TiS₂and ZrS₂single- and double-wall nanotubes: First-principles study

Abstract

Hybrid density functional theory has been applied for investigations of the electronic and atomic structure of bulk phases, nanolayers, and nanotubes based on titanium and zirconium disulfides. Calculations have been performed on the basis of the localized atomic functions by means of the CRYSTAL-2009 computer code. The full optimization of all atomic positions in the regarded systems has been made to study the atomic relaxation and to determine the most favorable structures. The different layered and isotropic bulk phases have been considered as the possible precursors of the nanotubes. Calculations on single-walled TiS2 and ZrS2 nanotubes confirmed that the nanotubes obtained by rolling up the hexagonal crystalline layers with octahedral 1T morphology are the most stable. The strain energy of TiS2 and ZrS2 nanotubes is small, does not depend on the tube chirality, and approximately obeys to D(-2) law (D is nanotube diameter) of the classical elasticity theory. It is greater than the strain energy of the similar TiO2 and ZrO2 nanotubes; however, the formation energy of the disulfide nanotubes is considerably less than the formation energy of the dioxide nanotubes. The distance and interaction energy between the single-wall components of the double-wall nanotubes is proved to be close to the distance and interaction energy between layers in the layered crystals. Analysis of the relaxed nanotube shape using radial coordinate of the metal atoms demonstrates a small but noticeable deviation from completely cylindrical cross-section of the external walls in the armchair-like double-wall nanotubes.

Application of zone‐folding approach to the first‐principles estimation of thermodynamic properties of carbon and ZrS2‐based nanotubes

“…[5] However, the deviation from D 22 may be significant. A better approximation has been obtained with a power function [34] : Table 4 lists the values of c and b calculated for E str and A str at 300 and 600 K. The power c is very close to 2 only for the E str of SWCNTs calculated through the internal energy. The values of c and b do not depend on the temperature considerably for E str of both graphene and disulfide NTs.…”

“…[34] After the rolling procedure, the symmetry of the achiral (n, 0), (n, n) and chiral (n, m) SWZNTs is described by line groups L(2n) n/ m, L(2n) n mc, and L(N) S belonging to families 4 (point symmetry C 2nh ), 8 (point symmetry C 2nv ), and 1 (point symmetry C N ), accordingly. [11,34] [a] Graphite value from Ref. [30].…”

First‐Principles Calculations of Phonons and Thermodynamic Properties of Zr(Hf)S2‐Based Nanotubes

“…The values obtained in this work are given in Table S4. [37,56] There is no appreciable difference between strain energy of ac and zz nanotubes. Figure 5 shows the strain energy dependence on average diameter D for ZrS 2 and HfS 2 nanotubes.…”

Thermodynamic properties of nanotubes: zone-folding approach

“…The parent hexagonal layers have layer group 72 (P -3/ml) which is the subgroup of space group 164 (P -3/ml) -the symmetry group of the most stable bulk TiS 2 and ZrS 2 phases [28]. As follows from Refs.…”

“…As follows from Refs. [27,28], after the rolling procedure the symmetry of the achiral (n, 0), (n, n) and chiral (n, m) NTs is described by line groups L(2n) n /m, L(2n) n mc, and L(N) S belonging to families 4 (point symmetry C 2nh ), 8 (point symmetry C 2nv ) and 1 (point symmetry C N ), respectively. The models for the zigzag and armchair NTs with hexagonal morphology are presented in Figs.…”