The Journal of
Physical Chemistry
0 Copyright, 1989, by the American Chemical Society
VOLUME 93, NUMBER 8 APRIL 20, l?89
LETTERS Icosahedral Shell Structure in Metal-Doped Rare Gas Clusters Kenneth E. Schriver, Mee Y. Hahn, John L. Persson, Michael E. LaVilla, and Robert L. Whetten* Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90024- 1569 (Received: August 23, 1988; In Final Form: February 17, 1989)
Threshold photoionization experiments on beams of rare gas atomic clusters doped with a single metal atom ( A k N ; N = 1-200) reveal pronounced discontinuitiesin cluster abundances as a function of N . Abundanm at the photoionization thresholds for clusters containing up to 60 atoms and fragmentation probabilities measured on a 5 0 - p ~time scale provide compelling evidence that the neutral clusters, as well as the corresponding ions, pack in icosahedral shells.
The optimal packing of a finite number of equivalent spheres follows a noncrystallographic motif characterized by concentric icosahedral shells.' Filled-shell structures consist of N* = 13, 5 5 , 147, 309, ... spheres and are called Mackay icosahedra.2 Icosahedral structure in finite-size systems has been suggested by several different experiments, including electron diffraction of polydisperse argon cluster jet^^,^ and scanning electron microscopy of supported metal atom particle^.^ The icosahedral packing sequence has been rationalized by computer simulations of neutral atomic clusters' and has provided guidance in understanding the structures of disordered and quasi-ordered bulk materials, e.g., glasses and quasi crystal^.^*'
The most compelling evidence in support of icosahedral packing in finite-size systems has come from mass spectrometry experiments on beams of rare gas atomic clusters AN (A = Ne, Ar,Kr, Xe).*v9 In these experiments on clusters composed solely of rare gas atoms, however, the magic number sequence has been observed only for the corresponding ionized clusters, AN+. Within the cluster ions, the excess charge is believed to be localized on a tightly bound center, whose binding energy alone often exceeds that of the remaining cluster. Although most early calculations indicated that Arz+ is the ionic core,I0 recent experiments have indicated that Ar3+ is the chromophore in small argon clusters,l* and Arl3' has been proposed as the core for larger clusters as well as bulk argon.12 The reorganization of the cluster upon ionization may
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(1) Hoare, M. R. Adu. Chem. Phys. 1979, 40, 49. (2) Mackay, A. C. Acta Crystallogr. 1962, 15, 916. For a review see: Phillips, J. C. Chem. Rev. 1986, 86, 619. (3) Farges, J.; deFeraudy, M. F.;Raoult, B.; Torchet, G. J . Chem. Phys. 1986,84, 3491; 1983, 78, 5067. (4) Lee, J. W.; Stein, G. D. J . Phys. Chem. 1987, 91, 2540. (5) Iijima, S.;Ichihashi, T. Phys. Reo. Lett. 1986,56,616, and references therein. Such particles are often referred to as "multiply twinned particles". (6) Jbnsson, H.; Andersen, H. C. Phys. Rev. Letr. 1988, 60, 2295. Steinhardt, P. J.; Nelson, D. R.; Ronchetti, M. Phys. Reu. 1983, 828, 784. (7) Steinhardt, P. J. Science 1987, 238, 1242.
0022-3654/89/2093-2869$01.50/0
(8) Echt, 0.;Sattler, K.; Recknagel, E. Phys. Reu. Lett. 1981.47, 1121. For a review of electron impact experiments, see: Echt, 0. In Elemental and Molecular Clusters; Benedek, G . , Martin, T. P., Pacchioni, G., Eds.; Springer-Verlag: New York, 1988. (9) Harris, I. A.; Kidwell, R. S.;Northby, J. A. Phys. Reu. Lett. 1984, 53, 2390. (10) For examole. see: Haberland. H. Surf. Sci. 1985. 156. 305. ( l l j Levinger,'N.'E.; Ray, D.; Alexander,'M. L.; Lineberger, W. C. J . Chem. Phys. 1988,89, 5654. (12) Carnovale, F.; Peel, J. B.; Rothwell, R. G.; Valldorf, J.; Kuntz, P. J. J . Chem. Phys. 1989, 90, 1452.
