GTBL042-03 GTBL042-Callister-v2 September 6, 2007 15:33
90 • Chapter 3 / Structures of Metals and CeramicsMetallic Crystal Structures
Most common metals exist in at least one of three relatively simple crystal structures:
face-centered cubic (FCC), body-centered cubic (BCC), and hexagonal close-packed
(HCP). Two features of a crystal structure are coordination number (or number of
nearest-neighbor atoms) and atomic packing factor (the fraction of solid sphere
volume in the unit cell). Coordination number and atomic packing factor are the
same for both FCC and HCP crystal structures.Ceramic Crystal Structures
Density Computations—Ceramics
For ceramics both crystalline and noncrystalline states are possible. The crystal struc-
tures of those materials for which the atomic bonding is predominantly ionic are
determined by the charge magnitude and the radius of each kind of ion. Some of the
simpler crystal structures are described in terms of unit cells; several of these were
discussed (rock salt, cesium chloride, zinc blende, diamond cubic, graphite, fluorite,
perovskite, and spinel structures).
Theoretical densities of metallic and crystalline ceramic materials may be com-
puted from unit cell and atomic weight data.Close-Packed Crystal Structures
Generation of face-centered cubic and hexagonal close-packed crystal structures is
possible by the stacking of close-packed planes of atoms. For some ceramic crystal
structures, cations fit into interstitial positions that exist between two adjacent close-
packed planes of anions.Silicate Ceramics
Carbon
For the silicates, structure is more conveniently represented by means of inter-
connecting SiO^44 −tetrahedra. Relatively complex structures may result when other
cations (e.g., Ca^2 +,Mg^2 +,Al^3 +) and anions (e.g., OH−) are added. The structures
of silica (SiO 2 ), silica glass, and several of the simple and layered silicates were pre-
sented.
Structures for the various forms of carbon—diamond, graphite, the fullerenes,
and carbon nanotubes—were also discussed.Point Coordinates
Crystallographic Directions
Crystallographic Planes
Crystallographic points, directions, and planes are specified in terms of indexing
schemes. The basis for the determination of each index is a coordinate axis system
defined by the unit cell for the particular crystal structure. The location of a point
within a unit cell is specified using coordinates that are fractional multiples of the
cell edge lengths. Directional indices are computed in terms of the vector projection
on each of the coordinate axes, whereas planar indices are determined from the
reciprocals of axial intercepts. For hexagonal unit cells, a four-index scheme for both
directions and planes is found to be convenient.