Page 136 - Materials Science and Engineering An Introduction

108 • Chapter 4 / Imperfections in Solids

EXAMPLE PROBLEM 4.1

Number-of-Vacancies Computation at a Specified Temperature
Calculate the equilibrium number of vacancies per cubic meter for copper at 1000 C. The
energy for vacancy formation is 0.9 eV/atom; the atomic weight and density (at 1000 C) for
3
copper are 63.5 g/mol and 8.4 g/cm , respectively.
Solution
This problem may be solved by using Equation 4.1; it is first necessary, however, to determine
the value of N—the number of atomic sites per cubic meter for copper, from its atomic weight
A Cu , its density r, and Avogadro’s number N A , according to
Number of N A r
atoms per N = (4.2)
unit volume A Cu
for a metal
6
23
3
3
3
(6.022 * 10 atoms/mol)(8.4 g/cm )(10 cm /m )
=
63.5 g/mol
28
= 8.0 * 10 atoms/m 3
Thus, the number of vacancies at 1000 C (1273 K) is equal to
Tutorial Video Q y
N y = N expa - b
kT
(0.9 eV)
3
28
= (8.0 * 10 atoms/m ) expc - d
-5
(8.62 * 10 eV/K)(1273 K)
25
= 2.2 * 10 vacancies/m 3
4.3 IMPURITIES IN SOLIDS

A pure metal consisting of only one type of atom just isn't possible; impurity or foreign
atoms are always present, and some exist as crystalline point defects. In fact, even with
relatively sophisticated techniques, it is difficult to refine metals to a purity in excess
of 99.9999%. At this level, on the order of 10 22 to 10 23 impurity atoms are present in
alloy 1 m 3 of material. Most familiar metals are not highly pure; rather, they are alloys, in
which impurity atoms have been added intentionally to impart specific characteristics
to the material. Ordinarily, alloying is used in metals to improve mechanical strength
and corrosion resistance. For example, sterling silver is a 92.5% silver/7.5% copper al-
loy. In normal ambient environments, pure silver is highly corrosion resistant, but also
very soft. Alloying with copper significantly enhances the mechanical strength without
depreciating the corrosion resistance appreciably.
solid solution The addition of impurity atoms to a metal results in the formation of a solid solution
and/or a new second phase, depending on the kinds of impurity, their concentrations,
and the temperature of the alloy. The present discussion is concerned with the notion
of a solid solution; treatment of the formation of a new phase is deferred to Chapter 9.
Several terms relating to impurities and solid solutions deserve mention. With re-
solute, solvent gard to alloys, solute and solvent are terms that are commonly employed. Solvent is the
element or compound that is present in the greatest amount; on occasion, solvent atoms
are also called host atoms. Solute is used to denote an element or compound present in
a minor concentration.