Diffusive atomistic dynamics of edge dislocations in two dimensions

Abstract

The fundamental dislocation processes of glide, climb, and annihilation are studied on diffusive time scales within the framework of a continuum field theory, the phase field crystal model. Glide and climb are examined for single edge dislocations subjected to shear and compressive strain, respectively, in a two-dimensional hexagonal lattice. It is shown that the natural features of these processes are reproduced without any explicit consideration of elasticity theory or ad hoc construction of microscopic Peierls potentials. Particular attention is paid to the Peierls barrier for dislocation glide or climb and the ensuing dynamic behavior as functions of strain rate, temperature, and dislocation density. It is shown that the dynamics are accurately described by simple viscous motion equations for an overdamped point mass, where the dislocation mobility is the only adjustable parameter. The critical distance for the annihilation of two edge dislocations as a function of separation angle is also presented.

Marginal stability analysis of the phase field crystal model in one spatial dimension

“…As originally formulated in a parabolic form, the PFC model allows simulations on diffusive time scales which can be many orders of magnitude larger than molecular dynamics simulations 6,14 . More recently a hyperbolic 24 or modified 25 PFC model was introduced that includes faster degrees of freedom in a form of inertia and as such leads to the description of both fast and slow dynamics.…”

“…It can be related to other continuum fields theories such as classical density-functional theory 8,9 and the atomic density function theory 10 . The PFC-model may also be considered as a conserved version of the Swift-Hohenberg equation and provides an efficient method for simulating liquid-solid transitions 11,12 , colloidal solidification 13 , dislocation motion and plasticity 14,15 , glass formation 16 , epitaxial growth 6,17 , grain boundary premelting 18 , surface reconstructions 19 , and grain boundary energies 20 .…”

Multiscale Modeling of Point and Line Defects in Cubic Lattices

“…Note that for uniaxial strain of the form F 11 = 1 +ε, with screw dislocations oriented parallel to the X 1 -direction, the defect energy in Eq. (69) degenerates to…”

“…However, this work constitutes an initial step toward computing energies used in continuum defect theories from physics-based, multiscale computations, as opposed to phenomenological curve fitting of the material response to macroscopic stress data, for example. Intermediate scale methods, such as phase field models [68,69] or discrete dislocation simulations [70][71][72], may ultimately be needed to address nonideal defect configurations and finite temperature defect kinetics to bridge scales of atomistic resolution and continuum crystal mechanics for arbitrarily disordered states of the material.…”

DDFT calibration and investigation of an anisotropic phase-field crystal model

“…Since its introduction, this phase-field crystal (PFC) method [2,3,4,5,6] has emerged as a computationally efficient alternative to molecular dynamics (MD) simulations for problems where the atomic and the continuum scale are tightly coupled. The reason is that it operates for atomic length scales and diffusive time scales.…”