Ab initio systematic study of chirality effects on phonon spectra, mechanical and thermal properties of narrow single walled carbon nanotubes H. Tashakori a , B. Khoshnevisan a,⇑ , F. Kanjuri b a Faculty of Physics, University of Kashan, Kashan, Islamic Republic of Iran b Physics department, Kharazmi University, Karaj, Islamic Republic of Iran article info Article history: Received 2 July 2013 Received in revised form 7 October 2013 Accepted 13 October 2013 Available online 21 November 2013 Keywords: DFPT calculation Chirality Phonon DOS Young modulus RBM Poisson ratio abstract Pseudo-potential method under frame work of density functional perturbation theory (DFPT) has been utilized to calculate the phonon spectrum, phonon DOS, specific heat capacity and mechanical properties of narrow armchair and zigzag single walled carbon nanotubes (SWCNTs). Our calculations show that although their Young modulus are about 1 TPa, but armchair SWCNTs have greater compressive modulus than the zigzag tubes while the situation would be vice versa for tensile modulus. On the other hand, it was found out that specific heat capacity of narrow tubes shows chirality independence and decreases by increasing the radius of nanotube whereas, this is not the case for the wider ones. In addition, chirality dependence of the radial breadth mode (RBM) frequency of narrow SWCNTs has been shown. Ó 2013 Elsevier B.V. All rights reserved. 1. Introduction Carbon nanotubes (CNTs) have the most applicable perspective among the other carbon based structures in new technologies because of their specific electronic, thermal and mechanical properties which are depending on their curvatures and chiralities. On the other hand, geometry of CNTs makes it possible to fabricate low dimension physical systems in order to achieve higher advan- tages in technology [1–9]. Considering the thermal and mechanical properties, multi walled CNTs have the biggest tensile strength among the known materials; about 63 GPa [10] (1000 times of car tiers) and also very high axial thermal conductivity. Their specific heat capacities and phonon spectra are the important quantities for industrial applications and experimental researches [11–13]. The zone-folding method gives a general approach for obtaining the phonon dispersion relations of CNTs, whereby the phonon dis- persion relations of a graphene sheet (2D) are folded into the 1D Brillouin zone of the tubes. However, in the zone-folding method, some lower-frequency phonon modes of nanotubes cannot be ex- pressed by graphenes due to the decoupled in-plane and out of planed modes. In order to avoid this difficulty, Saito et al. [14] have used tight-binding molecular dynamic (MD) method. Saxena and Sanyal [15] have also employed force constants tensor to find out the phonon dispersive relations for (10,10) and wider SWCNTs [14,15]. Full electron ab initio calculation has been done by Lier et al. [22] for Young modulus and Poisson ratio for nanotubes with diameters around 7 Å. Recently Vallabhanani et. al. [23] have used mode projection MD technique to investigate flexure modes of the acoustic phonons and also their lifetimes for armchair nanotubes. To the best of our knowledge, for narrow CNTs (diameter <7 Å) some anomalies originated from p–r re-hybridization effect have been predicted [3]. In addition, the full electron ab initio methods are much time-consuming, therefore in order to get reasonable quantitative results and understanding of the phonon dynamics, we have utilized pseudopotential DFPT calculations to conduct a systematic study of influence of the SWCNT’s chirality on their thermal and mechanical properties. In this regard, phonon disper- sion, phonon density of states (DOSs), specific heat capacity, Young modulus, Poisson ratio, elastic constants and RBM frequencies of the narrow carbon nanotubes have been re-calculated. 2. DFPT calculation methods As is well known in harmonic approximation, a SWCNT consists of a periodic array of carbon ions that will oscillate around their equilibrium positions on the surface of an empty tube by thermal 0927-0256/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.commatsci.2013.10.019 ⇑ Corresponding author. Tel.: +98 9123147358. E-mail address: b.khosh@kashanu.ac.ir (B. Khoshnevisan). Computational Materials Science 83 (2014) 16–21 Contents lists available at ScienceDirect Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci