不同近邻作用下一维双原子链晶格振动色散关系

在简谐近似和周期性边界条件下,推导出最近邻近似、次近邻近似和所有原子相互作用下一维双原子链晶格振动的色散关系.数值模拟表明：随着原子间库仑作用的增强,3种色散关系的频率不断降低、频隙逐渐减小,但最近邻近似的色散关系曲线形状基本保持不变,而次近邻近似和所有原子相互作用的色散关系在布里渊区中心的光学模频率向低频方向移动,并且所有原子相互作用下布里渊区中心的光学模软化更快.

Comparative Study of Dispersion Relations of One-dimensional Diatomic Chain Lattice Vibration with Different Neighbor Interactions

Based on the harmonic approximation and the periodic boundary condition of lattice vibration,the expressions of the dispersion relations of one-dimensional diatomic chain are derived under the nearest neighbor approximation and the secondary neighbor approximation and all atoms interaction.Numerical simulation shows that： with the enhancement of the Coulomb force constant ｜β｜;the frequency of dispersion relations reduces;frequency-gap position lowers;and the frequency gap gradually decreases until it disappears.Furthermore,the differences of three kinds of dispersion relations increase with the value of ｜β｜.In Brillouin zone center,optical modes of secondary neighbor approximation and all atoms interaction move to the low-frequency due to a large value of ｜β｜;and the optical mode by all atoms interaction softens faster and more pronounced than the mode of the secondary neighbor approximation.