Crystal structures close-packed, metals

Most metals active in cyclization belong to Group VIIIB and have either face-centered-cubic (fee) or hexagonal close packed (hep) crystal structure. 

The metal substrates used in the LEED experiments have either face centered cubic (fee), body centered cubic (bcc) or hexagonal closed packed (hep) crystal structures. For the cubic metals the (111), (100) and (110) planes are the low Miller index surfaces and they have threefold, fourfold and twofold rotational symmetry, respectively. 

A summary of physical and chemical constants for beryllium is compiled in Table 1 (3—7). One of the more important characteristics of beryllium is its pronounced anisotropy resulting from the close-packed hexagonal crystal structure. This factor must be considered for any property that is known or suspected to be structure sensitive. As an example, the thermal expansion coefficient at 273 K of single-crystal beryllium was measured (8) as 10.6 x 10-6 parallel to the -axis and 7.7 x 10-6 parallel to the t-axis. The actual expansion of polycrystalline metal then becomes a function of the degree of preferred orientation present and the direction of measurement in wrought beryllium. 

The hardest of the transition-metal borides are the diborides. Their characteristic crystal structure (Figure 10.6) consists of plane layers of close-packed metal atoms separated by plane openly-patterned layers of boron atoms ( chicken-wire pattern). If the metal atoms in the hexagonal close-packed layer have a spacing, d, then the boron atoms have a spacing of d/V3. 

The concept of close packing is particularly useful in describing the crystal structures of metals, most of which fall into one of three classes hexagonal close packed, cubic close packed (i.e., fee), and body-centered cubic (bcc). The bcc unit cell is shown in Fig. 4.8 its structure is not close packed. The stablest structures of metals under ambient conditions are summarized in Table 4.1. Notable omissions from Table 4.1, such as aluminum, tin, and manganese, reflect structures that are not so conveniently classified. The artificially produced radioactive element americium is interesting in that the close-packed sequence is ABAC..., while one form of polonium has... 

Further, it is observed experimentally that electron-pair bonds are frequently associated with anisotropic, i.e. directed, atomic orbitals. This gives rise to open structures. However, the electrostatic (Madelung) energy associated with ionic crystals favors close packing Therefore largely ionic crystals favor more close-packed, two-sublattice structures such as rock salt versus zinc blende. In the case of two-sublattice structures induced by d electrons, electron-pair bonds are generally prohibited by the metallic or ionic outer s and p electrons that favor close packing. Nevertheless, it will be found in Chapter III, Section II that, if transition element cations are small relative to the anion interstice and simultaneously have Rti RCf electron-pair bonds may be formed below a critical temperature. 

Stable. In this case the electronic structure ordinarily approximates that of a free-elcctron gas and may be analyzed with methods appropriate to free-electron gases. Again, the crystal structure is the determining feature for the classification. When tin has a tetrahedral structure it is a covalent solid when it has a close-packed white-tin structure, it is a metal. Even silicon and germanium, when melted, become close-packed and liquid metals. 

The simplest examples of the closest packing of identical units are the structures of crystalline metals or noble gases and of crystals built of molecules of one kind only. In the latter the molecules must either be approximately spherical in shape or become effectively spherical by rotation or random orientation. Metals provide many examples of hexagonal and cubic closest packing and a few examples of more complex sequences (for example, he. La, Pr, Nd, Am, and chh Sm). Close-packed molecular crystals include the noble gases, hydrogen, HCl, H2S, and CH4. 

FIG. 24.7. The crystal structures of metallic borides (a) close-packed metal layer in UBj (AIB2) with B in trigonal prism holes between layers, (b) metal layer in UB4 with positions of 6- and 8-coordination between layers, (c) metal layer in CaB (ThBg) structure, (d) the UB4... 

Most pure metals adopt one of three crystal structures, Al, copper structure, (cubic close-packed), A2, tungsten structure, (body-centred cubic) or A3, magnesium structure, (hexagonal close-packed), (Chapter 1). If it is assumed that the structures of metals are made up of touching spherical atoms, (the model described in the previous section), it is quite easy, knowing the structure type and the size of the unit cell, to work out their radii, which are called metallic radii. The relationships between the lattice parameters, a, for cubic crystals, a, c, for hexagonal crystals, and the radius of the component atoms, r, for the three common metallic structures, are given below. 

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