^{1}and Y. T. Gu

^{1,a)}

### Abstract

Based on the molecular dynamics (MD) simulation and the classical Euler-Bernoulli beam theory, a fundamental study of the vibrational performance of the Ag nanowire (NW) is carried out. A comprehensive analysis of the quality (Q)-factor, natural frequency, beat vibration, as well as high vibration mode is presented. Two excitation approaches, i.e., velocity excitation and displacement excitation, have been successfully implemented to achieve the vibration of NWs. Upon these two kinds of excitations, consistent results are obtained, i.e., the increase of the initial excitation amplitude will lead to a decrease to the Q-factor, and moderate plastic deformation could increase the first natural frequency. Meanwhile, the beat vibration driven by a single relatively large excitation or two uniform excitations in both two lateral directions is observed. It is concluded that the nonlinear changing trend of external energy magnitude does not necessarily mean a non-constant Q-factor. In particular, the first order natural frequency of the Ag NW is observed to decrease with the increase of temperature. Furthermore, comparing with the predictions by Euler-Bernoulli beam theory, the MD simulation provides a larger and smaller first vibration frequencies for the clamped-clamped and clamped-free thin Ag NWs, respectively. Additionally, for thin NWs, the first order natural frequency exhibits a parabolic relationship with the excitation magnitudes. The frequencies of the higher vibration modes tend to be low in comparison to Euler-Bernoulli beam theory predictions. A combined initial excitation is proposed which is capable to drive the NW under a multi-mode vibration and arrows the coexistence of all the following low vibration modes. This work sheds lights on the better understanding of the mechanical properties of NWs and benefits the increasing utilities of NWs in diverse nano-electronic devices.

This work sheds lights on the better understanding of the mechanical properties of NWs, and the simulation techniques and analysis methods delineated in this work should also be applicable to other NWs (such as pinned-pinned thin NWs, as well as thick NWs with smaller slenderness). The study in this work would also benefit the increasing utilities of NWs in diverse nano-electronic devices.

I. INTRODUCTION

II. NUMERICAL AND THEORETICAL FUNDAMENTS

A. Molecular dynamics implementation

B. Theoretical basics

III. RESULTS AND DISCUSSION

A. Velocity excitation

B. Displacement excitation

C. Beat vibration

D. Temperature influence

E. High vibration modes

IV. CONCLUSION

### Key Topics

- Structural beam vibrations
- 15.0
- Plasticity
- 13.0
- Exoelectron emission
- 11.0
- Molecular dynamics
- 11.0
- Number theory
- 8.0

##### B82B1/00

## Figures

Schematic of a clamped-clamped Ag NW model. Boundary regions “B” are fixed in all directions, with the rest as the deformation region. The NW has a square cross-section with the lateral size of *h*, and the NW length is denoted as *L*. (a) Front sight view. (b) Cross-section view.

Schematic of a clamped-clamped Ag NW model. Boundary regions “B” are fixed in all directions, with the rest as the deformation region. The NW has a square cross-section with the lateral size of *h*, and the NW length is denoted as *L*. (a) Front sight view. (b) Cross-section view.

Simulation results of the 6*a* × 6*a* × 34*a* Ag NW with the initial velocity amplitude equals 1 Å/ps under the temperature of 0.1 K. (a) The time history of *EE* during vibration. Circle markers highlighted the magnitudes of *EE* during each vibration circle. (b) First half of the periodogram, regarding the power of DFT versus frequency.

Simulation results of the 6*a* × 6*a* × 34*a* Ag NW with the initial velocity amplitude equals 1 Å/ps under the temperature of 0.1 K. (a) The time history of *EE* during vibration. Circle markers highlighted the magnitudes of *EE* during each vibration circle. (b) First half of the periodogram, regarding the power of DFT versus frequency.

Simulation results of the 6*a* × 6*a* × 34*a* Ag NW under velocity excitation at the temperature of 0.1 K. (a) The first vibration frequency as a function of the velocity amplitude. (b) The time history of *EE* during vibration for the Ag NW when the initial velocity amplitude equals 2 Å/ps. Circle markers highlighted the magnitudes of *EE* during each vibration circle. The inset figure (c) represents the atomic configurations of this NW at 100 ps, atoms with the *csp* value between 0.5 and 12 are visualized.

Simulation results of the 6*a* × 6*a* × 34*a* Ag NW under velocity excitation at the temperature of 0.1 K. (a) The first vibration frequency as a function of the velocity amplitude. (b) The time history of *EE* during vibration for the Ag NW when the initial velocity amplitude equals 2 Å/ps. Circle markers highlighted the magnitudes of *EE* during each vibration circle. The inset figure (c) represents the atomic configurations of this NW at 100 ps, atoms with the *csp* value between 0.5 and 12 are visualized.

