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By Marcelo Kuroda1, Salvador Barraza-Lopez2, J. P. Leburton3
1. Auburn University 2. Virginia Tech 3. University of Illinois at Urbana-Champaign
Calculates the phonon band structure of carbon nanotubes using the force constant method.
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Version 1.1.1w - published on 17 Mar 2015
doi:10.4231/D3WW77124 cite this
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11 Feb 2010
4.0 out of 5 stars
The CNTphonons tool from the nanoHUB calculates the phonon dispersion relation (E or omega vs. q) and the phonon density of states (DOS) for carbon nanotubes (CNTs) with nearly any (n,m) chiral index. The tool uses the force constant method with the parameters for graphite described in the paper from Saito, et al. (Phys. Rev. B 57, 4145 (1998)). The range of the n index value is 5 to 20, while there are no restrictions on the integral values for the m index. The number of q-points used for the E(or omega) versus q calculation can range from 2 to 500, while the number of points into which the energy range is divided for calculating the phonon DOS simply must be greater than 10.
The simulation time depends strongly on the number of q-points, as one expects. However, the number of “DOS points” does not strongly affect the computational time. Simulations for zig-zag or armchair CNTs run significantly more quickly than simulations for chiral CNTs, holding all other simulation parameters constant. In fact, attempting to calculate the phonon dispersion and density of states for a (9,5) CNT did not give a result.
The user interface is easy to use and navigate. Each of the 3 plots generated can be printed as an image or exported for plotting with a different software package. It would be nice to have an output log file to display the (n,m) indices for the simulation, the number of q-points, the number of DOS points, and the kind and number of phonon modes.
While the CNTbands tool can calculated the E-k relation and electronic DOS for both CNTs and carbon nanoribbons (CNRs) (also known as graphene nanoribbons (GNRs)), CNTphonons does not have the capability of calculating the phonon dispersion relation and density of states for GNRs. However this calculation would not be straightforward, since the boundary conditions and types of phonon modes would be different than those for CNTs. However, integrating the ability to calculate (or just show) the phonon dispersion relation and density of states for bulk graphene could be useful for comparison with those calculated for the CNTs.
The tool cites a paper by Dubay and Kresse (Phys. Rev. B 67, 035401 (2003)) that delineates the limitations of the model used to calculate the phonon band structure in this tool. The main problems seem to be neglecting the effects of curvature when using the zone-folding technique and possible inaccuracy in the predicted frequencies, since the force constants are usually fitted to the phonon dispersion relation for graphite measured experimentally. According to the paper, this problem is more severe for low-frequency modes (in the elastic regime). A more recent paper by Lazzeri, et al. (Phys. Rev. B 78, 081406 (2008)), critiques ab-initio computations for the electron-phonon interaction and the phonon dispersions using the generalized gradient approximation (GGA) and local-density approximation (LDA). The authors purport to show that the GW approximation can be used to calculate the electron-phonon interaction and the phonon dispersion and that the other methods underestimate portions of the phonon dispersion.
In summary, this tool provides very a good qualitative calculation for the phonon dispersion of CNTs. Quantitatively, the values calculated might be slightly incorrect. However, anybody desiring greater accuracy should run an ab-initio¬ (or other method) calculation for the phonon dispersion. The tool has a good user interface; however, the phonon dispersion for bulk graphene would be a useful addition for reference.
Justin Koepke (UIUC)
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12 May 2009
I reviewed this nanoHUB tool as part of ECE539 ( at University of Illinois at Urbana-Champaign). The tool is quite useful to gain an understanding of the phonon band structure and DOS for different carbon nanotubes. However, the tool could not successfully calculate and display the phonon band structure for a (9,5) tube. Calculations for zig-zag and armchair CNTs were quite fast though. It might be useful to have the phonon dispersion relation for bulk graphene as a reference for comparison with the phonon dispersions calculated for the CNTs.