Machine learning empowered compositional design of multiple rare-earth principal component disilicates for environmental barrier coatings applications

The targeted design of multi-RE-principal-component RE₂Si₂O₇ disilicates ((nRE_xi)₂Si₂O₇) for environmental barrier coatings (EBCs) applications requires customizing the multi-RE compositions to achieve maximal optimization on the target properties, with a prerequisite to control their high-temperature stabilized phase as β or γ polymorphs. This is challenged by their rich polymorphic phases varied with the elemental properties on the RE cationic sites. In this study, a random forest (RF) model is developed with high accuracy to classify the four types of high-temperature stabilized phase composition − single-β, single-γ, single-δ/mixed δ+γ, and phase separation – identifying the average RE³⁺ cationic radius ( ) and the deviation of RE³⁺ cationic radius ( ) as the most influential factors. The well-trained model is validated on the prediction of (Gd_x1Ho_x2Yb_x3Lu_x4)₂Si₂O₇ and (Nd_x1Ho_x2Yb_x3Lu_x4)₂Si₂O₇ systems, supported by experimental characterization of six representative compositions. High-throughput DFT calculations reveal that the formation of their high-temperature stabilized phases correlates with the the low energy costs to accommodate configurational randomness into the multicomponent system, characterized by rapid convergence of the configurational entropy of mixing with increased excitation energy. The design criteria for single-phase β-(nRE_xi)₂Si₂O₇ and γ-(nRE_xi)₂Si₂O₇ disilicates are established. This work provides an investigation paradigm enabling the targeted design of (nRE_xi)₂Si₂O₇ EBCs materials.