Page 139 - Materials Science and Engineering An Introduction

4.4 Specification of Composition • 111

strains, the atom just touches the two adjacent host atoms, which 4R
are corner atoms of the unit cell. The drawing shows atoms on √ 3
the (100) face of a BCC unit cell; the large circles represent the
host atoms—the small circle represents an interstitial atom that R R
is positioned in an octahedral site on the cube edge. 2r
On this drawing is noted the unit cell edge length—the
distance between the centers of the corner atoms—which, from
Equation 3.4, is equal to

4R
Unit cell edge length =
13
Also shown is that the unit cell edge length is equal to two times
the sum of host atomic radius 2R plus twice the radius of the interstitial atom 2r; i.e.,
Unit cell edge length = 2R + 2r
Now, equating these two unit cell edge length expressions, we get

4R
2R + 2r =
13
and solving for r in terms of R
4R 2
2r = - 2R = a - 1b(2R)
13 13
or
2
r = a - 1bR = 0.155R
13

Concept Check 4.1 Is it possible for three or more elements to form a solid solution?
Explain your answer.

[The answer may be found at www.wiley.com/college/callister (Student Companion Site)].

Concept Check 4.2 Explain why complete solid solubility may occur for substitutional
solid solutions but not for interstitial solid solutions.

[The answer may be found at www.wiley.com/college/callister (Student Companion Site)].

4.4 SPECIFICATION OF COMPOSITION
5
composition It is often necessary to express the composition (or concentration) of an alloy in terms
of its constituent elements. The two most common ways to specify composition are
weight percent weight (or mass) percent and atom percent. The basis for weight percent (wt%) is
the weight of a particular element relative to the total alloy weight. For an alloy that

5 The terms composition and concentration will be assumed to have the same meaning in this book (i.e., the relative
content of a specific element or constituent in an alloy) and will be used interchangeably.