Page 147 - Materials Science and Engineering An Introduction

4.6 Interfacial Defects • 119

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.
The bonds of these surface atoms that are not satisfied give rise to a surface energy,
2
expressed in units of energy per unit area (J/m 2 or erg/cm ). To reduce this energy,
materials tend to minimize, if at all possible, the total surface area. For example, liquids
assume a shape having a minimum area—the droplets become spherical. Of course, this
is not possible with solids, which are mechanically rigid.

Grain Boundaries
Another interfacial defect, the grain boundary, was introduced in Section 3.14 as the
boundary separating two small grains or crystals having different crystallographic orien-
tations in polycrystalline materials. A grain boundary is represented schematically from
an atomic perspective in Figure 4.8. Within the boundary region, which is probably just
several atom distances wide, there is some atomic mismatch in a transition from the
crystalline orientation of one grain to that of an adjacent one.
Various degrees of crystallographic misalignment between adjacent grains are
possible (Figure 4.8). When this orientation mismatch is slight, on the order of a few
degrees, then the term small- (or low-) angle grain boundary is used. These boundaries
can be described in terms of dislocation arrays. One simple small-angle grain boundary
is formed when edge dislocations are aligned in the manner of Figure 4.9. This type is
called a tilt boundary; the angle of misorientation, u, is also indicated in the figure. When
the angle of misorientation is parallel to the boundary, a twist boundary results, which
can be described by an array of screw dislocations.
The atoms are bonded less regularly along a grain boundary (e.g., bond angles are
longer), and consequently there is an interfacial or grain boundary energy similar to the
surface energy just described. The magnitude of this energy is a function of the degree of mi-
sorientation, being larger for high-angle boundaries. Grain boundaries are more chemically
reactive than the grains themselves as a consequence of this boundary energy. Furthermore,
impurity atoms often preferentially segregate along these boundaries because of their higher

Angle of misalignment Figure 4.8 Schematic diagram showing small-
and high-angle grain boundaries and the adjacent
atom positions.

High-angle
grain boundary

Small-angle
grain boundary

Angle of misalignment