On ionisation induced unimolecular dissociation of sodium clusters

  • M. M. Kappes
  • M. Schär
  • E. Schumacher
  • A. Vayloyan


Fragmentation of sodium cluster ions (Na x + ,x<42) was studied via photoionisation of neutral precursors. Expansions of metal vapor out of cylindrical and conical nozzles yielded supersonic beams with differing cluster compositions. Measurements of photoionisation efficiency curves in the 3–6 eV range for both types of expansion allow quantitative separation of direct ionisation and unimolecular dissociation contributions to specific ion signals. Data for Na 8 + and Na 7 + are analysed to yield lower limits on bond energies. Results obtained for larger clusters are also discussed.


35.20.Gs 35.20.Vf 36.40.+d 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Kappes, M., Kunz, R., Schumacher, E.: Chem. Phys. Lett.91, 413 (1982)Google Scholar
  2. 2.
    Kappes, M., Schär, M., Radi, P., Schumacher, E.: J. Chem. Phys.84, 1863 (1986)Google Scholar
  3. 3.
    Kappes, M., Radi, P., Schär, M., Schumacher, E.: Chem. Phys. Lett.119, 11 (1985)Google Scholar
  4. 4.
    In contrast, ionisation induced fragmentation even at threshold can be of great importance for van der Waals and hydrogen bonded aggregates. Here neutral and ionic ground state geometries may be very different. Then, vertical ionisation leads to the production of ions with significant internal excitation; see for example: Harris, I., Kidwell, R., Northby, J.: Phys. Rev. Lett.53, 2390 (1984)Google Scholar
  5. 5.
    Knight, W., Clemenger, K., Heer, W. de, Saunders, W., Chou, M., Cohen, M.: Phys. Rev. Lett.52, 2141 (1984)Google Scholar
  6. 5a.
    Knight, W., Heer, W. de, Clemenger, K., Saunders, W.: Solid State Commun.53, 445 (1985)Google Scholar
  7. 5b.
    Saunders, W., Clemenger, K., Heer, W. de, Knight, W.: Phys. Rev. B32, 1366 (1985)Google Scholar
  8. 6.
    We define a dominant maximum as corresponding to a cluster ion Mn+ with more than 3 × greater abundance than Mn+1+. Dominant maxima occur atn=2, (4), 8, 20, 40, ..., see Ref. 2 and 5. Figure 1 shows mass spectra obtained at an irradiation energy sufficient to ionize all species Nax,x>2 upon absorption of one photon. Absolute Na2 to Na3 ratios under the beam conditions used were typically 50:1Google Scholar
  9. 7.
    Chou, M., Cleland, A., Cohen, M.: Solid State Commun.52, 645 (1984);Google Scholar
  10. 7a.
    Ekardt, W.: Phys. Rev. B29, 1558 (1984)Google Scholar
  11. 8.
    Clemenger, K.: Phys. Rev. B32, 1359 (1985)Google Scholar
  12. 9.
    Kappes, M., Schär, M., Schumacher, E.: J. Phys. Chem.89, 1499 (1985)Google Scholar
  13. 10.
    Handbook of Chemistry and Physics. 60th Edn. Boca Raton: CRC Press 1980Google Scholar
  14. 11.
    Kappes, M., Schär, M., Schumacher, E.: J. Phys. Chem. (in press)Google Scholar
  15. 12.
    Schär, M., Kappes, M., Schumacher, E. (to be published)Google Scholar
  16. 13.
    Wild, U., Holzwarth, A., Good, H.: Rev. Sci. Instrum.48, 1621 (1977)Google Scholar
  17. 14.
    Grinvald, A., Steinberg, I.: Anal. Biochem.59, 583 (1974)Google Scholar
  18. 15.
    At oven temperatures of 850 °C we have observed sodium cluster ions with up to 85 atoms using this type of conical nozzle. Collisional “amplification” of conical nozzle clustering relative to cylindrical apertures has yet to be quantified. Measurements in this laboratory have established that terminal beam velocities are roughly independent of nozzle geometry for identical aperture diameters and stagnation conditionsGoogle Scholar
  19. 16.
    It is common literature practice todivide ion signal by lamp spectrum to obtain PIE curves normalised to differential photon flux. This does not take into account the finite monochromator slit function and can lead to erroneous results. Note that (broad band) mass spectral intensities are proportional to the integral over theuncorrected photoion yieldGoogle Scholar
  20. 17.
    Hagena, O., Obert, W.: J. Chem. Phys.56, 1793 (1972)Google Scholar
  21. 18.
    One might attempt to explain the discrepancy in post threshold ionisation efficiency in terms of nozzle dependent variance in terminal temperature or shape distributions (isomers). It seems likely, that all neutral clusters studied here (Nax,x>4) are molten. Internal temperature cannot be quantified at this timeGoogle Scholar
