Theoretical hardness calculated from crystallo-chemical data for MoS₂ and WS₂ crystals and nanostructures

The calculation of the hardness of Mo and W disulfides using a crystallo-chemical model provides a unique opportunity to obtain separate quantitative information on the maximum hardness H_max governed by strong intra-layer covalent bonds acting within the (0001) plane versus the minimum hardness H_min governed by weak inter-layer van der Waals bonds acting along the c-axis of the hexagonal lattice. The penetration hardness derived from fundamental crystallo-chemical data (confirmed by experimental determinations) proved to be far lower in MS₂ (M = Mo, W) than in graphite and hexagonal BN, both for H_max (H_graph/H_MoS2 = 3.85; H_graph/H_WS2 = 3.60; H_hBN/H_MoS2 = 2.54; H_hBN/H_WS2 = 2.37) as well as for H_min (H_graph/H_MoS2 = 6.22; H_graph/H_WS2 = 5.87; H_hBN/H_MoS2 = 4.72; H_hBN/H_WS2 = 4.46). However, the gap between H_max and H_min is considerably larger in MS₂ (M = Mo,W), as indicated by H_max/H_min being 279 in 2H-MoS₂, 282 in 2H-WS₂, 173 in graphite and 150 in hBN. The gap was found to be even larger in MS₂ (M = Mo, W) nanostructures. These findings help to explain the excellent properties of MS₂ (M = Mo, W) as solid lubricants in high tech fields, either as bulk 2H crystals (inter-layer shear and peeling off lubricating mechanisms), or especially as onion-like fullerene nanoparticles (rolling/sliding mechanisms).