Page 80 - Materials Science and Engineering An Introduction

WHY STUDY The Structure of Crystalline Solids?

The properties of some materials are directly related to Furthermore, significant property differences exist
their crystal structures. For example, pure and unde- between crystalline and noncrystalline materials hav-
formed magnesium and beryllium, having one crystal ing the same composition. For example, noncrystalline
structure, are much more brittle (i.e., fracture at lower ceramics and polymers normally are optically transparent;
degrees of deformation) than are pure and undeformed the same materials in crystalline (or semicrystalline) form
metals such as gold and silver that have yet another tend to be opaque or, at best, translucent.
crystal structure (see Section 7.4).

Learning Objectives
After studying this chapter, you should be able to do the following:
1. Describe the difference in atomic/molecular 5. Given three direction index integers, sketch the
structure between crystalline and noncrystalline direction corresponding to these indices within a
materials. unit cell.
2. Draw unit cells for face-centered cubic, body- 6. Specify the Miller indices for a plane that has
centered cubic, and hexagonal close-packed been drawn within a unit cell.
crystal structures. 7. Describe how face-centered cubic and hexagonal
3. Derive the relationships between unit cell edge close-packed crystal structures may be generated
length and atomic radius for face-centered cubic by the stacking of close-packed planes of atoms.
and body-centered cubic crystal structures. 8. Distinguish between single crystals and poly-
4. Compute the densities for metals having face- crystalline materials.
centered cubic and body-centered cubic crystal 9. Define isotropy and anisotropy with respect to
structures given their unit cell dimensions. material properties.

3.1 INTRODUCTION
Chapter 2 was concerned primarily with the various types of atomic bonding, which are
determined by the electron structures of the individual atoms. The present discussion
is devoted to the next level of the structure of materials, specifically, to some of the
arrangements that may be assumed by atoms in the solid state. Within this framework,
concepts of crystallinity and noncrystallinity are introduced. For crystalline solids, the
notion of crystal structure is presented, specified in terms of a unit cell. The three com-
mon crystal structures found in metals are then detailed, along with the scheme by which
crystallographic points, directions, and planes are expressed. Single crystals, polycrys-
talline materials, and noncrystalline materials are considered. Another section of this
chapter briefly describes how crystal structures are determined experimentally using
x-ray diffraction techniques.

Crystal Structures

3.2 FUNDAMENTAL CONCEPTS
Solid materials may be classified according to the regularity with which atoms or ions
crystalline are arranged with respect to one another. A crystalline material is one in which the
atoms are situated in a repeating or periodic array over large atomic distances—that is,
long-range order exists, such that upon solidification, the atoms will position themselves

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