Number Of Atoms In Cluster

Figure 4.3. Mass spectrum of Pb clusters. [Adapted from M. A. Duncan and D. H. Rouvray, Sci. Am. 110 (Dec. 1989).]

atom. The maximum ionization potentials occur for the rare-gas atoms 2He, 10Ne, and 18Ar because their outermost s and p orbitals are filled. More energy is required to remove electrons from filled orbitals than from unfilled orbitals. Figure 4.4b shows the ionization potential of sodium clusters as a function of the number of atoms in a cluster. Peaks are observed at clusters having two and eight atoms. These numbers are referred to as electronic magic numbers. Their existence suggests that clusters can be viewed as superatoms, and this result motivated the development of the jellium model of clusters. In the case of larger clusters stability, as discussed in Chapter 2, is determined by structure and the magic numbers are referred to as structural magic numbers.

4.2.2. Theoretical Modeling of Nanoparticles

The jellium model envisions a cluster of atoms as a large atom. The positive nuclear charge of each atom of the cluster is assumed to be uniformly distributed over a sphere the size of the cluster. A spherically symmetric potential well is used to represent the potential describing the interaction of the electron with the positive spherical charge distribution. Thus the energy levels can be obtained by solving the Schrodinger equation for this system in a fashion analogous to that for the hydrogen atom. Figure 4.5 compares the energy level scheme for the hydrogen atom and the energy-level scheme for a spherical positive-charge distribution. The superscripts refer to the number of electrons that fill a particular energy level. The electronic magic number corresponds to the total number of electrons on the superatom when

ATOMIC NUMBER (a)

Figure 4.4. (a) A plot of the ionization energy of single atoms versus the atomic number. The ionization energy of the sodium atom at atomic number 11 is 5.14eV (b) plot of the ionization energy of sodium nanopartides versus the number of atoms in the cluster. [Adapted from A. Herman et al., J. Chem. Phys. 80,1780 (1984).]

NUMBER OF ATOMS <b)

Figure 4.4. (a) A plot of the ionization energy of single atoms versus the atomic number. The ionization energy of the sodium atom at atomic number 11 is 5.14eV (b) plot of the ionization energy of sodium nanopartides versus the number of atoms in the cluster. [Adapted from A. Herman et al., J. Chem. Phys. 80,1780 (1984).]

ATOMIC NUMBER (a)

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