Formation and fragmentation of the tungsten clusters in gas phase

  • Ján MatúškaEmail author
  • Ivan Sukuba
  • Jan Urban
Original Paper


We present a theoretical study of accumulation of clusters consisting of up to 100 tungsten atoms based on information extracted from molecular dynamics trajectory simulations. The description is based on the rates corresponding to the single W atom attachment to Wn clusters and their dissociation processes. The results display a strong Arrhenius dependence of the dissociation rate constant on temperature. The preferred products of dissociation of the clusters composed of more than ten atoms are single W atoms and fragments with six to nine atoms. On the other hand, the association rate constants depend weakly on temperature. The obtained rate constants are used to calculate the chemical equilibrium of the W clusters that results in significant traces of small clusters only at high initial W atoms concentrations.


Molecular dynamics Thermal equilibrium rate constants Tungsten clusters Chemical equilibrium 



This work is supported by the Slovak Grant Agency VEGA, project Nr. V-1/0601/15. Also, we are grateful to the HPC center at the Slovak University of Technology in Bratislava, which is a part of the Slovak Infrastructure of High Performance Computing (SIVVP project, ITMS code 26230120002, funded by the European region development funds, ERDF), for the computational time and resources made available.

Supplementary material

894_2019_4072_MOESM1_ESM.pdf (92 kb)
ESM 1 (PDF 91 kb)


