Example 5
For both $\mathrm{FCC}$ and $\mathrm{BCC}$ crystal structures there are two different types of interstitial sites. In each case, one site is larger than the other, and is normally occupied by impurity atoms. For FCC, this larger one is located at the center of each edge of the unit cell; it is termed an octahedral interstitial site. On the other hand, with BCC the larger site type is found at $0 \frac{1}{2} \frac{1}{4}$ positions - that is, lying on \{100\} faces, and situated midway between two unit cell edges on this face and one-quarter of the distance between the other two unit cell edges; it is termed a tetrahedral interstitial site. For both $\mathrm{FCC}$ and $\mathrm{BCC}$ crystal structures, compute the radius $r$ of an impurity atom that will just fit into one of these sites in terms of the atomic radius $R$ of the host atom.