Insights on Phase Formation from Thermodynamic Calculations and Machine Learning of 2436 Experimentally Measured High Entropy Alloys

Both CALPHAD and machine-learning (ML) approaches were employed to analyze the phase formation in 2,436 experimentally measured high entropy alloy (HEA) compositions consisting of various quinary mixtures of Al, Co, Cr, Cu, Fe, Mn, and Ni. CALPHAD was found to has good capabilities in predicting the BCC/B2 and FCC phase formation for the 1,761 solid-solution-only compositions, excluding HEAs containing an amorphous phase (AM) or/and intermetallic compound (IM). Phase selection rules were examined systematically using several parameters and revealed that valence electron concentration (VEC) < 6.87 and VEC > 9.16 are the conditions for the formation of single-phase BCC/B2 and FCC, respectively. Both CALPHAD predictions and experimental observations show that more BCC/B2 alloys are formed over FCC alloys as the atomic size difference between the elements increases. Four machine learning (ML) algorithms were employed to study the phase selection rules for two different datasets, one consisting of 1,761 solid-solution (SS) HEAs without AM and/or IM phases, and the other set consisting of all the 2,436 HEA compositions. Cross validation (CV) was performed to optimize the ML models and the CV accuracies are found to be 89.1 to 93.1 in predicting the formation of BCC/B2, BCC/B2 + FCC, and FCC; and 92.7 to 95.5% in predicting SS, AM, SS + AM, and IM phases. VEC is found to be most important parameter in phase prediction for BCC/B2, BCC/B2 + FCC, and FCC phases. Electronegativity difference and FCC-BCC-index (FBI) are the two additional dominating features in determining the formation of SS, AM, SS + AM, and IM. A separation was found in the VEC-vs mixing enthalpy plot to predict the formation of single-phase BCC/B2 or FCC with a 96.2% accuracy. These insights will be very valuable for designing HEAs with targeted crystal structures.