Data-driven discovery of formation ability descriptors for high-entropy rare-earth monosilicates

Herein we establish formation ability descriptors of high-entropy rare-earth monosilicates (HEREMs) via the data-driven discovery based on the high-throughput solid-state reaction and machine learning (ML) methods. Specifically, adequate high-quality data are generated with 132 samples synthesized by the self-developed high-throughput solid-state reaction apparatuses, and 30 potential descriptors are considered in ML simultaneously. Two classifications are proposed to study the phase formation of HEREMs via the ML approach combined with the genetic algorithm: (Ⅰ) to distinguish pure HEREMs (X) from other phases and (Ⅱ) to categorize the detail phases of HEREMs (X2, X1, or X2+X1). Four formation ability descriptors ( r Me ¯ $\overline{r_{\text{Me}}}$ , E F ¯ $\overline{E_{\mathrm{F}}}$ , δ E g ${\delta }_{E_{\text{g}}}$ , and δ Z ∗ ${\delta }_{Z^{\ast }}$ ) with a high validation accuracy (96.2%) are proposed as the optimal combination for Classification Ⅰ, where a smaller r Me ¯ $\overline{r_{\text{Me}}}$ is determined to have the most significant influence on the formation of HEREMs. For Classification Ⅱ, a 100% validation accuracy is achieved by using only two formation ability descriptors ( r ion ¯ $\overline{r_{\text{ion}}}$ and δ Z ∗ ${\delta }_{Z^{\ast }}$ ), where the r ion ¯ $\overline{r_{\text{ion}}}$ is analyzed to be the dominant feature and a lower r ion ¯ $\overline{r_{\text{ion}}}$ is beneficial to the formation of X2-HEREMs. Based on our established formation ability descriptors, 6,045 unreported multicomponent silicates are explored, and 3,478 new HEREMs with 2,700 X2-and 423 X1-HEREMs are predicted.