Machine-learning-assisted multi-objective optimization of thermal conductivity, thermal expansion coefficient, and fracture toughness in rare-earth zirconate ceramics

Abstract

Although rare-earth zirconates (RE2Zr2O7) are promising top-coat candidates for thermal barrier coatings, their thermal conductivity (TC) still requires further reduction, and their limited thermal expansion coefficient (TEC) and fracture toughness (KIC) restrict further performance improvement. However, trial-and-error experiments and first-principles calculations are not well suited for rapid screening of the large RE2Zr2O7 compositional space, while empirical models usually have limited transferability to complex multi-component systems. To address these challenges, this study develops an interpretable machine learning (ML) framework that integrates multi-property prediction, feature interpretation, and multi-objective composition optimization for RE2Zr2O7 ceramics. Experimental data sets are selected from the literature and handbooks, including 1167, 660, and 309 samples for TC, TEC, and KIC, respectively. Composition-derived features related to atomic mass, configurational entropy, electronegativity, ionic radius, and ionic volume are generated, and a four-step feature selection strategy is applied to obtain compact feature subsets. Multiple ML algorithms are evaluated, and random forest is found to provide the best performance for TC, while extra trees perform best for TEC and KIC. The selected models show strong agreement between predicted and experimental values on both test sets and independent compositions. SHapley Additive exPlanations are further employed to interpret the role of temperature, mass disorder, electronegativity dispersion, and ionic-radius mismatch in governing the predictions. Finally, the trained ML predictors are integrated with non-dominated sorting genetic algorithm II to perform multi-objective optimization in the (Gd–Yb–Sc)2Zr2O7 compositional system, enabling the identification of composition regions with coordinated thermophysical and mechanical performance.