Insights on phase formation from thermodynamic calculations and machine learning of 2436 experimentally measured high entropy alloys

Abstract

Both CALPHAD (CALculation of PHAse Diagrams) and machine learning (ML) approaches were employed to analyze the phase formation in 2436 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 have good capabilities in predicting the BCC/B2 and FCC phase formation for the 1761 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 it was 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; and CALPHAD could predict this with essentially 100% accuracy. 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 ML algorithms, decision tree (DT), k-nearest neighbor (KNN), support vector machine (SVM), and artificial neural network (ANN), were employed to study the phase selection rules for two different datasets, one consisting of 1761 solid-solution (SS) HEAs without AM and/or IM phases, and the other set consisting of all the 2436 HEA compositions. Cross validation (CV) was performed to optimize the ML models and the CV accuracies are found to be 90.4%, 94.1%, 93.8%, 89.7% for DT, KNN, SVM, and ANN respectively in predicting the formation of BCC/B2, BCC/B2 + FCC, and FCC; and 92.9%, 96.3%, 96.9%, 92.3% for DT, KNN, SVM, and ANN respectively in predicting SS, AM, SS + AM, and IM phases. Sixty-six experimental bulk alloys with SS structures are predicted with the trained ANN model, and the accuracy reaches 80.3%. VEC was 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 dominating features in determining the formation of SS, AM, SS + AM, and IM. A separation line ΔHmix=29×VEC−247 was found in the ΔHmix-vs-VEC plot to predict the formation of single-phase BCC/B2 or FCC with a 96.2% accuracy (ΔHmix = mixing enthalpy). These insights will be very valuable for designing HEAs with targeted crystal structures.