Near-surface lattice instability in 2D fiber and half-space

We study the vibrational stability of model 2D solids with surfaces when large strains are present. For a fiber under compression, the phonon analysis correctly predicts the behavior of the buckling instability. For half-space under tension and compression, we find that (a) instabilities of the surface phonons, which are localized near the surface, almost always occur before bulk phonon instabilities; (b) with exceptions, short-wavelength or optical surface phonons usually go unstable first, rather than long-wavelength acoustic or elastic surface phonons; and (c) linear instability of a surface phonon triggers surface-initiated defect nucleation, such as dislocations or microcracks. The instability pattern seems to depend more on the surface structure than the interatomic potential model used.