超晶格的位错模型与系统的动力学稳定性

THE DISLOCATION MODEL OF SUPERLATTICE AND DYNAMIC STABILITIES OF THE SYSTEM

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.

The dynamic behavior in the vicinity of the superlattice＇s interface is discussed in the classical mechanics framework with the use of Seeger equation. By introducing damping term, Seeger equation for general dislocation motion is reduced to generalized pendulum equation for superlattice system. The properties of the phase plane of a non-perturbed system are analyzed by means of Jacobian elliptic function and the elliptic integral, and then the solution of the equation and the period of the dislocation motion are obtained analytically. Next,the global bifurcation and a chaotic behavior with the Smale horseshoe for the 3-kind orbit on a phase plane are analyzed by Melnikov method. Based on these,the critical conditions of system bifurcation or chaos are given,with close relation with system parameters. By regulating the system parameters properly,the bifurcation or the chaos can be avoided or controlled; as a result,the superlattice system can grow steadily and no delamination or fracture occurs.