大学物理 ›› 2024, Vol. 43 ›› Issue (9): 15-.doi: 10.16854/j.cnki.1000-0712.230447

• 教学研究 • 上一篇    下一篇

动力学矩阵方程法求解一维至三维晶格声子色散关系

鲁勇   

  1. 北京化工大学数理学院,北京100029
  • 收稿日期:2023-12-04 修回日期:2024-02-27 出版日期:2024-11-05 发布日期:2024-11-13
  • 作者简介:鲁勇(1985—),男,山东青岛人,北京化工大学数理学院,博士,主要从事计算物理方面的研究工作和固体物理及固体理论方面的教学工作. E-mail: luy@mail.buct.edu.cn
  • 基金资助:
    国家自然科学基金(12074028)资助

Solution of dynamic matrix equation of phonon dispersion relations  in one-dimensional to three-dimensional lattice

LU Yong   

  1. College of Mathematics and Physics, Beijing University of Chemical Technology, Beijing 100029, China
  • Received:2023-12-04 Revised:2024-02-27 Online:2024-11-05 Published:2024-11-13

摘要: 本文通过动力学矩阵方程求解了一维到三维晶格振动的声子色散关系.与传统的本科生固体物理课程中通过哈密顿正则方程方法求解一维原子链经典模型相比,构建动力学矩阵,使得从一维拓展到三维晶格声子色散关系的求解方程在形式上更具有统一性和普适性,有助于从思维方式上建立一维到三维晶格振动的连续的物理图像.在数值求解三维晶格振动以及考虑非谐效应的影响时,该方法亦提供了更好的便利性.

关键词: 晶格振动, 动力学矩阵方程, 声子色散关系

Abstract: In this paper, the phonon dispersion relation of lattice vibrations from one-dimension to three-dimension is solved by constructing dynamic matrix equation. Compared to traditional method of solving one-dimensional atomic chain classical model using Hamilton’s canonical equations in solid state physics courses, constructing a dynamic matrix provides a more unified and universal form for solving phonon dispersion relation from one-dimensional to three-dimensional lattice. It is helpful to establish a continuous physical picture of one-dimensional to three-dimensional lattice vibration from the way of thinking. In terms of numerically solving three-dimensional lattice vibrations and considering the effects of anharmonicity, this method also offers greater convenience.

Key words: lattice vibration, dynamic matrix equation, phonon dispersion relations