A universally applicable composite modulated structure approach to ordered BaxMyTi8−yO16 hollandite-type solid solutions

Abstract A wide range of barium titanate hollandites of the form Ba x 2 + M x 2 + Ti 8 - x 4 + O 16 ( M =Zn, Co, Mg, Fe and Mn) and Ba x 2 + M 2 x 3 + Ti 8 - 2 x 4 + O 16 ( M =Fe) with nominal x ranging from 1.0 to 1.4 have been synthesized and examined to investigate the solid solution range and the nature of the ordering of the Ba ions. Electron diffraction studies confirm that the barium titanate hollandites are composite modulated single phase solid solutions made up of mutually incommensurable (along b ) framework and Ba ion sub-structures. The overall superspace group symmetry was found to be I ′2/ m (0, x 2 ,0)1. The symbol I ′ here refers to the superspace centering operation { x 1 + 1 2 , x 2 + 1 2 , x 3 + 1 2 , x 4 + 1 2 } (see below). Both the framework and the Ba sub-structures have the same I 2/ m average structure space group symmetry. The solid solution ranges for the hollandites were calculated from the positions of well-defined superlattice peaks in X-ray diffraction patterns. The effect of cooling rate on Ba ion ordering is also examined.