Space lattice rhombohedral

There is only one space lattice in the rhombohedral crystal system. This crystal is sometimes called hexagonal R or trigonal R, so don t confnse it with the other two similarly-named crystal systems. The rhombohedral crystal has nniform lattice parameters in all directions and has equivalent interaxial angles, bnt the angles are nonorthogonal and are less than 120°. 

Only fourteen space lattices, called Bravais lattices, are possible for the seven crystal systems (Fig. 328). Designations are P (primitive), / (body-centered), F (face-centered),34 C pace-centered in one set of laces), and R (rhombohedral) Thus our monoclinic structure P2Jc belongs to the monoclinic crystal system and has a primitive Bravais lattice. 

X-ray Data.—The structure of black phosphorus has been calculated from the X-ray reflection spectrum, using the powder method of Debye and Scherrer. It is a rhombohedral space-lattice having a characteristic angle of 60° 47, and a side of 5-96 A. The unit cell contains 8 atoms, and therefore the volume of the unit molecular aggregate is ... 

Other Space Lattices in Metals. The three lattices previously described are by far the most common in metals, but we must briefly refer to three others which are occasionally encountered. These are (a) The rhombohedral hexagonal lattice, in which the atoms are arranged in repeated double layers so that each atom has three close neighbours in the one layer and three at a greaier distance in I he other layer. Such a lattice is found in antimony and bismuth, in which the grouping of the atoms into... 

Fig. 2. Orthographic projections of rhombohedral graphite space lattice. Scale is the same as that used in Fig, 1.

Designations of the space-lattice types P - - primitive, C - - side-centered (base-centered), I - - body-centered, F - face-centered, R - rhombohedral. ... 

Yet another type of canal structure has been reported for the urea inclusion compound of 1,4-dichlorobutane 51). Even though the canals are pseudo-hexagonal in dimension, there is a significant difference in their symmetry. The host lattice is orthorhombic, space group Pbcn. The difference lies in the directions of the six pseudo-3j helices of host molecules around the walls of each canal the sequence is cyc/o-RRRLLL, as opposed to cyc/o-RRRRRR in the hexagonal inclusion compounds and cvc/o-RLRLRL in the rhombohedral. This orthorhombic host structure probably occurs also in the urea inclusion compounds with 1,5-dichloropentane and 1,6-dibromohexane 51). 

The substance can be crystallized from toluene or CS2. It forms orange-red rhombohedral crystals with a density of 2.209 gm/cm , the highest density of any known sulfur allotrope. Eighteen Sg molecules occupy a unit cell with the space group SS-C i. The lattice constants are... 

In referring to any particular space-group, the symbols for the symmetry elements are put together in a way similar to that used for the point-groups. First comes a capital letter indicating whether the lattice is simple (P for primitive), body-centred (I for inner), side-centred (A, B, or C), or centred on all faces (F). The rhombohedral lattice is also described by a special letter R. Following the capital letter for the lattice type comes the symbol for the principal axis, and if there is a plane of symmetry or a glide plane perpendicular to it, the two symbols... 

Lattice parameters of Sm2Fel A.Co c)17C3, with various x and y values are listd in Table 10.2. The XRD lines observed on all the Sm2(Fe, xCox) 7Cy compounds were completely assignable to the Th2Zn]7-type crystal lattice of rhombohedral symmetry (space group = R3m), and the lattice parameters were in good agreement with reported values.3,35 The unit cell volume decreased with the concentration of Co but increased with the carbon content. This indicates that carbon atoms share the interstitial 9e sites.36... 

Designate space groups by a combination of unit cell type and point group symbol, modified to include screw axes and glide planes (Hermann-Mauguin) 230 space groups are possible. Use italic type for conventional types of unit cells (or Bravais lattices) P, primitive I, body-centered A, A-face-centered B, B-face-centered C, C-face-centered P, all faces centered and R, rhombohedral. 

Single-crystal X-ray results (9) point to strict alternation of Si and Al (the 4 0 ordering scheme) in accordance with Loewenstein s rules (10), but this model was recently challenged on the basis of 29si NMR measurements (1, 2) and our discovery that the sodium derivative can be rhombohedral (11,12). However, the controversy has now been resolved and the correctness of the X-ray model reaffirmed (13,14). A consequence of the Si, Al ordering is that the lattice parameter of the cubic cell is ca. 24.6 A, not 12.3 A as reported in earlier work, a feature reflected in weak superlattice reflections. The space group is Fm3c. 

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