Unit cell cubic closest-packed

Returning to Figure 9-3, we could also place the third layer atoms over neither of the first two layers, so that one atom is a position C. More layers can be added, following the ABCABC. . . pattern. This arrangement, called cubic closest packing, has an fee unit cell (the closest packed layers can be seen as planes of atoms perpendicular to the diagonal of the unit cell in Figure 9-2). 

The structure of iodine at four different pressures. The outlined face-centered unit cell in the 30-Gpa figure corresponds to that of a (distorted) cubic closest-packing of spheres. At 24.6 GPa four unit cells of the face-centered approximant structure are shown the structure is incommensurately modulated, the atomic positions follow a sine wave with a wave length of 3.89 x c. The amplitude of the wave is exaggerated by a factor of two. Lower left Dependence of the twelve interatomic contact distances on pressure... 

Unit cells for hexagonal (left) and cubic closest-packing of spheres. Top row projections in the stacking direction. 

In cubic closest-packing, consideration of the face-centered unit cell is a convenient way to get an impression of the arrangement of the interstices. The octahedral interstices are situated in the center of the unit cell and in the middle of each of its edges [Fig. 17.3(a)], The octahedra share vertices in the three directions parallel to the unit cell edges. They share edges in the directions diagonal to the unit cell faces. There are no face-sharing octahedra. 

Face-centered unit cell of cubic closest-packing ... 

Cl 6c +(u,u,u +m, + m, + m + w, + w, +m) w= This structure has a rhombohedral symmetry but is usually described in terms of a triple-volume hexagonal cell, which makes comparison with the idealized Cdl2 structure simpler. The idealized unit cell is adequate for the purposes of this book. In this representation the anion layers are in cubic closest packing. .. ABC ABC ABC... The metal and nonmetal stacking sequence is... 

Unit cells for hexagonal (left) and cubic closest-packing of spheres. Top row projections in the stacking direction. Spheres are dr awn smaller than then actual size. Spheres with the same coloring form hexagonal layers as in Fig. 14.1... 

One could follow a similar practice and construct a similar hexagonal sandwich with two layers (B, Q of filler, but a cubic cell of higher symmetry can be. constructed the second system is thus characterized as cubic closest packed. The relation between the cubic unit cell (which is identical to the face-centered cubic cell we <... 

Fig. 4.14 Unit cells in the cubic closest packed systems, (a) A face-ccntcred array of atoms. Note that the exposed layer consists of a closest packed array of fifteen atoms. Consider this the A layer , (b) A closest packed layer of six atoms placed on (a). Consider this the B layer, (c) The final atom, a member of the C layer, is added to complete the cube. The fee unit cell is redrawn in (d. Note that the single atom that composes the C layer does net lie above any atom in the A layer (as it would if ths were hep).

Silver metal crystallizes in a cubic closest-packed arrangement with the edge of the unit cell having a length d = 407 pm. What is the radius (in picometers) of a silver atom ... 

Cubic closest-packing uses a face-centered cubic unit cell. Looking at any one face of the cube head-on shows that the face atoms touch the corner atoms along the diagonal... 

The a-R12 allotrope consists of an approximately cubic closest packing arrangement of icosahedral B12 units bound to each other by covalent bonds. The parameters of the rhombohedral unit cell are a = 505.7 pm, a = 58.06° (60° for regular ccp). In space group Rim, the unit cell contains one B12 icosahedron. A layer of interlinked icosahedra perpendicular to the threefold symmetry axis is illustrated in Fig. 13.2.1. There are 12 neighboring icosahedra for each icosahedron six in the same layer, and three others in each of the upper and lower layers, as shown in Fig. 9.6.21(b). 

A structure that is exhibited by many metals is the face-centered cubic (fee) structure, which is also referred to as cubic closest packing. This structure has a unit cell consisting of one atom on each comer of a cube as well as one atom on each face that is shared between... 

The aba arrangement has the hexagonal unit cell shown in Fig. 16.14, and the resulting structure is called the hexagonal closest packed (hep) structure. The abc arrangement has a face-centered cubic unit cell, as shown in Fig. 16.15 on page 779, and the resulting structure is called the cubic closest packed (ccp) structure. Note that in the hep structure the spheres in every other layer occupy the same vertical position (ababab. . . ), while in the ccp structure the spheres in every fourth layer occupy the same vertical position (abcabca. . . ). A characteristic of both structures is that each sphere has 12 equivalent nearest... 

Density is mass per unit volume. Thus we need to know how many silver atoms occupy a given volume in the crystal. The structure is cubic closest packed, which means the unit cell is face-centered cubic, as shown in the figure at left. 

Recall that in the cubic closest packing arrangement, the unit cell is face-centered cubic and contains four net spheres. Thus the volume occupied by spheres in the unit cell is four times the volume of each sphere ... 

Cubic closest packed (cep) structure a solid modeled by the closest packing of spheres with an abcabc arrangement of layers the unit cell is face-centered cubic. (16.4)... 

The sequence ABC ABC... possesses cubic symmetry, that is, 3-fold axes of symmetry in four directions parallel to the body-diagonals of a cube, and is therefore described as cubic closest packing (c.c.p.). A unit cell is shown in Fig. 4.1(e) (p. 120) and the packing is also illustrated in Fig. 4.14. The close-packed layers seen in plan in Fig. 4.12 are perpendicular to any body-diagonal of the cube. Since the atoms in c.c.p. are situated at the corners and mid-points of the faces of the cubic unit cell the alternative name face-centred cubic (f.c.c.) is also applied to this packing. All atoms have their twelve nearest neighbours at the vertices of a cuboctahedron. (Fig. 4.5(b)). 

This account of these structures has been based on the mode of packing of the c.p. layers. For the alternative description in terms of the way in which the octahedral BX groups are joined together by sharing X atoms, see Chapter 5. The structures based on cubic closest-packing are normally illustrated and described in terms of the cubic unit cell. We noted earlier that the cryolite structure is a superstructure of perovskite the relation between the perovskite, cryolite, and K2PtQg structures is described in Chapter 10 (p. 388). 

Figure 12.29 Cubic closest packing of frozen argon (face-centered cubic unit cell).

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