Face-centered cubic structure close packed planes

Fig. XXIV-l.—The face-centered cubic structure, (a) atoms at the corners of a cube and the centers of the faces. (b) the same atoms connected up in planes perpendicular to the cube diagonal, (c) view of successive planes looking along the cube diagonal, illustrating the close-packed nature of the structure.

A close-packed structure is defined as a structure in which hard spheres that represent atoms can be placed with the maximum filling of space. In the plane, each atom has six neighbors in a hexagonal arrangement. The adjustment layer can be stacked in one of two ways (Figure 4.2) if the given plane is labeled A, then two possible positions for the next plane can be labeled as B and C. The face-centered cubic structure (fee) is the cubic close-packed structure which can be viewed as... 

Plastic crystals are characterized by orientational disorder but positional order of the structural motif. Molecules of plastic crystals are close to spherical, which are generally packed in body- or face-centered cubic structures [7]. T)q)ical examples are proAdded by the structure of ball-like hydrocarbon molecules as adamantane and norbornane. The name plastic crystals derives from the softness and easy of deformation of these materials, due to the large number of slip planes in close packed structures [5,7]. 

Colloidal crystals can have a large variety of structures that depend on the nature of the colloids (hard sphere, charged, mixed sizes, and charges) [23]. The equilibrium crystalline phase of single-sized hard spheres has the face-centered cubic structure. Its energy is only about 10 k T lower than that of the hexagonal close-packed crystal [24]. Equivalently, the stacking faults on the close-packed planes in both... 

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. 

Slip occurs along specific crystal planes (slip planes) and in specific directions (slip directions) within a crystal structure. Slip planes are usually the closest-packed planes, and slip directions are the closest-packed directions. Both face-centered-cubic (FCC) and hexagonal-close packed (HCP) structure are close packed structures, and slip always occurs in a close packed direction on a closepacked plane. The body-centered-cubic (BCC) structure is not, however, close packed. In a BCC system, slip may occur on several nearly close packed planes or directions. Slip planes and directions, as well as the number of independent slip systems (the product of the numbers of independent planes and directions), for these three structures are listed in Table 7.2. 

Energy bands for the transition-metal series Ti. V. Cr, (Mn, with a complex structure, is omitted). Fe. Co, Ni, and Cu. as a function of wave number along a symmetry line in the appropriate Brillouin Zone. For the face-centered cubic (fee) and body-centered cubic (bcc) structures, the symmetry line is in a [100] direction for the hexagonal close-packed (hep) structure, it is parallel to a nearest-neighbor distance in the basal plane. Pashed lines indicate estimated bands. [After Mattheiss. 1964.]... 

There are two possible cps arrangements, the hexagonal close-packed (hep) and the face centered cubic (fee) crystal lattice. In both cases the planes of highest atomic density, (0001) and (111), respectively, have the same two-dimensional (2D) hexagonal close-packed (2D hep) structure, Fig. 2.1. The sequence of consecutive planes forming the bulk cps structure, however, are different ... 

In many metals, each atom is in contact with twelve others six in a plane, three above, and three below. These are termed close-packed hexagonal (e.g., magnesium), or face-centered cubic (e.g., copper). In other metals (e.g., iron), each atom is in contact with eight others at the corners of a cube such structures are called body-centered cubic. 

Therefore lattice structures with closely packed planes allow more plastic deformation than those that are not closely packed. Also, cubic lattice structures allow slippage to occur more easily than non-cubic lattices. This is because of their symmetry which provides closely packed planes in several directions. Most metals are made of the body-centered cubic (BCC), face-centered cubic (FCC), or hexagonal close-packed (HCP) crystals, discussed in more detail in the Module 1,... 

The atoms in a grain comprise a lattice structure such as a body-centered cubic (bcc) lattice, a face-centered cubic (fee) lattice, or a hexagonal close-packed (hep) lattice. The atoms in a lattice are arranged regularly in a plane of the lattice, and a smooth plane becomes an active slip plane in which dislocations can move. In an fee lattice, the plane packed most closely with atoms is the (1 1 1) plane, in which atoms are located at apexes of regular triangles to cover the plane as shown in Fig. 4. There are four equivalent planes with different orientations in an fee lattice. 

Table 3 Different structures of simple metals with the corresponding d 2/4m ratio, hep-hexagonal close-packed,/cc = face-centered cubic, and rhomb. = rhombohedral. The layering pattern between hexagonal planes is given, a corresponds to the angle between in plane and out of plane bonds in the hep structure, and the angle between two bonds (a) in the rhombohedral...

Colloid crystal templates originate from studies done by Luck in 1963 where they observed that the color of dried latexes related to the Bragg diffraction of the incident light indicating crystal planes that they attributed to face-centered cubic (FCC) orientations of stacked latex particles. The small size distribution of the latex particles allowed for a close-packed ordered structure forming the FCC orientation. Under controlled drying, three- as well as two- dimensional films... 

The structural representations shown in Fig. 3.2 are useful for visualizing the slip-planes that may exist in various metal crystal systems. For example, from the face-centered cubic (fee) lattice shown in Fig. 3.2a, it is easy to see how planes of atoms might slide rather easily over one another from the upper left to the lower right. This lattice also has several other such slip planes. While it is not readily apparent from the figure, a three-dimensional model of these crystal systems would show that the body-centered cubic (bcc) lattice offers the least number of slip planes of the three shown, and the hexagonal-close-packed (hep) system falls in between the fee and bcc systems. 

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