Page 186 - Carbon Nanotubes

et
178 U. ZIMMERMAN at.
ber of electrons bonded by SO2 and 0. What effect there is some correlation between the two sets of num-
does C60 as an impurity have on the electronic shell bers, but no exact agreement. If we make the simpli-
structure? Will it merely shift the shell closings by 6 fying assumption that six Cs atoms transfer their
(the number of electrons possibly transferred to the valence electrons to the c60 molecule and that these
c60 molecule)? We will investigate this in the follow- electrons will no longer contribute to tne sea of quasi-
ing paragraphs. free electrons within the metal portion of the cluster,
Up to this point, we have always studied the clus- the number 6 should be subtracted from the shell clos-
ters using brute force (i.e., heating them so strongly ings observed for metal-coated c60. This improves
that they evaporate atoms). But the electronic shell the agreement between the two sets of shells. How-
structure of clusters can also be investigated more gen- ever, it is really not surprising that the agreement is
tly by keeping the photon flux low enough to prevent still not perfect, because a c60 molecule present in a
the clusters from being heated and using photon en- metal cluster will not only bond a fixed number of
ergies in the vicinity of the ionization energy of the electrons but will also act as a barrier for the remain-
clusters. ing quasi-free metal electrons. Using the bulk density
The ionization energy of alkali metal clusters os- of Cs, a spherical cluster Cs,,, has a radius of ap-
cillates with increasing cluster size. These oscillations proximately 24 A. A Cm molecule with a radius of
are caused by the fact that the s-electrons move almost approximately 4 A should, therefore, constitute a bar-
freely inside the cluster and are organized into so- rier of noticeable size. To get some idea of the effect
called shells. In this respect, the clusters behave like such a barrier has on the shell closings, let us consider
giant atoms. If the cluster contains just the right num- the following simple model.
ber of electrons to fill a shell, the cluster behaves like The metal cluster will be modeled as an infinitely
an inert gas atom (Le., it has a high ionization energy). deep spherical potential well with the C60 represented
Howeve?, by adding just one more atom (and, there- by an infinitely high spherical barrier. Let us place this
fore, an additional s-electron), a new electronic shell barrier in the center of the spherical cluster to simplify
must be opened, causing a sharp drop in the ioniza- the calculations. The simple Schrodinger equation,
tion energy. It is a tedious task to measure the ioniza- containing only the interaction of the electrons with
tion energy of each of hundreds of differently sized the static potential and the kinetic energy term and ne-
clusters. Fortunately, shell oscillations in the ioniza- glecting any electron-electron interaction, can then be
tion energy can be observed in a much simpler exper- solved analytically, the solutions for the radial wave
iment. By choosing the wavelength of the ionizing light functions being linear combinations of spherical Bessel
so that the photon energy is not sufficient to ionize and Neumann functions.
closed-shell clusters, but is high enough to ionize open- Such a simple model, without the barrier due to the
shell clusters, shell oscillations can be observed in a c60 at the center, has been used to calculate the elec-
single mass spectrum. Just as in the periodic table of tronic shell structure of pure alkali metal clusters[9].
elements, the sharpest change in the ionization energy
occurs between a completely filled shell and a shell
containing just one electron. In a threshold-ionization
mass spectrum this will be reflected as a mass peak of Table 1. Comparison of experimentally observed electronic
zero intensity (closed shell) followed by a mass peak shell closings with model calculations*
at high intensity (one electron in a new shell). This be- -
havior is often seen. However, it is not unusual to find Experiment Potential well
that this step in the mass spectrum is ‘washed out’ for c6@, M, [21,23] With barrier Without barrier
large clusters due to the fact that the ionization thresh-
old of a single cluster is not perfectly sharp. 12 f 0 8 8 8
Figure 13 shows a set of spectra of C60Cs, clusters 27 f 1 20 20 20
for three different wavelengths of the ionizing laser. 33 f 1 34 32 34
44 f 0
40
40
Note the strong oscillations in the spectra. Plotted on 61 f 1 58 50 58
a n1’3 scale, these oscillations occur with an equal 80
spacing. This is a first hint that we are dealing with 98 * 1 92 90 92
a shell structure. Because this spacing is almost iden- 146 f 2 138 130 138
tical to the one observed in pure alkali metal clusters, 198 i 0 198 i2 178 186
196
these oscillations are most certainly due to electronic 255 f 5 263 f 252 254
5
rather than geometric shells. The number of atoms at 352 f 10 341 f 5 330 338
which the shell closings occur are labeled in Fig. 13 445 f 10 443 a 5 428 440
and listed in Table 1. Note that these values do not *See text. The first two columns give the numbers of
correspond to the minima in the spectra as long as metal atoms at which electronic shell closings have been ob-
these have not reached zero signal. served in experiment for Cscovered C,, and for pure alkali
Also listed in Table 1 are the shell closings observed metal clusters, respectively. The columns on the right list the
in pure alkali metal clusters[9,21,23]. These values and number of electrons required for shell closings in an infinitely
deep potential well with and without a central barrier. The
the ones observed for the Cs-covered Cm have been numbers in the different columns are mainly arranged in a
arranged in the table in such a way as to show that manner to show correlations.