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.

DISLOCATION EMISSION AND EQUATION OF ENERGY BARRIERS AT MODEL I CRACK TIP

The propagation for the model I crack in aluminum single crystal has been directly studied by in-situ TEM observation.The equation of energy barrier of the dislocation building-up and emission at the model I crack tip has been established by means of Peierls-Nabarro dislocation model and starting from angle of energy.By means of calculation,the critical value of spontaneous emission of the dislocations from tip of the model I crack was obtained.

Low Energy Dislocation Structure in Deformed Metals

In this paper,the dislocation distribution struc- ture in deformed metal is discussed.The flow stress of material for the heterogeneous dislocation distri- bution which tends to the flow stress for the homo- geneous dislocation distribution in the limiting case is derived.The causes and the effects of the long range internal stresses are discussed.The total deformation energy of material system is obtained and the trend of evolution of dislocation distribu- tion in deformed metals is discussed simultaneously. No micromechanisms of dislocations are involved in the discussion,therefore the theory developed in this paper is universal.

Interaction energy of interface dislocation loops in piezoelectric bi-crystals

Interface dislocations may dramatically change the electric properties, such as polarization, of the piezoelectric crystals. In this paper, we study the linear interactions of two interface dislocation loops with arbitrary shape in generally anisotropic piezoelectric bi-crystals. A simple formula for calculating the interaction energy of the interface dislocation loops is derived and given by a double line integral along two closed dislocation curves. Particularly, interactions between two straight segments of the interface dislocations are solved analytically, which can be applied to approximate any curved loop so that an analytical solution can be also achieved. Numerical results show the influence of the bi-crystal interface as well as the material orientation on the interaction of interface dislocation loops.

A theoretical investigation of glide dislocations in BN/AlN heterojunctions

Glide dislocations with periodic pentagon-heptagon pairs are investigated within the theory of one-dimensional misfit dislocations in the framework of an improved Peierls–Nabarro(P–N)equation in which the lattice discreteness is fully considered.We find an approximate solution to handle misfit dislocations,where the second-order derivative appears in the improved P–N equation.This result is practical for periodic glide dislocations with narrow width,and those in the BN/AlN heterojunction are studied.The structure of the misfit dislocations and adhesion work are obtained explicitly and verified by first-principles calculations.Compared with shuffle dislocations,the compression force in the tangential direction of glide dislocations has a greater impact on the normal direction,and the contributions of the normal displacement to the interfacial energy cannot simply be ignored.

Modification of the Peierls-Nabarro model for misfit dislocation

For a misfit dislocation,the balance equations satisfied by the displacement fields are modified,and an extra term proportional to the second-order derivative appears in the resulting misfit equation compared with the equation derived by Yao et al.This second-order derivative describes the lattice discreteness effect that arises from the surface effect.The core structure of a misfit dislocation and the change in interfacial spacing that it induces are investigated theoretically in the framework of an improved Peierls-Nabarro equation in which the effect of discreteness is fully taken into account.As an application,the structure of the misfit dislocation for a honeycomb structure in a two-dimensional heterostructure is presented.

Effective Stacking Fault Energy in Face-Centered Cubic Metals

As a typical configuration in plastic deformations, dislocation arrays possess a large variation of the separation of the partial dislocation pairs in face-centered cubic（fcc） metals. This can be manifested conveniently by an effective stacking fault energy（SFE）. The effective SFE of dislocation arrays is described within the elastic theory of dislocations and verified by atomistic simulations. The atomistic modeling results reveal that the general formulae of the effective SFE can give a reasonably satisfactory prediction for all dislocation types, especially for edge dislocation arrays. Furthermore, the predicted variation of the effective SFE is consistent with several previous experiments, in which the measured SFE is not definite, changing with dislocation density. Our approach could provide better understandings of cross-slip and the competition between slip and twinning during plastic deformations in fcc metals.