Local Lattice Instability Analysis on Silicon by Tersoff Potential
Kisaragi YASHIRO and Masahiro FUJIHARA
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 ƒ°5 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, Bƒ¿ij , is evaluated numerically by ƒ¢ƒÐƒ¿i/ƒ¢ƒÃj(Voigt notation) against local strain perturbation. The change in the average, standard deviation of det Bƒ¿ij and the number of det Bƒ¿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 Bƒ¿ij began to increase at the peak of (1) and then the average of det Bƒ¿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 Bƒ¿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. Key Words:Molecular dynamics simulation, Local lattice instability analysis, Silicon, Tersoff potential, surface, Twist grain boundary