Delocalized nonlinear vibrational modes in fcc metals

Abstract Nonlinear lattices support delocalized nonlinear vibrational modes (DNVMs) that are exact solutions to the dynamical equations of motion dictated by the lattice symmetry. Since only lattice symmetry is taken into consideration for derivation of DNVMs, they exist regardless the type of interaction between lattice points, and for arbitrary large amplitude. Here, considering space symmetry group of the fcc lattice, we derive all one-component DNVMs, whose dynamics can be described by single equation of motion. Twelve such modes are found and their dynamics are analyzed for Cu, Ni, and Al based on ab initio and molecular dynamics simulations with the use of two different interatomic potentials. Time evolution of atomic displacements, kinetic and potential energy of atoms, and stress components are reported. Frequency-amplitude dependencies of DNVMs obtained in ab initio simulations are used to assess the accuracy of the interatomic potentials. Considered interatomic potentials (by Mendelev et al. and Zhou et al.) for Al are not as accurate as for Cu and Ni. Potentials by Mendelev can be used for relatively small vibration amplitudes, not exceeding 0.1 A, while potentials by Zhou are valid for larger amplitudes. Overall, the presented family of exact solutions of the equations of atomic motion can be used to estimate the accuracy of the interatomic potentials of fcc metals at large displacements of atoms.