Anharmonicity effects in the frictionlike mode of graphite

Abstract

Graphite is a prototypical solid lubricant demanding a thorough understanding of its low-friction behavior. The ${E}_{2g}$(1) Raman active vibrational mode of graphite is associated with the rigid-layer relative movement of its graphene sheets. Thus, this mode can provide a good means of exploring the low resistance of graphene layers to slip with respect to each other. To take advantage of this fact, the anharmonicity of the ${E}_{2g}$(1) mode has to be carefully characterized and evaluated since the atomic arrangement of carbon atoms in the ambient condition ABA stacking of graphite evidences potential asymmetry. The calculated one-dimensional energetic profile of the ${E}_{2g}$(1) mode reveals this local anisotropy around the energy minima and can be microscopically interpreted in terms of electron density interactions. Morse-type potentials accurately fit the energetic profiles at different interlayer separations, and provide simple analytical expressions for evaluating harmonic and anharmonic contributions to the $\mathrm{\ensuremath{\Gamma}}$-point ${E}_{2g}$(1) frequency ${\ensuremath{\omega}}_{{E}_{2g}(1)}$ under a perturbative algebraic treatment. We quantify how the anharmonic contribution increases with the available energy ($E$) at zero pressure, and how this contribution decreases as hydrostatic pressure ($p$) or uniaxial stress is applied for a given available energy. The calculated ${\ensuremath{\omega}}_{{E}_{2g}(1)}\ensuremath{-}p$ and ${\ensuremath{\omega}}_{{E}_{2g}(1)}\ensuremath{-}E$ trends indicate an increasing (decreasing) of frictional forces in graphite with pressure (temperature). Our conclusions are supported by the good agreement of the calculated frequencies with existing Raman experiments under hydrostatic pressure conditions.