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Research Interests

Prof. Dr. Paul Bechthold

Electronic Structure of Free and Deposited Mass-Selected Clusters

1. What are clusters, where are clusters, what are they good for?

Clusters are aggregates of atoms or molecules with a well defined number n of constituents [1]. As a form of matter intermediate between atoms (or molecules) and the bulk they allow a study of the evolution of a physical property from the atom towards the solid. This concerns, for example, the formation of an electronic band structure or the development of many-electron phenomena, such as solid state magnetism or superconductivity. However, clusters are not simply rigid fractions of the respective solid but each cluster comprises its unique geometric and electronic structure. Clusters can exhibit pentagonal, decahedral or icosahedral structures (see the figure of our logo) which cannot simply grow into periodic lattices. Therefore, the transition from the atom to the bulk is by no means smooth, but the cluster properties can change drastically with cluster size - particularly in the smaller size range. For example, the chemical reactivity can change by orders of magnitude from one cluster size to the next [2]. As a consequence, clusters of each size have to be inspected individually.

Clusters can significantly modify the properties of materials. In church windows they are responsible for the coloring, in laser crystals and optical fibers they may cause concentration quenching, in metals they change their hardness. The Ag4 cluster is presumably the preferred carrier of the latent image in silverhalide photography [3]. Clusters may even form completely new materials as has been demonstrated in the case of the fullerenes, a group of hollow caged carbon clusters [4]. The discovery of the most prominent of these species, the soccer ball shaped C60 cluster has been honoured by the Nobel price to Kroto, Curl and Smalley in 1996. These clusters may even be condensed into a new type of solid carbon. When doped with alkali atoms they may form metallic and even superconducting solids with transition temperatures up to 33 K being second only to high Tc superconductors. Carbon clusters are dominated by strong directed s,px-hybridized covalent bonds (x=1-3) which enable the hollow cage structure (x=2-3). Very small carbon clusters n<12 favor linear structures (x=1). In contrast, metal clusters prefer more compact structures and can be forced into linear atomic nanowires only by the additional interaction with an adequately prepared substrate [5]. Free metal clusters often tend to follow an icosahedral growth pattern which optimizes the number of atomic nearest neighbors and thus the number of direct metal - metal bonds and the total binding energy.

Clusters are characterized by a large surface to volume ratio, that is, a large fraction of the atoms occupies low coordinated surface sites. For a cluster of 2000 atoms a fraction of about 30 % is still at the surface. This makes clusters very sensitive to their chemical environment. They may form very specific and very selective catalysts. Metal clusters, therefore, are technologically used as catalysts, for instance, in catalytic exhaust pipes of cars.

The large surface to volume ratio also has strong implications for cluster magnetism which is in the focus of our present research interest. The surface atoms are lower coordinated than the bulk and therefore have a more atom-like character than interior atoms and - in accordance with findings for thin films and surfaces - contribute more to the magnetic moment of the cluster. Thus, clusters provide not only model catalysts but also model systems for nanoelectronics and nanostructured magnetism. The magnetic moments of clusters can be measured directly in Stern-Gerlach like experiments. This topic has been reviewed in recent lecture notes [6]. The associated electronic structures can be gained from spectroscopic techniques like photoelectron spectroscopy (PES) and x-ray absorption spectroscopy - specifically x-ray magnetic circular dichroism (XMCD) which according to sum rules enables a discrimination of spin- and orbital contributions to the magnetic moments.

2. Laser induced photoemission of mass-selected gas-phase cluster anions.

2a. Experimental arrangement.

In our institute we run an experiment on Laser induced photoemission of mass-selected gas-phase cluster anions. Fig. 1 shows a sketch of the experimental arrangement which comprises three essential parts in a vacuum environment. These are framed in the scheme of Fig. 1. The first part contains a laser-vaporization cluster source [7]. An intense focused laser pulse is used to vaporize a small amount of metal from a target rod, which performs a periodic spiral motion. This rod adjoins a tube, into which a pulse of inert helium gas is injected synchronously. Clusters grow inside this tube. The helium supports the condensation and cooling of the clusters by multiple collisions and simultaneously serves as a transport medium. The energy of condensation is partly transferred to the tube wall. At the end of the tube the cluster-helium mixture expands adiabatically into the vacuum vessel, thus further cooling the clusters and forming a supersonic molecular beam. The cooling occurs because part of the irregular thermal motion is transformed into center-of-mass motion. Note, that in the adiabatic expansion the clusters do not reach thermal equilibrium. Translational, rotational, and vibrational temperatures are then defined by the population of the respective degrees of freedom.

