Robust Bessel-function-based method for determination of the (n,m) indices of single-walled carbon nanotubes by electron diffraction

Hua Jiang (Corresponding Author), David P. Brown, Albert G. Nasibulin, Esko I. Kauppinen

Research output: Contribution to journalArticleScientificpeer-review

17 Citations (Scopus)

Abstract

We report a calibration-free method for the determination of chiral indices (n, m)
of single-walled carbon nanotubes from their electron diffraction patterns based on Bessel function analysis of the diffracted layer lines. An approach has been developed for confident identification of the orders of the Bessel functions from the intensity modulations of the diffraction layer lines, to which (n, m) are correlated. In particular, we critically evaluate the effect of nanotube inclination on the validity of the method and show that the layer lines governed by high-order Bessel functions tolerate higher tilt angles than those of low-order Bessel functions and thus are favored for (n, m) evaluation. The method is of particular significance in that it considerably enhances the precision of chiral indexing and makes possible the analysis of high-order Bessel functions, especially when EDPs are of relatively low pixel resolution. The technique can be extended to structural analysis of double-walled carbon nanotubes.
Original languageEnglish
Article number035427
Number of pages8
JournalPhysical Review B: Condensed Matter and Materials Physics
Volume74
Issue number3
DOIs
Publication statusPublished - 2006
MoE publication typeA1 Journal article-refereed

Fingerprint

Bessel functions
Single-walled carbon nanotubes (SWCN)
Electron diffraction
electron diffraction
carbon nanotubes
Carbon Nanotubes
structural analysis
Structural analysis
Nanotubes
Diffraction patterns
inclination
Carbon nanotubes
nanotubes
diffraction patterns
Diffraction
Pixels
pixels
Modulation
Calibration
modulation

Keywords

  • carbon nanotubes
  • nanotubes
  • single-walled carbon nanotubes
  • chirality
  • Bessel functions
  • electron diffraction analysis
  • diffraction

Cite this

@article{82802e112c684eba9f9e58dcf8f52839,
title = "Robust Bessel-function-based method for determination of the (n,m) indices of single-walled carbon nanotubes by electron diffraction",
abstract = "We report a calibration-free method for the determination of chiral indices (n, m)of single-walled carbon nanotubes from their electron diffraction patterns based on Bessel function analysis of the diffracted layer lines. An approach has been developed for confident identification of the orders of the Bessel functions from the intensity modulations of the diffraction layer lines, to which (n, m) are correlated. In particular, we critically evaluate the effect of nanotube inclination on the validity of the method and show that the layer lines governed by high-order Bessel functions tolerate higher tilt angles than those of low-order Bessel functions and thus are favored for (n, m) evaluation. The method is of particular significance in that it considerably enhances the precision of chiral indexing and makes possible the analysis of high-order Bessel functions, especially when EDPs are of relatively low pixel resolution. The technique can be extended to structural analysis of double-walled carbon nanotubes.",
keywords = "carbon nanotubes, nanotubes, single-walled carbon nanotubes, chirality, Bessel functions, electron diffraction analysis, diffraction",
author = "Hua Jiang and Brown, {David P.} and Nasibulin, {Albert G.} and Kauppinen, {Esko I.}",
year = "2006",
doi = "10.1103/PhysRevB.74.035427",
language = "English",
volume = "74",
journal = "Physical Review B",
issn = "2469-9950",
publisher = "American Physical Society",
number = "3",

}

Robust Bessel-function-based method for determination of the (n,m) indices of single-walled carbon nanotubes by electron diffraction. / Jiang, Hua (Corresponding Author); Brown, David P.; Nasibulin, Albert G.; Kauppinen, Esko I.

In: Physical Review B: Condensed Matter and Materials Physics, Vol. 74, No. 3, 035427 , 2006.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Robust Bessel-function-based method for determination of the (n,m) indices of single-walled carbon nanotubes by electron diffraction

AU - Jiang, Hua

AU - Brown, David P.

AU - Nasibulin, Albert G.

AU - Kauppinen, Esko I.

PY - 2006

Y1 - 2006

N2 - We report a calibration-free method for the determination of chiral indices (n, m)of single-walled carbon nanotubes from their electron diffraction patterns based on Bessel function analysis of the diffracted layer lines. An approach has been developed for confident identification of the orders of the Bessel functions from the intensity modulations of the diffraction layer lines, to which (n, m) are correlated. In particular, we critically evaluate the effect of nanotube inclination on the validity of the method and show that the layer lines governed by high-order Bessel functions tolerate higher tilt angles than those of low-order Bessel functions and thus are favored for (n, m) evaluation. The method is of particular significance in that it considerably enhances the precision of chiral indexing and makes possible the analysis of high-order Bessel functions, especially when EDPs are of relatively low pixel resolution. The technique can be extended to structural analysis of double-walled carbon nanotubes.

AB - We report a calibration-free method for the determination of chiral indices (n, m)of single-walled carbon nanotubes from their electron diffraction patterns based on Bessel function analysis of the diffracted layer lines. An approach has been developed for confident identification of the orders of the Bessel functions from the intensity modulations of the diffraction layer lines, to which (n, m) are correlated. In particular, we critically evaluate the effect of nanotube inclination on the validity of the method and show that the layer lines governed by high-order Bessel functions tolerate higher tilt angles than those of low-order Bessel functions and thus are favored for (n, m) evaluation. The method is of particular significance in that it considerably enhances the precision of chiral indexing and makes possible the analysis of high-order Bessel functions, especially when EDPs are of relatively low pixel resolution. The technique can be extended to structural analysis of double-walled carbon nanotubes.

KW - carbon nanotubes

KW - nanotubes

KW - single-walled carbon nanotubes

KW - chirality

KW - Bessel functions

KW - electron diffraction analysis

KW - diffraction

U2 - 10.1103/PhysRevB.74.035427

DO - 10.1103/PhysRevB.74.035427

M3 - Article

VL - 74

JO - Physical Review B

JF - Physical Review B

SN - 2469-9950

IS - 3

M1 - 035427

ER -