Elastic Moduli of Crystalline Solid Thin Films: How To Get the Intrinsic Coefficients from Molecular Simulations?

Molecular simulation is a powerful tool to model nanometric solids, in particular to predict the elastic properties of nanometric rods or films with realistic potentials. However, when implementing simulations, several questions arise. For instance, in a mechanical test, where should the forces be applied? On the outermost atoms, or on the virtual Gibbs surface? Which deformation should be considered? That deduced from the displacement of the outermost atoms, or from the displacement of the Gibbs surface? As a matter of fact, the responses differ depending on whether one is more interested in theoretical considerations or practical implementation in molecular simulations. This leads to two definitions of the elastic constants, with significant differences when considering small systems. This work proposes a simple formalism, allowing anyone interested in elastic properties to switch between these two points of view. A simple Lennard-Jones model of crystalline thin film is used to illustrate this formalism, with an application to the study of the impact of the film thickness on its elastic constants at zero temperature.