用不变本征算符法求晶面吸附原子的振动模  

Invariant eigen-operator calculated vibration mode of lattice in the case of absorbing an atom onto crystal surface

作　　者：张科 范承玉[1] 范洪义 Zhang Ke;Fan Cheng-Yu;Fan Hong-Yi(Key Laboratory of Atmospheric Composition and Optical Radiation,Anhui Institute of Optics and Fine Mechanics Chinese Academy of Sciences,Hefei 230031,China;Science Island Branch of Graduate School,University of Science and Technology of China,Hefei 230031;School of Electronic Engineering,Huainan Normal University,Huainan 232038,China)

机构地区：[1]中国科学院安徽光学精密机械研究所中国科学院大气光学重点实验室,合肥230031 [2]中国科学技术大学研究生院科学岛分院,合肥230031 [3]淮南师范学院电子工程学院,淮南232038

出　　处：《物理学报》2018年第17期44-50,共7页Acta Physica Sinica

基　　金：安徽高校省级自然科学研究项目(批准号:KJ2014A236)资助的课题~~

摘　　要：晶体表面的扩散和缺陷对晶体振动模式的影响是表面物理学研究的一个重要和基本的课题.晶格振动的频率对应于系统的能带.由于晶格中原子的振动不是孤立的,并且晶格具有周期性,所以在晶体中形成格波.格波代表晶体中所有原子都参与的频率相同的振动,又常称为一种振动模.本文讨论在表面吸附位势系数β_0与晶体内部原子的周期位势系数β不同的情况下,晶体表面吸附一个质量为m_0(与晶格原子质量m不同)的原子以后晶格的振动模.采用不变本征算符方法,严格地导出此振动模为ω=((2β(1-coshα))/(hm))^(1/2),其中α=ln[-(mβ_0+m_0(-2β+β_0)+(β_0)^(1/2)((-4mm_0β+(m+m_0)~2β_0))^(1/2)/2m_0β].此结果表明,ω不但取决于吸附位势与吸附原子的质量,也与晶格原子的质量与内位势有关.The influence of diffusion and defects of crystal surface on the crystal vibration mode are an important and basic subject in surface physics research. The frequency of lattice vibration corresponds to the energy band of the system.Since the vibrations of the atoms in the crystal lattice are not isolated from each other, and the crystal lattice is periodic,thereby forming a lattice wave in the crystal. The lattice wave represents that all the atoms in the crystal vibrate at an identical frequency, which is often called a vibration mode. The lattice chain model has been studied as the vibrating mode of phonon and the energy-band in solid state physics. The vibrating modes of the lattice chain model have been analyzed with the Newton equation and the Born-von-Karman boundary condition in the literaure. In general,it is difficult to solve this problem due to the complex nonlinear characteristic of the interactions between the matter particles and the environment. Noting the complicacy in directly diagonalizing quantum Hamiltonian operator of a long chain, we introduce the invariant eigenoperator method（IEO） for deriving the energy gap of a given crystal lattice without solving its eigenstates in the Heisenberg picture. The Heisenberg equation is as important as the Schrodinger equation. However, it has been seldom used for directly deriving the energy-gap in previous studies. Following the Heisenberg＇s original idea that most observable physical quantity in quantum mechanics is energy spectrum, Hong-yi Fan, one of the authors of the present paper, developed the IEO method. This method provides a natural result of combining both the Schrodinger operator and the Heisenberg equation. Using the IEO method, we study the vibration modes of crystal lattice,which are affected by absorbing an atom with mass m0,which is different from the mass of atom in the crystal. Moreover, the attractive potential constant β0 of the lattice surface differs from the inner constantβ.With the help of invariant eigen-operator method,

关 键 词：振动模 表面吸附位势 不变本征算符 

分 类 号：O73[理学—晶体学]