晶格振动色散关系与均匀杆纵振动色散关系的比较分析  

Comparative analysis of dispersion law of lattice vibration with that of the longitudinal vibration of a uniform bar

作　　者：田强[1] 

机构地区：[1]北京师范大学物理系,北京100875

出　　处：《大学物理》2006年第5期7-9,共3页College Physics

基　　金：教育部国家理科基地创建名牌课程项目;北京师范大学创新研究群体资助计划项目

摘　　要：一维单原子链晶格振动与均匀杆自由纵振动的运动方程在数学上存在内在的联系.将均匀杆自由纵振动运动方程中对空间的偏导数用差商代替,就得到一维单原子链晶格振动的运动方程.对于离散的一维单原子链晶格振动与连续的均匀杆自由纵振动的色散关系进行了比较分析.一维单原子链晶格振动的波矢具有特定的取值范围,即布里渊区,这是原子离散周期排布的结果.随着质量分布由离散逐渐向连续变化,一维单原子链晶格振动的色散关系逐渐演变为均匀杆纵振动的色散关系.The equation of lattice vibration of one-dimensional monatomie lattice and the equation of longitudinal vibration of a uniform bar are discussed. Raplaeing the spatial derivatives by spatial differences in the equation of the latter, we get the equation of the former. The dispersion laws of the two systems are compared. The Brillioun zone of discrete system is intimately connected with the interpartiele distance. With the changing of mass distribution from diseretization to continuum, the dispersion law of the lattice vibration changes to that of the longitudinal vibration of a uniform bar.

关 键 词：晶格振动 色散关系 一维单原子链 均匀杆 

分 类 号：O472[理学—半导体物理]