二维正方格子晶体中位错的晶格理论

The theory of dislocation in two-dimensional square crystal lattice

自从Orowan,Polanyi和Taylor等提出晶体中位错的概念并用弹性力学进行分析后,位错问题已经得到深入广泛的研究,并提出了一些著名的模型.但是,这些模型往往是连续的或半离散的,虽然能解决位错的许多问题,但是不能给出位错芯的精确描述.对此,建立在完全离散模型的基础上,作者只考虑最近邻原子间相互作用,运用格林函数方法对二维正方格子晶体中位错的Peierls模型进行计算,发现晶体没有切应力,二维问题变为一维,得出一维F-K模型方程.至此得出一个定量给出F-K模型方程的方法.

Since Orowan,Polanyi and Taylor defined the dislocation in crystal and analysed it by using elastic dynamics,dislocation has been deeply studied.Some models has been built.But that models are usually consecutive or halfdiscrete.Though they can resolve many problems about dislocation,they do not resolve the core of dislocation.Based on discrete model,the author only considers the affect of nearest atoms,using Green's function,calculates Peierls model of the dislocation in twodimensional square crystal lattice.It is found that there is no stress of shere,so twodimensional problem becomes onedimensional.From the outcome,the author finds the FK equation.