Ordered phases of lithium nickelite Li1−x−zNi1+xO2

A symmetry analysis of ordering in lithium nickelite Li_1−x−z Ni_1+x O₂ (Li_1−x−z □_yNi_1+x O₂) was performed with regard to the substitution of Li and Ni atoms and the occurrence of structural vacancies □ in the metal sublattice. For all the ordered phases, the k ₉ ⁽³⁾ ray of the Lifshitz {k ₉} star is present in the order-disorder transition channel. This ray determines the consecutive alternation of atomic planes filled with only Ni atoms or only Li atoms and vacancies in the [1[`1]1]_B1[1\bar 11]_{B1} direction. It was shown that the rhombohedral ordered LiNiO₂ phase is formed in the defect-free lithium nickelite, whereas a family of three monoclinic Li₃□Ni₄O₈ (C2/m space group) and Li₂□Ni₃O₆ (C2/m and C2 space groups) superstructures arises as the concentration of structural vacancies increases. For all the superstructures, the order-disorder phase-transition channels were determined and the distribution functions of Li and Ni atoms have been calculated. The long-range order parameters describing each superstructure were found as functions of the Li_{1−x− z} Ni_1+x O₂ composition.