Crystal systems table

The symmetries of crystals can be divided into six basic types or crystal systems (Table 6) ... 

Polycrystalline silicon carbide obtained by the Acheson process exhibits a large number of different structures (polytypes), some of which dominate. These can be classified in the cubic, hexagonal, and rhombohedral crystal systems (Table 1). 

In three dimensions, there are seven crystal systems (Table 6.2). The crystal systems are further divided according to centerings (Figure 6.3) into 14 Bravais lattices cubic (3), tetragonal (2), orthorhombic (4), hexagonal (1), trigonal (1), monoclinic (2), and triclinic (1). Auguste Bravais was a French mathematician. 

Crystal Systems Table 4.2. Seven Crystal Systems... 

These 14 Bravais Lattices are unique in themselves. If we arrange the crystal systems in terms of symmetry, the cube has the highest symmetry and the triclinic lattice, the lowest symmetry, as we showed above. The same hierarchy is maintained in 2.2.4. as in Table 2-1. The symbols used by convention in 2.2.4. to denote the type of lattice present are... 

At this point, you may find that the subject of symmetry in a crysted structure to be confusing. However, by studying the terminology carefully in Table 2-2, one can begin to sort out the various lattice structures and the symbols used to delineate them. All of the crystal systems can be described by use of either Schoenflies or Hermaim-Mauguin S5mbols, coupled with the use of the proper geometrical symbols. 

Table 3.1 The 32 crystal classes and the corresponding crystal systems...

More systematic (but not always unambiguous) is the designation by Pearson symbols their use is recommended by IUPAC (International Union of Pure and Applied Chemistry). A Pearson symbol consists of a lower case letter for the crystal system (cf. the abbreviations in Table 3.1, p. 24), an upper case letter for the kind of centering of the lattice (cf. Fig. 2.6, p. 8) and the number of atoms in the unit cell. Example sulfur-< F128 is orthorhombic, face centered and has 128 atoms per unit cell (a-sulfur). 

General discussions of the basic ideas have been presented in (33) and (34). Their applications to crystallization systems were reported in (3 ) and (36), and to polymerization reactors in (5) and (37) to (4J) (see also Table I). 

Table 3 Differentiation of Crystal Systems by the Character of Extinction System Character of observed extinction...

Seven crystal systems as described in Table 3.2 occur in the 32 point groups that can be assigned to protein crystals. For crystals with symmetry higher than triclinic, particles within the cell are repeated as a consequence of symmetry operations. The number of asymmetric units within the unit cell is related but not necessarily equal to the number of molecules in a unit cell, depending on how the molecules are related by symmetry operations. From the symmetry in the X-ray diffraction pattern and the systematic absence of specific reflections in the pattern, it is possible to deduce the space group to which the crystal belongs. 

The liquid effluent, which consists of water from the evaporator/crystallizer used to produce the solid filter cake produced by the brine-recovery operation, should not pose a significant hazard to human health or to the environment. While the evaporator/crystallizer system has not been tested yet, the composition of the water and solid filter cake can be readily determined from an analysis of the SCWO liquid effluent. As shown in Table 5-10, the liquid effluent is essentially free of organics. The source of the chromium and nickel that were found in some of the effluents is generally believed to be corrosion products from the SCWO reactor components. These elevated levels of metals indicate that the solid filter cake will need to be treated (e.g., by stabilization) prior to disposal in a hazardous waste landfill. 7... 

The recently determined X-ray crystal structure of cyclopentacorannulene 25 provides an additional opportunity to test the performance of theory in predicting the minimum energy structures of nonplanar conjugated systems. Table 4 presents the C-C bond lengths in the crystal and a comparison with ab initio values calculated at HF/3-21G and HF/6-3IG levels. The agreement between experimental and theoretical bond lengths is very satisfactory with root mean square devia-... 

Crystals are grouped into seven crystal systems based on their s)unmetry. Table 4.3 describes the... 

Symmetry restrictions for a number of crystal systems are summarized in Table B.l. The local symmetry restrictions for a site on a symmetry axis are the same as those for the crystal system defined by such an axis, and may thus be higher than those of the site. This is a result of the implicit mmm symmetry of a symmetric second-rank tensor property. For instance, for a site located on a mirror plane, the symmetry restrictions are those of the monoclinic crystal system. 

Table 2. Crystal Systems, Laue Classes, Non-Centrosymmetric Crystal Classes (Point Groups) and the Occurrence of Enantiomorphism and Optical Activity 31...

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