Analytical evaluation of unstable deformation criterion of atomic structure and its application to nanostructure

An analytical method for evaluating the unstable deformation modes of atomic structure is proposed. The instability criterion is given as positiveness of the minimum eigenvalue of the matrix, which consists of second order differential of potential energy with respect to atomic coordinates. The eigenvector for the minimum eigenvalue indicates the relative displacement of atoms at the instability (unstable deformation mode). The method is applied to tensile strengths of (1) thin film and (2) cracked body. The thin film with the thickness under 10 nm is weaker than bulk. The crack propagation mode in (2) is dependent on the boundary condition, and the mode is successfully distinguished by the method.