An atomistic instability condition and applications

We present an atomic-level criterion for material stability in an atomic system. The criterion draws on the strong ellipticity condition in continuum elasticity theory; however, it is formulated directly in terms of atomic potential without resorting to the continuum concepts. Since the criterion is based on local energetics at an atomic site, we expect it to be applicable to pre-defected systems, provided that the site energy can be reasonably defined. The kinetic implication of the stability condition is also discussed. The application in nanotubes shows that the criterion can capture the tensile limit strain of both perfect and defective nanotubes, and the predictions agree well with the atomistic simulations reported in the literature.