Ab initioprediction of vacancy properties in concentrated alloys: The case of fcc Cu-Ni

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.

Thermal vacancies in random alloys in the single-site mean-field approximation

“…This contrasts with the results obtained in Ref. 10 where much smaller supercells have been used. From a general point of view, such a dependence should not exist in the macroscopic limit, unless a ghost of the removed atom is still in the site.…”

“…This topic has recently been recently attracted attention of several groups doing first-principles simulations. [7][8][9][10][11] In contrast to those investigations, in this work a simplified model for the energetics of vacancies will be presented for completely random alloys with the purpose to get a qualitative picture of the configurational effects.…”

“…Nowadays, it can be obtained in first-principles calculations using, for instance, the so-called "local cluster expansion". 7,10 If a supercell approach is used to determine local vacancy formation energies in random alloys, these effects can be naturally reproduced since the fluctuations of the local environment around each site are inevitable.…”

Perspectives on the Theory of Defects

“…Consequently, there is not just one vacancy formation energy but a range of these energies, depending on the local environment. A good example is the random alloy Cu 0.5 Ni 0.5 investigated in Ruban (2016) and Zhang and Sluiter (2015). Depending on the number of Ni atoms in the nearestneighbor shell, the vacancy formation energies range from 1.4eV (no Ni in the first coordination shell) to 2.4eV (only Ni in the first coordination shell) (Ruban, 2016): vacancies prefer to be surrounded by Cu atoms.…”

“…Dealing with such a wide range of vacancy formation energies means that a proper statistical model is needed (Zhang and Sluiter, 2015;Ruban, 2016). The reason is the following: At 0K, vacancies are created only at the lowest-energy sites.…”