Data-driven design of high-entropy silicate ceramics with low thermal conductivity

High-entropy rare earth silicate ceramics represent promising candidates for environmental barrier coatings (EBCs) due to their low thermal conductivity, compatible coefficients of thermal expansion (CTE), and high-temperature stability. In this study, we present a data-driven approach that integrates machine learning and experimental validation to efficiently screen and design high-entropy rare earth pyrosilicate ceramics with low thermal conductivity. Principal Component Analysis (PCA) and K-means clustering were applied to the sample dataset to predict the rare earth element compositions associated with low thermal conductivity in high-entropy rare earth silicate ceramics. Five HECs were successfully synthesized through screening, exhibiting minimum thermal conductivities ranging from 0.93 to 1.22 W·m⁻¹·K⁻¹, and average coefficients of thermal expansion between 3.14 ∼ 3.84 × 10⁻⁶ K⁻¹ over the temperature range from room temperature to 1500 °C. This validates the reliability of our machine learning predictions. The optimized material ((Yb_0.2Y_0.2Er_0.2Lu_0.2Dy_0.2)₂Si₂O₇ (Abbr. YbYErLuDy)) was selected for evaluating coating application performance. Si/HEC coatings were fabricated using atmospheric plasma spraying (APS), and high-temperature stability and thermal conductivity were systematically evaluated. The successful implementation of this data-driven approach demonstrates its potential in accelerating the design and development of novel EBCs materials with targeted performance attributes, thus offering new avenues for advancing high-performance ceramic coatings across various applications. Through this screening process, we successfully identified and synthesized five rare earth silicate materials. Experimental measurements indicate that these materials have the thermal conductivity minimum range from 0.93 to 1.22 W·m⁻¹·K⁻¹, with an average coefficient of thermal expansion between room temperature and 1500 °C measured at (3.14 ∼ 3.84 × 10⁻⁶ K⁻¹). This validates the reliability of our machine learning predictions. The optimized material ((Yb_0.2Y_0.2Er_0.2Lu_0.2Dy_0.2)₂Si₂O₇ (referred to as YbYErLuDy)) was selected for evaluating coating application performance, with samples prepared using Atmospheric Plasma Spraying (APS) technology, while investigating the high-temperature stability of HECs/Si composite coatings and assessing the differences in thermal conductivity between the (YbYErLuDy) coating and substrate materials.