Pseudopotential theory for self-diffusion and impurity diffusion: Defect-energy calculations for fcc metals

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Abstract
Generalized formulations for the calculation of energies of multivacancy formation and migration in pure and impure lattices and a multi-interstitial formation in otherwise pure lattices have been obtained with use of a pseudopotential scheme. The energies caused by relaxations of the surrounding neighbors are incorporated in these processes. Formulas relating self-diffusion and impurity diffusion via a vacancy mechanism have been discussed. Calculations of the vacancy-formation energy, the migration energy, and hence the activation energy for self-diffusion and impurity diffusion and their changes have been done with use of standard model potentials. My calculations show that the effect of relaxations of the surrounding neighbors of the migrating atom at its activated position is significant while it has negligible effect in vacancy-formation process. The calculations also show that a Heine-Abarenkov model explains successfully all the defect parameters but the Aschroft model does not. A more sophisticated multiparameter model or the Heine-Abarenkov two-parameter model with approximate explanation of all the atomic properties is perhaps a better choice. It is also noted that careful numerical computation is essential for achieving satisfactory agreement with experiment.