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在经典力学框架内,把Seeger方程化为广义的Sine-Gordon方程,从行波解出发,把Sine-Gordon方程进一步化为带有固定力矩的摆方程。用Jacobian椭圆函数和椭圆积分解析地描述了系统的相平面特征。基于物理学的功能原理,提出了用能量法对系统进行分析,再借助相面积概念,引入能量释放系数进一步刻画了位错的能量释放机制。结果表明,由于晶格常数不匹配或外延条件不理想,在一定条件下位错聚集的能量是可以完成转移与释放的。
In the framework of classical mechanics, the Seeger equation is transformed into a generalized Sine-Gordon equation. From the traveling wave solutions, the Sine-Gordon equation is further transformed into a pendulum equation with a fixed moment. The phase plane features of the system are analytically described by Jacobian elliptic functions and elliptic integrals. Based on the functional principle of physics, this paper proposes a method of energy analysis of the system, and then introduces the concept of phase area and introduces the energy release coefficient to further depict the energy release mechanism of dislocation. The results show that due to lattice mismatch or unsatisfactory epitaxial conditions, the energy of dislocation aggregation can be transferred and released under certain conditions.