正弦平方势与应变超晶格位错动力学  

The sine-squared potential and dislocation dynamics for strained superlattice

作　　者：罗诗裕[1] 邵明珠[2] 罗晓华[2,3] 

机构地区：[1]东莞理工大学电子工程学院,东莞523106 [2]重庆交通大学图书馆,重庆400074 [3]重庆大学电气工程学院,重庆400044

出　　处：《中国科学：物理学、力学、天文学》2010年第2期207-212,共6页Scientia Sinica Physica,Mechanica & Astronomica

基　　金：广东省自然科学基金资助项目(编号:9151065005000008)

摘　　要：引入正弦平方势描述了应变超晶格系统的弹性势能,并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,指出了系统的分叉或混沌将导致位错的运动与堆积,造成超晶格的分层或断裂.首先,引入阻尼项,在小振幅近似下,把描述一般位错运动的Seeger方程化为了超晶格系统的广义Duffing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方法分析了异宿轨道和周期轨道的分叉性质与进入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,保证了超晶格的完整性和性能的稳定性.Sine-squared potential is introduced to describe the elastic potential energy for the strained superlattice, the dynamic behavior in the vicinity of the interface for the superlattice is discussed in the classical mechanics frame based on Seeger equation. It is indicated that the motion and the accumulations of the dislocations by the bifurcation and chaos may give rise to the layer or the fracture of the superlattice. At first, by introducing damping term, the Seeger equation described the dislocation motion is reduced to the generalized duffing equation described superlattice in the small amplitude approximation. The properties of the phase plane for a non-perturbed system are analyzed by means of Jacobian elliptic function and the elliptic integral, and the solution of the equation and a period of the dislocation motion for this system are expressed exactly. Secondary, the bifurcation and a chaotic behaviors with the Smale horseshoe for the herteroclinic orbit and the periodic orbit in a phase plane are analyzed by Melnikov method. The critical condition of the system entering in a bifurcation or a chaos is found. The results show that the critical condition is related to the parameters of the system, then by regulating a parameters of the system, the bifurcation or the chaos can be avoided or controlled in principle, then the stabilities and the perfect of the superlattice materials may be further ensured.

关 键 词：位错动力学 稳定性 超晶格 分叉 混沌 

分 类 号：O469[理学—凝聚态物理]