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在经典力学框架内和Seeger方程基础上,讨论了超晶格界面附近的位错动力学行为,指出了由于系统的分叉或混沌将导致位错的运动与堆积,造成了超晶格的分层或断裂;同时,也指出了,将生长过程中的超晶格置于适当的声场中将应力减至最小,或者适当调节系统参数就可最大限度的保证系统的动力学稳定性.首先,引入阻尼项,把描述一般位错运动的Seeger方程化为了超晶格系统的广义摆方程.利用Jacobian椭圆函数和椭圆积分分析了无扰动系统的相平面特征,并解析地给出了系统的解和粒子振动周期.其次,利用Melnikov方法分析了系统相平面上三类轨道的分叉性质和进入Smale马蹄意义下的混沌行为,找到了系统的全局分叉与系统进入混沌的临界条件.结果表明,系统的临界条件与它的物理参数有关,只需适当调节这些参数就可以原则上避免、控制分叉或混沌的出现,进一步保证生长过程的稳定性和超晶格材料的完整性.
Based on the classical mechanics framework and the Seeger equation, the dislocation dynamics in the vicinity of the superlattice interface are discussed. It is pointed out that the dislocation and chaos will lead to the movement and accumulation of dislocations, Layer or fracture. At the same time, it is also pointed out that the superlattice in the process of growth is placed in the appropriate sound field to minimize the stress or the system parameters can be adjusted properly to ensure the dynamic stability of the system to the maximum.Firstly, The damping term is introduced and the Seeger equation describing the general dislocation motion is transformed into the generalized pendulum equation of the superlattice system.The phase plane characteristics of the perturbed system are analyzed by Jacobian elliptic function and elliptic integral and the system solutions are given analytically And the period of particle vibration.Secondly, Melnikov method is used to analyze the bifurcation properties of three kinds of orbits and the chaos behavior in the sense of Smale horseshoe, and find the critical condition of global bifurcation and chaos entering system. The results show that , The critical condition of the system is related to its physical parameters, which can be avoided and controlled in principle by adjusting these parameters as appropriate, further guaranteeing The stability of the growth process and the integrity of the superlattice material.