Face-centered cubic close-packed

Figure 5 The face-centered cubic, close-packed solid-state structure of copper metal...

D20.6 In a face-centered cubic close-packed lattice, there is an octahedral hole in the center. The rock-salt structure can be thought of as being derived from an fee structure of Cl ions in which Na+ ions have filled the octahedral holes. 

There is, in fact, a near-continuum of nonstoichiometric phases. As x in the formula CeOx varies from 2 to 1.7, the lattice expands in a nearly linear manner due to the larger radius of Ce " compared with Ce". Both metal and oxygen atoms remain face-centered, cubic-close-packed. 

The close-packed crystalline structures are either hexagonal close-packed (hep) or face-centered cubic close-packed (fcc) In a hexagonal close-packed structure, the atoms of the first layer are directly over those of the third layer and this planar arrangement is shown in Fig. 3.9a and 3.9b. The layer sequence is expressed as ABAB and the resulting crystal has a hexagonal symmetry. 

In a face-centered cubic close-packed structure, the successive layers are repeated in the layer sequencei4fiC4fiC as shown in Fig. 3.10a and 3.10b. 

As can be seen in Table 10.2, many different compositions are known and of these, the most common and important is the mononitride, usually expressed as MNj. (M = metal). This notation shows that the nitrogen content is variable and is the result of incomplete filling of the available sites. The mononitrides (with the exception of WN) have a face-centered cubic close-packed structure (fee) where the successive layers follow the sequence ABCABC the coordination number of the metal atom is 12 (see Sec. 4.0 of Ch, 3). A typical fee strueture, that of TiN, is shown in Fig. 10.4.I9]... 

Iridium metal, Ir, crystallizes in a face-centered cubic (close-packed) stmcture. The edge length of the unit cell was found by x-ray diffraction to be 383.9 pm. The density of iridium is 22.42 g/cm. Calculate the mass of an iridium atom. Use Avogadro s number to calculate the atomic weight of iridium. 

Cerium oxide (Ce02) has the fluorite-type structure, shown in Figure 25.3 (space group Fm3m), consisting of a face-centered cubic close-packed array of Ce atoms with all tetrahedral holes filled by oxygen [11,12]. 

Austenitic stainless steels are a class of materials that are extremely relevant for conventional and advanced reactor technologies. They are Fe-Cr-Ni alloys with a fully or quasifuUy face-centered-cubic close-packed crystal structure which imparts most of their physical and mechanical properties [7]. Various chemical additions enhance their properties over a wide range of temperatures. Three main alloy classes are to be considered here 304, 316, and alloy 800 series. 

Figure 28.3 Closest Packing of Spheres, (a) Layers of spheres, (b) The hexagonal close-packed unit cell. This figure shows that the third layer has each sphere directly over a sphere of the first layer, (c) The face-centered cubic close-packed unit cell. This unit cell is oriented so that the layers of atoms in Figure 28.3a are parallel to a plane that passes through the lattice point at the top rear of the cell, the lower left of the cell, and the lower right of the cell.

Figure 2.12. Representations of hexagonal close-packing (hep) and face-centered cubic (fee) packing. Reproduced with permission from Silberberg, M. S. Chemistry The Molecular Nature of Matter, 2nd ed., McGraw-Hill New York, 2000.

Eig. 1. SoHd—Hquid phase diagram for ( ndashrule ) He and (—) He where bcc = body-centered cubic, fee = face-centered cubic, and hep = hexagonal close-packed (53). To convert MPa to psi, multiply by 145. 

Properties. Thallium is grayish white, heavy, and soft. When freshly cut, it has a metallic luster that quickly dulls to a bluish gray tinge like that of lead. A heavy oxide cmst forms on the metal surface when in contact with air for several days. The metal has a close-packed hexagonal lattice below 230°C, at which point it is transformed to a body-centered cubic lattice. At high pressures, thallium transforms to a face-centered cubic form. The triple point between the three phases is at 110°C and 3000 MPa (30 kbar). The physical properties of thallium are summarized in Table 1. 

The electronic stmcture of cobalt is [Ar] 3i/4A. At room temperature the crystalline stmcture of the a (or s) form, is close-packed hexagonal (cph) and lattice parameters are a = 0.2501 nm and c = 0.4066 nm. Above approximately 417°C, a face-centered cubic (fee) aHotrope, the y (or P) form, having a lattice parameter a = 0.3544 nm, becomes the stable crystalline form. The mechanism of the aHotropic transformation has been well described (5,10—12). Cobalt is magnetic up to 1123°C and at room temperature the magnetic moment is parallel to the ( -direction. Physical properties are Hsted in Table 2. 

It is well known that the 0 of a metal depends on the surface crystallographic orientation.6,65,66 In particular, it is well established that 0 increases with the surface atomic density as a consequence of an increase in the surface potential M. More specifically, for metals crystallizing in the face-centered cubic (fee) system, 0 increases in the sequence (110) <(100) <(111) for those crystallizing in the body-centered cubic (bcc) system, in the sequence (111) < (100) <(110) and for the hexagonal close-packed (hep) system, (1120) < (1010) < (0001). 

FIGURE 5.28 A fragment ot the structure constructed as described in Fig. 5.27. This fragment shows the origin of the names "cubic close-packed" or "face-centered cubic" for this arrangement. The layers A, B, and C can be seen along the diagonals of the faces of the cube and are indicated by the different colors of the atoms. 

Buckminsterfullerene is an allotrope of carbon in which the carbon atoms form spheres of 60 atoms each (see Section 14.16). In the pure compound the spheres pack in a cubic close-packed array, (a) The length of a side of the face-centered cubic cell formed by buckminsterfullerene is 142 pm. Use this information to calculate the radius of the buckminsterfullerene molecule treated as a hard sphere, (b) The compound K3C60 is a superconductor at low temperatures. In this compound the K+ ions lie in holes in the C60 face-centered cubic lattice. Considering the radius of the K+ ion and assuming that the radius of Q,0 is the same as for the Cft0 molecule, predict in what type of holes the K ions lie (tetrahedral, octahedral, or both) and indicate what percentage of those holes are filled. 

FCC. Face-centered cubic the FCC structure is a close-packed structure. 

Figure 5.1. Unit cells of the face-centered cubic (fee), body-centered cubic (bcc), and hexagonally closed packed (hep) lattices.

The term crystal structure in essence covers all of the descriptive information, such as the crystal system, the space lattice, the symmetry class, the space group and the lattice parameters pertaining to the crystal under reference. Most metals are found to have relatively simple crystal structures body centered cubic (bcc), face centered cubic (fee) and hexagonal close packed (eph) structures. The majority of the metals exhibit one of these three crystal structures at room temperature. However, some metals do exhibit more complex crystal structures. 

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