Truncated decahedron

In work of Nava and coworkers (2003), Pd clusters were studied using the spin-polarized DFT method in the range N = 2-309. The N = 13 cluster was foimd to have an icosahedral structure with a high spin state. It is seen to undergo a very slight Jahn-Teller distortion, which increases the cohesive energy only by 0.01 eV. The truncated decahedron and the cuboctahedron are found to be less stable. 

The truncated octahedron and the rhombic dodecahedron provide periodic cells that are approximately spherical and so may be more appropriate for simulations of spherical molecules. The distance between adjacent cells in the truncated octahedron or the rhombic df)decahedron is larger than the conventional cube for a system with a given number of particles and so a simulation using one of the spherical cells will require fewer particles than a comparable simulation using a cubic cell. Of the two approximately spherical cells, the truncated octahedron is often preferred as it is somewhat easier to program. The hexagonal prism can be used to simulate molecules with a cylindrical shape such as DNA. 

Fig. 3.7. Most common stable shapes of nanoparticles (a) icosahedron, (b) truncated octahedon (Wulff shape), (c) Marks decahedron...

In experiments, the most common shapes have truncated vertices and correspond to particles named Marks decahedron and the round decahedron. 

The first structure [54] contains extra 111 facets and turns out to be quite stable. In particularly clean growth conditions (weak interactions with substrates), it results one of the predominant shapes for the size interval taken into account. An alternative way to describe the Marks decahedron is as a regular decahedron, which has truncations on its facets, as shown in Fig. 3.11 (3y, 3x and 3z). 

In Fig. 3.11 we observe for the perpendicular polarization, that the optical response of the regular decahedron does not change for small truncations, in both cases, the Marks and rounded decahedra. For both parallel polarizations, the spectra of the truncated decahedra show differences with respect to the regular ones. The observed effects are similar to those already seen in the case of truncated cubes (Fig. 3.10) as a result of the increment of the faces, the main resonance is blue-shifted and its FWHM decreases. Finally, as for more regularly shaped nanoparticles, also for such kind of NPs the spectra show a red-shift with increasing size as a consequence of the radiation effects. 

By starting from the maximum truncation of a regular decahedron which corresponds to a star decahedron (r = 1/2), in this section we will have a look at the optical behavior of multi-tips objects with the unique surface geometry consisting of several corners or thorns protruding from a central body. 

The two Qabs spectra obtained by exciting the nanoparticle with an incident field polarized parallel to the plane of the pentagonal motif result both broad and quite similar, while for the perpendicular polarization, the response of the star decahedron is completely different since it shows a sharp resonance at 400 nm with a FWHM of 50 nm. For the three polarizations, it should be noted, how the presence of the tips make this particle very peculiar and different from the other decahedron truncations (Fig. 3.11). 

Fig. 19.4 Atomic configurations of a an fee dot of 9 shells with K — 3.3, b an fee rod of 3 shells with K = 1.9, and c an fee plate of AT = 1.7 thick, d an icosahedron with N]47 atoms, e a marks decahedron with Njoi, and f an fee truncated octahedron with N201 atoms (reprinted with...

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