Hydrogen–vacancy interaction in bcc iron: ab initio calculations and thermodynamics

Abstract

The paper presents results of ab initio modelling of formation energies of vacancy–hydrogen complexes VHn and an extended variant of thermodynamic theory describing equilibrium concentrations of such complexes. A single H atom is shifted from vacancy to a neighbouring O-site by 1.19 Å. Two H atoms in a vacancy form a dumbbell with H–H distance of 2.38 Å being much greater than in H2 molecule. Configurations of three, four and five H atoms in a vacancy are more complex, and H–H distances gradually increase showing repulsion between hydrogen atoms. Binding energy of a VHn−1 complex with the next hydrogen atom to form VHn is 0.60, 0.61, 0.39, 0.37 and 0.31 for n = 1–5, which is close to other researchers’ data. These results were used to construct an improved variant of thermodynamic description of vacancy–hydrogen interaction in a bcc solid solution taking into account both binding energies and hydrogen atom configurations in different VHn complexes. Calculations show that at low temperatures most vacancies are bound to several hydrogen atoms, and the equilibrium concentration of vacancies themselves significantly increases, in accordance with existing experiments.