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

A symmetry analysis of ordering in lithium nickelite Li1−x−zNi1+xO2 (Li1−x−z□yNi1+xO2) 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 k9(3) ray of the Lifshitz {k9} 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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$[1\bar 11]_{B1} $$ \end{document} 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 Li1−x− zNi1+xO2 composition.