Both CALPHAD (CALculation of PHAse Diagrams) 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 have 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 it revealed that valency 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 machine learning (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 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 91.4%, 93.1%, 90.2%, 89.1% for DT, KNN, SVM, and ANN respectively in predicting the formation of BCC/B2, BCC/B2 + FCC, and FCC; and 93.6%, 93.3%, 95.5%, 92.7% 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 trained ANN model, and the accuracy reaches 81.8%. 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 line ΔH_mix=28.97×VEC-246.77 was found in the VEC-vs-ΔH_mix plot to predict the formation of single-phase BCC/B2 or FCC with a 96.2% accuracy (ΔH_mix = mixing enthalpy). These insights will be very valuable for designing HEAs with targeted crystal structures.
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Phase Prediction of High-Entropy Alloys by Integrating Criterion and Machine Learning Recommendation Method
The comprehensive properties of high-entropy alloys (HEAs) are highly-dependent on their phases. Although a large number of machine learning (ML) algorithms has been successfully applied to the phase prediction of HEAs, the accuracies among different ML algorithms based on the same dataset vary significantly. Therefore, selection of an efficient ML algorithm would significantly reduce the number and cost of the experiments. In this work, phase prediction of HEAs (PPH) is proposed by integrating criterion and machine learning recommendation method (MLRM). First, a meta-knowledge table based on characteristics of HEAs and performance of candidate algorithms is established, and meta-learning based on the meta-knowledge table is adopted to recommend an algorithm with desirable accuracy. Secondly, an MLRM based on improved meta-learning is engineered to recommend a more desirable algorithm for phase prediction. Finally, considering poor interpretability and generalization of single ML algorithms, a PPH combining the advantages of MLRM and criterion is proposed to improve the accuracy of phase prediction. The PPH is validated by 902 samples from 12 datasets, including 405 quinary HEAs, 359 senary HEAs, and 138 septenary HEAs. The experimental results shows that the PPH achieves performance than the traditional meta-learning method. The average prediction accuracy of PPH in all, quinary, senary, and septenary HEAs is 91.6%, 94.3%, 93.1%, and 95.8%, respectively.
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- Award ID(s):
- 1943445
- NSF-PAR ID:
- 10327500
- Date Published:
- Journal Name:
- Materials
- Volume:
- 15
- Issue:
- 9
- ISSN:
- 1996-1944
- Page Range / eLocation ID:
- 3321
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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