Icosahedral glass

Note that the low-temperature structure is neither a quasicrystal nor an icosahedral glass. Given the molecular symmetry, one might have predicted the latter, whereas icosahedral quasicrystals require two distinct structural units to satisfy space filling. While the precise energetic requirements for crystal versus icosahedral glass formation are not understood, it seems likely that the structural order at low T is driven both by a preference for close packing and,by local orientational order. 

Boron s chemistry is so different from that of the other elements in this group that it deserves separate discussion. Chemically, boron is a nonmetal in its tendency to form covalent bonds, it shares more similarities with carbon and silicon than with aluminum and the other Group 13 elements. Like carbon, boron forms many hydrides like silicon, it forms oxygen-containing minerals with complex structures (borates). Compounds of boron have been used since ancient times in the preparation of glazes and borosilicate glasses, but the element itself has proven extremely difficult to purify. The pure element has a wide diversity of allotropes (different forms of the pure element), many of which are based on the icosahedral Bj2 unit. 

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

Sc considerably lowers the glass forming ability of Al alloys compared to rare earth metals (Ce). No amorphous phase was formed in rapidly solidified binary Al-Sc alloys. An unstable quasicrystalline icosahedral phase was first found in the alloy A185Sci5. Substitution of Ce for Sc in Al91Ce9 xScx alloys caused a transfer to a mixed amorphous-nanocrystalline and then to nanocrystalline structure. In Al85Nii0Ce5 xScx alloys a mixed amorphous-nanocrystalline structure appeared in the alloy with x=5 at a lowered solidification rate (increased ribbon thickness). 

Fig. 1.2 Model of solute-centered icosahedral type atom packing in an Ni8oP2o binary glass obtained through Monte Carlo modeling (from Sheng et al. (2006) courtesy of Nature).

Crystal lattices have symmetry elements such as rotation axes, mirror planes, inversion points, and combinations of these. A crystalline lattice has translation symmetry, except for quasi-crystals or icosahedral phases, which have lattices with point symmetry elements only. Glasses are amorphous solids that do not have any symmetry element in their lattices. 

H. Tanaka, Roles of local icosahedral chemical ordering in glass and quasicrystal formation in metallic glass formers. J. Phys. Condens. Matter , L491-L498 (2003). 

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],... 

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