Icosahedral order

D. R. Nelson and B. I. Halperin, Pentagonal and icosahedral order in rapidly cooled metals. Science 229, 233-238 (1985). 

To monitor the progress of the reconstruction, the resolution test would be performed as a function of particle numbers. As shown in Fig. 6, the resolution would be expected to improve as the number of particles increases. Thus such a plot could allow the prediction of the number of particles needed to achieve a certain resolution. The required number of particles varied somewhat in practice (Table I), probably because of variations in the robustness of icosahedral symmetry in the particle, the image quality, as well as the effectiveness of the data processing procedures used. It should be pointed out that the FSC should approach unity at low resolution and generally decrease rapidly closer to the resolution limit for perfectly icosahedrally ordered particles. The presence... 

Jonsson, H., and Andersen, H. C. Icosahedral ordering in the Lennard-Jones crystal and glass. Phys. Rev. Lett. 60, 2295 (1988). 

Kelton, K.F. Lee, G.W. Gangopadhyay, A.K. Hyers, R.W. Rathz, T.J. Rogers, J.R. Robinson, M.B. Robinson, D.S. First X-ray scattering studies on electrostatically levitated metallic liquids demonstrated influence of local icosahedral order on the nucleation barrier. Phys. Rev. Lett. 2003, 90, 195504 (1-4). 

The main result of the calculations is that they demonstrate an enhancement in icosahedral order at increasing supercooling of melt. 

A. Di. Cicco, A. Trapananti, S. Fraggioni, A. Fihpponi. Is there icosahedral ordering in liquid and supercooled metals . Phys. Rev. Lett, 91, N13, pp. 135505-1-135505 (2003). 7. N. Jakse, A. Pasturel. Ab-initio molecular dynamics simulations of local structure of supercooled Ni. J. Chem. Phys., 120, N13, pp. 6124-6127 (2004). 

At high tanperatures the local icosahedral order in the liquid state is shortlived and the distorted (e.g., cubic) configurations at the equivalent minima of the APES are oriented arbitrarily with a complicated dynamics of transition between them. Below the critical tanperature an ordering of these distortions takes place due to their interaction, and the system transforms into a crystal with the symmetry determined by the local distorted configurations and their interaction, similar to phase transitions in crystals (see Section Vll). Another possibility is that the liquid state transforms into an amorphous (glass) state if, dependent on the interaction between the centers, a freeze of the randomly oriented distortions takes place before their ordering [67],... 

At higher frequencies (above 200 cm ) the vibrational spectra for fullerenes and their cry.stalline solids are dominated by the intramolecular modes. Because of the high symmetry of the Cgo molecule (icosahedral point group Ih), there are only 46 distinct molecular mode frequencies corresponding to the 180 6 = 174 degrees of freedom for the isolated Cgo molecule, and of these only 4 are infrared-active (all with Ti symmetry) and 10 are Raman-active (2 with Ag symmetry and 8 with Hg symmetry). The remaining 32 eigcnfrequencies correspond to silent modes, i.e., they are not optically active in first order. 

Whereas only hh0 can diffract with the beam along a fivefold axis of the icosatwin because of the tilt of the cubic crystals, any plane in the zone 110 of the decatwin can diffract because the seed orients the cubic crystals with this zone axis parallel to the fivefold axis of the twin. It is seen from Fig. 1 (b) that the meridional spots of decagonal FeAl are the same as for icosahedral MnAl6, representing orders of hh0, but that there are many more equatorial spots, eleven instead of three. Indices are assigned in Table II some spots involve double... 

In order to describe derivatives of B12 or B12H122 having icosahedral structures, it is necessary to have a way to designate positions of atoms or substituent groups. In order to do that, the positions are identified by a numbering system that is illustrated as shown in Figure 13.5. 

We now describe the individual molecules in Fig. 3.103 (as well as the limiting icosahedral Bi2Hi22 species to be introduced below), giving details of the NBOs, relative weightings of alternative styx structures, and NRT bond orders for each species. 

In a famous paper by Shechtman et al. (1984) electron diffraction patterns were shown of rapidly quenched and solidified aluminium-manganese alloys. Sharp diffraction peaks, suggesting long-range translational order, were observed with the presence however of five-fold symmetry (that is of a non-crystallographic symmetry see 3.6.1.1). By different orientation of the specimen five-fold axes (in 6 directions), three-fold axes (in 10 directions) and two-fold axes (in 15 directions) were identified with the subsequent observation of the existence also of an inver-sion centre the assignment of this phase to the icosahedral point group, m36, was defined. 

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