0 1989 American Chemical Society
Letters
2870 The Journal of Physical Chemistry, Vol. 93, No. 8, 1989
Figure 1. Energy level diagram relevant to AIArNclusters. At left the ionization potential of the AI atom (IP, = 5.986 eV) is contrasted with the first excited-state energy (1 1.55 eV) and ionization energy (15.76 eV) of the AI atom. Dashed lines indicate the binding energies of AI and AIt to an ArNcluster and their relations to the cluster ionization potential (IPN). The inset illustrates the laser vaporization nozzle source used to prepare pulsed AlAr, cluster beams.
N (no. of Ar atoms) Figure 3. Photoionization thresholdsof AIAr, clusters as a function of N. The experimentally measured thresholds are marked with circler and err- bars; the calculated vertical ionization potentials are marked with shaded squares. The clusters in the regions 27 5 N 5 34 and N 2 5 0 have thrhesholds below 5.51 eV, which was the lowest photon energy uscd in these experiments.
04
N
Figure 4. Photoionization mass spectra of AIAI, clusters at three different photon energies under otherwise identical conditions: (a) 5.71 eV, (b) 5.66 eV, (c) 5.61 eV. Framed shows the fraction of clusters undergoing an AIAr,+ AIAmwlt evaporation event during the 1-50-ps postmeasurement periods at 5.74 eV (circles) and 5.61 eV (squares); R(N) = I ( N - I)/(I(N) + I ( N - I)), where I ( N ) is the intensity of the N-cluster peak in the mass spatrum and I(N - I) is the intensity of the corresponding fragment peak. This data indicates that abundance maxima are retained or enhanced and that the decay fraction tends to zero as hv E,,M.
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ION FLIGHT TIME Figure 2. Photoionization mass spectra of AIAr, (upper) and AI(N2), (lower) cluster beams taken at 6.41 eV. Particularly abundant ion signals are indicated for N + 1 = 13,19,55. and 147 (Ar) and 13.33, and 55 (NJ.
result in extensive, ultrafast f~agmentation,'~which precludes verification of the relevance of the icosahedral packing principle to neutral finite systems. To overcome these difficulties, in which measured ion abundances fail to reflect neutral ahundances in the cluster beam, we have developed a molecular beam source of metal-atom-doped rare gas clusters, where the atomic radius of the metal atom is nearly equal to that of the rare gas atoms comprising the rest of the cluster. The large disparity between the ionization potentials of the metal and rare gas atoms, as illustrated in Figure 1, makes photoionization possible at energies arbitrarily close to the metal atom ionization threshold. By ionizing a t the threshold of the metal atom within a given cluster, fast fragmentation may be largely avoided, and detected ion ahundances reflect neutral abundances. In this Letter we present the results of threshold photoionization experiments which suggest that neutral metal-rare (13) Kreisle, D.;Echt, 0.;Knapp, M.; Recknagel. E. Phys. Reo. 1986, A33, 168. Echt, 0.; Cook, M.C.: Castleman Jr., A. W . Chem. Phys. Leu. 1987, 135, 229. These pawrs describe the slow d a y believed to be the termindl cvcnts of this p;&m It has k n rationald b) ~ a k u l i t ~ oul:n ~ Slenr. J. J :Soln,J. M.;Garcia. U. C h m Phyr. Leu 1985.111. IS. Seharf. S.;Jortner. J.. Landman. L'. J . Chem Phyr. 1988. 88. 4273.