Simulation results of the 6*a* × 6*a* × 34*a* C-C Ag NW under displacement excitation at the temperature of 0.1 K. (a) The time history of *EE* during vibration for the Ag NW with the initial displacement amplitude equals 5.91 Å. Circle markers highlighted the magnitudes of *EE* during each vibration circle. (b) The first vibration frequency as a function of the displacement amplitude. The inset figure (c) represents the Q-factor as a function of the displacement amplitude.

Simulation results of the 6*a* × 6*a* × 34*a* C-C Ag NW under displacement excitation at the temperature of 0.1 K. (a) The time history of *EE* during vibration for the Ag NW with the initial displacement amplitude equals 5.91 Å. Circle markers highlighted the magnitudes of *EE* during each vibration circle. (b) The first vibration frequency as a function of the displacement amplitude. The inset figure (c) represents the Q-factor as a function of the displacement amplitude.

Simulation results of the 6*a* × 6*a* × 34*a* C-C Ag NW under the temperature of 0.1 K with the initial displacement amplitude equals 13.91 Å. (a) The time history of *EE* during vibration. Circle markers highlighted the magnitudes of *EE* during each vibration circle. (b) Atomic configuration at 1600 ps reveals the vibration *u*(*z*) in *x* direction. (c) Atomic configuration at 1600 ps reveals the vibration *v*(*z*) in *y* direction. In the atomic configurations, atoms with the *csp* value between 0.5 and 12 are visualized.

Simulation results of the 6*a* × 6*a* × 34*a* C-C Ag NW under the temperature of 0.1 K with the initial displacement amplitude equals 13.91 Å. (a) The time history of *EE* during vibration. Circle markers highlighted the magnitudes of *EE* during each vibration circle. (b) Atomic configuration at 1600 ps reveals the vibration *u*(*z*) in *x* direction. (c) Atomic configuration at 1600 ps reveals the vibration *v*(*z*) in *y* direction. In the atomic configurations, atoms with the *csp* value between 0.5 and 12 are visualized.

Simulation results of the 6*a* × 6*a* × 34*a* C-C Ag NW under two uniform velocity stimuli (velocity amplitudes of 0.75 Å/ps) in both *x* and *y* directions at the temperature of 0.1 K. (a) The time history of *EE* during vibration. Circle markers highlighted the magnitudes of *EE* during each vibration circle. (b) First half of the periodogram regarding the power of DFT versus frequency.

Simulation results of the 6*a* × 6*a* × 34*a* C-C Ag NW under two uniform velocity stimuli (velocity amplitudes of 0.75 Å/ps) in both *x* and *y* directions at the temperature of 0.1 K. (a) The time history of *EE* during vibration. Circle markers highlighted the magnitudes of *EE* during each vibration circle. (b) First half of the periodogram regarding the power of DFT versus frequency.

Simulation results of thin Ag NWs under velocity stimuli at various temperatures ranging from 0.1 K to 400 K. (a) The first order natural frequency as a function of temperature for the C-C NWs. (b) The first order natural frequency as a function of temperature for the C-F NWs.

Simulation results of thin Ag NWs under velocity stimuli at various temperatures ranging from 0.1 K to 400 K. (a) The first order natural frequency as a function of temperature for the C-C NWs. (b) The first order natural frequency as a function of temperature for the C-F NWs.

Simulation results of C-C 6*a* × 6*a* × 124*a* Ag NWs under velocity stimuli at the temperature of 10 K. (a) The first vibration frequency as a function of the velocity amplitude. (b) Comparison of the normalized frequency for different vibration modes between simulation results and theoretical calculations. Error bars describe the standard deviation of the normalized frequency under different velocity magnitudes.

Simulation results of C-C 6*a* × 6*a* × 124*a* Ag NWs under velocity stimuli at the temperature of 10 K. (a) The first vibration frequency as a function of the velocity amplitude. (b) Comparison of the normalized frequency for different vibration modes between simulation results and theoretical calculations. Error bars describe the standard deviation of the normalized frequency under different velocity magnitudes.

Simulation results of thin Ag NWs under a combined velocity excitation at the temperature of 10 K. (b) First half of the periodogram, regarding the power of DFT versus frequency for the 6*a* × 6*a* × 124*a* Ag NW. (b) Comparison of the normalized frequency at different vibration modes between simulation results and theoretical calculations for NW with three different lengths, i.e., 124*a*, 154*a*, and 184*a*.

Simulation results of thin Ag NWs under a combined velocity excitation at the temperature of 10 K. (b) First half of the periodogram, regarding the power of DFT versus frequency for the 6*a* × 6*a* × 124*a* Ag NW. (b) Comparison of the normalized frequency at different vibration modes between simulation results and theoretical calculations for NW with three different lengths, i.e., 124*a*, 154*a*, and 184*a*.

Article metrics loading...

Full text loading...

Commenting has been disabled for this content