Modeling the oscillations of a copper nanorod using the molecular dynamics method

Abstract

937Nanorods (NRs) and nanowires (NWs) are the pri mary elements of nanoelectromechanical sensors and nanoswitches [1,2]. The natural frequency of metallic NRs lies in the gigahertz range, and the study of the dynamics of oscillations of such nanoresonators with the use of the molecular dynamics (MD) method allowed the researchers to characterize its specifics [3][4][5]. Analysis of the most widely studied system (metallic nanobeams (NWs) fixed at both ends) revealed the influence of surface effects on natural fre quency of this system f 0 and the emergence of beats in its oscillations [4,5]. The natural frequencies of nan oresonators were often determined from the time dependence of the periodic variation of their potential energy [3][4][5]. However, this f 0 determination method does not allow one to trace their spatial oscillations. This is especially important in the studies of oscilla tions of an NR fixed at one side. The oscillations of such an NR may take place in different planes and are coupled. Using the example of the dynamics of oscil lations of a copper NR, we show in the present paper that the determination of the resonance frequency from the data on periodic variations of the potential energy of this NR produces results that differ from the frequency value determined based on the data on the time variation of spatial NR oscillations. It is demon strated that the distribution of oscillation energy over different degrees of freedom may allow the NR poten tial energy to remain constant while the NR itself con tinues oscillating. It is found that predominantly lon gitudinal oscillations arise in the process of relaxation in a stressed NR. The Young's modulus of a copper NR is determined based on the results of measure ments of the frequency of its longitudinal oscillations. The obtained value is almost 2.5 times lower than the Young's modulus of bulk material.The modeling was performed with the use of an MDEAM software package of our own development [6]. This software package incorporates a calculation module and atomic structure visualization tools utiliz ing an OpenGL graphics library of our own develop ment. The Cu-Cu interatomic interaction was calcu lated with the use of the embedded atom method (EAM potential) [7]. The equations of motion were integrated using a leapfrog algorithm with a time step of 10 -15 s. The constancy of the number of particles, the volume, and the energy (NVE ensemble) was maintained in the process of modeling. The initial model temperature was set to 1 K. The coordinates of atoms were output to a file with an interval of 10 -13 s. This allowed tracing oscillations in the system with frequencies lower than 1 THz.The NR was an 8a × 8a × 90a (3.0 × 3.0 × 16.5 nm) parallelepiped with a 20a × 20a × 9a (7.2 × 7.2 × 1.5 nm) base cleaved from a bulk FCC (100) copper crystal with its lattice constant a = 0.3615 nm (Fig. 1a). The number of atoms in the NR equaled 18848. The lower two atomic layers of the base were fixed. Periodic boundary conditions in the XY plane were used to imit...