原子质量对一维三原子链色散关系的影响

The influence of atomic mass on the dispersion relation of one-dimensional three-atom chain

本文采用数值分析方法研究原胞中原子质量对一维三原子链色散关系的影响,建立了频谱宽度和频率禁带宽度随原子质量变化的基本规律.结果表明,在原胞内只有一个原子质量发生变化的情况下,声学波频谱宽度随任一原子质量的增加而减小,光学波的频谱宽度随小原子质量的增加而增大,随大原子质量的增加而减小;两个频率禁带均随小原子质量的增加而变窄,随大原子质量的增加而增宽;随中间原子质量的增加,低频光学波和声学波间的频率禁带逐渐变窄,而高、低频光学波间的频率禁带逐渐增宽.相关结果可为晶体带通滤波器设计提供理论依据.

In this paper,the numerical analysis method is used to study the influence of the atomic mass in the primitive cell on the dispersion relationship of one-dimensional three-atom chain.The basic law of the spectral width and the frequency band gap changing with the atomic mass are established.The results show that when the mass of only one atom in the primitive cell changes,the width of the acoustic wave spectrum decreases with the increase of any atomic mass.The spectral width of optical waves increases with the increase of the mass of small atoms,and decreases with the increase of the mass of large atoms.Both frequency band gaps are narrowed with increasing the mass of the small atom,and widened with increasing the mass of the large atom.As the mass of the intermediate atoms increases,the frequency forbidden band between low-frequency optical waves and acoustic waves gradually is narrowed,while the frequency forbidden band between high-and low-frequency optical waves is gradually widened.The relevant results provide a theoretical basis for the design of crystal band-pass filters.