Page 141 - Materials Science and Engineering An Introduction

4.4 Specification of Composition • 113

C 1 = C 1 A 1 * 100 (4.7a)
Conversion of C 1 A 1 + C 2 A 2
atom percent to
weight percent (for
a two-element alloy) C 2 = C 2 A 2 * 100 (4.7b)
C 1 A 1 + C 2 A 2
Because we are considering only two elements, computations involving the preced-
ing equations are simplified when it is realized that
C 1 + C 2 = 100 (4.8a)
C 1 + C 2 = 100 (4.8b)
In addition, it sometimes becomes necessary to convert concentration from weight
percent to mass of one component per unit volume of material (i.e., from units of
3
wt% to kg/m ); this latter composition scheme is often used in diffusion computations
(Section 5.3). Concentrations in terms of this basis are denoted using a double prime
(i.e., C 1 and C 2 ), and the relevant equations are as follows:

C 1 = C 1 * 10 3 (4.9a)
£ C 1 C 2 ≥
+
Conversion of weight r 1 r 2
percent to mass per
unit volume (for a
two-element alloy) C 2
C 2 = * 10 3 (4.9b)
£ C 1 C 2 ≥
+
r 1 r 2
3
3
For density r in units of g/cm , these expressions yield C 1 and C 2 in kg/m .
Furthermore, on occasion we desire to determine the density and atomic weight of
Tutorial Video:
Weight Percent a binary alloy, given the composition in terms of either weight percent or atom percent.
If we represent alloy density and atomic weight by r ave and A ave , respectively, then
and Atom Percent
Calculations
r ave = 100 (4.10a)
C 1 C 2
Computation of +
density (for a two- r 1 r 2
element metal alloy)
C 1 A 1 + C 2 A 2
r ave = (4.10b)
C 1 A 1 C 2 A 2
+
r 1 r 2
100
A ave = (4.11a)
C 1 C 2
+
Computation of A 1 A 2
atomic weight (for a
two-element metal
alloy) C 1 A 1 + C 2 A 2
A ave = (4.11b)
100
It should be noted that Equations 4.9 and 4.11 are not always exact. In their deriva-
tions, it is assumed that total alloy volume is exactly equal to the sum of the volumes of
the individual elements. This normally is not the case for most alloys; however, it is a