Dynamics of a Square Lattice I. Frequency Spectrum
Dynamics of a Square Lattice I. Frequency Spectrum
复制标题
方晶格的动力学 I. 频谱
DOI：
--
复制
发表时间：
1947
期刊：
影响因子：
--
通讯作者：
E. Montroll
中科院分区：
文献类型：
--
作者：
E. Montroll
单原子方晶格的简正振动模式的频率分布是作为晶格的力常数的函数而获得的。由于晶格中原子对之间的力是短程的，因此除了最近和次最近邻居之外的所有原子之间的相互作用都被忽略。两个常数 α 和 γ 用于描述晶格。 α 是从最近邻的相互作用导出的力常数，γ 是从下一个最近邻的相互作用导出的力常数。根据德拜连续统理论，频谱或简正模态的密度应该是频率的线性函数。在本文使用的玻恩-卡门原子模型中，表明这只在非常低的频率下出现这种情况，并且频谱中实际上存在两个尖锐的无穷大。我们定义g(ν)，使得g(ν)dν是频率在ν和ν+dν之间的简正振动模式的数量。涉及完全椭圆积分的闭合表达式...
The distribution of frequencies of normal modes of vibration of a monatomic square lattice is obtained as a function of the force constants of the lattice. Since the forces between pairs of atoms in the lattice are short ranged, interactions between all atoms, other than nearest and next nearest neighbors, are neglected.Two constants, α and γ, are used to describe the lattice. α is a force constant derived from the interaction of nearest neighbors, and γ is that derived from the interaction of next nearest neighbors.According to the Debye continuum theory the frequency spectrum, or density of normal modes, should be a linear function of the frequency. In the Born‐Karman atomic model used in the present paper it is shown that this is only the case at very low frequencies and that there actually exist two sharp infinities in the frequency spectrum.We define g(ν) so that g(ν)dν is the number of normal modes of vibration with frequencies between ν and ν+dν. A closed expression involving complete elliptic inte...