Face-centered crystals

Figure 3.13. Top Model of an ideal (100) surface of a face-centered crystal (fee) lattice. Center and bottom Model of a vicinal surface of an fee cut at 12° to the (100) plane a) with straight monatomic steps and (Z ) monatomic steps with kinks along the steps. (From Ref. 11, with permission from Pergamon Press.)...

Figure 11.5. The face-centered crystal structure of orthorhombic oxalic acid. On the left is the cell projected along the a0 axis. Only one molecule at a corner and three molecules in the centers of the faces are shown for clarity. On the right, a packing drawing shows all molecules in the cell with the same view.

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

If, for example, a face-centered crystal having four atoms per unit cell were to lose its face atoms to become a simple cubic cell with only one atom per unit cell, the volume per mole would be four times Table IV shows a comparison of 4Kq with from Eyring s papers. ... 

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. 

The relative number of vacancies which are formed at the intersection of dislocations Cin for face-centered crystals is given by [81]... 

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. 

Cubic close-packed (face-centered) crystal structure... 

For the face-centered crystal structure, the centers of the third plane are situated over the C sites of the first plane (Figure 3.18a). This yields an ABCABCABC. . . stacking sequence that is, the atomic alignment repeats every third plane. It is more difficult to correlate the stacking of close-packed planes to the FCC unit cell. However, this relationship is demonstrated in Figure 3.186. These planes are of the (111) type an FCC unit cell is outlined on the upper left-hand front face of Figure 3.186 to provide perspective. The significance of these FCC and HCP close-packed planes will become apparent in Chapter 7. 

Face-centered cubic crystals of rare gases are a useful model system due to the simplicity of their interactions. Lattice sites are occupied by atoms interacting via a simple van der Waals potential with no orientation effects. The principal problem is to calculate the net energy of interaction across a plane, such as the one indicated by the dotted line in Fig. VII-4. In other words, as was the case with diamond, the surface energy at 0 K is essentially the excess potential energy of the molecules near the surface. 

A LEED pattern is obtained for the (111) surface of an element that crystallizes in the face-centered close-packed system. Show what the pattern should look like in symmetry appearance. Consider only first-order nearest-neighbor diffractions. 

Except for helium, all of the elements in Group 18 free2e into a face-centered cubic (fee) crystal stmeture at normal pressure. Both helium isotopes assume this stmeture only at high pressures. The formation of a high pressure phase of soHd xenon having electrical conductivity comparable to a metal has been reported at 33 GPa (330 kbar) and 32 K, and similar transformations by a band-overlap process have been predicted at 15 GPa (150 kbar) for radon and at 60 GPa (600 kbar) for krypton (51). 

The stmcture of Pmssian Blue and its analogues consists of a three-dimensional polymeric network of Fe —CN—Fe linkages. Single-crystal x-ray and neutron diffraction studies of insoluble Pmssian Blue estabUsh that the stmcture is based on a rock salt-like face-centered cubic (fee) arrangement with Fe centers occupying one type of site and [Fe(CN)3] units randomly occupying three-quarters of the complementary sites (5). The cyanides bridge the two types of sites. The vacant [Fe(CN)3] sites are occupied by some of the water molecules. Other waters are zeoHtic, ie, interstitial, and occupy the centers of octants of the unit cell. The stmcture contains three different iron coordination environments, Fe C, Fe N, and Fe N4(H20), in a 3 1 3 ratio. 

URANIUM compounds), Pb from the thorium series, and Pb from the actinium series (see Actinides and transactinides). The crystal stmcture of lead is face-centered cubic the length of the edge of the cell is 0.49389 nm the number of atoms per unit cell is four. Other properties are Hsted in Table 1. 

Elemental composition, ionic charge, and oxidation state are the dominant considerations in inorganic nomenclature. Coimectivity, ie, which atoms are linked by bonds to which other atoms, has not generally been considered to be important, and indeed, in some types of compounds, such as cluster compounds, it caimot be appHed unambiguously. However, when it is necessary to indicate coimectivity, itaUcized symbols for the connected atoms are used, as in trioxodinitrate(A/,A/), O2N—NO . The nomenclature that has been presented appHes to isolated molecules (or ions). Eor substances in the soHd state, which may have more than one crystal stmcture, with individual connectivities, two devices are used. The name of a mineral that exemplifies a particular crystal stmcture, eg, mtile or perovskite, may be appended. Alternatively, the crystal stmcture symmetry, eg, rhombic or triclinic, may be cited, or the stmcture may be stated in a phrase, eg, face-centered cubic. 

Silver chloride crystals are face-centered cubic (fee), having a distance of 0.28 nm between each ion in the lattice. Silver chloride, the most ionic of the halides, melts at 455°C and boils at 1550°C. Silver chloride is very ductile and can be roUed into large sheets. Individual crystals weighing up to 22 kg have been prepared (10). 

Calcium has a face-centered cubic crystal stmcture (a = 0.5582 nm) at room temperature but transforms into a body-centered cubic (a = 0.4477 nm) form at 428 2° C (3). Some of the more important physical properties of calcium are given in Table 1. For additional physical properties, see references 7—12. Measurements of the physical properties of calcium are usually somewhat uncertain owing to the effects that small levels of impurities can exert. 

In bulk form cerium is a reactive metal that has a high affinity for oxygen and sulfur. It has a face centered cubic crystal stmcture, mp 798°C, bp 3443°C, density 6.77 g/mL, and a metallic radius of 182 pm. Detailed chemical and physical property information can be found in the Hterature (1,2). 

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