Revisiting the phase stability rules in the design of high-entropy alloys: A case study of quaternary alloys produced by mechanical alloying

High-entropy alloys (HEAs) are potential candidates for many structural applications because of their outstanding mechanical properties. Achieving solid solution (SS) in HEAs is desirable since intermetallic compounds (IMs) can, in most cases, be deleterious. While empirical phase stability rules have been widely used to predict SS or IM phases in HEAs, there are substantial reported cases of their breakdown. To assess the effectiveness of the empirical rules—atomic size difference (δ), mixing enthalpy (ΔHmix), mixing entropy (ΔSmix), entropy to enthalpy ratio (Ω), electronegativity difference (△χ), and valence electron concentration (VEC), a systematic study that isolates the effect of processing pathway was conducted. As a starting point and as a benchmark, an existing equiatomic AlCoCrFe BCC HEA was correctly predicted (following the classical empirical rules) and developed. This was followed by the SS FCC prediction and development of five novel semi-equiatomic AlTiCuZn-based quaternary HEAs (Al0.57TiCuZn, AlTi0.45CuZn, Al0.45TiCuZn, AlTiCu1.76Zn, and AlTiCu2Zn) by mechanical alloying. Among the AlTiCuZn-based HEAs, only AlTi0.45CuZn showed SS, but with FCC + HCP phase contradicting the traditional VEC rule that predicts FCC. Using AlTi0.45CuZn as a guide, conservative SS formation criteria for AlTiCuZn-based HEAs were determined—Ω ≥ 1.6, δ≤ 5%, and ΔHmix ≥ -8 kJ/mol, while retaining conventional ΔSmix and △χ range. Also, FCC + HCP phase formation is stable at 7.5 ≤ VEC ≤ 8.4. The revised rules were verified by correctly predicting the phases in newly-fabricated non-equiatomic HEAs—AlTi0.37CuZn0.97 and AlTi0.56Cu1.24Zn1.2. This study shows that the range of empirical phase stability model values is not fixed, but alloy-dependent due to the differences in bonding nature of HEA-constituting elements.