Page 137 - Materials Science and Engineering An Introduction

4.3 Impurities In Solids • 109

Figure 4.2 Two-dimensional schematic representations
of substitutional and interstitial impurity atoms.
(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, NY.
Reprinted by permission of John Wiley & Sons, Inc.)

Substitutional
impurity atom

Interstitial
impurity atom

Solid Solutions
A solid solution forms when, as the solute atoms are added to the host material, the
crystal structure is maintained and no new structures are formed. Perhaps it is useful
to draw an analogy with a liquid solution. If two liquids that are soluble in each other
(such as water and alcohol) are combined, a liquid solution is produced as the molecules
intermix, and its composition is homogeneous throughout. A solid solution is also com-
positionally homogeneous; the impurity atoms are randomly and uniformly dispersed
within the solid.
Impurity point defects are found in solid solutions, of which there are two types:
substitutional solid substitutional and interstitial. For the substitutional type, solute or impurity atoms re-
solution place or substitute for the host atoms (Figure 4.2). Several features of the solute and
solvent atoms determine the degree to which the former dissolves in the latter. These
interstitial solid are expressed as four Hume–Rothery rules, as follows:
solution
1. Atomic size factor. Appreciable quantities of a solute may be accommodated in
this type of solid solution only when the difference in atomic radii between the
two atom types is less than about 15%. Otherwise, the solute atoms create sub-
stantial lattice distortions and a new phase forms.
2. Crystal structure. For appreciable solid solubility, the crystal structures for metals
of both atom types must be the same.
3. Electronegativity factor. The more electropositive one element and the more elec-
tronegative the other, the greater the likelihood that they will form an intermetal-
lic compound instead of a substitutional solid solution.
4. Valences. Other factors being equal, a metal has more of a tendency to dissolve
another metal of higher valency than to dissolve one of a lower valency.
An example of a substitutional solid solution is found for copper and nickel. These
two elements are completely soluble in one another at all proportions. With regard to
Tutorial Video: the aforementioned rules that govern degree of solubility, the atomic radii for copper
Defects
What are and nickel are 0.128 and 0.125 nm, respectively; both have the FCC crystal structure; and
their electronegativities are 1.9 and 1.8 (Figure 2.9). Finally, the most common valences
the Differences
between Interstitial are 1 for copper (although it sometimes can be 2) and 2 for nickel.
and Substitutional For interstitial solid solutions, impurity atoms fill the voids or interstices among the
Solid Solutions? host atoms (see Figure 4.2). For both FCC and BCC crystal structures, there are two
types of interstitial sites—tetrahedral and octahedral—these are distinguished by the
number of nearest neighbor host atoms—that is, the coordination number. Tetrahedral