We perform the molecular dynamics simulations for crystalline solid which can be regarded as a thin film. Particles are arranged to form a body-centered cubic structure. The periodic boundary conditions are imposed only along x- and y-axes. The system is composed of n layers and the top layer is considered as solid surface. We use either the harmonic potential or the anharmonic potential for each simulation and the interaction potentials include the nearest neighbor and the second nearest neighbor interactions. Our system is designed so that the bottom layer is connected to the heat bath and the equations of motions of particles in the bottom layer are described as the Langevin equations.
After impulsive force is applied to the surface, time-dependent profiles of the displacement of the surface along z-axis are calculated. From these time-domain data, pulse spectra are obtained by Fourier transformation. On the other hand, applying monochromatic perturbation on the surface, we observe the amplitude of surface oscillation. Sweeping the frequencies, system gain is calculated for given frequency. From these frequency-domain data, continuous-wave spectra are obtained. As expected by linear response theory, these two methods produce the same spectra.
In case of harmonic potential, our system can be explained by 1-dimensional coupled Brownian harmonic oscillator, when coherent phonons are induced. Each layer is considered as an effective particle and their equations of motions are expressed by linear ordinary differential equations. The simulation results are compared with analytical results of 1-dimensional model and show satisfactory agreement. The positions and widths of peaks in spectra can be calculated from eigenvalues of the evolution matrices. When the anharmonicity is introduced to the interaction potential, positions of peaks are shifted and shapes of peaks are changed asymmetrically. Cubic nonlinearity makes red-shift and quartic nonlinearity blue-shift. Also overtone is observed. The effect of each anharmonic terms can be understood from perturbative solutions of anharmonic oscillators. Finally, systems with defects are studied. Vacancies and impurities with large mass are considered. As increasing the ratio of defects, peaks broaden, but peak shift is not large. As increasing the mass of impurity, new peak appears.
