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

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

Important Terms and Concepts • 91

Linear and Planar Densities

Crystallographic directional and planar equivalencies are related to atomic linear and

planar densities, respectively. The atomic packing (i.e., planar density) of spheres in

a crystallographic plane depends on the indices of the plane as well as the crystal

structure. For a given crystal structure, planes having identical atomic packing yet

different Miller indices belong to the same family.

Single Crystals

Polycrystalline Materials

Single crystals are materials in which the atomic order extends uninterrupted over

the entirety of the specimen; under some circumstances, they may have flat faces

and regular geometric shapes. The vast majority of crystalline solids, however, are

polycrystalline, being composed of many small crystals or grains having different

crystallographic orientations.

Crystal Systems

Polymorphism and Allotropy

Anisotropy

Noncrystalline Solids

Other concepts introduced in this chapter were: crystal system (a classification

scheme for crystal structures on the basis of unit cell geometry); polymorphism

(or allotropy) (when a specific material can have more than one crystal structure);

anisotropy (the directionality dependence of properties), and noncrystalline solids

[solid materials (including the silica glasses) for which there is an absence of long-

range atomic regularity or order].

X-Ray Diffraction: Determination of Crystal Structures

X-ray diffractometry is used for crystal structure and interplanar spacing determina-

tions. A beam of x-rays directed on a crystalline material may experience diffraction

(constructive interference) as a result of its interaction with a series of parallel atomic

planes according to Bragg’s law. Interplanar spacing is a function of the Miller indices

and lattice parameter(s) as well as the crystal structure.

IMPORTANT TERMS AND CONCEPTS

Allotropy

Amorphous

Anion

Anisotropy

Atomic packing factor (APF)

Body-centered cubic (BCC)

Bragg’s law

Cation

Coordination number

Crystal structure

Crystal system

Crystalline

Diffraction

Face-centered cubic (FCC)

Grain

Grain boundary

Hexagonal close-packed (HCP)

Isotropic

Lattice

Lattice parameters

Miller indices

Noncrystalline

Octahedral position

Polycrystalline

Polymorphism

Single crystal

Tetrahedral position

Unit cell