Ni ordering in the van der Waals gap of Ni-intercalated 2H-NbS$_2$: from disorder through $2\times2$ and $\sqrt{3}\times\sqrt{3}$ order to stripe order
We report a synchrotron x-ray diffraction study of Ni-intercalated 2H-NbS$_2$ over the range $0.18 \le x \le 0.57$, with Ni contents measured by energy-dispersive x-ray spectroscopy. Powder diffraction on the whole series shows that the NbS$_2$ host is preserved, while the Ni ions in the van der Waals gap evolve from a disordered arrangement to $2\times2$ order at $x=1/4$ and $\sqrt{3}\times\sqrt{3}$ order at $x=1/3$, through a range where both motifs coexist, to an orthorhombic stripe-type order at $x=0.57$. The in-plane lattice parameter increases with Ni content, whereas the interlayer spacing remains nearly constant except for a pronounced minimum at $x=1/4$, which density-functional calculations reproduce for the ordered structure. Single-crystal diffraction on the two commensurate phases shows that the $x=1/4$ structure, with Ni on a single site and a trimerized Nb lattice, is free of stacking faults, whereas the chiral $x=1/3$ structure contains Ni on the nominally empty site, inversion twins and stacking faults of the Ni layers. The comparison between powders and crystals shows that grinding mainly degrades the stacking of the Ni layers. These results establish the structural phase diagram of Ni$_x$NbS$_2$ and the intercalant disorder to be taken into account in the interpretation of its magnetic properties.