School of Chemistry, Physics and Mechanical Engineering, Queensland University of Technology, GPO Box 2434, Brisbane, QLD 4001, Australia.
Nanoscale. 2012 Nov 7;4(21):6779-85. doi: 10.1039/c2nr31545a. Epub 2012 Sep 20.
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.
1D 纳米结构（如纳米线）的弹性性质通常通过在其共振频率下驱动纳米线来实验测量，并使用基本梁理论将共振频率与弹性刚度相关联。在本工作中，我们利用大规模分子动力学模拟来报告 [110] 取向 Ag 纳米线中出现的一种新的拍现象。发现这种拍现象是由于[110]纳米线正交基本方向（即[110]和[001]方向）中晶格间距的不对称性引起的，这导致了两个不同的主转动惯量。因此，发现沿着任何其他方向施加的激励会根据相对于这两个基本方向的激励角度分解为两个正交的振动分量，这种现象可推广到不同材料（Cu、Au、Ni、Pd 和 Pt）的<110> FCC 纳米线。通过基于硬球假设的离散转动惯量模型来解释拍现象；该模型用于表明表面效应增强了拍现象，而随着纳米线横截面尺寸或纵横比的增加，效应会降低。最重要的是，由于存在拍现象，我们证明在共振实验中仅预期观察到单个频率分量，特别是当阻尼比相对较大或非常小时。此外，对于较大的激励角度范围，更有可能检测到较低的频率而不是较高的频率，这意味着通过共振获得的杨氏模量的实验预测实际上可能是低估的。因此，本研究对通过共振测试获得的杨氏模量的实验解释具有重要意义。
