Random stacking of a commensurate guest layer in an ordered host: Ni/Al layer-double-hydroxides

In the solid solution layer double hydroxides with the general composition [Ni_1-xAl_x(OH)₂] [(CO₃)_x/2·yH₂O], 0 ≤ x ≤ 0.4 the Ni²⁺/Al³⁺ ions decorate a positively charged triangular lattice that is sandwiched between two hydroxyl layers to form brucite-like host layers. Guest layers of co-intercalated water molecules and carbonate anions oriented with their three-fold axes perpendicular to the basal plane occupy the galleries. For x = 0.30, the carbonate ions form a (√13 × √13)R13.9° in-plane superlattice structure relative to the host layers which themselves exhibit an ABC stacking sequence that is only slightly (20%) disordered. Despite their commensurate structure, the guest layers yield Warren line shape X-ray reflections characteristic of a random stacking arrangement. This unusual result is attributed to the high (26-fold) degeneracy of the ground state structure of the guest layer.