Page 140 - Materials Science and Engineering An Introduction

112 • Chapter 4 / Imperfections in Solids

contains two hypothetical atoms denoted by 1 and 2, the concentration of 1 in wt%,
C 1 , is defined as

Computation of m 1 (4.3a)
weight percent (for a C 1 = * 100
two-element alloy) m 1 + m 2
where m 1 and m 2 represent the weight (or mass) of elements 1 and 2, respectively. The
concentration of 2 is computed in an analogous manner. 6
atom percent The basis for atom percent (at%) calculations is the number of moles of an element
in relation to the total moles of the elements in the alloy. The number of moles in some
specified mass of a hypothetical element 1, n m1 , may be computed as follows:

m 1
n m1 = (4.4)
A 1
Here, m 1 and A 1 denote the mass (in grams) and atomic weight, respectively, for element 1.
Concentration in terms of atom percent of element 1 in an alloy containing element
1 and element 2 atoms, C 1 is defined by 7

Computation of n m1
atom percent (for a C 1 = * 100 (4.5a)
two-element alloy) n m1 + n m2
In like manner, the atom percent of element 2 is determined. 8
Atom percent computations also can be carried out on the basis of the number of
atoms instead of moles, because one mole of all substances contains the same number
of atoms.
Composition Conversions
Sometimes it is necessary to convert from one composition scheme to another—for
example, from weight percent to atom percent. We next present equations for making
these conversions in terms of the two hypothetical elements 1 and 2. Using the conven-
tion of the previous section (i.e., weight percents denoted by C 1 and C 2 , atom percents
by C 1 and C 2 , and atomic weights as A 1 and A 2 ), we express these conversion equations
as follows:

C 1 A 2
C 1 = * 100 (4.6a)
Conversion of C 1 A 2 + C 2 A 1
weight percent to
atom percent (for a
two-element alloy) C 2 = C 2 A 1 * 100 (4.6b)
C 1 A 2 + C 2 A 1

6 When an alloy contains more than two (say n) elements, Equation (4.3a) takes the form

C 1 = m 1 * 100 (4.3b)
m 1 + m 2 + m 3 + c + m n
7 In order to avoid confusion in notations and symbols being used in this section, we should point out that the prime
(as in C 1 and m 1 ) is used to designate both composition in atom percent and mass of material in grams.
8 When an alloy contains more than two (say n) elements, Equation (4.5a) takes the form

C 1 = n m1 * 100 (4.5b)
n m1 + n m2 + n m3 + g + n mn