Centered crystal lattice

Translational symmetry is the most important symmetry property of a crystal. In the Hermann-Mauguin symbols the three-dimensional translational symmetry is expressed by a capital letter which also allows the distinction of primitive and centered crystal lattices (cf. Fig. 2.6, p. 8) ... 

Crystal Structure Periclase has a cubic face-centered crystal lattice iso-morphous with that of sodium chloride and calcium oxide see Figure 8.1. 

The y-phase is a solid solution with a face-centered crystal lattice and randomly distributed different species of atoms. By contrast, the y -phase has an ordered crystalline lattice of II2 type (Figure 10.2). In pure intermetallic compound NisAl the atoms of aluminum are placed at the vertices of the cubic cell and form the sublattice A. Atoms of nickel are located at the centers of the faces and form the sublattice B. The y -phase has remarkable properties, in particular, an anomalous dependence of strength on temperature. The y -phase first hardens, up to about 1073 K, and then softens. The interatomic bondings Ni-Al are covalent. 

At low temperatures they solidify. The solid noble gases have the cubic face-centered crystal lattice. The molecules of solid noble gases are glued by very weak fluctuating dipole forces. The atoms are distorted from the stable configuration and this creates a potential that holds atoms of solid together. This attractive potential depends on the interatomic distance r as the inverse sixth power. The repulsive force depends inversely on the distance to the twelfth power. An empirical formula for potential is known as Leimard-Jones potential (11.26). It is appropriate to use this equation in the dimensionaUy-handy form... 

The exponent n is an important quantity in the empirical description of the interatomic interactions. This quantity uniquely determines the dependence of energy on distance, E r) Series of the type of (15.18) have been calculated and tabulated (see [7]). For n < 3 these series diverge. As n ooA approaches the number of nearest neighbors, which is 12 for the face-centered crystal lattice. 

Magnesium oxide is a highly ionic crystal, with the Mg O bonds having about 80% ionic character, and with a cubic face-centered crystal lattice (space group Fm3m). MgO has no polymorph transitions from room temperature to melting point at 3073 K. The physical properties of the MgO single crystal are listed in Table 1.3. 

Only body-centered cubic crystals, lattice constant 428.2 pm at 20°C, are reported for sodium (4). The atomic radius is 185 pm, the ionic radius 97 pm, and electronic configuration is lE2E2 3T (5). Physical properties of sodium are given ia Table 2. Greater detail and other properties are also available... 

Acid-treated clays were the first catalysts used in catalytic cracking processes, but have been replaced by synthetic amorphous silica-alumina, which is more active and stable. Incorporating zeolites (crystalline alumina-silica) with the silica/alumina catalyst improves selectivity towards aromatics. These catalysts have both Fewis and Bronsted acid sites that promote carbonium ion formation. An important structural feature of zeolites is the presence of holes in the crystal lattice, which are formed by the silica-alumina tetrahedra. Each tetrahedron is made of four oxygen anions with either an aluminum or a silicon cation in the center. Each oxygen anion with a -2 oxidation state is shared between either two silicon, two aluminum, or an aluminum and a silicon cation. 

The geometry of ionic crystals, in which there are two different kinds of ions, is more difficult to describe than that of metals. However, in many cases the packing can be visualized in terms of the unit cells described above. Lithium chloride, LiCl, is a case in point Here, the larger Cl- ions form a face-centered cubic lattice (Figure 9.18). The smaller Li+ ions fit into holes between the Cl- ions. This puts a Li+ ion at the center of each edge of the cube. 

Magnesia forms solid solutions with NiO. Both MgO and NiO have face-centered cubic lattices with NaCl-type structures. The similarity between the ionic radii of the metals (Ni2+ = 0.69 A, Mg2+ = 0.65 A) allows interchangeability in a crystal lattice, and thus the formation of solid solutions with any proportion of the two oxides is possible. Such solid solutions are more difficult to reduce than NiO alone. Thus Takemura et al. (I) demonstrated that NiO reduced completely at 230°-400°C (446°-752°F) whereas a 10% NiO-90% MgO solid solu-... 

