A Recommender System for High-Entropy Alloys Exploration: Uncovering Non-Entropic Rules from Latent Space Similarity

The properties of high-entropy alloys (HEAs) are governed by their phase formation. However, entropy is often insufficient to suppress compound formation in as-cast alloys, making the stabilization of a single-phase solid solution notoriously difficult and its prediction a central research challenge. Herein, we present a similarity-based representation learning approach to identify and explore HEA phases. Our model integrates a variational autoencoder with an affinity propagation clustering algorithm to create a powerful tool for phase classification. When trained on a data set of 632 alloys comprising 24 elements, the model achieves 86.8% accuracy and identifies seven distinct classes of HEAs. Analysis demonstrates that nonentropic factors significantly influence phase formation. Leveraging this reliable model, we generated 560 phase diagrams across the compositional space of eight metal elements ({Mo, V, Ti, Nb, Zr, Ta, Hf, and Al}). These diagrams elucidate key stabilization rules: high concentrations of V and Mo jointly stabilize the BCC phase, whereas high concentrations of V and Al favor intermetallic formation. This work provides an invaluable roadmap for the targeted design of single-phase refractory HEAs.