计及次近邻作用二维单原子正方晶格振动的色散关系  

Dispersion relation of two-dimensional monatomic square Lattice vibration with the secondary neighbor coupling

作　　者：陈志远[1] 张全坤 谢菊芳[3] 

机构地区：[1]湖北科技学院核技术与化学生物学院,湖北咸宁437100 [2]武汉大学物理科学与技术学院,湖北武汉430072 [3]湖北大学物理学与电子技术学院,湖北武汉430062

出　　处：《湖北大学学报（自然科学版）》2013年第4期507-512,共6页Journal of Hubei University：Natural Science

基　　金：国家自然科学基金(51272072);湖北省教育厅优秀中青年人才项目(Q20122803);湖北省高校青年教师深入企业行动计划项目(XD2012351)资助

摘　　要：基于晶格动力学理论推导了计及次近邻原子作用下二维单原子正方晶格振动的色散关系,得到第一布里渊区中3种特殊对称方向的色散关系表达式,每一对称方向仅有两支声学波.分析讨论次近邻原子间作用对色散关系的影响,结果表明:在缺乏次近邻原子作用下Γ-X方向横波频率为零,X-M方向高频声学波是无色散的,Γ-M方向纵波与横波简并;随着次近邻原子间作用的增强,Γ-X和X-M方向声子频率增大,Γ-M方向纵波频率也增大,并且当4γ2>γ1时纵波频率出现极大值,而其横波频率不变,但是Γ点和M点声子频率始终不变并分别简并.Based on lattice dynamics, we had derived the dispersion relations of two-dimensional monatomic square lattice under the secondary neighbor coupling, and obtained the expressions of the dispersion relations along three symmetry directions in the first Brillouin zone and had only two pieces of acoustic branches. The effect of second neighbor coupling to the dispersion relations had been discussed. The result showed that in absence of second neighbor coupling, transverse wave phonon has zero frequencies along Г-X direction, the acoustic branch of high frequencies was dispersionless along X-M direction, longitudinal wave and transverse wave degenerated along Г-M direction. With the enhancement of the secondary neighbor coupling, the phonon frequencies increase along Г-X and X-M directions, the longitudinal wave phonon frequencies also increased and they arised to maximum value when four times second neighbor coupling constant was larger than the nearest neighbor coupling constant along Г-M direction, but the transverse wave phonon frequencies keeped no change. Further more, the phonon frequencies degenerated at Г and M points whereas they retained fixedness.

关 键 词：晶格动力学 次近邻原子作用 色散关系 第一布里渊区 单原子正方晶格 

分 类 号：O731[理学—晶体学]