gas atomic clusters pack in icosahedral shells. The apparatus for generating intense beams of metal-doped rare gas clusters is shown schematically in Figure 1 (inset). This design is a modification of similar sources used to generate cold beams of neat metal atom clusters." Time-of-flight mass spectra of AIAr, and AI(N,), clusters generated from this source are shown in Figure 2; photoionization was via an ArF excimer laser (6.41 eV). Over a wide range of operating parameters the abundance distributions in these spectra correspond closely to those predicted by the icosahedral model, including strong discontinuities a t the major magic numbers of N + 1 = 13, 55, and 147 units and most minor numbers as well (19, 23, 26,29,49, 71, and 3 1 for AI; 33 for NJ. The spectra also show certain anomalous regions, such as the swells in the AIAr, spectrum around N + 1 = 41 and 140. Because the ionization potential of the aluminum atom within an argon cluster is close to the gas-phase value of 5.99 eV, the photon energy may exceed the ionization potential of the cluster by ca. 0.5 eV. The binding energy of individual argon atoms is no larger than 0.1 eV;" substantial fragmentation may therefore he expected. By continuously scanning the ionizing laser photon energy between 5.6 and 6.0 eV, the ionization potentials of AIAr, clusters containing up to 60 atoms were determined. The experimental ionization potentials were determined for N up to 21 by finding (!4) Schrivcr. K. E.; Perssan, J. L.; Hahn, M. Y.: Whetten, R. L.. tobe published. See also: Gardner. J. M.;Lester, M.1. Chem. Phys. Lett. 1987, 137, 301.
The Journal of Physical Chemistry, Vol. 93, No. 8, 1989 2871
Letters the intercept of the base line with the best straight line through the threshold curve in the region of the threshold. For N > 21, ionization potentials were bracketed by using data from individual mass spectra taken at specific photon energies. To N = 4 the photoionization cross sections are characterized by steplike drops (0.01 eV wide) at a well-defined energy, but for larger clusters the cross section follows a smooth descent over a 0.04-0.10-eV range. The shallowness of the ionization potential vs N curve, shown in Figure 3, suggests that it is possible to photoionize groups of clusters at threshold and thereby determine their relative neutral abundances directly. A set of mass spectra taken in this manner are shown in Figure 4a-c. These data demonstrate that at threshold (i) the magic number effects at the major and minor shell closings are retained or enhanced and (ii) the anomalous regions, such as that observed around N = 44-50 in Figure 2, return to the expected form, indicating that at 6.41 eV the distributions in these regions are strongly affected by cluster ion fragmentation. For example, the virtual absence of signal for the 50-atom cluster in the 5.61-eV spectrum reflects the relative stability of the 49-atom cluster, formed by removing one cap from the 55-atom ic~sahedron.~ These abundance distributions suggest that a substantial fraction of the neutral clusters in the beam are produced with closed or nearly closed icosahedral shells. The general features of the ionization potential vs N curve can be explained in terms of the sudden-polarization effect, whereby ionization of an impurity atom induces dipoles on closed-shell solvent atoms.Is Specifically, by assumingI6 a pair-potential decomposition of the neutral AIArN interactions along with additional ion-induced dipole and dipoledipole interactions in the ionized cluster, it is possible to calculate the vertical ionization potentials from the Born-Haber cycle: IPN - IPO = E(N+)- E(N0) where IP and E represent the ionization potential and total binding energy, respectively, of an N-sized cluster. The results of these calculations are shown along with the experimentally measured thresholds in Figure 3.17 Apparently, the small clusters’ experimentally measured thresholds reflect the adiabatic ionization potentials while the large clusters’ thresholds reflect the vertical ionization potentials, with a crossover occurring in the N = 6-10 region. There is an anomalous break at N = 34 in the IP vs N curve, Figure 3. One possibility is that the N = 30-40 region corresponds to the crossover from the 13-atom-based structure to the 5 5 atom-based structure. A change in cluster binding energy as the structure changes from interpenetrating icosahedra to a multilayer icosahedron has been predicted in Lennard-Jones clusters.’* A similar effect would be expected for the electron binding energy of a chromophore centered in such a cluster, as in the case of this work. That is, there is one curve that describes the ionization thresholds for N up to 35 atoms and then a second threshold curve (15) For a recent description of this effect, see: Kohler, A. M.; Saile, V.; Reininger, R.; Findley, G. L. Phys. Rev.Lett. 1988, 60, 2727. (16) The potentials and parameters used are, in standard notation: Ar-Ar, c = 120 K, u = 3.4 A; AI-Ar, 0.= 253 cm-’, Re = 3.62 A. For the ions, the additional electrostatic interaction is characterized by the atomic polarizability of Ar, aA,= 1.64 A’. (17) The reported calculated ionization potentials are averages over an ensemble generated by the Monte Carlo method in the temperature range T = 2-20 K. For a very similar model calculation on the XeAr,’ system, see: Bohmer. H.-U.: Peverimhoff. S.D. 2.Phvs. 1988. 0 8 . 91. (18) Farges, J.; DeFeraudy, M. F.; Raoult, B.; Torchet, G. Adv. Chem. Phys. 1988, 70,45.
