Learning phase selection and assemblages in High-Entropy Alloys through a stochastic ensemble-averaging model

Efficient alloy design requires a knowledge of phase selection, phase-fractions and microstructure of the material. Prediction of the phase equilibria, though well-established for traditional alloys, is still an open challenge for novel materials and concentrated multicomponent systems such as the High-Entropy Alloys (HEAs). In this paper, we present a novel data-driven approach for learning the phase-equilibria in HEAs through the use of a stochastic ensemble averaging method. The proposed model employs a model-averaging technique on an ensemble of 150 artificial neural networks that have been trained on a 323 alloy dataset. A seven-label classification is presented using a three-element vector description of phases. This allows us to fit the classification boundaries to a relatively larger number of phase combination labels while using only three target parameters for training thereby improving accuracy. The phase prediction capabilities (i.e., formation of FCC, BCC, intermetallics or different combinations of these phases) were tested on 320 alloys outside of the training dataset. Additionally, quantitative estimate of the phase equilibria, i.e., relative phase-fractions, were estimated and compared with experimental measurements and CALPHAD predictions in three different high-entropy systems, viz., Fex-Niy-(AlCoCr0.5)1-x-y, Alx-Tiy-(CrFeNi)1-x-y and Crx-Moy-(VNbTi)1-x-y. The model's capability of going a step beyond current state-of-the-art model allows greater insights into target composition spaces for the alloy designer and establishes the first such approach for HEAs.