Temperature effects on the friction-like mode of graphite

Abstract

Since the anharmonicity of the vibrational mode related to the relative rigid motion of graphene layers plays a decisive role in the friction behavior of graphite, a quantitative account of the temperature dependence of the frequency of this $E_{2{\rm g}}$(1) mode is worth to be investigated. Starting with the solution of the Morse quantum-mechanical oscillator, a relationship between the populated averaged vibrational quantum number and temperature is proposed. This expression is applied to our previous computed Morse fittings describing the anharmonic potential of this mode (Menéndez et al. in Phys Rev B 93:144112-1–144112-9, 2016) with the aim at providing the available vibrational energy at different pressures and temperatures. We show that the average vibrational quantum number decreases under pressure but the available vibrational energy is almost independent on pressure at a given temperature. As a result, the calculated temperature coefficient shows that inter-layer friction in graphite lowers as temperature increases with a similar trend regardless the pressure applied.