First-principles concentration-wave approach to predict incipient order in high-entropy alloys: case of Ti${}_{0.25}$CrFeNiAl${}_x$

Abstract

Multi-principal-element alloys, including high-entropy alloys, experience segregation or partially-ordering as they are cooled to lower temperatures. For Ti${}_{0.25}$CrFeNiAl${}_x$, experiments suggest a partially-ordered B2 phase, whereas CALculation of PHAse Diagrams (CALPHAD) predicts a region of L2${}_1$+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 ($x\le 0.75$) and with CALPHAD in Al-rich region ($0.75\le x\le 1$), 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.

arXiv comment9 pages, 5 figures

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