The formation of surface defects of a crystal lattice. It was observed while using crystal compounds of transition metals as catalysts [e.g. as was shown by Arlman (171, 173), for a TiCl3 surface defects appear on the lateral faces of the crystal]. In this case low surface concentration of the propagation centers should be expected, as is illustrated in the case of polymerization by titanium dichloride (158). The observed... 

As has been shown by the X-ray diffraction method the parent metals (i.e. Pd or Ni), the a-phase, and /3-phase all have the same type of crystal lattice, namely face centered cubic of the NaCl type. However, the /9-phase exhibits a significant expansion of the lattice in comparison with the metal itself. Extensive X-ray structural studies of the Pd-H system have been carried out by Owen and Williams (14), and on the Ni-H system by Janko (8), Majchrzak (15), and Janko and Pielaszek (16). The relevant details arc to be found in the references cited. It should be emphasized here, however, that at moderate temperatures palladium and nickel hydrides have lattices of the NaCl type with parameters respectively 3.6% and 6% larger than those of the parent metals. Within the limits of the solid solution the metal lattice expands also with increased hydrogen concentration, but the lattice parameter does not depart significantly from that of the pure metal (for palladium at least up to about 100°C). 

Explain why the density of vanadium (6.1 L g-cm 3) is significantly less than that of chromium (7.19 g-cm-3). Both vanadium and chromium crystallize in a body-centered cubic lattice. 

Consider some vanadium ions in aqueous solution. Pale violet solutions of vanadium(ii) salts contain the [V(H20)6] ion. The vanadium(ii) center is only weakly polarizing, and the hexaaqua ion is the dominant solution species. Aqueous vanadium(ii) solutions are observed to be unstable with respect to reduction of water by the metal center. In contrast, vanadium(ni) is more highly polarizing and an equilibrium between the hexaaqua and pentaaquahydroxy ion is set up. The of 2.9 means that the [V(OH2)6] ion (Eq. 9.17) only exists in strongly acidic solution or in stabilizing crystal lattices. 

It has been found that adamantane crystallizes in a face-centered cubic lattice, which is extremely unusual for an organic compound. The molecule therefore should be completely free from both angle strain (since all carbon atoms are perfectly tetrahedral) and torsional strain (since all C—C bonds are perfectly staggered), making it a very stable compound and an excellent candidate for various applications, as wUl be discussed later. 

Yet another common crystal lattice based on the simple cubic arrangement is known as the face-centered cubic structure. When four atoms form a square, there is open space at the center of the square. A fifth atom can fit into this space by moving the other four atoms away from one another. Stacking together two of these five-atom sets creates a cube. When we do this, additional atoms can be placed in the centers of the four faces along the sides of the cube, as Figure 11-28 shows. 

The family of true clathrates based on hydrocarbons only is further enriched by the inclusion compounds of 48 with benzene (1 1) and p-xylene (2 1) 90> (Table 19). Figure 28 illustrates the structure of 48 benzene (1 1). The structure of the p-xylene clathrate shows intercalated guest molecules at centers of symmetry in the crystal lattice. Both clathrates are rather unstable at ambient temperatures and decompose easily, e.g. on exposure to X-rays (even in the presences of mother liquor). The 48 p-xylene clathrate is unstable to such a degree that decomposition occurs at low temperature. 

For simple monovalent metals, the pseudopotential interaction between ion cores and electrons is weak, leading to a uniform density for the conduction electrons in the interior, as would obtain if there were no point ions, but rather a uniform positive background. The arrangement of ions is determined by the ion-electron and interionic forces, but the former have no effect if the electrons are uniformly distributed. As the interionic forces are mainly coulombic, it is not surprising that the alkali metals crystallize in a body-centered cubic lattice, which is the lattice with the smallest Madelung energy for a given density.46 Diffraction measurements... 

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