  22. 19.
    Jena, P., Rao, B., Nieminen, R.: Solid State Commun. (in press)Google Scholar
  23. 20.
    Koutecky, J., Fantucci, P.: Chem. Reviews86, 539 (1986);Google Scholar
  24. 20a.
    Martins, J., Buttet, J., Car, R.: Phys. Rev. Lett.53, 655 (1984) and Phys. Rev. B31, 1804 (1985)Google Scholar
  25. 21.
    Klots, C.: J. Chem. Phys.83, 5854 (1985)Google Scholar
  26. 22.
    PIE curves obtained for Na6+ do not provide evidence for significant post threshold fragmentation contribution. Furthermore the ratio of Na6 to Na7 is roughly the same in both expansionsGoogle Scholar
  27. 23.
    In the absence of accurate data, one can assume that ionisation cross section scales with geometric cross section. Then the correction necessary is (8/7)2/3=1.09Google Scholar
  28. 24.
    Ions produced upon dissociation during transit of the mass filter do not reach the multiplierGoogle Scholar
  29. 25.
    Herrmann, A., Schumacher, E., Wöste, L.: J. Chem. Phys.68, 2327 (1978)Google Scholar
  30. 26.
    Kittel, C.: Introduction to Solid State Physics. New York: Wiley 1976Google Scholar
  31. 27.
    Classical considerations predict that cluster total energies comprise a volume (αN) and a surface energy (αN 2/3) term. Then bond energy per atom is given by:A(1 −b*N −1/3), whereA andb may be used as fittable parameters andN is the number of atoms in the cluster. If we use dimer and bulk cohesive energies as determinants forA andb, then we would expect a cohesive energy of 0.651 eV/atom for Na8. A variant of this interpolation divides cluster volume into a surface and bulk portion: Stwalley, W., Llano, M. de: Z. Phys. D — Atoms, Molecules and Clusters2, 153 (1986); Here bond energies per atom are given byA(1 −b(3N −1/3-3N −2/3+N −1)) which for Na8 results in 0.459 eV/atom (using the same interpolation boundaries)Google Scholar
  32. 28.
    Gole, J., Green, G., Pace, S., Preuss, D.: J. Chem. Phys.76, 2247 (1982)Google Scholar
  33. 29.
    Peterson, K., Dao, P., Farley, R., Castleman, A. Jr.: J. Chem. Phys.80, 1780 (1984)Google Scholar
  34. 30.
    Helm, H., Möller, R.: Rev. Sci. Instr.54, 837 (1983)Google Scholar
  35. 31.
    Several Nax ionisation potentials have been previously determined at lower resolution. Preliminary analysis of the new measurements indicates that where data sets overlap, agreement is good to within the respective error limits. Furthermore none of the essential conclusions of Ref. 2 regarding spherical droplet or jellium models are in any way modified due to the extended data setGoogle Scholar
  36. 32.
    Average bond energy per atom and consequently dissociation energies are expected to increase with particle size, see Ref. 27. Together with the increased number of vibrational modes available, this should lead to longer metastable lifetimes for the same level of internal excitationGoogle Scholar
  37. 33.
    Brucat, P., Zheng, L., Petiette, C., Yang, S., Smalley, R.: J. Chem. Phys.84, 3078 (1986)Google Scholar
  38. 34.
    Ionization induced fragmentation of bismuth clusters (Bix, x <39) has recently been studied by a similar method: Walstedt, R., Bell, R.: Phys. Rev. A,33, 2830 (1986)Google Scholar
  39. 35.
    Dominant maxima are in fact accentuated upon fragmentation correctionGoogle Scholar
  40. 36.
    Clearly ionisation induced fragmentation thresholds will be smaller for heavier alkali metalsGoogle Scholar
  41. 37.
    References 20 lists total energies,E(x), calculated for Lix, (x<10). It has been proposed that for “near-equilibrium” alkali cluster beams, the second difference in total energy, δ2(x)=E(x+1)+E(x−1)−2E(x), may be related to cluster abundances, Ref. 5. On this basis, Nax abundances obtained from conical nozzle expansions and δ2(x) from ab-initio computations for Lix (scaled to Na8) are in remarkably good agreementGoogle Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • M. M. Kappes
    • 1
  • M. Schär
    • 1
  • E. Schumacher
    • 1
  • A. Vayloyan
    • 1
  1. 1.Institute of Inorganic and Physical ChemistryUniversity of BernBernSwitzerland

Personalised recommendations