Ab initio prediction of vacancy properties in concentrated alloys

Abstract

Vacancy properties in concentrated alloys continue to be of great interest because nowadays ab initio supercell simulations reach a scale where even defect properties in disordered alloys appear to be within reach. We show that vacancy properties cannot generally be extracted from supercell total energies in a consistent manner without a statistical model. Essential features of such a model are knowledge of the chemical potential and imposition of invariants. In the present work, we derive the simplest model that satisfies these requirements and we compare it with models in the literature. As illustration we compute ab initio vacancy properties of fcc Cu-Ni alloys as a function of composition and temperature. Ab initio density functional calculations were performed for SQS supercells at various compositions with and without vacancies. Various methods of extracting alloy vacancy properties were examined. A ternary cluster expansion yielded effective cluster interactions (ECIs) for the Cu-Ni-Vac system. Composition and temperature dependent alloy vacancy concentrations were obtained using statistical thermodynamic models with the ab initio ECIs. An Arrhenius analysis showed that the heat of vacancy formation was well represented by a linear function of temperature. The positive slope of the temperature dependence implies a negative configurational entropy contribution to the vacancy formation free energy in the alloy. These findings can be understood by considering local coordination effects.