Crystal structure and cationic ordering in ludwigites Co$_{3-x}$Ni$_x$BO$_5$

The structure and composition of two solid solutions of Co$_{3-x}$Ni$_x$BO$_5$ with the ludwigite structure, the nickel ion concentrations in which are $x$ = 0.33 and $x$ = 0.59, are determined. Within the framework of the first-principles calculation, the cationic ordering for three concentrations $x$ = 0.25, 0.5, 0.75. It was found that nickel cations prefer to occupy positions 2a and 4g.