Analysis of partial dislocations in wurtzite GaN using gradient elasticity

Abstract

A non‐singular gradient elasticity solution for the dislocation self‐energy is employed and compared to previous results for 1/6〈20$ \bar 2 $3〉 partial dislocations fault in wurtzite GaN obtained by empirical potential calculations. Twenty‐four previously obtained stable dislocation cores, twelve for each GaN polarity, are considered. It is shown that the gradient elasticity solution can be fitted to the atomistic simulations with good agreement and can be employed to trace the energetically favourable cores without the requirement of defining a core radius. As a byproduct of this continuum approach, a dislocation self‐energy quantity is derived as a constant material property in terms of a gradient coefficient. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Gradient Nanomechanics: Applications to Deformation, Fracture, and Diffusion in Nanopolycrystals

“…As has been shown elsewhere, [23][24][25][26] the self-energy per unit length of a screw dislocation within the gradient theory of nanoelasticity summarized by Eqs. [5] is given by the expression…”

“…It turns out [23][24][25][26] that for a loaded NC or UFG material weakened by a (nano) crack, the stress tensor r ij is given by the inhomogeneous Helmholtz equation:…”

Nonsingular dislocation and crack fields: implications to small volumes

“…The strain energy per unit dislocation length for a cylinder of radius R surrounding the dislocation line within the gradient elasticity theory (Aifantis 2003) is given by (Kioseoglou et al 2006 and references quoted therein)…”

“…The above expressions were adopted to calculate the self-energy of a 1=6\20 " 23 [ partial dislocation in wurtzite GaN (Kioseoglou et al 2006). As the classical elasticity expressions for W s;e ð¼ A s;e ln½R=r 0 Þ are singular for r 0 !…”

Exploring the applicability of gradient elasticity to certain micro/nano reliability problems

“…1 can be obtained on the basis of recently developed highresolution optical methods in conjunction with the nonsingular solutions obtained for the strain field of dislocation (see, for example, the recent paper by Kioseoglou et al 2006) and crack problems. This is possible due to the fact that the model of Eq.…”