STRUCTURES

• Face-Centered Cubic (fee)

The ABCABC . . . layers, of which there are four sets, are
perpendicular to the body diagonals of the cube. The 12 nearest neighbors at a distance D (the
diameter of a sphere) form a cubo-octahedron about each sphere, as shown in Fig. 1.14. There are
six next nearest neighbors at a distance V2 D and 24 third-nearest neighbors at a distance V5 D.
The symmetry of the structure is cubic F in Fig. 1.5. The following metals adopt the fee structures
as one of their polymorphs: Al, Ca, Fe, Co, Ni, Cu, Sr, Y, Rh, Pd, Ag, Ir, Pt, Au, and Pb.

• Hexagonal Close-Packed (hep)

.There is only one close-packed direction with a packingsequence ABAB . . . The hexagonal symmetry is shown in Fig. 1.5. As in the fee structure, there are
12 nearest neighbors, but their configuration is different in the form of a twinned cubooctahedron,
as shown in Fig. 1.14. There are six next nearest neighbors, as in the fee structure, but only two
third-nearest neighbors at a distance V% D or 1.63 3D, the distance from one sphere to the spheres in the second layer above or below the given sphere. The c/a ratio = 1.633 is defined in Fig. 1.5
for the hexagonal lattice. If the shape of the atoms is ellipsoidal rather than spherical, then the c/a
ratio deviates from the 1.633 value. Metals with the hep structure and their c/a ratio are 

• Body-Centered Cubic (bcc)

There, the distance of the next nearest neighbors is close to
the nearest-neighbor distance. Thus, the effective coordination number is 14, comparable to the fee
and hep structures. Metals that have the bcc structure are Li, Na, K, Ca, V, Ti, Cr, Fe, Rb, Sr, Nb,
Mo, Cs, Ba, Hf, Ta, and W.
The structure of a particular metal adopts cannot be explained only in terms of volume occupied
or number of nearest neighbors. The energy differences between fee, hep, and bcc structures are very
small. The nature of the bonding and the electronic configuration also play important roles.