Lattice resistance and Peierls stress in finite size atomistic dislocation simulations

Atomistic computations of the Peierls stress in fcc metals are relatively scarce. By way of contrast, there are many more atomistic computations for bce metals, as well as mixed discrete-continuum computations of the Peierls-Nabarro type for fcc metals, One of the reasons for this is the low Peierls stresses in fcc metals. Because atomistic computations of the Peierls stress take place in finite simulation cells, image forces caused by boundaries must either be relaxed or corrected for if system size-independent results are to be obtained. One of the approaches that has been developed for treating such boundary forces is by computing them directly and subsequently subtracting their effects, as developed in (Shenoy V B and Phillips R 1997 Phil. Mag. A 76 367), That work was primarily analytic, and limited to screw dislocations and special symmetric geometries. We extend that work to edge and mixed dislocations, and to arbitrary two-dimensional geometries, through a numerical finite element computation. We also describe a method for estimating the boundary forces directly on the basis of atomistic calculations. We apply these methods to the numerical measurement of the Peierls stress and lattice resistance curves for a model aluminium (fcc) system using an embedded-atom potential.