The cluster beam always contains a mixture of clusters of various sizes. Mainly it is made up of neutrals but comprises also smaller amounts of charged clusters. They have to be selected and mass separated before information on clusters of a particular size can be obtained. Consequently, the beam is skimmed and enters the second part of the experiment, which consists of a time-of-flight mass spectrometer. Here, we are interested in cluster anions. Therefore, the negatively charged clusters are accelerated in a pulsed electric field of a Wiley-McLaren ion source [8]. Thereafter they enter a grounded drift tube and, depending on their times-of-flight, separate into sequenced bunches of defined cluster size.


Fig. 1 Scheme of the three essential parts of the experiment. Cluster anions are formed in a laser vaporization cluster source and transferred to a pulsed time-of-flight mass spectrometer. The separated anions enter the source region of a "magnetic bottle"-type electron spectrometer where photoelectrons are detached. The kinetic energy of the photoelectrons is measured by a time-of-flight technique.

The drift tube contains an electrostatic mirror (in the newer version a quadrupole deflector), which is used to deflect the cluster anions from the neutral beam path. An ion detector at the end of the drift region can be used to analyze their mass distribution. Since smaller clusters acquire larger velocities they arrive first. The others appear as the sequence of their masses. Before the anions reach the ion detector they pass the source region of a "magnetic bottle" time-of- flight electron spectrometer, which is the third essential part of the experiment [9]. Here, a selected bunch of cluster anions is irradiated by a UV laser pulse (photon energy hν = 3 - 6.4 eV), and the kinetic energy of the detached photoelectrons is measured. The advantage of the magnetic-bottle type spectrometer is that it permits the collection of all the emitted electrons irrespective of their direction of emission. A strongly inhomogeneous magnetic field at the location of the electron emission acts as a magnetic mirror and deflects all the electrons toward the electron detector. This sufficiently increases the electron yield. Prior to electron detachment a mass gate allows the selection of a particular cluster size. Clusters of other sizes are deflected out of the beam. Moreover, the cluster anions are decelerated prior to the electron detachment to prevent a Doppler shift of the emitted photoelectrons. Otherwise, the resolution of the spectrometer will be reduced. The spectrometer is calibrated with some atomic lines. Ideally, the cluster anions are in their ground electronic state when they enter the electron spectrometer. This is, in fact, often the case. However, with transition-metal clusters, which usually exhibit a high density of states very close to their electronic ground state, some low lying excited states may also be populated. This will lead to the simultaneous presence of different isomers in the cluster beam.

2b. The photoemission process.

The photoemission process is a transition from the initial anionic state to a neutral final state, but in the geometry of the anion. Thus, considering the initial anionic state as fixed, a photoemission spectrum is a mapping of the neutral final states. In the majority of cases the first peak corresponds to the creation of a neutral ground state. If correlation effects are omitted the process can be described in a simplified single particle picture. In this picture the binding energy (BE) of the electron in the anion is deduced from the difference of the photon energy and the measured electron kinetic energy Ekin:

BE = h ν – Ekin .

This equation is used to evaluate binding-energy spectra from measured photoemission data (also when correlation effects are visible). The photoemission process in the single particle picture is illustrated for Cu2 and Ni2 in Fig. 2. In this simple picture the features in the photoemission spectrum are directly related to the molecular orbitals of the particle. Starting from occupied molecular orbitals with specified configurations as deduced from the atomic 3d and 4s -orbitals the photoelectrons are excited above the vacuum level. The photon excess energy is released as electron kinetic energy.

When two Cu or Ni atoms come together to form a dimer the atomic 4s -orbitals form a bonding σg and an antibonding σu molecular orbital. For the anions the extra electron occupies the σu orbital. The main difference between the Cu2 and Ni2 spectra results from the relative position of the 3d orbitals which despite the open d -shell of the Ni atom are only very weakly hybridized. Note, that in neutral Ni2 the HOMO (Highest Occupied Molecular Orbital) is a d -orbital while in neutral Cu2 the HOMO is the 4s -derived σg -orbital.

The figure compares the level scheme of molecular orbitals (left position) with the respective experimental spectra (right position). The spectra show the energetic position of the single particle states in the geometry of the anion. The emission from the σu level corresponding to the peak with the lowest binding energy results in photoelectrons with the highest kinetic energy and leaves behind a neutral particle in its electronic ground state. A second significant peak corresponds to emission from the doubly occupied σg orbital. For neutral Cu2 the energy difference of both these peaks corresponds to the HOMO-LUMO (Lowest Unoccupied Molecular Orbital) gap of the neutral particle. Often, the geometrical structure of the anion does not deviate very much from the ground-state geometry of the neutral. In such a case, the peak at the lowest binding energy (i.e., the vertical detachment energy) corresponds to the creation of the neutral cluster in its electronic ground state. However, its energetic position may be shifted according to the Franck-Condon overlap of the anionic and the neutral cluster.


