Three-Dimensional Representation of Curved Nanostructures
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Three-Dimensional Representation of Curved Nanostructures Z. Huang, D.A. Dikin, W. Ding, Y. Qiao, Y. Fridman1 and R.S. Ruoff Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208, USA 1 Department of Computer Science, University of North Carolina, Chapel Hill, NC 27599, USA ABSTRACT Nanostructures, such as nanowires, nanotubes, and nanocoils, can be described in many cases as quasi one-dimensional (1D) curved objects projecting in three-dimensional (3D) space. A parallax method to reconstruct the correct three-dimensional geometry of such 1D nanostructures is presented. A series of images were acquired at different view angles, and from those image pairs, 3D representations were constructed using a MATLAB program. Error analysis as a function of view-angle between the two images is discussed. As an example application, we demonstrate the importance of knowing the true 3D shape of Boron nanowires. Without precise knowledge of the nanowire’s dimensions, diameter and length, mechanical resonance data cannot be properly fit to obtain an accurate estimate of the Young’s modulus. INTRODUCTION The mechanical properties of nanostructures such as wires, tubes, coils, ribbons (for discussion purposes, we will refer only to nanowires, NWs, below) are of both fundamental and practical interest. One method of determining a NW’s stiffness (Young’s modulus, E) is to drive them in a mechanical resonance. This method requires that the geometry, density (mass per unit length), and resonant frequency of the NWs be known. The 4th power dependence of the defined value of E on the length, L, is such that an error in L of 5% leads to an error in E of ~20%. The most common method of detecting mechanical resonance of NWs is to use scanning or transmission electron microscopy (SEM or TEM)[1-4]. It is well known that the electron microscope has high resolution in the plane orthogonal to the electron beam (the XOY plane) but low resolution in the z direction due to a high depth of focus. Determining L for a NW from one two-dimensional (2D) image only yields a good value when the NW happens to lie almost exactly in the XOY plane. Since this is not typically the case in many experiments, L would be poorly determined from a single image. This motivates developing rapid methods to determine the true 3D geometry of the NW, which will also assist in the maneuverability of the NW and other tools used to configure nanoscale experiments in 3D space. There is a long list of experiments done with the aim to realize stereo vision by electron microscopy[5-7]. All of these experiments utilize a similar method that involves the creation of a series of micrographs with defined varying angles of incidence of the primary electron beam. For example, Cheng et al.[8] and Hein[9] have used the parallax method to generate 3D representations of cytoskeleton or measuring topography of rough surface region under an electron microscope (EM). Images are acquired from two different viewpoints, and the object’s 3D coordinates are calcula
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