具有长程相互作用正方晶格的色散关系和热容

根据晶格动力学理论计算具有长程相互作用二维单原子正方晶格的色散关系,在简谐近似下,得到了考虑任意近邻原子色散关系的一般表达式。 分析了最近邻和次近邻近似下的结果,当近邻数 p 较大时,第 p近邻的原子对第一布里渊区内平均振动频率的贡献随近邻数的增大以幂律形式衰减。 以长程库仑相互作用为例,进行数值计算和分析。 在此微观动力学的基础上,研究了长程相互作用对宏观热容的影响。 数值计算长程库仑相互作用系统的热容,且发现热容随近邻数的增大以幂律形式衰减。

Dispersion Relations and Heat Capacity with Long Range Interactions in a Square Lattice

The dispersion relation of a monoatomic two-dimensional lattice with long-range interactions isderived according to the theory of lattice dynamics. Based on a simple harmonic approximation, a generaldispersion relation that takes into account arbitrary neighbor interactions is obtained. The results of thenearest neighbor and the second nearest neighbor approximation are analyzed. When the order of thenearest neighbors p is large, the contribution of the pth nearest neighbors to the average vibrationfrequency in the Brillouin zone decays in a power law form with the increase of the neighbor number.Moreover, the long-range Coulomb interaction is analyzed as an example. Based on this microscopicdynamics, the effect of long-range interaction on macroscopic heat capacity is numerically investigated,and the heat capacity of the system decays in a power law form with the increase of the neighbor number.