as the cluster rearranges to accommodate a new icosahedral shell. There should be additional breaks in the curve at each subsequent shell closing. RRK estimates of the rate of fragmentation of a hot cluster ion containing N > 10 atoms indicate some fragmentation will occur on the lo-’ to 10” s time scale as the photoelectron energy approaches zero. It is therefore desirable to have a means of directly measuring the probability of fragmentation occurring on a time scale less than or equal to that required for mass measurement. While this is generally not yet possible for such large clusters, it is possible to assess the fragmentation on the to lo4 s time scale, Le., during the time that the ion spends in the field-free region of the mass ~pectr0meter.I~ Preliminary results for smaller clusters are shown in Figure 4d. For clusters of fewer than ca. 20 atoms, the probability of fragmentation (specifically, loss of a single neutral argon) on these slower time scales decreases as the photon energy approaches threshold; significant fragmentation on faster time scales is very unlikely.” For larger clusters, it appears that there is some fragmentation occurring on the microsecond time scale even as the excess energy above the observed photoionization threshold tends to zero. This data is also indicative of a vertical ionization process in which the cluster ion is formed in a vibrationally excited state which leads to subsequent evaporation. The results illustrated in Figure 4, which show full retention or enhancement of closed-shell abundances at threshold, are quite remarkable and provide strong evidence for icosahedral packing in neutral clusters. Despite this, all the evidence presented here is necessarily indirect. A more convincing demonstration that the abundance maxima of Figure 4 correspond to neutral clusters involves observing the effect of changing the source conditions, since at very low temperatures the stabilities of clusters in any particular size range should be nearly equal. We have carried out experiments in which the carrier gas was changed to a 15% Ar in He mixture in order to further cool the clusters in the source expansion; however, the resulting abundance distributions reflected in the mass spectra were not significantly different from those obtained with 100% Ar. Experiments are under way to combine laser vaporization techniques with very cold (e.g., liquid nitrogen cooled) beam sources in order to test the above hypothesis. The use of metal-doped inert-gas clusters has made it possible to demonstrate the importance of icosahedral packing in these clusters. We have also been able to measure some elementary electronic and kinetic properties of these clusters. Preliminary spectroscopic experiments in the regions of A1 atom absorption indicate that investigations of the unique thermal and dynamical properties of the icosahedral lattice will now be achievable on a size-specific basisL4 Furthermore, there is no intrinsic limitation to extending these experiments to clusters of lo3 or more atoms or small molecules, making possible investigations of the transition from icosahedral to macroscopic crystalline or quasicrystalline states.
Acknowledgment. This research was supported in part by the Office of Naval Research, the Ford Motor Co., and the Exxon Educational Fund. The assistance of David S. Levy in analyzing the decay data recorded here is acknowledged. Robert L. Whetten acknowledges support from a National Science Foundation Presidential Young Investigator Award and a Sloan Research Fellowship. (19) Schriver, K. E.; LaVilla, M. E.; Levy, D. S.;Whetten, R. L., to be published.
