Dislocation Equation Of The Simple Cubic Lattice With Anisotropy

Recently dislocation equation based on the crystal lattice dynamics has been derived considering interacts of atoms by means of Green Function in two-dimensional triangular crystal and isotropic simple-cubic crystal. This lattice theory of dislocation considers discreteness of crystal and reflects the character of lattice. The result from this theory accords with data from experiment well. The new theory makes it possible to derive dislocation in different types of crystal. The approximation of isotropy was considered in simple cubic which makes the mathematics be simple, but the result is only described by number which doesn't reflect essence in physic. Dislocation equation in anisotropic simple-cubic crystal has been studied mainly and the content is as follows:1) Concept's and theories development,models confirmation about dislocation have been introduced briefly. And some most important models are described in detail. We analyze the background,results and both virtue and lack of these models combining with the character of crystal material.2) With Green function dislocation equation in anisotropic simple-cubic crystal has been derived rigorously using crystal dislocation analytic theory on the base of crystal dynamics considering the central force interact during the first-nearest-neighbor atoms and the second–nearest-neighbor atoms and the angular force interact between the first-nearest-neighbor atoms. The universal structure of dislocation equation that the equation was nonlinear differential-integral expression has been discovered. Different interacting models and different types of crystal lattices only reflect interrelated coefficients. The coefficients in equation are first described accurately by the expression of every interacting parameter and that how coefficients vary with parameters changing also is discussed. The result is that the second order differential coefficient can be described by elastic coefficient and the first order differential coefficient in integral agree well with energy coefficient in elastic dislocation theory when angular force parameter equal zero.3) With the truncation approximation the dislocation equation has been solved on the base of character dislocation's slowly-varying. The solution of dislocation is described as the function every interacting parameter. When analyzing the effect from interacting parameters to dislocation width, the result that dislocation width c1...