Frictional Anisotropy and the Role of Lattice Relaxation in Molecular Tribology of Crystalline Interfaces

Abstract

A statistical thermodynamic description of the atomic force microscope is summarized and applied to the sliding of a single-atom tip over 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 to be Lennard-Jones (12,6). Sliding is treated as a quasistatic (reversible) process. The force of static friction (i.e., the maximum of the lateral component of the force anti-parallel to the direction of movement of the tip) is computed for several crystallographic directions at T = 0K. The frictional force is found to be strongly anisotropic, consistent with the recent experiment by Sheehan and Lieber (Science, 1158 (1996)). The tip slides with minimum resistance along a particular pathway where rows of substrate atoms form a `'groove.'' Sliding perpendicular to the groove offers frictional forces up to an order of magnitude greater. For hard substrates the frictional force is nearly linear with load (i.e., the coefficient of static friction is constant). As the substrate gets softer (i.e., the force constant decreases), the force of friction decreases and the coefficient of friction declines with load, even becoming negative for sufficiently soft substrates.