Introduction to Nanotechnology

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4.2. METAL NANOCLUSTERS 79
orbital calculations based on the density functional method predict that the
icosahedral form has a lower energy than the other forms, suggesting the possibility
of a structural change. There are no experimental measurements of the Al13 structure
to verify this prediction. The experimental determination of the structure of small
metal nanoparticles is difficult, and there are not many structural data available. In
the late 1970s and early 198Os, G. D. Stien was able to determine the structure of
BiN, PbN, InN, and AgN nanoparticles. The particles were made using an oven to
vaporize the metal and a supersonic expansion of an inert gas to promote cluster
formation. Deviations from the face-centered cubic structure were observed for
clusters smaller than 8 nm in diameter. Indium clusters undergo a change of structure
when the size is smaller than 5.5 nm. Above 6.5 nm, a diameter corresponding to
about 6000 atoms, the clusters have a face-centered tetragonal structure with a c/a
ratio of 1.075. In a tetragonal unit cell the edges of the cell are perpendicular, the
long axis is denoted by c, and the two short axes by a. Below -6.5 nm the c/a ratio
begins to decrease, and at 5 nm c/a = 1, meaning that the structure is face-centered
cubic. Figure 4.7 is a plot of c/a versus the diameter of indium nanoparticles. It
needs to be pointed out that the structure of isolated nanoparticles may differ from
that of ligand-stabilized structures. Ligand stabilization refers to associating nonme-
tal ion groups with metal atoms or ions. The structure of these kinds of nanos-
tructured materials is discussed in Chapter 10. A different structure can result in a
i
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DIAMETER (nm)
Figure 4.7. Plot of the ratio of the length of the c axis to the a axis of the tetragonal unit cell of
indium nanoparticles versus the diameter of nanoparticles. [Plotted from data in A. Yokozeki and
G. D. Stein, J. Appl. Phys. 49, 224 (1 978).]