Group-subgroup schemes for MoNi4, Nb4N5, KxFe2−ySe2, Nd10Au3As8O10 and CsInCl3: i5 superstructures of I 4/m allowing atom, charge or vacancy ordering

Abstract

Abstract Isomorphic symmetry reductions are a special class of klassengleiche symmetry reductions where the subgroup has the same space group type. The present contribution highlights five different isomorphic transitions of index 5 (i5), all from I 4/m to I 4/m. These superstructure formations allow (i) atom ordering in MoNi4, (ii) vacancy ordering in Nb4N5, KxFe2−ySe2 and Nd10Au3As8O10 and (iii) charge ordering in CsInCl3 (≡Cs2InIInIIICl6). The group-subgroup schemes in the Bärnighausen formalism are discussed along with the crystal chemical consequences.