Static frictional forces at crystalline interfaces

A statistical thermodynamic description of the atomic force microscope is developed and used to compute the force of static friction for a single-atom tip on a hexagonal close-packed substrate surface under constant load in vacuum. The substrate atoms are taken to be independent isotropic harmonic oscillators, and the tip-substrate interaction is taken to be Lennard-Jones (12,6). Movement of the tip is treated as a quasistatic (reversible) process. The force of static friction (i.e., the maximum of the component of the force parallel to the direction of movement of the tip) is computed by the Monte Carlo technique for several crystallographic directions (paths) and found to be strongly anisotropic. The frictional force is minimum along a particular path where rows of substrate atoms form a "groove"; it is up to 2 orders of magnitude greater for the path perpendicular to the groove. The dependence of the frictional force on the hardness of the substrate (as measured by the force constant of the substrate harmonic potential) and on temperature was examined for these two extreme paths. For hard substrates the frictional force is nearly linear with load. As the substrate gets softer, or as the temperature increases at fixed hardness, the frictional force declines. The results of the computations are correlated with recent experimental observations on the sliding of nanocrystals of MoO₃ over an MoS₂ substrate.