A unified equation is presented for dislocations on the basis of lattice statics and symmetry principles. The equation satisfied by the displacement field defined on the two-dimensional misfit-plane can be applied to curved dislocations as well as straight dislocations. The correction for discreteness, which is important for the core structure, is included in the equation and related to the acoustic phonon velocity and lattice geometry structure. The dislocation equation of the new theory can be viewed as a kind of unification of the Peierls–Nabarro and Frenkel–Kontorva models of dislocations.
A dislocation equation satisfied by both horizontal displacement parallel to the glide plane and vertical displacement perpendicular to the glide plane has been derived generally from the lattice dynamics. In the slow-varying approximation that can be well applied to the dislocation, the equation has been changed into an integro-differential equation that possesses a universal form except the coefficients. If the higher-order derivatives of the displacement are canceled, the classic Peierls equation is recovered. The terms proportional to the higher-order derivatives represent the lattice effects that cannot be obtained in the continuum theory, and cannot be neglected in the core of the dislocation. The results are helpful to link the plasticity with the electronic structure of material because it is rigorously shown that the dislocation structure is mainly controlled by a few factors.
Based on the solution of the balance problem for a semi-infinite lattice, we propose a generalization of the Peierls–Nabarro equation that is applicable to an interfacial misfit dislocation array. We obtain a relationship between the mass center displacement and the relative displacement. Under the assumption that the change in the interfacial layer spacing is sufficiently small that it can be ignored, this relationship allows us to reveal the core structure of the misfit dislocation and determine the interfacial atomic coordinates. As an example, a boron nitride/aluminum nitride heterostructure with a large lattice mismatch is studied using the equation. We find a good match between the theoretically predicted interfacial atomic configuration and that obtained from a first-principles calculation. Furthermore, the adhesion energy of the heterostructure is also evaluated, and the theoretical result coincides with that obtained from first-principles simulations.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.