计及次近邻作用二维单原子正方晶格振动的色散关系

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Г-X方向横波频率为零，X-M方向高频声学波是无色散的，Г-M方向纵波与横波简并；随着次近邻原子间作用的增强，Px和X-M方向声子频率增大，Г-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11点和M点声子频率始终不变并分别简并．

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

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.