Elastic calculation of self-interstitial formation energies in fcc metals

An elastic calculation of self-interstitial formation energies in fcc metals is presented. The formation energy of an interstitial is identified with the elastic deformation energy inside an infinite crystal containing an extra atom. The following configurations of interstitials in fcc metals are analyzed: octahedral and tetrahedral single interstitials and single $〈100〉$, $〈110〉$, and $〈111〉$ splits. The deformation resulting from the insertion of an extra atom into the metallic lattice consists of two distinct parts: the deformation of the interstitial atom (eventually, in a split configuration, the deformation of an interstitial atomic pair), and the deformation of the region adjacent to the occupied interstitial site. In the first ("inner") region the local volume change is relatively significant, whereas in the second ("outer") region the deformation is merely a shear deformation with a zero average volume change (at least for an infinite crystal). The linear Hooke's approximation becomes insufficient for the inner region, and a pressure dependence of the lattice elastic constants has to be introduced explicitly. The formation energies calculated here for different interstitial configurations are more differentiated than those reported elsewhere. The calculation corroborates the conclusion that in fcc metals a split $〈100〉$-type interstitial has the lowest formation energy among interstitial configurations. Experimental data about interstitial formation energies in fcc are very scarce, but the agreement of the calculation with them can be considered as very good.