Compositional design and phase formation capability of high-entropy rare-earth disilicates from machine learning and decision fusion

A key strategy for designing environmental barrier coatings is to incorporate multiple rare-earth (RE) components into β- and γ-RE₂Si₂O₇ to achieve multifunctional performance optimization. However, the polymorphic phase presents significant challenges for the design of multicomponent RE disilicates. Here, employing decision fusion, a machine learning (ML) method is crafted to identify multicomponent RE disilicates, showcasing notable accuracy in prediction. The well-trained ML models evaluated the phase formation capability of 117 (RE₁₀.₂₅RE₂₀.₂₅Yb₀.₂₅Lu₀.₂₅)₂Si₂O₇ and (RE₁₁/₆RE₂₁/₆RE₃₁/₆Gd₁/₆Yb₁/₆Lu₁/₆)₂Si₂O₇, which are unreported in experiments and validated by first-principles calculations. Utilizing model visualization, essential factors governing the formation of (RE₁₀.₂₅RE₂₀.₂₅Yb₀.₂₅Lu₀.₂₅)₂Si₂O₇ are pinpointed, including the average radius of RE³⁺ and variations in different RE³⁺ combinations. On the other hand, (RE₁₁/₆RE₂₁/₆RE₃₁/₆Gd₁/₆Yb₁/₆Lu₁/₆)₂Si₂O₇ must take into account the average mass and the electronegativity deviation of RE³⁺. This work combines material-oriented ML methods with formation mechanisms of multicomponent RE disilicates, enabling the efficient design of superior materials with exceptional properties for the application of environmental barrier coatings.