Friction between incommensurate crystals

Abstract

We present an overview of friction processes expected between two ideal crystals of strong layers (graphite, MoS₂, etc.) when one crystal is rotated with respect to the other by a certain angle θ. We assume perfect conditions: no impurities; no preexisting dislocations in the bulk of the crystals; slow gliding velocities. Two regimes show up: (a) Weak coupling when , where are typical intra- (inter-) layer interactions. Here we expect weak friction, controlled by two-phonon processes, and analyzed by Sokoloff et al. However, we point out that surface waves at the interface also play a role. (b) Strong coupling () where two orthogonal sets of screw disclinations should build up in the contact plane, as shown long ago by F.C. Frank. Here (to a first approximation) the dislocations are arranged in ladders, and we expect solid friction with a Peierls–Nabarro threshold stress.

Acknowledgements

We thank J.M. Martin who introduced us to the problem of superlubrication, C. Girit, who gave us a description of the existing literature, and C. Caroli, for some very useful comments.

Notes

†The dominant Fourier component of the surface forces has a wavevector 2π/b. There are other components (down to ∼2π/d) but the leading term is the first one. This is the basis of equation (16).