Page 150 - Materials Science and Engineering An Introduction

122 • Chapter 4 / Imperfections in Solids

material between these boundaries is appropriately termed a twin. Twins result from
atomic displacements that are produced from applied mechanical shear forces (mechan-
Tutorial Video: ical twins) and also during annealing heat treatments following deformation (annealing
Defects twins). Twinning occurs on a definite crystallographic plane and in a specific direction,
Differences among both of which depend on the crystal structure. Annealing twins are typically found in
Point, Linear, and metals that have the FCC crystal structure, whereas mechanical twins are observed in
Interfacial Defects
BCC and HCP metals. The role of mechanical twins in the deformation process is dis-
cussed in Section 7.7. Annealing twins may be observed in the photomicrograph of the
polycrystalline brass specimen shown in Figure 4.14c. The twins correspond to those
regions having relatively straight and parallel sides and a different visual contrast than
the untwinned regions of the grains within which they reside. An explanation for the
variety of textural contrasts in this photomicrograph is provided in Section 4.10.

Miscellaneous Interfacial Defects
Other possible interfacial defects include stacking faults and ferromagnetic domain
walls. Stacking faults are found in FCC metals when there is an interruption in the
ABCABCABC . . . stacking sequence of close-packed planes (Section 3.12). For ferromag-
netic and ferrimagnetic materials, the boundary that separates regions having different
directions of magnetization is termed a domain wall, which is discussed in Section 20.7.

Associated with each of the defects discussed in this section is an interfacial energy, the
magnitude of which depends on boundary type, and which varies from material to material.
Normally, the interfacial energy is greatest for external surfaces and least for domain walls.

Concept Check 4.3 The surface energy of a single crystal depends on crystallographic ori-
entation. Does this surface energy increase or decrease with an increase in planar density? Why?

[The answer may be found at www.wiley.com/college/callister (Student Companion Site).]

4.7 BULK OR VOLUME DEFECTS
Other defects exist in all solid materials that are much larger than those heretofore
discussed. These include pores, cracks, foreign inclusions, and other phases. They are
normally introduced during processing and fabrication steps. Some of these defects and
their effects on the properties of materials are discussed in subsequent chapters.

4.8 ATOMIC VIBRATIONS
Every atom in a solid material is vibrating very rapidly about its lattice position within
atomic vibration the crystal. In a sense, these atomic vibrations may be thought of as imperfections or de-
fects. At any instant of time, not all atoms vibrate at the same frequency and amplitude
or with the same energy. At a given temperature, there exists a distribution of energies
for the constituent atoms about an average energy. Over time, the vibrational energy of
any specific atom also varies in a random manner. With rising temperature, this average
energy increases, and, in fact, the temperature of a solid is really just a measure of the
average vibrational activity of atoms and molecules. At room temperature, a typical vi-
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brational frequency is on the order of 10 vibrations per second, whereas the amplitude
is a few thousandths of a nanometer.
Many properties and processes in solids are manifestations of this vibrational
atomic motion. For example, melting occurs when the vibrations are vigorous enough to
rupture large numbers of atomic bonds. A more detailed discussion of atomic vibrations
and their influence on the properties of materials is presented in Chapter 19.