Fig. 2 Illustration of the photoemission process in terms of single particle orbitals exemplified by Cu2 and Ni2 spectra.

The pronounced similarity of the Cu2 and Ni2 spectra occurs due to the high degree of localization of the 3d -orbitals. They do not essentially contribute to the chemical bonding although in Ni they are "open shell". However, this similarity gets lost very rapidly as the clusters become bigger and the s/d - hybridization increases while the d -states more and more adopt the itinerant character of bulk nickel. In fact, already for clusters with more than 7 atoms the similarity is completely gone. Moreover, in more general cases, the photoemission spectra of clusters are complicated by many body effects: multiplet splittings, shake up processes, and configuration-interaction effects may lead to considerable deviations from the simple single particle picture displayed in Fig.2 [10,11].

2c. Transition-metal clusters exhibit large valence-densities of states.

Fig.3 shows photoemission spectra of Con clusters [11]. The molecule-like sharper features observed for the smaller clusters rapidly develop into a broader structure at the onset of photoemission. This structure is caused by the high density of states generated by the partially filled d-orbitals and will gradually develop into the 3d - emission band of bulk Co located directly at the Fermi energy. This, although here the onset at about 2.3 eV (the so called electron affinity) is still quite a distance apart from the onset of bulk photoemission (called the work function) at about 5 eV. The bandwidth of the 3d -derived structure shows a remarkable minimum for Co13. This indicates a high degree of degeneracy as is expected for a highly symmetric structure like the icosahedral structure. An icosahedral structure is also expected for Ni13.

The appearance of the broad 3d -structure at the photoemission threshold results from the high density of states derived from the partially filled atomic d -orbitals. Such behavior is typical for d - transition metal clusters and is in contrast to other metals like alkalis or silver where the valence band at the Fermi level is dominated by features derived from s,p - orbitals. In these metals the d -states are either completely empty like in sodium or completely filled like in silver and therefore are positioned away from the photoemission threshold. In clusters of such metals the s -valence electrons are delocalized throughout the cluster. Due to quantum confinement and the much lower density of states they populate discrete energy levels. Consequently, photoemission spectra of noble and simple metal clusters show sharp and well separated peaks up to large cluster sizes. This behavior can be interpreted in terms of a simple electronic shell model. This model is widely used to describe cluster abundances and spectral features up to cluster sizes where calculations at the ab initio level are not available [12].


Fig. 3 Photoelectron spectra of Con clusters recorded at a photon energy of hν = 4.0 eV.

The marked difference due to the d-derived density of states can clearly be observed even in the smallest clusters. This has been verified by femtosecond pump-probe spectroscopy of clusters as small as Na3 [13] and Ni3 [14]. In such experiments the relaxation rate of electrons in excited states can be measured in real time. For Na3 the rather discrete electronic structure leads to a low probability of inelastic electron-electron scattering. Therefore, after excitation by a broadband femtosecond laser pulse Na3 shows a typical molecular like wavepacket dynamics on a picosecond timescale. In contrast to this, Ni3 shows an ultrafast inelastic electro-electron scattering relaxation dynamics with a relaxation time of 215 fs.


FIG. 4 Femtosecond pump-probe photoelectron spectra of Ni3 taken with pulse lengths of 80 fs. (a) Single-photon photoemission with 3 eV photons. (b) Time-resolved photoemission spectra using a 1.5 eV pump and a 3 eV probe photon. The rapid changes of the intensity distribution above the HOMO (dotted line at 1.3 eV) indicate the ultrafast relaxation of the optically excited electrons by inelastic electron scattering.

3. Deposition of mass-selected cluster ions.

At present we are setting up a new experimental apparatus in our laboratory devoted to the deposition of mass-selected cluster ions onto a substrate surface under UHV conditions. The machine also consists of a three stage setup containing a continuously operating magnetron-sputter source for cluster production, a quadrupole-mass analyzer, and a deposition chamber providing soft landing conditions (Ekin/atom < 1 eV).

Future projects will focus on the size-selected deposition of magnetic clusters (open d - or f -shells). The clusters will be available for investigations using STM and STS (scanning tunneling microscopy and spectroscopy) and XAS (X-ray absorption spectroscopy) - specifically XMCD- and XPS (X-ray photoelectron spectroscopy).

