An electron and X-ray diffraction study of the compositely modulated barium nickel hollandite Ba_x(Ni_xTi_8-x)O₁₆, 1.16 < x < 1.32, solid solution

Hollandite samples, Ba_x(NixTi_8-x)O₁₆ (1.1 < x < 1.40) made by ceramic techniques, have been studied by electron and X-ray diffraction. As a result, the barium nickel hollandite system is described as a composite modulated single phase solid solution made up of mutually incommensurable (along b) framework and Ba ion sub-structures. The magnitude of the incommensurate primary modulation wave-vector when defined with respect to the framework sub-structure q = b_Ba (measured directly from electron diffraction patterns (EDPs)) acts as a chemical ruler in that it is directly related to composition and given by x/2. The superspace group symmetry was found to be I′2/ m(0. x/2, 0)1. Both the framework and the Ba sub-structures have the same I2/m average structure space group symmetry. The solid solution limits for Ba_x(Ni_xTi_8-x)O₁₆ were found to correspond to 1.16 < x < 1.32. These limits were found by calculating the lattice parameters of both the frame work and sub-lattice from the powder X-ray diffraction patterns.