Study On The Multifold Structure Of Screw Dislocations In Body-Centered Cubic Crystals

It is 1/2?111? screw dislocation that dominates the plasticity in body-centered cubic(BCC)crystal.There exist two kinds of nonplanar structure,3-fold structure and 6-fold structure,in BCC crystal.It is controversial which structure is the most stable one.In BCC crystal,nonplanar structures are also called multifold structures because of their structural characteristics.This paper aims to study the multifold structure of BCC crystals within the framework of the P-N model,and gives the equilibrium state structure of 1/2?111? screw dislocations.This paper first solves the problem of the ground state of the multifold structure screw dislocation under the sinusoidal force law.The problems mainly are the follows,the derivation of generalized Peierls equations,the exact solution of the generalized Peierls equation,the dislocation energy,the stress fields,and the displacement fields.All along,physicist can only deal with multifold dislocation equation by approximated solutions.In this paper,the author gives the exact solution of the generalized Peierls equation for the first time.It is found that the solution defined on each individual fold is given by the tail cut from the original Peierls solution.In viewpoint of energetics,a screw dislocation has a tendency to spread the distribution on all possible slip planes which are contained in the dislocation line zone.The stress field and displacement field of multi-fold structure are also evaluated explicitly.The stress field shows obvious multifold structure characteristics.The strength of the stress field of the six-fold structure is significantly smaller than that of the planar structure,and it indicates smaller elastic energy density of the six-fold structure.The displacement field near the dislocation center has a discontinuous leap when crosses the fold.The leap magnitude equals to the value of the mismatch field(exact solution).After given the exact solution,the generalized Peierls equation in BCC crystal is improved by including the contact interaction resulting from the lattice discreteness and replacing the sinusoidal-force law by the g-surface.The full g-surface of six typical BCC metals(Ta,Mo,Cr,W,Nb,V)is given.Based on the exact solution,the approximated solution of the multifold dislocation equation is proposed.Applying the model to the 1/2 ?111? screw dislocation in BCC metals,it is found that the six-fold structure has the lowest energy.Thus six-fold structure is the most stable structure compared to the planar and three-fold structure.From the energetics point of view,the stable structures of the VB and VIB metals should all be six-fold structures.At last,the effect of elastic anisotropy on screw dislocations in multifold structures is discussed beyond the isotropic model.After summarizing the interaction energy between dislocations in the anisotropic approximation,the dislocation equations for multifold structures are determined,and the approximated solutions based on the exact solutions are given.Applying the model to 1/2 ?111? screw dislocations in BCC metals(Ta,Mo,Cr,W,Nb,V),it is found that the energy of the six-fold structure is the lowest one compare to three-fold and two-fold structure.In addition,the anisotropy on the screw dislocations of nonplanar structures cannot be neglected when the ratio of the shear module from g-surface to the energy factor deviates 1.The influence of the ratio of the shear module to the energy factor on the anisotropy of screw dislocations is greater than the interaction in dislocation equation.The model corresponding to the generalized Peierls equation under sinusoidal force can be solved exactly.The dislocation tends to distribute on all possible slip planes.Under the framework of P-N theory,the ground state structure of screw dislocations in BCC crystals is six-fold structure,and three-fold structure and planar structure are metastable structures.Under the anisotropic elastic approximation,the conclusion is still valid.