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

The nonlinear localized vibrational modes in an anharmonic atomic chain wit h uniform mass but two alternating force constants between nearest-neighbor s are studied by means of multiple-scale expansion. This atomic chain model s the vibrations of an arrow of atoms in the [111] direction of a diamond-s tructure 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 re sults are somewhat different from that of the diatomic chain with uniform f orce constants but two alternating masses. The reason may be that the trans lational symmetry of diamond-structure lattice is comparetively lower.