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 (interlayer shear and peeling off lubricating mechanisms), or especially as onion-like fullerene nanoparticles (rolling/sliding mechanisms).