  1. 1.
    Pintsuk G (2012) Tungsten as a plasma-facing material. Compr Nucl Mater 4:551–581. CrossRefGoogle Scholar
  2. 2.
    Pitts RA, Carpentier S, Escourbiac F, Hirai T, Komarov V, Lisgo S, Kukushkin AS, Loarte A, Merola M, SashalaNaik A, Mitteau R, Sugihara M, Bazylev B, Stangeby PC (2013) A full tungsten divertor for ITER: physics issues and design status. J Nucl Mater 438:S48–S56. CrossRefGoogle Scholar
  3. 3.
    Pitts RA, Carpentier S, Escourbiac F, Hirai T, Komarov V, Kukushkin AS, Lisgo S, Loarte A, Merola M, Mitteau R, Raffray AR, Shimada M, Stangeby PC (2011) Physics basis and design of the ITER plasma-facing components. J Nucl Mater 415:S957–S964. CrossRefGoogle Scholar
  4. 4.
    Tavassoli F (2013) Eurofer steel, development to full code qualification. Proc Eng 55:300–308. CrossRefGoogle Scholar
  5. 5.
    Kytka M, Brumovsky M, Falcnik M (2011) Irradiation embrittlement characterization of the EUROFER 97 material. J Nucl Mater 409:147–152. CrossRefGoogle Scholar
  6. 6.
    Roth J, Sugiyama K, Alimov V, Höschen T, Baldwin M, Doerner R (2014) EUROFER as wall material: reduced sputtering yields due to W surface enrichment. J Nucl Mater 454:1–6. CrossRefGoogle Scholar
  7. 7.
    Widdowson A, Alves E, Ayres CF, Baron-Wiechec A, Brezinsek S, Catarino N, Coad JP, Heinola K, Likonen J, Matthews GF, Mayer M, Rubel M (2014) Material migration patterns and overview of first surface analysis of the JET ITER-like wall. Phys Scr T159:14010. CrossRefGoogle Scholar
  8. 8.
    Brezinsek S, Widdowson A, Mayer M, Philipps V, Baron-Wiechec P, Coenen JW, Heinola K, Huber A, Likonen J, Petersson P, Rubel M, Stamp MF, Borodin D, Coad JP, Carrasco AG, Kirschner A, Krat S, Krieger K, Lipschultz B, Linsmeier C, Matthews GF, Schmid K (2015) Beryllium migration in JET ITER-like wall plasmas. Nucl Fusion 55:63021. CrossRefGoogle Scholar
  9. 9.
    Baldwin MJ, Doerner RP, Nishijima D, Buchenauer D, Clift WM, Causey RA, Schmid K (2007) Be-W alloy formation in static and divertor-plasma simulator experiments. J Nucl Mater 363–365:1179–1183. CrossRefGoogle Scholar
  10. 10.
    Ahlgren T, Heinola K, Vörtler K, Keinonen J (2012) Simulation of irradiation induced deuterium trapping in tungsten. J Nucl Mater 427:152–161. CrossRefGoogle Scholar
  11. 11.
    Träskelin P, Juslin N, Erhart P, Nordlund K (2007) Molecular dynamics simulations of hydrogen bombardment of tungsten carbide surfaces. Phys Rev B 75:174113. CrossRefGoogle Scholar
  12. 12.
    Nordlund K, Björkas C, Ahlgren T, Lasa A, Sand AE (2014) Multiscale modelling of plasma–wall interactions in fusion reactor conditions. J Phys D Appl Phys 47:224018. CrossRefGoogle Scholar
  13. 13.
    Baguenard B, Pinaré JC, Bordas C, Broyer M (2001) Photoelectron imaging spectroscopy of small tungsten clusters: direct observation of thermionic emission. Phys Rev A 63:23204. CrossRefGoogle Scholar
  14. 14.
    Staudenmaier G (1972) Clusters sputtered from tungsten. Radiat Eff 13:87–91. CrossRefGoogle Scholar
  15. 15.
    Hayakawa T, Yasumatsu H (2012) Two-dimensional to three-dimensional transition of tungsten clusters anchored on graphite surface. J Nanopart Res 14:1022. CrossRefGoogle Scholar
  16. 16.
    Wu ZJ (2003) Density functional study of W2 and W3 clusters. Chem Phys Lett 370:510–514. CrossRefGoogle Scholar
  17. 17.
    Zhang X, Ding X, Dai B, Yang J (2005) Density functional theory study of Wn (n=2-4) clusters. J Mol Struct THEOCHEM 757:113–118. CrossRefGoogle Scholar
  18. 18.
    Yamaguchi W, Murakami J (2005) Geometries of small tungsten clusters. Chem Phys 316:45–52. CrossRefGoogle Scholar
  19. 19.
    Yang X, Hassanein A (2014) Atomic scale calculations of tungsten surface binding energy and beryllium-induced tungsten sputtering. Appl Surf Sci 293:187–190. CrossRefGoogle Scholar
  20. 20.
    Sand AE, Aliaga MJ, Caturla MJ, Nordlund K (2016) Surface effects and statistical laws of defects in primary radiation damage: Tungsten vs. iron. Europhys Lett 115:36001. CrossRefGoogle Scholar
  21. 21.
    Salonen E, Nordlund K, Keinonen J, Wu CH (2002) Enhanced erosion of tungsten by atom clusters. J Nucl Mater 305:60–65. CrossRefGoogle Scholar
  22. 22.
    Juslin N, Erhart P, Träskelin P, Nord J, Henriksson KOE, Nordlund K, Salonen E, Albe K (2005) Analytical interatomic potential for modeling nonequilibrium processes in the W–C–H system. J Appl Phys 98:123520. CrossRefGoogle Scholar
  23. 23.
    Yang X, Hassanein A (2013) Molecular dynamics simulation of deuterium trapping and bubble formation in tungsten. J Nucl Mater 434:1–6. CrossRefGoogle Scholar
  24. 24.
    Klaver TPC, Nordlund K, Morgan TW, Westerhof E, Thijsse BJ, van de Sanden MCM (2016) Molecular dynamics simulations of ballistic he penetration into W fuzz. Nucl Fusion 56:126015. CrossRefGoogle Scholar
  25. 25.
    Wang K, Doerner RP, Baldwin MJ, Meyer FW, Bannister ME, Darbal A, Stroud R, Parish CM (2017) Morphologies of tungsten nanotendrils grown under helium exposure. Sci Rep 7:42315. CrossRefPubMedPubMedCentralGoogle Scholar
  26. 26.
    Li ZH, Truhlar DG (2008) Cluster and nanoparticle condensation and evaporation reactions. Thermal rate constants and equilibrium constants of Al m + Al n − m ↔ Al n with n = 2−60 and m = 1−8. J Phys Chem C 112:11109–11121. CrossRefGoogle Scholar
  27. 27.
    Yang H, Eirini G, Hogan CJ (2018) Condensation and dissociation rates for gas phase metal clusters from molecular dynamics trajectory calculations. J Chem Phys 148:164304. CrossRefPubMedGoogle Scholar
  28. 28.
    Matuska J, Sukuba I (2017) Thermal rate constants of beryllium clusters in gas phase. (2017). Acta Chimica Slovaca 10:115–122. CrossRefGoogle Scholar
  29. 29.
    Blais NC, Truhlar DG (1983) Third body efficiencies for collision-induced dissociation of diatomics. Rate coefficients for H+H 2 →3H. J Chem Phys 78:2388–2393. CrossRefGoogle Scholar
  30. 30.
    Zheng J, Li Z-H, Jasper AW, Bonhommeau DA, Valero R, Meana-Pañeda R, Mielke SL, Truhlar DG (2016) ANT, version 2016. University of Minnesota, Minneapolis Google Scholar
  31. 31.
    Tuckerman M, Berne BJ, Martyna GJ (1992) Reversible multiple time scale molecular dynamics. J Chem Phys 97:1990–2001. CrossRefGoogle Scholar
  32. 32.
    Martyna GJ, Klein ML, Tuckerman M (1992) Nosé–hoover chains: the canonical ensemble via continuous dynamics. J Chem Phys 97:2635–2643. CrossRefGoogle Scholar
  33. 33.
    Stillinger FH (1963) Rigorous basis of the Frenkel-band theory of association equilibrium. J Chem Phys 38:1486–1494. CrossRefGoogle Scholar

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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of Physical Chemistry and Chemical PhysicsFCHPT-STUBratislavaSlovakia
  2. 2.Department of Nuclear Physics and Biophysics, Faculty of Mathematics, Physics and InformaticsComenius UniversityBratislavaSlovakia

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