Fundamentals of Materials Science and Engineering: An Integrated Approach, 3e

GTBL042-03 GTBL042-Callister-v2 September 6, 2007 15:33

3.16 Close-Packed Crystal Structures • 79

Tetrahedral Octahedral

Figure 3.32 The stacking of one plane of close-packed (orange) spheres (anions) on top of

another (blue spheres); the geometries of tetrahedral and octahedral positions between the

planes are noted. (From W. G. Moffatt, G. W. Pearsall, and J. Wulff,The Structure and

Properties of Materials,Vol. I,Structure.Copyright©c1964 by John Wiley & Sons, New

York. Reprinted by permission of John Wiley & Sons, Inc.)

Ceramics

VMSE A number of ceramic crystal structures may also be considered in terms of close-

Close-packed

Structures

packed planes of ions (as opposed toatomsfor metals). Ordinarily, the close-packed

planes are composed of the large anions. As these planes are stacked atop each other,

small interstitial sites are created between them in which the cations may reside.

These interstitial positions exist in two different types, as illustrated in Figure

3.32. Four atoms (three in one plane, and a single one in the adjacent plane) surround

tetrahedral position one type; this is termed atetrahedral position,since straight lines drawn from the

centers of the surrounding spheres form a four-sided tetrahedron. The other site

type in Figure 3.32, involves six ion spheres, three in each of the two planes. Because

an octahedron is produced by joining these six sphere centers, this site is called an

octahedral position octahedral position.Thus, the coordination numbers for cations filling tetrahedral

and octahedral positions are 4 and 6, respectively. Furthermore, for each of these

anion spheres, one octahedral and two tetrahedral positions will exist.

Ceramic crystal structures of this type depend on two factors: (1) the stacking of

the close-packed anion layers (both FCC and HCP arrangements are possible, which

correspond toABCABC... andABABAB... sequences, respectively), and (2) the

manner in which the interstitial sites are filled with cations. For example, consider the

rock salt crystal structure discussed above. The unit cell has cubic symmetry, and each

cation (Na+ion) has six Cl−ion nearest neighbors, as may be verified from Figure 3.5.

That is, the Na+ion at the center has as nearest neighbors the six Cl−ions that reside

at the centers of each of the cube faces. The crystal structure, having cubic symmetry,

may be considered in terms of an FCC array of close-packed planes of anions, and all

planes are of the{ 111 }type. The cations reside in octahedral positions because they

have as nearest neighbors six anions. Furthermore, all octahedral positions are filled,

since there is a single octahedral site per anion, and the ratio of anions to cations is

1:1. For this crystal structure, the relationship between the unit cell and close-packed

anion plane stacking schemes is illustrated in Figure 3.33.

Other, but not all, ceramic crystal structures may be treated in a similar manner;

VMSE

Close-packed

Structures

Generate Spinal

Structure

included are the zinc blende and perovskite structures. Thespinel structureis one of

the AmBnXptypes, which is found for magnesium aluminate or spinel (MgAl 2 O 4 ).

With this structure, the O^2 −ions form an FCC lattice, whereas Mg^2 +ions fill tetrahe-

dral sites and Al^3 +reside in octahedral positions. Magnetic ceramics, or ferrites, have