Local Lattice Instability Analysis on Silicon by Tersoff Potential

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, B α ij , is evaluated numerically by Δσ α i /Δε j (Voigt notation) against local strain perturbation. The change in the average, standard deviation of det B α ij and the number of det B α ij < 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 B α ij began to increase at the peak of (1) and then the average of det B α ij 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 B α ij 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.