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Continuum model for low-frequency phonons of boron nitride nanotubes
Institution:1. Universidad Autónoma del Estado de Morelos, Ave. Universidad 1001, CP 62209, Cuernavaca, Morelos, Mexico;2. Universidad de Sancti Spiritus “José Martí Pérez”, Ave. de los Mártires 360, CP 62100, Sancti Spiritus, Cuba;3. CLAF – Centro Latino-Americano de Física, Avenida Venceslau Braz, 71, Fundos, 22290-140 Rio de Janeiro, RJ, Brasil;4. Instituto de Ciencia de Materiales de Madrid (ICMM), Consejo Superior de Investigaciones Científicas (CSIC), C/ Sor Juana Inés de la Cruz 3, 28049 Madrid, Spain;1. Institut de Physique et de Chimie des Matériaux de Strasbourg, Université de Strasbourg, CNRS UMR 7504, 23 rue du Loess, BP 43, F-67034 Strasbourg Cedex 2, France;2. Freiburg Institute for Advanced Studies, Albert-Ludwigs-Universität, Albertstr. 19, D-79104 Freiburg, Germany;1. Kantonsschule Frauenfeld, Ringstrasse 10, CH-8500 Frauenfeld, Switzerland;2. Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (UIB-CSIC), E-07122 Palma de Mallorca, Spain
Abstract:A continuum model is employed to calculate the low-frequency phonons of boron nitride nanotubes. We find an excellent agreement of the optically active modes calculated within this approach and those from more elaborate calculations within an energy and wavelength window that can be established beforehand, from the choice of the bulk input parameters. We verify that this model describes correctly the dependence of radial breathing mode with the radius, the existence of parabolic modes at small wavevectors, and other general characteristics of the dispersion relations of these systems.
Keywords:Oscillation modes  Phonons  Boron nitride nanotubes  Continuum model
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