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 MS(2) (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 MS(2) (M = Mo,W), as indicated by H(max)/H(min) being 279 in 2H-MoS(2), 282 in 2H-WS(2), 173 in graphite and 150 in hBN. The gap was found to be even larger in MS(2) (M = Mo, W) nanostructures. These findings help to explain the excellent properties of MS(2) (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).