Ordering Transformations in High-Entropy Alloys

The high-temperature disordered phase of multi-component alloys, including high-entropy alloys (HEA), generally must experience segregation or else passes through partially-ordered phases to reach the low-temperature, fully-ordered phase. Our first-principles KKR-CPA-based atomic short-range ordering (SRO) calculations (analyzed as concentration-waves) reveal the competing partially and fully ordered phases in HEA, and these phases can be then directly assessed from KKR-CPA results in larger unit cells [Phys. Rev. B 91, 224204 (2015)]. For Al$_x$CrFeNiTi$_{0.25}$, Liu et al. [J Alloys Compd 619, 610 (2015)] experimentally find FCC+BCC coexistence that changes to BCC with increasing Al (x from 0-to-1), which then exhibits a partially-ordered B2 at low temperatures. CALPHAD (Calculation of Phase Diagrams) predicts a region with L2$_1$+B2 coexistence. From KKR-CPA calculations, we find crossover versus Al from FCC+BCC coexistence to BCC, as observed, and regions for partially-order B2+L2$_1$ coexistence, as suggest by CALPHAD. Our combined first-principles KKR-CPA method provides a powerful approach in predicting SRO and completing long-range order in HEA and other complex alloys.