Machine-learning phase prediction of high-entropy alloys

High-entropy alloys (HEAs) have been receiving intensive attention due to their unusual properties that largely depend on the selection among three phases: solid solution (SS), intermetallic compound (IM), and mixed SS and IM (SS + IM). Accurate phase prediction is therefore crucial for guiding the selection of a combination of elements to form a HEA with desirable properties. It is widely accepted that the phase selection is correlated with elemental features such as valence electron concentration and the formation enthalpy, leading to a set of parametric phase-selection rules [1]. Previous studies on predicting the phase selection employed density functional theory (DFT) calculations to obtain some correlated parameters. But DFT calculations are time consuming and exhibit uncertainties in terms of treating the d orbitals of transition-metal atoms that are often components of HEAs. Here we employ machine learning (ML) algorithms to efficiently explore phase selection rules using a comprehensive experimental dataset consisting of 401 different HEAs including 174 SS, 54 IM, and 173 SS + IM phases. We adopt three different ML algorithms: K-nearest neighbours (KNN), support vector machine (SVM), and artificial neural network (ANN). To avoid overfitting, we divide the whole dataset into four nearly equal portions to perform a cross validation. For the classification of the three phases at the same time, the testing accuracy values from the KNN, SVM and ANN calculations achieve 68.6%, 64.3% and 74.3%, respectively. We then focus on the classification of two of the three phases using SVM and ANN. We find that the testing accuracy values using ANN in classifying the SS and IM phases, the SS + IM and IM phases, and the SS and SS + IM phases, are 86.7%, 94.3%, and 78.9%, respectively, which are higher than the corresponding testing accuracy values using SVM. As such, the trained ANN model performs the best among the three ML algorithms and is useful for predicting the phases of new HEAs. Our work provides an alternative route of computational design of HEAs, which is also applicable to accelerate the discovery of other metal alloys for modern engineering applications.