The extended core structure of the dissociated edge dislocation in Al, Au, Ag, Cu and Ni is determined within lattice theory of dislocation. The 2D dislocation equation governing the displacements is coupled by the restoring forces that are determined by the parameterization of the generalized stacking fault energies. The Ritz variational method is presented to solve the dislocation equation and the trial solution is constituted by two arctan-type functions with two undetermined parameters. The core widths of partial dislocations are wider than that obtained in generalized Peierls-Nabarro model due to the consideration of discreteness of crystal.
Applying the parametric derivation method, Peierls energy and Peierls stress are calculated with a non-sinusoidal force law in the lattice theory, while the results obtained by the power-series expansion according to sinusoidal law can be deduced as a limiting case of non- sinusoidal law. The simplified expressions of Peierls energy and Peierls stress are obtained for the limit of wide and narrow. Peierls energy and Peierls stress decrease monotonically with the factor of modification of force law. Present results can be used expediently for prediction of the correct order of magnitude of Peierls stress for materials.
The core structure of （110）{001} mixed disloca- tion in perovskite SrTiO3 is investigated with the modified two-dimensional Peierls-Nabarro dislocation equation con- sidering the discreteness effect of crystals. The results show that the core structure of mixed dislocation is independent of the unstable energy in the （100） direction, but closely related to the unstable energy in the （110） direction which is the direction of total Burgers vector of mixed dislocation. Furthermore, the ratio of edge displacement to screw one nearly equals to the tangent of dislocation angle for differ- ent unstable energies in the （110） direction. Thus, the con- strained path approximation is effective for the （110）{001} mixed dislocation in SrTiO3 and two-dimensional equation can degenerate into one-dimensional equation that is only related to the dislocation angle. The Peierls stress for （110） {001 } dislocations can be expediently obtained with the one-dimensional equation and the predictive values for edge, mixed and screw dislocations are 0.17, 0.22 and 0.46 GPa, respectively.
