Simple hexagonal

Figure Al.3.23. Phase diagram of silicon in various polymorphs from an ab initio pseudopotential calculation [34], The volume is nonnalized to the experimental volume. The binding energy is the total electronic energy of the valence electrons. The slope of the dashed curve gives the pressure to transfomi silicon in the diamond structure to the p-Sn structure. Otlier polymorphs listed include face-centred cubic (fee), body-centred cubic (bee), simple hexagonal (sh), simple cubic (sc) and hexagonal close-packed (licp) structures.

Fig. 3.8 Some basic Bravais lattices (a) simple cubic, (b) body-centred cubic, (c) face-centred cubic and (d) simple hexagonal close-packed. (Figure adapted in part from Ashcroft N V and Mermin N D 1976. Solid State Physics.

It has been mentioned above that bir-nessite-type samples can show a wide variety of different XRD patterns. Mostly, the samples show only XRD peaks around 240 pm (20 37° for CuKa radiation) and 142 pm (2 ss 66°). These peaks correspond to the (1 0 0) and (110) reflections of the simple hexagonal setting of the S - Mn02 unit cell. Additionally, in some natural as well in synthetic materials the basal plane (0 0 l) reflections (001) and (0 0 2) do occur at about 700 pm (26 312°) and 350 pm (26 25°), respectively. 

Benzene, C6H(l, is another molecule best described as a resonance hybrid. It consists of a planar hexagonal ring of six carbon atoms, each one having a hydrogen atom attached to it. One Lewis structure that contributes to the resonance hybrid is shown in (11) it is called a Kekulc structure. The structure is normally written as a line structure (see Section C), a simple hexagon with alternating single and double lines (12). 

The prototype hard metals are the compounds of six of the transition metals Ti, Zr, and Hf, as well as V, Nb, and Ta. Their carbides all have the NaCl crystal structure, as do their nitrides except for Ta. The NaCi structure consists of close-packed planes of metal atoms stacked in the fee pattern with the metalloids (C, N) located in the octahedral holes. The borides have the A1B2 structure in which close-packed planes of metal atoms are stacked in the simple hexagonal pattern with all of the trigonal prismatic holes occupied by boron atoms. Thus the structures are based on the highest possible atomic packing densities consistent with the atomic sizes. 

Perpendicular linkage from simple hexagonal net. Am. Mineral., 62 (7-8), 703-709. 

The structural sequence dhcp — ccp was also expected to occur in the next element, curium. But the ccp phase was not observed under pressure. In contrast, the simple hexagonal close-packed (hep) and, at still higher pressure, an as yet undetermined structure is formed. If these results are confirmed by further study, curium structures will have to be considered as another intermediate stage between the lighter and the heavier actinides. ... 

Many reflections which would be given by a simple hexagonal crystal are necessarily absent for a rhombohedral crystal. Only those reflections hH kH lH for which hH-]-2kH+lHy and — 2h>n—kH+lH are all divisible... 

The process of forming boron-boron bonds is carried on further in aluminum boride, AIB, which has a very simple hexagonal structure, consisting of hexagonal layers of boron a,toms, like the layers of carbon atoms in graphite, with aluminum atoms in the spaces between the layers (Pig. 11-15). The B—B bond length is 1.73 A, corresponding to n = 0.66 that is, two valence electrons per boron atom are used in the B—B bonds, which are two-thirds bonds. 

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