Interaction of Si, Ge, and Be solutes with vacancies and interstitials in Ni

Abstract

The solute-vacancy and the solute-interstitial binding energies for Si, Ge, and Be solutes in Ni matrix have been calculated, using the results of an augmented-plane-wave calculation of the electronic structure of the solute and the solvent atoms. The electronic wave function of the solute is expressed in terms of the wave functions of the unperturbed host lattice. This allows the partial densities of states (DOS) of different angular momentum type at the solute site to be written in terms of those at the solvent atom site and their energy-dependent phase shifts. It is found that the $d$ electron DOS which is large and dominant at the Ni site is rather small at the solute site for all the solutes studied here. At the Si and Ge sites the $p$ DOS is dominant while at the Be site both $s$ and $p$ components are important. The excess charge density displaced by the solute and the potential associated with it show the oscillatory behavior. The $3s$ and $4s$ electrons of Si and Ge, respectively, form bound states below the bottom of the Ni conduction band. These states influence in a profound manner the interaction of these solutes with both vacancies and interstitials. No bound state is formed in the case of Be, where the scattering states in the conduction band are the sole contributors to the interaction energy. We have found that Ge, even though oversized, has a positive binding energy of 0.28 eV with the interstitial in the mixed dumbbell configuration. The undersized Si and Be form mixed dumbbells with binding energies of 0.90 and 0.58 eV, respectively. Contrary to usual expectations the vacancy-solute binding is calculated to be rather strong, 0.73 and 0.55 eV, respectively, for Si and Ge in the nearest-neighbor vacancy-solute configuration. The corresponding interaction with Be is found to be repulsive with a binding energy of -0.32 eV.