Theory of energy dissipation in sliding crystal surfaces

The average force of kinetic friction that occurs when layered compounds (which are commonly used as solid lubricants) are sheared in steady state is calculated for a model for such substances, assuming that the dissipation is caused by the excitation of lattice vibrations in one surface by the other. Because at slow speeds shearing is believed to be due to dislocation motion, a model for slow-speed shearing due to dislocation motion has been formulated. The force of friction is found to be inversely proportional to the sliding velocity for velocity small compared to the velocity of sound in the material and proportional to the area of the slipping surfaces. The dissipative stress at a sliding speed of 1 cm/s is calculated to be ${10}^8$ dyn/${\mathrm{cm}}^2$. The dissipative stress, calculated for slippage of two incommensurate surfaces, is found to be only ${10}^{\mathrm{-}4}$ dyn/${\mathrm{cm}}^2$, however, which opens up the question of whether lubrication is caused by slippage of the lubricant relative to the sliding surfaces rather than by shearing of the solid lubricant crystal.