一般情况下一维双原子链的求解及其色散关系  

SOLUTION AND DISPERSION RELATION OF ONE-DIMENSIONAL DIATOMIC CHAIN IN GENERAL

作　　者：刘艳晶 胡建民[1,2] 王月媛[1,2] 牛丽 孙文军[1,2] LIU Yanjing;HU Jianmin;WANG Yueyuan;NIU Li;SUN Wenjun(Key Laboratory for Photonic and Electronic Bandgap Materials,Ministry of Education,Harbin Normal University,Harbin,Heilongjiang 150025;School of Physics and Electronic Engineering,Harbin Normal University,Harbin,Heilongjiang 150025)

机构地区：[1]哈尔滨师范大学光电带隙材料教育部重点实验室,黑龙江哈尔滨150025 [2]哈尔滨师范大学物理与电子工程学院,黑龙江哈尔滨150025

出　　处：《物理与工程》2022年第4期46-50,共5页Physics and Engineering

基　　金：黑龙江省自然科学基金项目(LH2019A019);教育部高等学校物理类专业教学指导委员会教研项目(JZW18GT01);黑龙江省高等教育教学改革研究项目(SJGY20190371/70);哈尔滨师范大学研究生培养质量提升工程项目、课程思政教学改革示范项目和混合式教学模式改革试点项目、哈尔滨师范大学高等教育教学改革研究项目(XJGYW2022003)。

摘　　要：本文在简谐近似下采用原胞法求解一般情况下的一维双原子链的格波解和色散关系,讨论原子链结构参数对其色散关系的影响以及原胞内原子的振动特点。研究结果表明,晶格常数一定的情况下一维双原子链的色散关系与近邻原子相对间距无关;在布里渊区中心,长声学支格波近似为连续的弹性介质波,而长光学支格波近似为原胞内原子相对振动而原胞质心不动的驻波;在近邻原子间距和恢复力系数均相等的情况下,在布里渊区边界处短声学支格波和短光学支格波分别近似为波节在小原子和大原子的驻波。本文相关内容可为固体物理教学提供优质教学素材。In this paper,the lattice wave solutions and dispersion relations of one-dimensional diatomic chains are solved by using the protocell cell under the harmonic approximation.The influence of structural parameters of atomic chains on dispersion relations and the vibration characteristics of atoms in the protocell are discussed.The research results show that the dispersion relation of a one-dimensional diatomic chain with a certain lattice constant has nothing to do with the relative distance of neighboring atoms.In the center of the Brillouin zone,the long acoustic wave is similar to a continuous elastic medium wave,while the long optical wave is similar to a standing wave in which the atoms in the protocell vibrate relative to each other and the protocell centroid does not move.When the distance between neighboring atoms and the coefficient of restoring force are equal,the short acoustic wave and short optical wave at the boundary of the Brillouin zone are approximated as standing waves with nodes at small and large atoms,respectively.The relevant contents of this paper can provide high quality teaching materials for solid state physics teaching.

关 键 词：固体物理学 一维双原子链 色散关系 

分 类 号：O562[理学—原子与分子物理]