^{1}, Rui Li

^{1}, Yong Ge

^{2}and Jinming Dong

^{1,a)}

### Abstract

Growth of single-walled silver and copper nanotubes (Ag- and Cu-SWNTs), confined in carbon nanotubes (CNTs), has been studied by using the classical molecular dynamics method. It is found that: (1) Four kinds of Ag-SWNTs, i.e., (3, 2), (4, 2), (4, 3), and (5, 3) ones, and five kinds of Cu-SWNTs, i.e., (3, 2), (4, 2), (4, 3), (4, 4), and (5, 3) ones, could be formed when the diameters of outside CNT containers are changed from 6.78 to 10.86 Å. (2) The formation of the Ag- and Cu-SWNTs in confined CNTs is less sensitive to the CNTs' tube indices, but heavily influenced by the CNTs’ diameters. And the Ag- and Cu-SWNTs, formed in confined CNTs, are radially compressed, when the CNTs’ diameters are small. (3) The frequencies of the radial breathing modes of Ag- and Cu-SWNTs are approximately to vary linearly with the inverse tube diameters.

The authors acknowledged financial supports from the State Key Program for Basic Research of China through the Grant Nos. 2010CB630704 and 2011CB922100Q. Our numerical calculations are performed in the High Performance Computing Center of Nanjing University. Y. Han gratefully acknowledged useful discussions with Dr. Aping Yang and Associate Professor J. Zhou.

I. INTRODUCTION

II. COMPUTATIONAL MODEL AND METHOD

III. RESULTS AND DISCUSSIONS

A. Ag- and Cu-SWNTs obtained by MD method

B. The phase transition of (3, 2) Cu-SWNT in confined (10, 0) CNT

C. The RBMs of Ag-SWNTs and Cu-SWNTs

IV. SUMMARY

## Figures

Schematic show for four kinds of formed Ag-SWNTs, respectively, in outside (11, 0), (7, 7), (13, 0), and (12, 2) CNT containers: (a) (3, 2), (b) (4, 2), (c) (4, 3), (d) (5, 3) Ag-SWNTs. Here, the outside carbon atoms and inside silver atoms are denoted by dark black and light blue colors, respectively.

Schematic show for four kinds of formed Ag-SWNTs, respectively, in outside (11, 0), (7, 7), (13, 0), and (12, 2) CNT containers: (a) (3, 2), (b) (4, 2), (c) (4, 3), (d) (5, 3) Ag-SWNTs. Here, the outside carbon atoms and inside silver atoms are denoted by dark black and light blue colors, respectively.

Schematic show for five kinds of formed Cu-SWNTs, respectively, in outside (10, 0), (11, 0), (9, 4), (12, 0), and (11, 2) CNT containers: (a) (3,2), (b) (4, 2), (c) (4, 3), (d) (4, 4), (e) (5, 3) Cu-SWNTs. Here, the outside carbon atoms and inside copper atoms are denoted by dark black and yellow colors, respectively.

Schematic show for five kinds of formed Cu-SWNTs, respectively, in outside (10, 0), (11, 0), (9, 4), (12, 0), and (11, 2) CNT containers: (a) (3,2), (b) (4, 2), (c) (4, 3), (d) (4, 4), (e) (5, 3) Cu-SWNTs. Here, the outside carbon atoms and inside copper atoms are denoted by dark black and yellow colors, respectively.

Schematic show of an unrolled (4, 2) Ag-SWNT, lying in a silver (111) sheet. Here, four unit cells of the silver tube are shown. There are 4 atoms in a unit cell. The and are the unit vectors of the two-dimensional triangular silver sheet. is the chiral vector along the circumference direction of the silver nanotube, and is the translational vector along its tube axis.

Schematic show of an unrolled (4, 2) Ag-SWNT, lying in a silver (111) sheet. Here, four unit cells of the silver tube are shown. There are 4 atoms in a unit cell. The and are the unit vectors of the two-dimensional triangular silver sheet. is the chiral vector along the circumference direction of the silver nanotube, and is the translational vector along its tube axis.

Multimedia file, a cartoon for the growth of a (3, 2) Ag-SWNT in a confined (11, 0) CNT at both fixed (left) and unfixed (right) cases, obtained in our MD simulations. When the CNT is not fixed, the Ag-Ag and C-C interactions are described by the EAM and Tersoff potentials, respectively. And the Ag-C interaction is described by the LJ potential with the related parameters given in Refs. 36 and 41–44 . Our simulation result clearly shows that the inner (3, 2) Ag-SWNT could still be formed in the MD simulation in the unfixed case and outer (11, 0) SWCNT is not destroyed except that its diameter becomes a little bit larger at finite temperature. For example, the diameters of inner Ag-SWNT and outside unfixed CNT reached 2.88 Å and 8.94 Å, respectively, in contrast to their previous values of 2.78 Å and 8.61 Å under the fixed CNT confinement. In a word, the condition of the fixed CNT would be appropriate for our MD simulations on the growth of transition metal tubes in it. (enhanced online). [URL: http://dx.doi.org/10.1063/1.4811368.1]doi: 10.1063/1.4811368.1.

