Local Lattice Instability Analysis on Silicon by Tersoff Potential

Abstract

We have long discussed the onset mechanism of inelastic deformation of crystalline/amorphous metals based on atomic elastic stiffness or atomic stability. In the present study, we have first applied our “local lattice instability analysis” to silicon with Tersoff interatomic potential. For a comprehensive discussion including the effect of thermal fluctuation and structural inhomogeneity such as surface and grain boundaries, we have performed various tensile simulations against bulk/nanowire of Si single crystal, laminate-bulk/bamboo-nanowire with Σ5 twist grain boundary. Here, we have prepared different 8 set changing the random number for initial Maxwell-Boltzmann velocity distribution for each simulation. Not only the stress-strain response, but also the atomic elastic stiffness at each atom point, Bαij, is evaluated numerically by Δσαi/Δεj(Voigt notation) against local strain perturbation. The change in the average, standard deviation of det Bαij and the number of det Bαij < 0 atoms have brought us many significant insights, especially in e.g. (1) in the case of bulk single crystal under T = 1K, we have found a slight and smooth stress peak before the unstable stress drop, (2) the standard deviation of det Bαij began to increase at the peak of (1) and then the average of det Bαij became negative or reached “global instability” at the stress drop, (3) even in the systems with thermal fluctuation and structural inhomogeneity, the standard deviation of det Bαij decreases at the initial stage of tension, but it increase again when the lower bound of the standard deviation reaches zero well before the unstable stress drop.