Kaleidoscopic Incommensurate Structures of Aluminum-Substituted Rhenium Silicides

Al substitution leads to kaleidoscopic vacancy-bearing crystal structures in the rhenium silicides, ReAl_xSi_1.75-0.75x□_0.25-0.25x (□ indicates Si/Al vacancies), including two incommensurate structures newly found and successfully solved with (3 + 1)-dimensional superspace groups in this work. The similarity and difference among these structures, especially the subtle difference in the ordered distribution of vacancies, are compared and discussed in detail. With synthetic, crystallographic, and computational investigations, we gained a comprehensive understanding of the composition-structure relationship in these compounds, especially the ordered distribution of Si/Al vacancies.