General energy-strain scheme for accurate evaluation of the Born elasticity term for solid and liquid systems under finite temperature and pressure conditions

Abstract

The stress fluctuation approach is well known for evaluation of elastic constants due to its remarkable advantages of rapid convergence and the use of unstrained systems. The major contribution to the elastic constants comes from the Born term of the formula. However, the demand of the second energy derivative sets challenges for systems with many-body potentials. In this study, a general energy-strain scheme is proposed to evaluate the Born term of the elastic constants of solids under finite temperature and pressure conditions. It is shown theoretically how the Born term can be extracted from the system’s potential energy variation under a small strain. Then this prediction is further verified by using a pairwise potential and a three-body potential, the Lennard-Jones (LJ) model and crystalline silicon with a Stillinger–Weber potential. The results show that the Born term from the energy-strain scheme agrees very well with the one obtained by analytical formula. Incorporating this term in the stress fluctuation formalism, we investigate the elastic constants of LJ system under various pressures and temperatures. It is found that this scheme is also valid for liquid state.