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

Abstract The targeted design of multi-RE-principal-component RE2Si2O7 disilicates ((nRExi)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 (Gdx1Hox2Ybx3Lux4)2Si2O7 and (Ndx1Hox2Ybx3Lux4)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-(nRExi)2Si2O7 and γ-(nRExi)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 (nRExi)2Si2O7 EBCs candidates.