Phase formation criteria for structurally ordered high-entropy intermetallics

Abstract

Structurally ordered high-entropy intermetallics (SOHEI), as the latest paradigm of high-entropy materials, exhibit a variety of excellent and attractive mechanical and functional properties, which are mainly derived from the formation of multi-principal element intermetallics. Nevertheless, the phase formation criteria for SOHEI have not been systematically investigated so far. In this work, a series of parameter formulas related to the mixing entropy (ΔSmix*), mixing enthalpy (ΔHmix*, ΔHmixA−B), atomic size difference (δr*, δrA−B), electronegativity difference (Δχ*, ΔχA−B), standard deviation of valence electron concentration (VEC) (σVEC*, σVECA−B), and total VEC (VECtot) based on the sublattice model were established. The universal criteria for phase formation of SOHEI were proposed, which states that various atoms occupying the common and different sublattice need to satisfy: − 8 kJ∙mol−1 ≤ ΔHmix*≤ 4 kJ∙mol−1, δr* ≤ 6.5%, Δχ*≤ 8%, σVEC*≤ 1.6, − 60 kJ∙mol−1 ≤ ΔHmixA−B ≤ 0 kJ∙mol−1, 2.5% ≤ δrA−B ≤ 16.5%, ΔχA−B ≥ 2.5% and 0.5 ≤ σVECA−B ≤ 3.5. Importantly, the VECtot of alloy system was identified as the crucial factor for determining the phase types of SOHEI, which can be utilized to design and regulate the desired type of intermetallic phase. The correctness and effectiveness of the proposed criteria based on sublattice model were well verified by designed experiments. The quantitative insights of phase formation criteria are greatly useful for the preliminary screening alloy components, and this contribution can provide meaningful guidance for the future development of SOHEI.