Influence of average radii of RE³⁺ ions on phase structures and thermal expansion coefficients of high-entropy pyrosilicates

High-entropy pyrosilicate element selection is relatively blind, and the thermal expansion coefficient (CTE) of traditional β-type pyrosilicate is not adjustable, making it difficult to meet the requirements of various types of ceramic matrix composites (CMCs). The following study aimed to develop a universal rule for high-entropy pyrosilicate element selection and to achieve directional control of the thermal expansion coefficient of high-entropy pyrosilicate. The current study investigates a high-entropy design method for obtaining pyrosilicates with stable β-phase and γ-phase by introducing various rare-earth (RE) cations. The solid-phase method was used to create 12 different types of high-entropy pyrosilicates with 4–6 components. The high-entropy pyrosilicates gradually transformed from β-phase to γ-phase with an increase in the average radius of RE³⁺ ions ($\overline{r}({\text{RE}}^{3+})$). The nine pyrosilicates with a small $\overline{r}({\text{RE}}^{3+})$ preserve β-phase or γ-phase stability at room temperature to the maximum of 1400 ℃. The intrinsic relationship between the thermal expansion coefficient, phase structure, and RE–O bond length has also been found. This study provides the theoretical background for designing high-entropy pyrosilicates from the perspective of $\overline{r}({\text{RE}}^{3+})$. The theoretical guidance makes it easier to synthesize high-entropy pyrosilicates with stable β-phase or γ-phase for the use in environmental barrier coatings (EBCs). The thermal expansion coefficient of γ-type high-entropy pyrosilicate can be altered through component design to match various types of CMCs.