Edward A. Bouchet Award Talk: Nanoparticles with Five-fold Symmetry

In materials science structure of bulk crystals play a paramount role. Bulk crystals abide by the rules of symmetry, order and periodicity which are fundamental characteristics of bulk crystals. It is well known that the only rotational symmetries that are allowed correspond to angular rotations of 2$\pi $, \textpm $\pi $, \textpm 2$\pi $/3 and \textpm $\pi $/2, which correspond to rotational symmetries of 1-fold, 2-fold, 3-fold and 4-fold. However, n$=$5, n$=$10 and n$=$7; are not allowed. There are no natural crystals with five-fold or ten-fold symmetry. Researchers have synthetize quasicrystals that indeed have five-fold symmetry. Two important differences make quasicrystals and crystals different. Quasicrystals a) have order but no translational symmetry and b) they are always formed by at least two different kinds of atoms. No quasicrystal form by only one single element has been found. In the case of small crystallites (or non-particles) it seems to be a different situation since decahedral and icosahedral particles are frequently and stubbornly observed. One important question is: Are the decahedral and icosahedral particles really five-fold or tenfold symmetry? Experimental evidence indicates that the five-fold symmetry comes from 5 or 20 twins arranged to form a decahedron or icosahedron polyhedral shape. Every twin crystal produces a diffraction pattern. When all the patterns are put together, a five-fold pattern is obtained. This is nevertheless a curios fact, and shows a remarkable preference for five-fold shapes. In this talk, we discuss the factors that result in a certain preference for five--fold shapes in nanoparticles and mechanisms that stabilize them.