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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 ( i 5), all from  I  4/ m  to  I  4/ m . These superstructure formations allow (i) atom ordering in MoNi 4 , (ii) vacancy ordering in Nb 4 N 5 , K x Fe 2−y Se 2  and Nd 10 Au 3 As 8 O 10  and (iii) charge ordering in CsInCl 3  (≡Cs 2 In I In III Cl 6 ). The group-subgroup schemes in the Bärnighausen formalism are discussed along with the crystal chemical consequences.

zeitschrift für kristallographie - crystalline materials 

Group-subgroup schemes for MoNi 4 , Nb 4 N 5 , K x Fe 2−y Se 2 , Nd 10 Au 3 As 8 O 10  and CsInCl 3 :  i 5 superstructures of  I  4/ m  allowing atom, charge or vacancy ordering