Elastic energy of a straight dislocation and contribution from core tractions

Abstract

We derive an expression of the core traction contribution to the dislocation elastic energy within linear anisotropic elasticity theory using the sextic formalism. With this contribution, the elastic energy is a state variable consistent with the work of the Peach-Koehler forces. This contribution needs also to be considered when extracting from atomic simulations core energies. The core energies thus obtained are real intrinsic dislocation properties: they do not depend on the presence and position of other defects. This is illustrated by calculating core energies of edge dislocation in bcc iron, where we show that dislocations gliding in {110} planes are more stable than the ones gliding in {112} planes.

Simulation of screw dislocations in wadsleyite

“…fitted value was 100.7 GPa and the value from anisotropic elasticity was 101.4 GPa.) The second approach involves plotting the difference between the total energy and the elastic part of the energy (using K from the elastic constants) this is shown in Figure 10 and converges to the core energy at large radius (Clouet, 2009). Using this approach gives somewhat smaller core energies and implies smaller core radii (∼1.4 eV/Å and ∼6Å for the…”

“…In the latter case it is important to consider interactions between the dislocation core fields and to include the contribution from core traction in the dislocation formation energy (Clouet, 2009 pressure olivine structure and the high pressure ringwoodite (spinel) structure and accounts for around 40% of the mantle by volume for a pyrolitic composition at depths between 410 and 520 km. An understanding of the deformation mechanisms of wadsleyite is particularly useful as a signature of mantle dynamics and, in particular, to discriminate between whole-mantle and layered convection.…”

Atomic-scale models of dislocation cores in minerals: progress and prospects

“…An alternative approach to finding the core energy is illustrated in Figure 6c where the difference between the elastic and calculated energies are plotted as a function of radius (Clouet, 2009). This graph (Figure 6c) converges on the core energy at large radii and the core radius can then be directly read from Figure 6b using the core energy.…”

“…There is also an elastic interaction energy between the two dislocations within the central simulation cell that must be corrected and removed. Finally, in order to allow rigourous comparisons with cluster calculations, it is necessary to include a correction for the core traction term (Clouet, 2009). …”

Simulation of defects in bubble clusters

“…The energy of a dislocation can be described by the well-known equations of the elastic strain field of an edge dislocation [23,[28][29][30]. The strain energy density w of a dislocation with Burgers vector B in an incompressible foam cluster is…”