Machine learning empowered compositional design of multiple rare-earth principal component disilicates

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 of the target properties. A critical prerequisite is the retention of a stable β- or γ-polymorphic phase under high-temperature service conditions. This, however, is challenged by their rich polymorphic phases, which varies with the elemental properties of the RE cationic sites. In this study, a random forest (RF) model with high accuracy is developed to classify the four types of phase composition − single-β, single-γ, single-δ/mixed δ+γ, and separate phase – identifying the average RE³⁺ cationic radius ( ) and the deviation of RE³⁺ cationic radius ( ) as the most influential factors. The well-trained model is validated by predicting the phase compositions of (Gd_x1Ho_x2Yb_x3Lu_x4)₂Si₂O₇ and (Nd_x1Ho_x2Yb_x3Lu_x4)₂Si₂O₇ systems, supported by experimental characterization of representative compositions. High-throughput DFT calculations reveal that the formation of their phases correlates with 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 quantitative design criteria for single-phase β-(nRE_xi)₂Si₂O₇ and γ-(nRE_xi)₂Si₂O₇ disilicates are established: (i)  < 0.885 Å for β-polymorphs and 0.885 Å <  < 0.900 Å for the γ-polymorphs; and (ii) sufficiently small , whose upper bound increases monotonically with , reaching  ~ 0.04 at the vicinity of  ~ 0.885 and 0.900 Å. This work provides an investigation paradigm enabling the targeted design of (nRE_xi)₂Si₂O₇ EBCs candidates.