Structure

Figure 2.6. Thirteen-atom nanoparticie set in its FCC unit ceH, showing the shape of the 14-sided polyhedron associated with the nanoduster. The three open circles at the upper right correspond to the atoms of the top layer of the nanoparticie sketched in Fig. 10.8 (of Chapter 10), the six solid circles plus the atom (not pictured) in the center of the cube constitute the middle hexagonal layer of that figure, and the open circle at the lower left corner of the cube is one of the three atoms at the bottom of the cluster of Fig. 10.18.

nanoparticles with the same polyhedral shape are obtained by adding more layers, and the sequence of numbers in the resulting particles, N = 1,13,55,147,309,561,..., which are listed in Table 2.1, are called structural magic numbers. For n layers the number of atoms N in this FCC nanoparticie is given by the formula

and the number of atoms on the surface N^ is

For each value of n, Table 2.1 lists the number of atoms on the surface, as well as the percentage of atoms on the surface. The table also lists the diameter of each nanoparticie, which is given by the expression (2n — 1 )d, where d is the distance between the centers of nearest-neighbor atoms, and d = a/J2, where a is the lattice constant. If the same procedure is used to construct nanoparticles with the hexagonal close-packed structure that was discussed in the previous section, a slightly different set of structural magic numbers is obtained, namely, 1,13,57,153,321,581,

Purely metallic FCC nanoparticles such as Au55 tend to be very reactive and have short lifetimes. They can be ligand-stabilized by adding atomic groups between their atoms and on their surfaces. The Au5J nanoparticie has been studied in the ligand-

Table 2.1. Number of atoms (structural magic numbers) in rare gas or metallic nanopartlcles with face-centered cubic close-packed structure'

Number of FCC Nanoparticle Atoms

Table 2.1. Number of atoms (structural magic numbers) in rare gas or metallic nanopartlcles with face-centered cubic close-packed structure'

Number of FCC Nanoparticle Atoms

Shell Number

Diameter

Total

On Surface

% Surface

0 0

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