Beat phenomena in metal nanowires, and their implications for resonance-based elastic property measurements

The elastic properties of 1D nanostructures such as nanowires are often measured experimentally through actuation of nanowires at their resonance frequency, and then relating the resonance frequency to the elastic stiffness using the elementary beam theory. In the present work, we utilize large scale molecular dynamics simulations to report a novel beat phenomenon in [110] oriented Ag nanowires. The beat phenomenon is found to arise from the asymmetry of the lattice spacing in the orthogonal elementary directions of [110] nanowires, i.e. the [110] and [001] directions, which results in two different principal moments of inertia. Because of this, actuations imposed along any other direction are found to decompose into two orthogonal vibrational components based on the actuation angle relative to these two elementary directions, with this phenomenon being generalizable to <110> FCC nanowires of different materials (Cu, Au, Ni, Pd and Pt). The beat phenomenon is explained using a discrete moment of inertia model based on the hard sphere assumption; the model is utilized to show that surface effects enhance the beat phenomenon, while effects are reduced with increasing nanowire cross-sectional size or aspect ratio. Most importantly, due to the existence of the beat phenomena, we demonstrate that in resonance experiments only a single frequency component is expected to be observed, particularly when the damping ratio is relatively large or very small. Furthermore, for a large range of actuation angles, the lower frequency is more likely to be detected than the higher one, which implies that experimental predictions of the Young's modulus obtained from resonance may in fact be under-predictions. The present study therefore has significant implications for experimental interpretations of the Young's modulus as obtained via resonance testing.