Molecular dynamics study on atomic elastic stiffness in Si under tension: homogenization by external loading and its limit

Abstract

As a series of studies that discuss the onset of inelastic deformation based on atomic elastic stiffness (AES), we investigated the AES in silicon by the Tersoff interatomic potential. For a comprehensive discussion including the effect of structural inhomogeneity by surface and grain boundaries, we performed tensile simulations on bulk/nanowire of Si single crystal, laminate bulk/bamboo nanowire with Σ5 twist grain boundary under a very low temperature (T = 1 K). Not only the stress–strain response, but also the AESs at each atom point, , were evaluated numerically by (Voigt notation) against local strain perturbation. The deviation of vanishes/diminishes by tension both in the homogeneous case of bulk perfect lattice and inhomogeneous ones with surface and grain boundaries; however, there is a certain limit for the homogenization. That is, the subtle deviation of AES in the perfect bulk vanishes by tension but it increases again like an onset of resonance, showing precursor stress decrease just before the unstable stress drop. In the inhomogeneous cases, we demonstrated that the near-zero AESs at the initial structural defects, e.g. surface or grain boundary, do not change but the positive AESs of other stable atoms approach zero by tension. When these distributions overlap each other, the standard deviation of AES increases again as if it were the first homogenization limit. However, the real homogenization starts at that point; that is, the AES distribution changes its shape to have a single peak at the border, suggesting that the difference of initial defects and other stable part vanishes before the system instability.