4. References.

[1] H. Haberland (Ed.), Clusters of Atoms and Molecules I and II, Springer-Verlag, Berlin, (1995)

[2] E.K. Parks, B.H. Weiller, P.S. Bechthold, W.F. Hoffmann III, G.C. Nieman, L.G. Pobo, and S.J. Riley, Chemical Probes of Metal Cluster structure: Reactions of Iron Clusters with Hydrogen, Ammonia and Water, J. Chem. Phys. 88, 1622 (1988)

[3] P. Fayet, F. Granzer, G. Hegenbart, E. Moisar, B. Pischel, and L. Wöste, Latent-image generation by deposition of monodisperse silver clusters, Phys. Rev. Lett. 55, 3002 (1985)

[4] M.S. Dresselhaus, G. Dresselhaus, P.C. Eklund, Science of Fullerenes and Carbon Nanotubes, Academic Press, San Diego (1996) (see also: page 50 in a: a, b)

[5] P. Gambardella, A. Dallmeyer, K. Maiti, M. C. Malagoli, W. Eberhardt, K. Kern, and C. Carbone, Ferromagnetism in one-dimensional monatomic metal chains, Nature 416, 301 (2002)

[6] P.S. Bechthold, Clusters to Nanowires, in: S. Blügel, T. Brückel, C.M. Schneider (eds.), Magnetism goes Nano, Electron Correlations, Spin Transport, Molecular Magnetism, Lecture Manuscripts of the 36th Spring School of the Institute of Solid State Research, Matter and Materials Vol. 26, Forschungszentrum Jülich (2005), ISSN 1433-5506, ISBN 3-89336-381-5 (download: pdf)

[7] D.E. Powers, S.G. Hansen, M.E. Geusic, A.C. Pulu, J.B. Hopkins, T.G. Dietz, M.A. Duncan, P.R.R. Langridge-Smith, and R.E. Smalley, Supersonic metal cluster beams: laser photoionization studies of Cu2, J. Phys. Chem. 86, 2556 (1982)

[8] W.C. Wiley, I.H. McLaren, Time-of-Flight Mass Spectrometer with Improved Resolution, Rev. Sci. Instr. 26, 1150 (1955)

[9] P. Kruit and F. H. Read, Magnetic field paralleliser for 2π electron-spectrometer and electron-image magnifier, J. Phys. E 16, 313 (1983)

[10] G. Ganteför and W. Eberhardt, Localization of 3d and 4d Electrons in Small Clusters: The "roots" of magnetism, Phys. Rev. Lett. 76, 4975 (1996)

[11] J. Morenzin, H. Kietzmann, P. S. Bechthold, G. Ganteför, and W. Eberhardt, Localization and bandwidth of the 3d-orbitals in magnetic Ni and Co clusters, Pure Appl. Chem. 72, 2149 (2000)

[12] W. Ekardt, W.-D. Schöne, and J. M. Pacheco, Application of the Jellium Model and its Refinements to the Study of the Electronic Properties of Metal Clusters, in: W. Ekardt (Ed.), Metal Clusters, John Wiley & Sons Ltd., Chichester (1999);

Walt A. de Heer, The physics of simple metal clusters: experimental aspects and simple models, Rev. Mod. Phys. 65, 611 (1993);

H. Handschuh, Chia-Yen Cha, H. Möller, P.S. Bechthold, G. Ganteför, and W. Eberhardt, The Validity of the Shell Model: Comparison of Nan, Cun, Agn and Aun-Clusters, Chem. Phys. Lett. 227, 496 (1994);

H. Handschuh, Chia-Yen Cha, P.S. Bechthold, G. Ganteför, and W. Eberhardt, Electronic Shells or Molecular Orbitals: Photoelectron Spectra of Agn--Clusters, J. Chem. Phys. 102, 6406 (1995);

G. Ganteför, H. Handschuh, H. Möller, Chia-Yen Cha, P.S. Bechthold, and W. Eberhardt, Comparison of Photoelectron Spectra of Cun-, Agn-, and Nan-: Molecular Orbitals versus Electronic Shells, Surface Review and Letters 3, 399 (1996)

[13] T. Baumert, R. Thalweiser, and G. Gerber, Femtosecond two-photon ionization spectroscopy of the B state of Na3 clusters, Chem. Phys. Lett. 209, 29 (1993); T. Baumert and G. Gerber, Molecules in intense femtosecond laser fields, Physica Scripta, T 72, 53 (1997)

[14] N. Pontius, M. Neeb, W. Eberhardt, G. Lüttgens, and P. S. Bechthold, Ultrafast relaxation dynamics of optically excited electrons in Ni3-, Phys. Rev. B 67, 035425 (2003)