Dislocation energy and calculation from Peierls stress： a rigorous the lattice theory

In the classical Peierls-Nabarro （P-N） theory of dislocation, there is a long-standing contradiction that the stable configuration of dislocation has maximum energy rather than minimum energy. In this paper, the dislocation energy is calculated rigorously in the context of the full lattice theory. It is found that besides the misfit energy considered in the classical P-N theory, there is an extra elastic strain energy that is also associated with the discreteness of lattice. The contradiction can be automatically removed provided that the elastic strain energy associated with the discreteness is taken into account. This elastic strain energy is very important because its magnitude is larger than the misfit energy, its sign is opposite to the misfit energy. Since the elastic strain energy and misfit energy associated with discreteness cancel each other, and the width of dislocation becomes wide in the lattice theory, the Peierls energy, which measures the height of the effective potential barrier, becomes much smaller than that given in the classical P-N theory. The results calculated here agree with experimental data. Furthermore, based on the results obtained, a useful formula of the Peierls stress is proposed to fully include the discreteness effects.

APPLICATION OF PARAMETRIC DERIVATION METHOD TO THE CALCULATION OF PEIERLS ENERGY AND PEIERLS STRESS IN LATTICE THEORY

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.

Peierls stress for <110>{001} mixed dislocation in SrTiO_3 within framework of constrained path approximation

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.

ON CORE STRUCTURE PROPERTIES AND PEIERLS STRESS OF DISSOCIATED SUPERDISLOCATIONS IN ALUMINIDES:NiAl AND FeAl

The study of dislocation properties in B2 structure intermetallics NiAl and FeAl is crucial to understand their mechanical behaviors. In this paper, the core structure and Peierls stress of collinear dissociated （111）{110} edge superdislocations in NiAl and FeAl are investigated with the modified P-N dislocation equation. The generalized stacking fault energy curve along （111） direction in {110} slip plane contains two modification factors that can assure the antiphase energy and the unstable stacking fault energy to change independently. The results show that the core width of superpartials decreases with the increasing unstable stacking fault energy, and increases with the increasing antiphase boundary energy. The calculated Peierls stress of （111）{ 110） edge superdislocations in NiAl and FeAl are 475 MPa and 3042 MPa, respectively. The values of Peierls stress in NiAl is in accordance in magnitude with the experimental and the molecular statics simulations results.

On the core structure and mobility of the〈100 〉{010} and〈100 〉 {01■} dislocations in B2 structure YAg and YCu

Dislocations are thought to be the principal mechanism of high ductility of the novel B2 structure intermetallic compounds YAg and YCu.In this paper, the edge dislocation core structures of two primary slip systems 〈100〉{010} and 〈100〉{01^-1} for YAg and YCu are presented theoretically within the lattice theory of dislocation.The governing dislocation equation is a nonlinear integro-differential equation and the variational method is applied to solve the equation.Peierls stresses for 〈100〉{010} and 〈100〉{01^-1} slip systems are calculated taking into consideration the contribution of the elastic strain energy.The core width and Peierls stress of a typical transition-metal aluminide NiAl is also reported for the purpose of verification and comparison.The Peierls stress of NiAl obtained here is in agreement with numerical results,which verifies the correctness of the results obtained for YAg and YCu.Peierls stresses of the 〈100〉{01^-1} slip system are smaller than those of 〈100〉{010} for the same intermetallic compounds originating from the smaller unstable stacking fault energy.The obvious high unstable stacking fault energy of NiAl results in a larger Peierls stress than those of YAg and YCu although they have the same B2 structure.The results show that the core structure and Peierls stress depend monotonically on the unstable stacking fault energy.

A Generalized Peierls-Nabarro Model for Curved Dislocations Using Discrete Fourier Transform

In this paper,we present a generalized Peierls-Nabarro model for curved dislocations using the discrete Fourier transform.In our model,the total energy is expressed in terms of the disregistry at the discrete lattice sites on the slip plane,and the elastic energy is obtained efficiently within the continuum framework using the discrete Fourier transform.Our model directly incorporates into the total energy both the Peierls energy for the motion of straight dislocations and the second Peierls energy for kink migration.The discreteness in both the elastic energy and the misfit energy,the full long-range elastic interaction for curved dislocations,and the changes of core and kink profiles with respect to the location of the dislocation or the kink are all included in our model.The model is presented for crystals with simple cubic lattice.Simulation results on the dislocation structure,Peierls energies and Peierls stresses of both straight and kinked dislocations are reported.These results qualitatively agree with those from experiments and atomistic simulations.