Callister - An introduction - 8th edition

98 • Chapter 4 / Imperfections in Solids
M¿ m¿ 1 m¿ 2
(4.12)
Using the definition of C¿ 1 (Equation 4.5) and incorporating the expression
for n m1 , Equation 4.4, and the analogous expression for n m2 yields
C¿ 1
n m1
n m1 n m2
100
m¿ 1
A 1
m¿ 1
A 1
m¿ 2
A 2
100
Rearrangement of the mass-in-grams equivalent of Equation 4.3 leads to
m¿ 1 C 1M¿
100
(4.13)
(4.14)
Substitution of this expression and its m¿ 2 equivalent into Equation 4.13 gives
C 1 M¿
C¿ 1
Upon simplification we have
100A 1
C 1 M¿
100A 1
C 2M¿
100A 2
100
(4.15)
C¿ 1
which is identical to Equation 4.6a.
C 1 A 2
C 1 A 2 C 2 A 1
100
EXAMPLE PROBLEM 4.3
Composition Conversion—From Weight Percent to Atom
Percent
Determine the composition, in atom percent, of an alloy that consists of
97 wt% aluminum and 3 wt% copper.
Solution
If we denote the respective weight percent compositions as C Al 97 and
C Cu 3, substitution into Equations 4.6a and 4.6b yields
C¿ Al
C Al A Cu
C Al A Cu C Cu A Al
100
1972163.55 g/mol2
1972163.55 g/mol2 132126.98 g/mol2 100
and
98.7 at%