Hexagonal crystal symmetry

Mechanical Properties. The hexagonal symmetry of a graphite crystal causes the elastic properties to be transversely isotropic ia the layer plane only five independent constants are necessary to define the complete set. The self-consistent set of elastic constants given ia Table 2 has been measured ia air at room temperature for highly ordered pyrolytic graphite (20). With the exception of these values are expected to be representative of... 

The adsorption of cyclohexene, cyclohexane, 1,3-cyclohexadiene, 1,4-cyclohexadiene, and benzene on Pt(l 11) was studied with STM [35, 36]. Figure 7.20a shows an STM image of 2 x 10-s Torr cyclohexene on Pt(l 11). The low-pressure structure shows a hexagonal symmetry with a periodicity of approximately 7 A that is rotated approximately 18-20° with respect to the [1 1 0] direction of the Pt crystal face. From prior... 

Attempts were made to include all hydrogen atoms explicitly in the simulations. This computationally demanding explicit-atom model shows (Fig. 1) that the crystal symmetry is orthorhombic, in agreement with the well-known experimental result for polyethylene single crystals, instead of the hexagonal symmetry seen in united-atom model simulations. 

The crystals obtained in this fashion have hexagonal symmetry (space group P63/mmc) with a = 3.314 A and c/2 = 6.04 A (c/2 is the basic S—Ta—S slab thickness). The d values given above for the polycrystalline material may be used to check the identity of a crushed crystal. 

In hexagonal diamond (wurtzite structure) the wrinkled sheets are stacked in an ABABAB sequence, as shown in the Figure 7. Looking down on the stack from above, hexagonal holes can be seen formed by the six-membered carbon rings. The crystal has hexagonal symmetry about this axis, hence the name hexagonal diamond, or wurtzitic carbon. 

The suggestion that in metal crystals the atoms are arranged in closest packing was made by Barlow before the development of the x-ray technique, in order to account for the observations that many metals crystallize with cubic or hexagonal symmetry and that in the latter case many of the observed values of the axial ratio lie near the ideal value 2y/2/ v 3 = 1.633 for hexagonal closest packing. 

Single crystals of /S-A1203 are essentially two dimensional conductors. The conducting plane has hexagonal symmetry (honeycomb lattice). This characteristic feature made -alumina a useful model substance for testing atomistic transport theory, for example with the aid of computer simulations. Low dimensionality and high symmetry reduce the computing time of the simulations considerably (e.g., for the calculation of correlation factors of solid solutions). 

Polyoxybenzoate is a stiff chain, lyotropic liquid crystalline material, as was discussed on the basis of its copolymers with ethylene terephthalate (see Sect. 5.1.4). The crystal structure of the homopolymer polyoxybenzoate was shown by Lieser 157) to have a high temperature phase III, described as liquid crystalline. X-ray and electron diffraction data on single crystals suggested that reversible conformational disorder is introduced, i.e. a condis crystal exists. Phase III, which is stable above about 560 K, has hexagonal symmetry and shows an 11 % lower density than the low temperature phases I and II. It is also possible to find sometimes the rotational disorder at low temperature in crystals grown during polymerization (CD-glass). 

Similar considerations of symmetry apply in other systems, for example nematic liquid crystals and aligned short fibre composites have symmetry D h, smectic A liquid crystals D , while in copolymers and certain fibre composites examples of hexagonal symmetry may be found and translational symmetry may also be present, which is not found in petrology. 

Fig. 20 (a) Stacked layers of parallel helices, with a 120° twist between adjacent layers, result in a sieve-like pattern with hexagonal symmetry, (b) A similar structure is obtained by inter-connected DNA strands and replicated into millimeter-sized crystals, as shown in the optical microscopy image in (c). Adapted with permission from [81]. (d) Design of a triangle from seven strands. The relative position of helices (1, 2, 3) at the vertices (a, b, c) is discussed in the text. Sticky ends mediate the aggregation of tiles into macroscopic rhombohedral crystals, shown in the optical microscopy image in (e). Adapted with permission from [82]... 

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