Lattice Dynamics and Interstitial Motion

Abstract

If an interstitial atom is introduced into a host crystal lattice, the surrounding host atoms will relax and thus lower the total energy. This relaxation energy, often called self — trapping energy, ranges typically from several 10eV for self interstitial atoms in metals to 0.1eV for H in Nb. This variation is roughly proportional to the square of the relative defect relaxation volume (ΔV/Vc), “size” of the defect. On the other hand, typical lattice vibration energies, e.g. the Debye energy kBΘD, are of the order of 0.01eV. Comparing these energies, we conclude that the interstitial atom and the host lattice will dynamically form a strongly coupled entity, even for the smaller interstitial atoms. This strong defect-host coupling in turn causes low — frequency resonant vibrational modes of the defect and its neighbours. These resonances are especially pronounced for the “large” self interstitial atoms [1] but have also been found for the “small” H in Nb [2]. The existence of resonant vibrations indicates a local softening of the lattice. One of the consequences of this softening are the low activation energies (Ea <0.1) found for interstitial atoms (in metals). In a simple-minded picture the activation energy can be approximated by $$ {E_a}\; \simeq \;\left( {1/8{\pi^2}} \right){G_d}^{{ - 1}} $$ (1) where d is the jump distance and Gd the static defect Green’s function in the jump direction.