| Dislocations are the most abundant defects in materials that affect electronic, optic, magnetic especially the mechanical properties of materials. The crucial proplem of dislocation theory is the core structure, which is closely related with the Peierls stress and the interaction between dislocations that is correlated with the ductility and work hardening of materials. In a word, the determination of the core structure is the first and the most important step while disclosing the properties of dislocations. The classical Peierls-Nabarro (P-N) model can determine the core structure and Peierls stress quantitily. However, P-N model is based on the linear elastic theory that neglects the lattice discrete effect. Recently, lattice theory of dislocation based on the lattice statics has been constructed and dislocation equation to discuss the core sturucture is provided that can recover the defect of P-N model. In this paper, the core structure and Peierls stress of compact <100>{010} dislocation and collinear dissociated <111>{110} superdislocation in the novel B2 structure intermetallics YAg and YCu, <110>{100} mixed dislocation in SrTiO3 and 1/2<110>{111} dislocation in FCC crystals have been disscussed. The main work and results involve:(1) Variational principle for dislocation equation and the method for Peierls stressThe variational principle is applied to solve the dislocation taking into account the discreteness effect. The dislocation equation is changed into the equivalent variational extreme problem. The trial solution is chosed to be the same as that in the truncate approximation method that is a good trial solution while the parameter is taken to be zero that is the same as the Peierls solution. The variational functional can be represented by parameter of core structure. Take the two-dimentional triangular lattice and the simple cubic lattice as an example, the value of parameters obtained by variational principle are 0.71 and 0.68 for sinusoidal force law,the value of parameters obtained by variational principle are 0.72 and 0.68 for sinusoidal force law. The results show that both variational principle and truncate approximation method are effective method to solve the dislocation equation. The modification of the sinusoidal force law show that variational parameter decreases as the increasing of the modification factor. The parametric derivation method of Foremanethod is applied to derive Peierls energy and Peierls stress considering the contribution of elastic strain energy that is neglected in P-N model and the term of modification of sinusoidal force law. The result for Peierls energy and Peierls stress are the same obtained by parametric derivation method and power series expansion method for the sinusoidal force law. But the expression obtained by parametric derivation method is much brief than that obtained by power series expansion method and is convenient to estimate the Peierls stress of specific materials.(2) <100>{010} dislocation in YAg and YCuYAg and YCu are the typical novel B2 structure intermetallics that possess the good mechanical properties. There is lack of the study of dislocation properties in literatures. The core structure and Peierls stress are calculated for the <100>{010} dislocation in novel B2 structure intermetallics YAg and YCu taking into account the modification of discrete effect. The core width of <100>{010} dislocation are 2.12b and 1.94b, the correspongding Peierls stress are 3.5×10 -3μand 5.8×10 -3μ, respectively. Furthermore, the core width and Peierls stress of <100>{010} dislocation in traditional B2 structure NiAl are also calculate for comparison, and the results are 1.38b and 5047MPa , that is in order agreement with the numerical result, the result is acceptable while evaluating the Peierls stress due to the approximation. The results show that the unstable stacking fault energy is the key parameter controlling the core width and Peierls stress. The unstable stacking fault energy of <100>{010} dislocations in YAg and YCu is smaller than that of <100>{010} dislocation in NiAl. Thus, core width of dislocation are wider and Peierls stress are smaller. Core width is wider as the increasing of discreteness effect factor and the decreasing of the modification factor of sinusoidal force law.(3) <100>{010} dissociated superdislocations in YAg and YCuDissociated <111>{110} superdislocations are the most easiest slip dislocations in B2 structure intermetallics. The dissociated properties result in some complex. The trial solution for <111>{110} dissociated superdislocations in YAg and YCu are presented, dissociated width and core width of superpartials are two core structure paramenters. The variatiaonal functional can be represented by the two parameters, and the core structure of edge and screw <111>{110} superdislocations in YAg and YCu are determined. The experimental vaule for edge <111>{110} superdislocations in YAg provided by Xie is 0.6nm, the theoretical value predicted by this paper is 0.572nm, the dissociated width obtained in P-N is 0.431nm that is underestimate the dissociated width with the elastic continuum approximation. The Peierls stress of <111>{110} superpartials in YAg and YCu are 1.80×10 -3μand 3.13×10 -3μ, respectively. The Peierls stress of <111>{110} superpartials are smaller than that of <100>{010} dislocation, although the unstable stacking fault energy of <111>{110} superpartials are larger than that of <100>{010} dislocation due to the dissociated effect. The dissociated effect leads to the geometric structure factor of <111>{110} dislocation that is larger than of <100>{010} dislocationand and Peierls stress exponential decreases as the increasing of the geometric strucuture factor.(4) <110>{001} mixed dislocation in SrTiO3 and dislocations in FCC crystalThe properties of <110>{001}45 mixed dislocation in perovskite structure SrTiO3 are discussed taking into account the discrete effect. It's necessary to deal with the mixed dislocation with two-dimensional dislocation equation due to the edge and screw components. The rationality of the constrained path approximation is stated. In the constrained path approximation, the two dimensional dislocation reduced into one dimensional mixed dislocation equation. While the discrete effect is neglected, the new equation is the same as the mixed dislocation equation in P-N model. Peierls stress of the <110>{001} mixed dislocation obtained with reduced dislocation equation is 0.22GPa and Peierls stress of <110>{001} edge and screw dislocations are 0.17GPa and 0.46GPa, respectively. This shows that the one dimensional dislocation equation is a valid method to deal with the mobility of mixed dislocation due to the Peierls stress of mixed dislocation in the region of edge and screw dislocations. The dissociated core structure of edge 1/2<110>{111} dislocation in FCC crystals(Al,Cu,Ag and Au) are examined. The core structure of these dislocations is complex, the dissociated width is determined by the elastic theory, the width of edge and screw component of partials are determined by variational principle. While the modification of discrete effect is taken into account the width obtained are wider than that obtained in P-N model.
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