Vacancy formation energy in CuNiCo equimolar alloy and CuNiCoFe high entropy alloy: ab initio based study

In this research, the interaction between the composing elements of CuNiCoFe high entropy alloy with vacancies was investigated employing EMTO-LSGF and EMTO-CPA codes based on DFT calculations. In this regard, for the equimolar CuNiCo and CuNiCoFe alloys with the face center cubic structure, variation of vacancy formation energy was calculated as a function of the number of the nearest neighbors of composing elements. The results reveal that copper atoms have the strongest interaction with vacancy among all elements in both CuNiCo and CuNiCoFe equimolar alloys. The mean local vacancy formation energy (< E-f >) was calculated based on its distribution function for both alloys. Since the differences between the interaction energy of Cu-vacancy and other metal-vacancies in these two equimolar alloys was significant, to calculate the distribution function of vacancy formation energy and its dependence to temperature, equimolar CuNiCo and CuNiCoFe were estimated by a quasi-binary alloy. In this quasi-binary alloy copper is one of the components and other elements could be other components. The results show that < E-f > of equimolar CuNiCoFe is 0.176 eV greater than that for CuNiCo equimolar alloy. The dependence of effective vacancy formation energy ((E) over bar (f)) and renormalized vacancy formation energy ((E) over tilde (f) ) to temperature is estimated using the single-site mean field approximations with energy parameters obtained in ab initio calculations. In these calculations, the alloy configurational entropy was used. The results indicate higher (E) over bar (f) and (E) over tilde (f) values with increasing temperature from 400 to 2500K in both alloys. The values of (E) over bar (f) and (E) over tilde (f) for CuNiCoFe are greater than those in CuNiCo within this range of temperature.