j.susc.2003.09.035

K. Christmann, O. Schober, G. Ertl, and M. Neumann, “Adsorption of hydrogen on nickel single crystal surfaces”, The Journal of Chemical Physics, 60(11), 4528–4540 (1974). https://doi.org/10.1063/1.1680935

How to Cite
Okseniuk, I. I., Litvinov, V. O., Shevchenko, D. I., Afanasieva, I. O., & Bobkov, V. V. (2024). A Simplistic Analytical Model for Hydrogen Surface Coverage Under the Influence of Various Surface-Related Processes and Ion Bombardment. East European Journal of Physics, (2), 99-110. https://doi.org/10.26565/2312-4334-2024-2-08

Most read articles by the same author(s)