An atomistically validated continuum model for strain relaxation and misfit dislocation formation

Abstract

In this paper, molecular dynamics (MD) calculations have been used to examine the physics behind continuum models of misfit dislocation formation and to assess the limitations and consequences of approximations made within these models. Without compromising the physics of misfit dislocations below a surface, our MD calculations consider arrays of dislocation dipoles constituting a mirror imaged "surface". This allows use of periodic boundary conditions to create © 2016. This manuscript version is made available under the Elsevier user license http://www.elsevier.com/open-access/userlicense/1.0/ 2 a direct correspondence between atomistic and continuum representations of dislocations, which would be difficult to achieve with free surfaces. Additionally, by using long-time averages of system properties, we have essentially reduced the errors of atomistic simulations of large systems to "zero". This enables us to deterministically compare atomistic and continuum calculations. Our work results in a robust approach that uses atomistic simulation to accurately calculate dislocation core radius and energy without the continuum boundary conditions typically assumed in the past, and the novel insight that continuum misfit dislocation models can be inaccurate when incorrect definitions of dislocation spacing and Burgers vector in latticemismatched systems are used. We show that when these insights are properly incorporated into the continuum model, the resulting energy density expression of the lattice-mismatched systems is essentially indistinguishable from the MD results.

Atomistic calculations of dislocation core energy in aluminium

“…This is not satisfactory for calculating dislocation energies, which are related to total energies of (dislocated and perfect) systems if the length along dislocation is fixed. Time-averaged properties of long time MD simulations, on the other hand, are found to converge satisfactorily regardless of the system dimensions [18]. This sounds surprising at a first sight but can be understood because the time averaged MD calculations not only average out the thermal noises, but also are analogous to performing ensemble averages of many MS simulations with different perturbations of initial configurations.…”

“…As shown in the appendix, the dipole array energy can be expressed analytically using isotropic linear elasticity theory for a chosen core radius r 0 . As discussed in Section III.C, fitting the MD data to this analytical equation then allows us to determine the core energy [18].…”

“…We have found that while molecular statics (MS) energy calculations based on the conjugate gradient method can give low relative errors, they produce large total errors that increase as the system dimension increases [18]. This is not satisfactory for calculating dislocation energies, which are related to total energies of (dislocated and perfect) systems if the length along dislocation is fixed.…”

“…During this stage of separation we lump all of the work done into a change in the core energy, leading to an energy change of [18] The total line energy of the extended dislocation is now Γ = Γ pf + ΔΓ. Using Eqs.…”

“…Recently, we have used molecular dynamics (MD) to calculate core energies of edge dislocations under periodic boundary conditions [18]. In our approach, we eliminate the alternation of dislocations in x, which prevents annihilation by glide.…”