北京邮电大学学报

  • EI核心期刊

北京邮电大学学报 ›› 2022, Vol. 45 ›› Issue (5): 60-65.

• 论文 • 上一篇    下一篇

具有长程相互作用正方晶格的色散关系和热容

李震东,谭振庭,方萍   

  1. 北京邮电大学 理学院
  • 收稿日期:2021-11-09 修回日期:2022-04-06 出版日期:2022-10-28 发布日期:2022-11-01
  • 通讯作者: 方萍 E-mail:pingfang@bupt.edu.cn
  • 基金资助:
    国家自然科学基金项目;中央高校基本科研业务费专项资金项目

Dispersion Relations and Heat Capacity with Long Range Interactions in a Square Lattice

LI Zhendong, TAN Zhenting, FANG Ping   

  • Received:2021-11-09 Revised:2022-04-06 Online:2022-10-28 Published:2022-11-01
  • Contact: FANG Ping E-mail:pingfang@bupt.edu.cn

摘要: 根据晶格动力学理论计算具有长程相互作用二维单原子正方晶格的色散关系,在简谐近似下,得到了考虑任意近邻原子色散关系的一般表达式分析了最近邻和次近邻近似下的结果,当近邻数 p 较大时, p近邻的原子对第一布里渊区内平均振动频率的贡献随近邻数的增大以幂律形式衰减以长程库仑相互作用为例,进行数值计算和分析在此微观动力学的基础上,研究了长程相互作用对宏观热容的影响数值计算长程库仑相互作用系统的热容,且发现热容随近邻数的增大以幂律形式衰减

关键词: 晶格振动, 色散关系, 简谐近似, 周期性边界条件, 正方晶格, 热容

Abstract: The dispersion relation of a monoatomic two-dimensional lattice with long-range interactions is derived according to the theory of lattice dynamics. Based on a simple harmonic approximation, a general dispersion relation that takes into account arbitrary neighbor interactions is obtained. The results of the nearest neighbor and the second nearest neighbor approximation are analyzed. When the order of the nearest neighbors p is large, the contribution of the pth nearest neighbors to the average vibration frequency in the Brillouin zone decays in a power law form with the increase of the neighbor number. Moreover, the long-range Coulomb interaction is analyzed as an example. Based on this microscopic dynamics, the effect of long-range interaction on macroscopic heat capacity is numerically investigated, and the heat capacity of the system decays in a power law form with the increase of the neighbor number.

Key words: lattice vibration, dispersion relation, harmonic approximation, periodic boundary conditions, square lattice, heat capacity

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