Temperature-dependent elasticity of single crystalline graphite

Despite its relevance in many high temperature processes, the elastic behavior of single crystalline graphite is so far entirely undocumented away from room temperature conditions. In this work we present a molecular dynamics investigation of graphite's second order elastic tensor dependence on temperature from 300 to 4000 K, using a series of popular interatomic potentials for carbon. Data and analytic expressions are presented for the elastic tensor under the two limiting situations known as isothermal, or quasi-static, and adiabatic deformation conditions, prevailing in the limits of slow and large deformation rates, respectively. Independently from the potential, we identify a strong non-linearity of elastic constants with respect to temperature. We show that despite conserving an important elastic anisotropy whatever the temperature, the latter is being reduced by a factor of similar to 5 when increasing temperature up to 4000 K. Also, we show that elastic anisotropy is about 20 times larger under isothermal conditions than under adiabatic conditions. Finally, we investigate the dynamics of the adiabatic to isothermal stress relaxations occurring right after ultra fast deformations such as those encountered under shock loading, showing that the relevant time and length scales are of the order of a few ps and nm, respectively, for deformations around a percent.