A unified dislocation equation from lattice statics

Abstract

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.

The Properties of Shuffle Screw Dislocations in Semiconductors Silicon and Germanium

“…Where θ is the dislocation angel, µ andν are the effective shear modulus and Poisson's ratio within {111} plane [1,5], 11 c and 12 c are the elastic constants, and 0 a is the lattice constant. The values for these constants are listed in Table 1.…”

“…However, because of treating the crystal as an elastic continuum body, the classical P-N model becomes increasingly inaccurate for narrow dislocations [5,7,8]. Recently, professor Wang have obtained the improved P-N equation which has relaxed the continuum approximation successfully [9][10][11]. The research results have shown that the improved P-N theory can remarkably improve the agreement between theoretical prediction and the numerical result [12,13].…”

On the core width and Peierls stress of bubble rafts dislocations within the framework of modified Peierls-Nabarro model

“…The modified P-N dislocation equation including the discrete lattice effect was obtained firstly by using the solvable models and secondly derived in a model-independent way, and takes the following form [17][18][19] − β…”

“…However, the fundamental dislocation equation in the P-N model is derived from the balance between the nonlinear interaction from the misfit gluing and the linear interaction form the deformation, which is obtained by the assumption that the crystal is taken to be elastic continuum. Recently, a modified P-N dislocation equation taking into account the discrete lattice effect is presented on the basis of lattice statics and symmetry principles, which is important for the dislocation core structure [17][18][19]. Today, the remaining key task to determine the dislocation core structure is to obtain the solution of the modified P-N dislocation equation combined with the restoring force law for bubble rafts.…”

Peierls stress for 〈110〉{001} mixed dislocation in SrTiO3 within framework of constrained path approximation

“…Recently, Ferré et al investigated dislocation properties in perovskite structure oxides based on the Peierls-Nabarro (P-N) model using the generalized stacking fault determined from first-principle calculations and some interesting results were obtained [8][9][10][11]. The major drawback of the P-N model is the adoption of the continuum elastic approximation and the discreteness effect of crystals is underestimated [12][13][14]. Especially, the displacement field varies so rapidly at the dislocation core region and the discreteness effect should be taken into account [15].…”