Decahedron

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. 

Figure 2 Schematic representation of a Marks-decahedron (111) (left) and (100) (right) projections. (From L.D. Marks [67].)...

Figure 3 Phase diagram of gold clusters as a function of their size. Ic icosahedron MTP, Dh decahedron MTP, SC single crystal, QM quasimelt, L liquid. (From P.M. Ajayan and L.D. Marks [77].)... 

Figure 3. Werfelmeir s growth sequence of small monoatomic models with N atoms. The construction of the decahedron N = 7 is explained in the text. The model N == 13 is the regular IC.

Figure 20. Calculated X-ray scattering patterns for various types and sizes of Pt nanocrystallites. Top left 3.5 nm (a) sphalerite (b) wurtzite (c) wurtzite with one stacking fault (d) experimental powder spectmm with ca. 3.5.nm avg. crystallites. Top right Experimental powder diffraction pattern of ca. 8.0 nm crystallites (dotted line) compared to (a) spherical and (b) prolate particles (solid line) Center (a) progression of habits of cuboctahedral shapes of nanocrystals, (b) change in shape as 111 faces increase and 100 decrease, (c) decahedron and icosahedron multiply twiimed forms. Bottom left to right three successive sizes of cuboctahedral nanociystallites three successive sizes of decahedral nanociystallites three successive sizes of icosahedral nanocrystallites. From Zanchet et al. (2000), used with permission of Wiley-VCH.

Fig. 14.19. A result of modern nanochemistry (formally) in the form of shells, that is two Plato and Archimedes look pleased viewing (H2O)20 dodecahedra and a rhombicosido-the nanodrop of water H20 ioo inside a decahedron (H2O)60- Note, as in liquid water...

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

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