Multimedia file, a cartoon for the growth of a (3, 2) Ag-SWNT in a confined (11, 0) CNT at both fixed (left) and unfixed (right) cases, obtained in our MD simulations. When the CNT is not fixed, the Ag-Ag and C-C interactions are described by the EAM and Tersoff potentials, respectively. And the Ag-C interaction is described by the LJ potential with the related parameters given in Refs. 36 and 41–44 . Our simulation result clearly shows that the inner (3, 2) Ag-SWNT could still be formed in the MD simulation in the unfixed case and outer (11, 0) SWCNT is not destroyed except that its diameter becomes a little bit larger at finite temperature. For example, the diameters of inner Ag-SWNT and outside unfixed CNT reached 2.88 Å and 8.94 Å, respectively, in contrast to their previous values of 2.78 Å and 8.61 Å under the fixed CNT confinement. In a word, the condition of the fixed CNT would be appropriate for our MD simulations on the growth of transition metal tubes in it. (enhanced online). [URL: http://dx.doi.org/10.1063/1.4811368.1]doi: 10.1063/1.4811368.1.

Diffusion coefficient versus temperature for a Cu system with total 208 Cu atoms, confined in a (10, 0) CNT. The relative radial density profiles (ρ(r)) of Cu atoms in the solid state at lower temperature of 820 K and in the fluid state at high temperature of 1000 K are given in the insets (a) and (b), respectively, in which their corresponding top-view geometrical configurations are also shown.

Diffusion coefficient versus temperature for a Cu system with total 208 Cu atoms, confined in a (10, 0) CNT. The relative radial density profiles (ρ(r)) of Cu atoms in the solid state at lower temperature of 820 K and in the fluid state at high temperature of 1000 K are given in the insets (a) and (b), respectively, in which their corresponding top-view geometrical configurations are also shown.

The RBM frequency variations of different diameter Ag- and Cu-SWNTs with their inverse tube diameters in units of 1/Å. Here, the red and black solid lines are the linear fittings for the Cu and Ag tubes, respectively. The insets (a) and (b) are schematic show for the RBMs of (5, 3) Ag-SWNT and (4, 4) Cu-SWNTs, respectively. For comparison, the RBM frequency of (4, 4) Ag-SWNT in Ref. 23 is also calculated, which is found to be 122 cm−1.

The RBM frequency variations of different diameter Ag- and Cu-SWNTs with their inverse tube diameters in units of 1/Å. Here, the red and black solid lines are the linear fittings for the Cu and Ag tubes, respectively. The insets (a) and (b) are schematic show for the RBMs of (5, 3) Ag-SWNT and (4, 4) Cu-SWNTs, respectively. For comparison, the RBM frequency of (4, 4) Ag-SWNT in Ref. 23 is also calculated, which is found to be 122 cm−1.

Variations of the total energy E per unit cell with the tube radius change for the (4, 2) Au-, Ag-, and Cu-SWNTs.

Variations of the total energy E per unit cell with the tube radius change for the (4, 2) Au-, Ag-, and Cu-SWNTs.

## Tables

The diameters (d confined) of Ag-SWNTs obtained in our MD simulations, which are confined in outer SWCNT templates with their diameters (d CNT). Here, d opt is the diameter of the optimized Ag tube at nearly zero temperature without the CNT confinement. And d first-principle is the diameter of the corresponding Ag-SWNTs, optimized by the first principles calculations in the free standing case. The length unit is Å.

The diameters (d confined) of Ag-SWNTs obtained in our MD simulations, which are confined in outer SWCNT templates with their diameters (d CNT). Here, d opt is the diameter of the optimized Ag tube at nearly zero temperature without the CNT confinement. And d first-principle is the diameter of the corresponding Ag-SWNTs, optimized by the first principles calculations in the free standing case. The length unit is Å.

The diameters (d confined) of Cu-SWNTs obtained in our MD simulations, which are confined in outer SWCNT templates with their diameters (d CNT). Here, d opt is the diameter of the optimized Cu tube at nearly zero temperature without the CNT confinement. And d first-principle is the diameter of the corresponding Cu-SWNTs, optimized by the first principles calculations in the free standing case. The length unit is Å.

The diameters (d confined) of Cu-SWNTs obtained in our MD simulations, which are confined in outer SWCNT templates with their diameters (d CNT). Here, d opt is the diameter of the optimized Cu tube at nearly zero temperature without the CNT confinement. And d first-principle is the diameter of the corresponding Cu-SWNTs, optimized by the first principles calculations in the free standing case. The length unit is Å.

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