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Chin. Phys. B, 2021, Vol. 30(11): 114301    DOI: 10.1088/1674-1056/abf4c0

Phonon dispersion relations of crystalline solids based on LAMMPS package

Zhiyong Wei(魏志勇)1,†, Tianhang Qi(戚天航)1, Weiyu Chen(陈伟宇)2, and Yunfei Chen(陈云飞)1
1 Jiangsu Key Laboratory for Design & Manufacture of Micro/Nano Biomedical Instruments and School of Mechanical Engineering, Southeast University, Nanjing 211189, China;
2 College of Mechanical and Electronic Engineering, Nanjing Forestry University, Nanjing 210037, China
Abstract  The phonon dispersion relations of crystalline solids play an important role in determining the mechanical and thermal properties of materials. The phonon dispersion relation, as well as the vibrational density of states, is also often used as an indicator of variation of lattice thermal conductivity with the external stress, defects, etc. In this study, a simple and fast tool is proposed to acquire the phonon dispersion relation of crystalline solids based on the LAMMPS package. The theoretical details for the calculation of the phonon dispersion relation are derived mathematically and the computational flow chart is present. The tool is first used to calculate the phonon dispersion relation of graphene with two atoms in the unit cell. Then, the phonon dispersions corresponding to several potentials or force fields, which are commonly used in the LAMMPS package to modeling the graphene, are obtained to compare with that from the DFT calculation. They are further extended to evaluate the accuracy of the used potentials before the molecular dynamics simulation. The tool is also used to calculate the phonon dispersion relation of superlattice structures that contains more than one hundred of atoms in the unit cell, which predicts the phonon band gaps along the cross-plane direction. Since the phonon dispersion relation plays an important role in the physical properties of condensed matter, the proposed tool for the calculation of the phonon dispersion relation is of great significance for predicting and explaining the mechanical and thermal properties of crystalline solids.
Keywords:  phonon dispersion relation      molecular dynamics      force constant      potential function  
Received:  23 February 2021      Revised:  20 March 2021      Accepted manuscript online:  05 April 2021
PACS:  43.35.+d (Ultrasonics, quantum acoustics, and physical effects of sound)  
  62.60.+v (Acoustical properties of liquids)  
  63.20.-e (Phonons in crystal lattices)  
Fund: Project supported by the National Key R&D Program of China (Grant No. 2017YFB0406000) and the Southeast University “Zhongying Young Scholars” Project.
Corresponding Authors:  Zhiyong Wei     E-mail:

Cite this article: 

Zhiyong Wei(魏志勇), Tianhang Qi(戚天航), Weiyu Chen(陈伟宇), and Yunfei Chen(陈云飞) Phonon dispersion relations of crystalline solids based on LAMMPS package 2021 Chin. Phys. B 30 114301

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