Lattice Instability Analysis of Silicon and Aluminum under [001] Uniaxial Tension by Means of ab initio Molecular Dynamics

Recent rapid progress in computers has made it possible to elucidate not only static atomic structure but also mechanical properties such as theoretical strength by using the ab-initio molecular dynamics. The theoretical strength, however, is evaluated on the assumption that crystals deform in a definite deformation path because of computational limitation, so that it is necessary to clarify the relationship between the theoretical strength and bifurcation criteria to the other deformation path. The lattice instability analysis based on the classical interatomic potentials has suggested that the bifurcation to the anisotropic transverse contraction becomes more important than the theoretical tensile strength in the uniaxial [001] tension. In this study, the bifurcation point under tension is investigated by means of ab-initio molecular dynamics. Si and Al single crystals are subjected to the uniaxial [001] tension under isotropic and anisotropic transverse contractions. The difference in energy shows that the deformation path of isotropic Poisson's contraction would bifurcate to anisotropic contraction at *ezz = 0.093 and *ezz = 0.051 for Si and Al, respectively, while the theoretical strengths under isotropic contractions reach *ezz = 0.25 (Si) and *ezz = 0.18 (Al). Then the lattice instability at these bifurcation points is investigated on the basis of the positive definiteness of the elastic stiffness coefficients. It is shown that the positiveness is violated after the bifurcation point and the instability is caused by the negativeness of the minor determinants of the stiffness matrix, which represents the compliance against the anisotropic transverse contractions.