Page 81 - Materials Science and Engineering An Introduction

3.3 Unit Cells • 53

(a) (b) (c)
Figure 3.1 For the face-centered cubic crystal structure, (a) a hard-sphere unit cell representation, (b) a reduced-
sphere unit cell, and (c) an aggregate of many atoms.
[Figure (c) adapted from W. G. Moffatt, G. W. Pearsall, and J. Wulff, The Structure and Properties of Materials, Vol. I, Structure,
p. 51. Copyright © 1964 by John Wiley & Sons, New York.]

in a repetitive three-dimensional pattern, in which each atom is bonded to its nearest-
neighbor atoms. All metals, many ceramic materials, and certain polymers form crystal-
line structures under normal solidification conditions. For those that do not crystallize,
this long-range atomic order is absent; these noncrystalline or amorphous materials are
discussed briefly at the end of this chapter.
crystal structure Some of the properties of crystalline solids depend on the crystal structure of the
material, the manner in which atoms, ions, or molecules are spatially arranged. There is
an extremely large number of different crystal structures all having long-range atomic
order; these vary from relatively simple structures for metals to exceedingly complex
ones, as displayed by some of the ceramic and polymeric materials. The present dis-
cussion deals with several common metallic crystal structures. Chapters 12 and 14 are
devoted to crystal structures for ceramics and polymers, respectively.
When crystalline structures are described, atoms (or ions) are thought of as be-
ing solid spheres having well-defined diameters. This is termed the atomic hard-sphere
model in which spheres representing nearest-neighbor atoms touch one another. An
example of the hard-sphere model for the atomic arrangement found in some of the
common elemental metals is displayed in Figure 3.1c. In this particular case all the atoms
lattice are identical. Sometimes the term lattice is used in the context of crystal structures; in
this sense lattice means a three-dimensional array of points coinciding with atom posi-
tions (or sphere centers).

3.3 UNIT CELLS
The atomic order in crystalline solids indicates that small groups of atoms form a repeti-
tive pattern. Thus, in describing crystal structures, it is often convenient to subdivide the
unit cell structure into small repeat entities called unit cells. Unit cells for most crystal structures
are parallelepipeds or prisms having three sets of parallel faces; one is drawn within the
aggregate of spheres (Figure 3.1c), which in this case happens to be a cube. A unit cell is