Atomic and global mechanical properties of systems described by the Stillinger-Weber potential

Analytical expressions for the stress and elasticity tensors of materials, in which the interactions are described by the Stillinger-Weber potential, are derived in the context of the stress fluctuation formalism. The derived formulas can be used both in Monte Carlo and molecular dynamics simulations. As an example of possible applications, they are employed to calculate the influence of the temperature and system size on the mechanical properties of crystalline cubic boron nitride. The system has been studied by molecular dynamics simulations. The computed mechanical properties are in good agreement with available experimental data and first principle calculations. In the studied crystalline cubic boron nitride system, the employed formalism is of higher accuracy than the 'small-strain' non-equilibrium method. The dominant contributions to the elastic constants stem from the Born and stress fluctuation terms. An increase in the system size reduces the statistical uncertainties in the computation of the mechanical properties. A rise of the temperature leads to a slight increase in the observed uncertainties. The derived expressions for the stress and elasticity tensors are further decomposed into sums of atomic level stress and atomic level elasticity tensors. The developed factorization enables us (i) to quantify the contribution of the various chemical groups, in the case under consideration of the different atoms, to the observed mechanical properties and (ii) to determine the elastic constants with reduced computational uncertainties. The reason is that the exact values of some terms of the proposed factorization can be determined theoretically beforehand. Thus, they can be substituted in the derived formulas leading to an enhanced convergence.