1.01.4.1 Atomic Structure of Self-Interstitials

The accommodation of an additional atom within a perfect crystal lattice remained a topic of lively debates at international conferences on radiation effects for many decades. The leading question was the configuration of this interstitial atom and its surrounding atoms. This scientific question has now been resolved, and there is general agreement that this additional atom, a self-interstitial, forms a pair with one atom from the perfect lattice in the form of a dumbbell. The configuration of these dumbbells can be illustrated well with hard spheres, that is, atoms that repel each other like marbles.

Let us first consider the case of an fcc metal. In the perfect crystal, each atom is surrounded by 12 nearest neighbors that form a cage around it as shown on the left of Figure 13. When an extra atom is inserted in this cage, the two atoms in the center form a pair
whose axis is aligned in a [001] direction. This [001] dumbbell constitutes the self-interstitial in the fcc lattice. The centers of the 12 nearest neighbor atoms are the apexes of a cubo-octahedron that encloses the single central atom in the perfect lattice, and it can be shown19 that the cubo-octahedron encloses a volume of V0 = 10O/3. However, around a self-interstitial dumbbell, this cubo-octahedron expands and distorts, and now it encloses a larger volume of V001 = 4.435O. The volume expansion is the difference

DV = V001 — V0 = 1.10164O [28]

which happens to be larger than one atomic volume. We shall see shortly that the volume expansion of the entire crystal is even larger due to the elastic strain field created by the self-interstitial that extends through the entire solid.

We consider next the self-interstitial defect in a bcc metal. Here, each atom is surrounded in the perfect crystal by eight nearest neighbors as shown on the left of Figure 14. When an extra atom is inserted, it again forms a dumbbell configuration with another atom, and the dumbbell axis is now aligned in the [011] direction, as shown on the right of Figure 14. The cage formed by the eight nearest neighbor atoms becomes severely distorted. It is surprising, however, that the volume change of the cage is only

DV = 0.6418 O [29]

less than the volume ofthe inserted atom to create the self-interstitial in the bcc structure.

The reason for this is that the bcc structure does not produce the most densely packed arrangement of atoms, and some ofthe empty space can accommodate the self-interstitial. In contrast, the fcc structure has in fact the densest arrangement of atoms, and disturbing it by inserting an extra atom only creates disorder and lower packing density.

As already mentioned, the large inclusion volume DV of self-interstitials leads to a strain field

throughout the surrounding crystal that causes changes in lattice parameter and that is the major source of the formation energy for self-interstitials. In order to determine this strain field, we treat in Appendix A the case of spherical defects in the center of a spherical solid with isotropic elastic properties. Although this represents a rather simplified model for self-interstitials, for vacancies, and for complex clusters of such defects, it is a very instructive model that captures many essential features.