First-principles prediction of incipient order in arbitrary high-entropy alloys: exemplified in Ti0.25CrFeNiAlx

Abstract

<p>Multi-principal-element alloys, including high-entropy alloys, experience segregation or partially-ordering as they are cooled to lower temperatures. For Ti0.25CrFeNiAl<em>x</em>, experiments suggest a partially-ordered B2 phase, whereas CALculation of PHAse Diagrams (CALPHAD) predicts a region of L21+B2 coexistence. We employ first-principles density-functional theory (DFT) based electronic-structure approach to assess stability of phases of alloys with arbitrary compositions and Bravais lattices (A1/A2/A3). In addition, DFT-based linear-response theory has been utilized to predict Warren-Cowley short-range order (SRO) in these alloys, which reveals potentially competing long-range ordered phases. The resulting SRO is uniquely analyzed using concentration-waves analysis for occupation probabilities in partially-ordered states, which is then be assessed for phase stability by direct DFT calculations. Our results are in good agreement with experiments and CALPHAD in Al-poor regions (<em>x</em> ≤ 0.75) and with CALPHAD in Al-rich region (0.75 ≤ <em>x</em> ≤ 1), and they suggest more careful experiments in Al-rich region are needed. Our DFT-based electronic-structure and SRO predictions supported by concentration-wave analysis are shown to be a powerful method for fast assessment of competing phases and their stability in multi-principal-element alloys.</p>