Rhombohedral system

Hemihydrate crystals have an SG of 2.71, are white in colour and belong to the rhombohedral system. Figure 3 shows photographs of industrial and laboratory hemihydrate. The crystals are needle-like with sizes up to 20 pm. 

When extended to rhombohedral systems, the mathematical equation is... 

This form of selenium can also be produced from amorphous selenium by heating with quinoline, pyridine, aniline or other basic organic solvent,7 and also by sublimation. In this latter case the sublimate also contains the amorphous form.8 Atmospheric oxidation of solutions of alkali selenides gives this variety of selenium as a granular deposit. When produced by these last three methods, leafy crystals may be obtained, and Muthmann (1890) discovered that crystals which he obtained by the sublimation method were of the trigonal (rhombohedral) system and isomorphous with those of tellurium. 

Trigonal (or Rhombohedral) System with one threefold axis. 

The trigonal system can be considered as a subdivision of the hexagonal unit. On this basis there would be only six different crystal systems, but conventionally, the trigonal system (also called the rhombohedral system) is retained separately. Figure 2.1 shows two rhombohedral cells within a hexagonal cell. 

The Seven Systems of Crystals are shown in Figure 2.2. The relationship between the trigonal and rhombohedral systems is shown in Figure B.la. The possibilities of body-centered and base-centered cells give the 14 Bravais Lattices, also shown in Figure 2.2. A face-centered cubic (fee) cell can be represented as a 60° rhombohedron, as shown in Figure B.lb. The fee cell is used because it shows the high symmetry of the cube. 

These systems can be described in terms of their symmetry elements. A triclinic crystal has only a center of symmetry. Monoclinic crystals have a single axis of twofold rotational symmetry. Orthorhombic crystals have three mutually perpendicular axes of twofold symmetry. With tetragonal symmetry, there is a single axis of fourfold symmetry. Cubic crystals are characterized by four threefold axes of symmetry, the <111> axes. There is a single axis of threefold symmetry in the rhombohedral system. The hexagonal system involves a single axis of sixfold symmetry. 

This is evident from the crystallographic measurements detailed below.1 The salts crystallise according to the rhombohedral system. 

Properties.—The pentoxide exists in crystalline and vitreous forms, the transformation temperature of which has been given as 440° C.5 Sublimation proceeds with moderate speed between 180° and 250° C.6 and the vapour pressure may reach 760 mm. at 860° C.7 When it is sublimed at 360° C. in a current of oxygen the oxide forms brilliant crystals together with some of the amorphous material which is considered to be a product of polymerisation. The crystalline form, by X-ray examination, is that of the rhombohedral system with 12P2Os in a unit cell the lengths of the axes are a = 11-12, b = 1-12 A.8... 

Above 160° C. the stable form of silver nitrate belongs to the rhombohedral system. At lower temperatures the crystals are rhombic, the transition-temperature between the two varieties being between 159-2° and 159-7° C.5... 

The lattice of points shown in Fig. A4-1 is rhombohedral, that is, it possesses the symmetry elements characteristic of the rhombohedral system. The primitive rhombohedral cell has axes ai(R), ajCR), and a3(R). The same lattice of points, however, may be referred to a hexagonal cell having axes a,(H), ajCH), and c(H). The hexagonal cell is no longer primitive, since it contains three lattice points per unit cell (at 0 0 0, f and f f), and it has three times the volume of the rhombohedral cell. 

There is then the problem of determining the lattice parameters and a of the rhombohedral unit cell. But the dimensions of the rhombohedral cell can be determined from the dimensions of the hexagonal cell, and this is an easier process than solving the rather complicated plane-spacing equation for the rhombohedral system. The first step is to index the pattern on the basis of hexagonal axes. Then the parameters a and c of the hexagonal cell are calculated in the usual way. Finally, the parameters of the rhombohedral cell are determined from the following equations ... 

Most of the metals crystallize in the cubic system (face centered, body centered). Zn and Cd crystallize in the hexagonal system, Bi in the rhombohedral system, and Sn in the tetragonal system. In this chapter emphasis will be placed on the cubic system, for Au, Ag, Cu, Pb, and so forth, are face-centered-cubic metals (fee). 

Only for bismuth faces has the temperature effect been studied (for cyclohexanol adsorption in 50mM/Na2SO4 and H2SO4 aqueous solutions) from 281 to 321 The different behavior of the (111) face from that of the (Oil) and (211) faces, suggested that the chemical interactions between bismuth atoms and cyclohexanol are reinforced by temperature for the two last faces but that, for (111), there is only physical adsorption. This could explain why Fmax (surface excess at saturation) diminishes with increasing temperature for (111) and increases for the two other faces. Bismuth crystallizes in the rhombohedral system, the (111) face is less densely packed in atoms than the two other faces, and bismuth is a semimetal, not a metal. 

FIGURE 15.5 Variation in crystal morphology for identical unit cells, (a) Crystals in the rhombohedral system that only have faces present in the unit cell (001), (010), and (100). (b) Cubic system the leftmost picture is a cube, the rightmost one a regular octahedron in between are intermediate shapes, (c) Examples of the various shapes that an ot-lactose monohydrate crystal (monoclinic) can assume in practice. In (a) and (b) the shapes are shown in perspective. In (c) we have projections (all in the same direction with respect to the axes of the unit cell). 

A redetermination of the crystal structure of calcium orthoborate, Ca3(B03)2, reveals that it crystallizes in the rhombohedral system, space group R3c, and that there are six formula units in the hexagonal unit cell. The BO3 group is said to be non-planar, but the reported O—B—O angle of 119.95(4)° suggests that this is only marginally the case. The B—O bond distance is 1.3836(5) A. 

In 1955, for the first time, G. Natta obtained definite amounts of stereoregular polystyrene by polymerization, in the presence of titanium chloride Cl4Ti. This isotactic polystyrene has a crystallinity ratio which may reach 90 per cent. The melting temperature is 240 °C, The crystals belong to the rhombohedric system. 

The product is a green powder, extremely sensitive to moisture or oxygen. At room temperature in air, it is immediately oxidized giving a mixture of Ko.soCr02 and K2Cr04. It crystallizes in the rhombohedral system. The hexagonal parameters are a = 3.022 0.004 A, c= 17.76 0.03 A. Its structure consists of (Cr02) layers between which the K+ ions are inserted in an octahedral environment.4... 

The first letter denotes the crystal system triclinic (a), monoclinic (m), orthorhombic (o), tetragonal (t), hexagonal (h) and cubic (c). Trigonal (rhombohedral) system is denoted by combination hR. The second letter of Pearson s symbol denotes lattice type primitive (P), edge-(base-) centered (C), body-centered (I) or face-centered (F). The following number denotes number of atoms in the crystal unit cell. 

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