First-principles study of interaction energies of atomic defects in bcc ferromagnetic iron

Abstract

A comprehensive calculation of the solute formation energies, solute-solute and vacancy-solute binding energies in bcc iron is reported. An extended set of solutes with atomic numbers 1 to 54 has been considered. We used the projector augmented wave method of density functional theory with the generalized gradient approximation for the exchange-correlation energy functional. The prominent results are the following: (1) formation energies of solutes from fourth and fifth periods vary with their atomic numbers such that they reach maxima near the ends of the periods and a minimum in between, with a local increase near Cu and Ag (like a quasiparabolic valley). Solutes from second and third periods show similar trend like the elements near the ends of the fourth and fifth periods. (2) The size factors of the solutes also show similar variation with their atomic numbers like their formation energies. These trends corroborate the relatively smaller formation energies and size factors of the common alloying additions to Fe (such as $3d,4d$, and $sp$ elements) as compared to solutes that lack solubility (such as Li, Na, K, Rb, He, Ne, Ar, Kr, Xe, F, Cl, Br, I, Mg, Ca, Sr, Ag, Cd, In, Y). (3) The solubilities estimated from our formation energies are found to be in reasonable agreement with those from the phase diagram database. (4) Solute-solute and vacancy-solute binding energies are found to vary with the atomic number of the solutes in a manner inverse to solute formation energies and solute size factors, reaching strong binding energies near the ends of the periods which generally include the insoluble elements. (5) Another trend revealed by our work is that the size factors of isoelectronic sets of solutes increase down the groups with associated increase of formation energies, and strength of solute-solute and vacancy-solute binding energies. (6) A significant correlation is found between our vacancy-solute binding energies of $3d$ and $4d$ elements and the corresponding diffusion coefficients from literature whereby solutes with strong binding energies have higher diffusion coefficients and vice versa.