Date of Original Version
Copyright 2013 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The version of record may be found at http://dx.doi.org/10.1063/1.4774077
Abstract or Description
External loads typically have an indirect influence on phonon curves, i.e., they influence thephonon curves by changing the state about which linearization is performed. In this paper, we show that in nanotubes, the axial load has a direct first-order influence on the long-wavelength behavior of the transverse acoustic (TA) mode. In particular, when the tube is force-free, the TA mode frequencies vary quadratically with wave number and have curvature (second derivative) proportional to the square-root of the nanotube's bending stiffness. When the tube has non-zero external force, the TA mode frequencies vary linearly with wave number and have slope proportional to the square-root of the axial force. Therefore, the TA phonon curves—and associated transport properties—are not material properties but rather can be directly tuned by external loads. In addition, we show that the out-of-plane shear deformation does not contribute to this mode and the unusual properties of the TA mode are exclusively due to bending. Our calculations consist of 3 parts: First, we use a linear chain of atoms as an illustrative example that can be solved in close-form; second, we use our recently developed symmetry-adaptedphonon analysis method to present direct numerical evidence; and finally, we present a simple mechanical model that captures the essential physics of the geometric nonlinearity in slendernanotubes that couples the axial load directly to the phonon curves. We also compute thedensity of states and show the significant effect of the external load.
Journal of Applied Physics, 113, 023503.