Atomic simulation of phonon scattering by point defect in honeycomb lattice

In this paper, the impact of a single point defect on phonons with different frequencies in a two-dimensional honeycomb lattice is investigated. We first demonstrate the dynamic equations for the harmonic honeycomb lattice, along with the equations of motion for atoms near the point defect. Then, we derive the expression for a single-frequency phonon mode. To realize the incidence of phonons and eliminate boundary reflections, we adopt the two-way boundary condition with the single-frequency phonon mode as a source term. Numerical computations show that as the frequency of incident phonons increases, the scattering patterns become more pronounced, displaying symmetric water-like ripple images. Furthermore, the nonlinear honeycomb lattice with FPU- beta potential is also investigated. In a nonlinear lattice, it has been found that a point defect not only alters the propagation direction and vibration amplitude of phonons but also enhances the interaction between phonon modes, thereby generating a large number of high-frequency phonons, which may increase the randomness of the scattering pattern.