Rhombohedral crystal lattice

Fe203, known as ferric oxide or hematite, possesses rhombohedral crystal lattice... 

Texture. All limestones are crystalline, but there is tremendous variance in the size, uniformity, and arrangement of their crystal lattices. The crystals of the minerals calcite, magnesite, and dolomite are rhombohedral those of aragonite are orthorhombic. The crystals of chalk and of most quick and hydrated limes are so minute that these products appear amorphous, but high powered microscopy proves them to be cryptocrystalline. Hydrated lime is invariably a white, fluffy powder of micrometer and submicrometer particle size. Commercial quicklime is used in lump, pebble, ground, and pulverized forms. 

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... 

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°. 

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... 

Over several days rhombohedral crystals of Pt6Clj2 are obtained at room temperature.9 Unlike the Ni halides or PdF2, which are ionic and paramagnetic, these chlorides are molecular or polymeric and diamagnetic, and Bom-Haber calculations indicate that ionic lattices would be endothermic. 

Bravais in 1849 showed that there are only 14 ways that identical points can be arranged in space subject to the condition that each point has the same number of neighbors at the same distances and in the same directions.Moritz Ludwig Frankenheim, in an extension of this study, showed that this number, 14, could also be used to describe the total number of distinct three-dimensional crystal lattices.These are referred to as the 14 Bravais lattices (Figure 4.9), and they represent combinations of the seven crystal systems and the four lattice centering types (P, C, F, I). Rhombohedral and hexagonal lattices are primitive, but the letter R is used for the former. 

Fig 2. The 14 three-dimensional translation lattice types (Bravais, 1850). P = primitive C = c-face centred, F = all face centred, R = rhombohedral (crystals In the 7 rhombohedral space groups are described in relation to hexagonal axes). 

Figures 5.7, 5.8 and 5.9 show the diffraction pattern and transmission electron micrograph of the particles in the carbyne films produced by the combustion flame method. In Figures 5.7 and 5.8, the d-spacing of our particles is in good agreement with values of the a-modification of carbyne [47]. The evaluated lattice parameters were aQ = 0.892 nm, co=1.536nm. Figure 5.8 also shows that the interplanar spacing (21.0) and (30.0) of carbyne monocrystal obtained by combustion flame is coinciding with the value obtained by Heimann et al. [46]. The transmission electron micrograph shows the rhombohedral crystal flake of carbyne with a size of 230 X 274 nm.

The first complete description of crystalline Se was reported by Donohue et al. in 1961 on the basis of an X-ray diffraction study [64]. The rhombohedral structure was verified, and the molecular symmetry was ascertained to be D d. Since cyc/o-hexasulfur decomposes rapidly under X-ray irradiation at standard temperature-pressure (STP) conditions Steidel et al. reinvestigated the molecular and crystal structure at 183 K giving results with a higher accuracy [65]. The molecular and crystal lattice parameters are summarized in Tables 1 and 2. 

Boron carbide crystallizes in the trigonal-rhombohedral space group R3m the unit cell is shown in Figure 4.5. The structure is usually described as an arrangement of distorted icosahedra located at the nodes of a rhombohedral Bravais lattice. Parallel to the space diagonal, which is the c-axis in hexagonal notation, a linear chain of three... 

Let us demonstrate the procedure of finding the matrix of a symmetrical transformation (4.77) by the example of the rhombohedral crystal system where there is only one lattice type (R). The basic translation vectors of the initial lattice are the following ... 

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