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The crystal structure of MoS$_2$ with strong covalent bonds in plane and weak Van der Waals interactions out of plane gives rise to interesting properties for applications such as solid lubrication, optoelectronics, and catalysis, which can be enhanced by transition-metal doping. However, the mechanisms for improvement and even the structure of the doped material can be unclear, which we address with theoretical calculations. Building on our previous work on Ni-doping of the bulk 2H phase, now we compare to polytypes (1H monolayer and 3R bulk), to determine favorable sites for Ni and the doping effect on structure, electronic properties, and the layer dissociation energy. The most favorable intercalation/adatom sites are tetrahedral intercalation for 3R (like 2H) and Mo-atop for 1H. The relative energies indicate a possibility of phase change from 2H to 3R with substitution of Mo or S. We find structural and electronic properties that can be used to identify the doping sites, including metallic behavior in Mo-substituted 3R and 2H, and in-gap states for Mo- and S-substituted 1H, which could have interesting optoelectronic applications. We observe a large enhancement in the interlayer interactions of Ni-doped MoS$_2$, opposite to the effect of other transition metals. For lubrication applications, this increased layer dissociation energy could be the mechanism of low wear. Our systematic study shows the effect of doping concentration and we extrapolate to the low-doping limit. This work gives insight into the previously unclear structure of Ni-doped MoS$_2$ and how it can be detected experimentally, the relation of energy and structures of doped monolayers and bulk systems, the electronic properties under doping, and the effect of doping on interlayer interactions., 31 pages, 8 figures

Ni-doped MoS$_2$ is a layered material with useful tribological, optoelectronic, and catalytic properties. Experiment and theory on doped MoS$_2$ has focused mostly on monolayers or finite particles: theoretical studies of bulk Ni-doped MoS$_2$ are lacking and the mechanisms by which Ni alters bulk properties are largely unsettled. We use density functional theory calculations to determine the structure, mechanical properties, electronic properties, and formation energies of bulk Ni-doped 2H-MoS$_2$ as a function of doping concentration. We find four meta-stable structures: Mo or S substitution, and tetrahedral (t-) or octahedral (o-) intercalation. We compute phase diagrams as a function of chemical potential to guide experimental synthesis. A convex hull analysis shows that t-intercalation (favored over o-intercalation) is quite stable against phase segregation and in comparison with other compounds containing Ni, Mo, and S; the doping formation energy is around 0.1 meV/atom. Intercalation forms strong interlayer covalent bonds and does not increase the $c$-parameter. Ni-doping creates new states in the electronic density of states in MoS$_2$ and shifts the Fermi level, which are of interest for tuning the electronic and optical properties. We calculate the infrared and Raman spectra and find new peaks and shifts in existing peaks that are unique to each dopant site, and therefore may be used to identify the site experimentally, which has been a challenge to do conclusively., 34 pages, 7 figures