Interaction of vacancies with substitutional solute atoms in alpha iron

The paper presents the results of ab initio calculations in WIEN2k package of binding energy of a vacancy in a iron with Pd, Ti, V and Cr impurity atoms located in the first, second and third spheres of coordination with respect to the vacancy. The binding energy reaches 0.3 eV for Pd and Cr being less than 0.1 eV for V and Cr. It is positive and monotonically decreases with increasing distance from the vacancy to Pd and Cr atoms, while for Ti and V atoms it is positive in the first and the third spheres of coordination and negative in the second sphere. A statistical and thermodynamic theory of vacancy formation in dilute substitutional solutions is proposed that takes into account the short-range interaction of vacancies with impurity atoms. Calculations show that palladium and titanium additions to a iron may lead to multiple increase of equilibrium vacancy concentration, while the effect of vanadium and chromium is much smaller.