Symmetry and Models of Double-Wall BN and TiO₂Nanotubes with Hexagonal Morphology

Abstract

The line symmetry groups for one-periodic (1D) nanostructures with rotohelical symmetry have been applied for symmetry analysis of double-wall boron nitride and titania nanotubes (DW BN and TiO 2 NTs) formed by rolling up the stoichiometric two-periodic (2D) slabs of hexagonal structure with the same or opposite orientation of translation and chiral vectors. We have considered the two sets of commensurate DW BN and TiO 2 NTs with either armchair-or zigzag-type chiralities, i.e., (n 1 ,n 1 )@(n 2 ,n 2 ) or (n 1 ,0)@(n 2 ,0), respectively. To establish the equilibrium interwall distances corresponding to the minima of energy, we have varied chiral indices n 1 and n 2 of the constituent single-wall (SW) nanotubes. To analyze the structural and electronic properties of hexagonal DW NTs, we have performed ab initio LCAO calculations using the hybrid HartreeÀFock/KohnÀSham exchange-correlation functional PBE0 as implemented in CRYSTAL-09 code. The inversely stacked structure of zigzag-type DW BN NT, characterized by arrangement of positively and negatively charged rings in each atomic cross section (consisting of either B or N atoms, respectively), has been found to be energetically more preferable as compared to the straightly stacked structure containing nanotube rings consisting of the same type of atoms in cross sections, i.e., B(N) and B(N). In armchair-type DW BN NTs, each atomic ring contains the whole number of BÀN bonds, which reduces the electrostatic interaction between both walls. On the other hand, main contribution to interwall bonding in DW TiO 2 NTs is provided by interaction between the nearest oxygen and titanium ions of neighboring shells. The interaction between the walls results in a decrease of band gaps for double-wall NTs as compared to those for SW NTs, which is substantially larger for TiO 2 .

Structure and stability of SnS2-based single- and multi-wall nanotubes

“…Y calculated for the SnS 2 layer directly: (n,n), DI corr. The stability of MWNT in respect to their SWNT constituents can be 451 measured by the so-called binding energy E bind [65],…”

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“…The graph of the Titania Nanotubes TiO 2 (m,n) is presented in Fig.1, where m denotes the number of octagons in a column and n denotes the number of octagons in a row of the Titania Nanotubes. We encourage the reader to consult papers [19][20][21][22][23][24][25][26][27][28][29][30] , for further study and more information of Titania Nanotubes TiO 2 . …”

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“…A 2-dimensional lattice of the Titania Nanotubes, TiO 2 [m,n], is shown in Fig. 1 and for more chemical properties of TiO 2 Nanotubes and TiO 2 nano-composite, see [15][16][17][18] . In TiO 2 [m,n], m and n denotes the number of octagons in a column and the number of octagons in a row 19 -37 .…”