CHAOTIC AND REGULAR BEHAVIOR IN 2-DIMENSIONAL ANHARMONIC CRYSTAL LATTICES

A two-dimensional anharmonic lattice model to describe the behavior of coupled nonlinear displacement modes is constructed. The equations of motion and the underlying Hamiltonian of the anharmonic lattice are f ound. The equations of motion are analyzed using the fourth-order Rung e-Kutta method. The integrability of the system is found to depend on its energy as well as the regularity of the system potential. A contin uous transition between regular and chaotic behavior is found and is i llustrated using Poincare sections. As an example, the effects of orde ring on a (100) tungsten surface are discussed in this context.