Role of allowance for interaction of distant neighbors in loss of stability in an extended anharmonic atomic chain

Abstract

We investigate the problem of loss of stability in an anharmonic atomic chain whose ends are subject to a constant tensile stress when we allow for interaction of not only immediate neighbors, but distant neighbors as well. Using the approximation of self-consistent phonons, we obtain general expressions for the law of dispersion for natural oscillations of the chain and the equilibrium interatomic distance. We perform a concrete analysis for the pairwise interatomic Morse potential. Together with the case of first and second neighbors, we consider the general case of interaction of all atoms with each other. We show that instability appears simultaneously in all oscillation modes. Allowance for the interaction of more distant neighbors as well as closer neighbors increases the domain of stability of a chain relative to external stresses.