IMPERFECTIONS IN SOLIDS

POINT DEFECTS IN METALS

The simplest of the point defects is a vacancy, or vacant lattice site, one normally occupied from which an atom is missing (Figure 1). All crystalline solids contain vacancies and, in fact, it is not possible to create such a material that is free of these defects,

 

FIGURE 1 Two-dimensional representations of a vacancy and a self-interstitial. (Adapted from W. G. Moffatt, G. W. Pearsall, and J. Wulff, The Structure and Properties of Materials, Vol. I, Structure, p. 77. Copyright © 1964 by John Wiley & Sons, New York. Reprinted by permission of John Wiley & Sons, Inc.)

A self-interstitial is an atom from the crystal that is crowded into an interstitial site, a small void space that under ordinary circumstances is not occupied.

POINT DEFECTS IN CERAMICS

The anion is relatively large, and to fit into a small interstitial position, substantial strains on the surrounding ions must be introduced. Anion and cation vacancies  and a cation interstitial are represented in Figure 2.

 FIGURE 2 Schematic representations of cation and anion vacancies and a cation interstitial.

The expression defect structure is often used to designate the types and concentrations of atomic defects in ceramics. Because the atoms exist as charged ions, when  defect structures are considered, conditions of electroneutrality must be maintained.

Electroneutrality is the state that exists when there are equal numbers of positive and negative charges from the ions. As a consequence, defects in ceramics do not occur alone. One such type of defect involves a cation–vacancy and a cation– interstitial pair. This is called a Frenkel defect (Figure 3). It might be thought of as being formed by a cation leaving its normal position and moving into an interstitial site. There is no change in charge because the cation maintains the same positive charge as an interstitial.

Another type of defect found inAXmaterials is a cation vacancy–anion vacancy pair known as a Schottky defect, also schematically diagrammed in Figure 3. This defect might be thought of as being created by removing one cation and one anion from the interior of the crystal and then placing them both at an external surface. Since both cations and anions have the same charge, and since for every anion vacancy there exists a cation vacancy, the charge neutrality of the crystal is maintained.

 FIGURE 3 Schematic diagram showing Frenkel and Schottky defects in ionic solids. (From W. G. Moffatt, G. W. Pearsall, and J. Wulff, The Structure and Properties of Materials, Vol. 1, Structure, p. 78. Copyright © 1964 by John Wiley & Sons, New York. Reprinted by permission of John Wiley & Sons, Inc.)

MISCELLANEOUS IMPERFECT IONS

DISLOCATIONS—LINEAR DEFECTS

A dislocation is a linear or one-dimensional defect around which some of the atoms are misaligned. One type of  dislocation is represented in Figure 4: an extra portion of a plane of atoms, or half-plane, the edge of which terminates within the crystal. This is termed an edge dislocation; it is a linear defect that centers around the line that is defined along the end of the extra half-plane of atoms.

  FIGURE 4 The atom positions around an edge dislocation; extra half-plane of atoms shown in perspective. (Adapted from A. G. Guy, Essentials of Materials Science, McGraw-Hill Book Company, New York, 1976, p. 153.)

Another type of dislocation, called a screw dislocation, exists, which may be thought of as being formed by a shear stress that is applied to produce the distortion shown in Figure 5: the upper front region of the crystal is shifted one atomic distance to the right relative to the bottom portion.

 FIGURE 5 (a) A screw dislocation within a crystal. (b) The screw dislocation in (a) as viewed from above. The dislocation line extends  along line AB. Atom positions above the slip plane are designated by open circles, those below by solid circles. (Figure (b) from W. T. Read, Jr., Dislocations in Crystals, McGraw-Hill Book Company, New York, 1953.)

INTERFACIAL DEFECTS

Interfacial defects are boundaries that have two dimensions and normally separate regions of the materials that have different crystal structures and/or crystallographic orientations. These imperfections include external surfaces, grain boundaries, twin boundaries, stacking faults, and phase boundaries.
 

EXTERNAL SURFACES

One of the most obvious boundaries is the external surface, along which the crystal structure terminates. Surface atoms are not bonded to the maximum number of nearest neighbors, and are therefore in a higher energy state than the atoms at interior positions.

GRAIN BOUNDARIES

Another interfacial defect, the grain boundary,  as the boundary separating two small grains or crystals having different crystallographic orientations in polycrystalline materials.

FIGURE 6 Schematic diagram showing lowand high-angle grain boundaries and the adjacent atom positions.

TWIN BOUNDARIES

A twin boundary is a special type of grain boundary across which there is a specific mirror lattice symmetry; that is, atoms on one side of the boundary are located in mirror image positions of the atoms on the other side. The region of material between these boundaries is appropriately termed a twin. Twins result from atomic displacements that are produced from applied mechanical shear forces (mechanical twins), and also during annealing heat treatments following deformation (annealing twins).

FIGURE 7  Schematic diagram showing a twin plane or boundary and the adjacent atom positions (dark circles).