Page 138 - Materials Science and Engineering An Introduction

110 • Chapter 4 / Imperfections in Solids

Figure 4.3 Octahedral
Locations of 0 1 1
tetrahedral and 1 1 1 2
octahedral interstitial 2 2 2
sites within (a) FCC
and (b) BCC unit
cells. Tetrahedral
Tetrahedral
1 3 1 1 1 1
4 4 4 2 4
1 1 0
2
Octahedral
(a) (b)

sites have a coordination number of 4; straight lines drawn from the centers of the sur-
rounding host atoms form a four-sided tetrahedron. However, for octahedral sites the
coordination number is 6; an octahedron is produced by joining these six sphere cent-
3
ers. For FCC, there are two types of octahedral sites with representative point coordi-
1
1 1 1
nates of 0 1 and . Representative coordinates for a single tetrahedral site type are
2 2 2
2
1 3 1 4
. Locations of these sites within the FCC unit cell are noted in Figure 4.3a. One type
4 4 4
of each of octahedral and tetrahedral interstitial sites is found for BCC. Representative
1 1
1
coordinates are as follows: octahedral, 1 0 and tetrahedral, 1 . Figure 4.3b shows the
2 4
2
positions of these sites within a BCC unit cell. 4
Metallic materials have relatively high atomic packing factors, which means that
these interstitial positions are relatively small. Consequently, the atomic diameter of an
interstitial impurity must be substantially smaller than that of the host atoms. Normally,
the maximum allowable concentration of interstitial impurity atoms is low (less than
10%). Even very small impurity atoms are ordinarily larger than the interstitial sites,
and as a consequence, they introduce some lattice strains on the adjacent host atoms.
Problems 4.8 and 4.9 call for determination of the radii of impurity atoms r (in terms of
R, the host atom radius) that just fit into tetrahedral and octahedral interstitial positions
of both BCC and FCC without introducing any lattice strains.
Carbon forms an interstitial solid solution when added to iron; the maximum con-
centration of carbon is about 2%. The atomic radius of the carbon atom is much less
than that of iron: 0.071 nm versus 0.124 nm.
Solid solutions are also possible for ceramic materials, as discussed in Section 12.5.
EXAMPLE PROBLEM 4.2

Computation of Radius of BCC Interstitial Site
Compute the radius r of an impurity atom that just fits into a BCC octahedral site in terms of
the atomic radius R of the host atom (without introducing lattice strains).
Solution
As Figure 4.3b notes, for BCC, the octahedral interstitial site is situated at the center of a unit
cell edge. In order for an interstitial atom to be positioned in this site without introducing lattice

3 The geometries of these site types may be observed in Figure 12.7.
4 Other octahedral and tetrahedral interstices are located at positions within the unit cell that are equivalent to these
representative ones.