Nonlinear localized modes in a one-dimensional diamond-structure lattice

The nonlinear localized vibrational modes in an anharmonic atomic chain with uniform mass but two alternating force constants between nearest-neighbors are studied by means of multiple-scale expansion. This atomic chain models the vibrations of an arrow of atoms in the [111] direction of a diamond-structure lattice or a molecular chain. It is shown that the distribution of the atomic displacements is governed by a perturbed nonlinear Schrodinger equation, and both the stationary and moving solutions are obtained. The results are somewhat different from that of the diatomic chain with uniform force constants but two alternating masses. The reason may be that the translational symmetry of diamond-structure lattice is comparetively lower.