The collective behavior of dislocations can be described thanks to dislocation dynamics codes. In order to reinforce the physical foundation, input data such as mobility laws can be obtained from atomistic calculations ofindividual dislocations. These defects can now be investigated using more accurate ab initio electronics structure methods. We exemplify these studies by focusing in the following section on the properties ofdislocations in bcc metals and especially
iron. In these materials, dislocation properties are known to be closely related to their core structure.

When dealing with dislocations, special care should be taken in the positioning ofthe dislocations and in the boundary conditions of the calculations. For instance, considering (111) screw dislocations, the two cell geometries proposed in the literature — the cluster approach85 and the periodic array of dislocation dipoles86 — have been thoroughly compared.87 The calculations of dislocations are extremely demanding as they can include up to 800 atoms, so studies usually use fast codes such as SIESTA.8 The construction of simulation cells appro­priate for such extended defects should be optimized for cell sizes accessible to DFT calculations, and the cell-size dependence of the energetics evidenced in both the cluster approach and the dipole approach for various cell and dipole vectors should be rationa­lized. The quadrupolar arrangement of dislocation dipoles is most widely used for such calculations87 although the cluster approach with flexible boundary conditions can be considered a reference method when no energies are necessary (i. e., only structures).

DFT calculations in bcc metals such as Mo, Ta, Fe, and W85,87-91 predict a nondegenerate structure for the core, as illustrated in Figure 9 using differential displacement maps as proposed by Vitek.92 The edge component reveals the existence of a significant core dilatation effect in addition to the Volterra field, which can be successfully accounted for by an aniso­tropic elasticity model.93

Thanks to good control of energy, it is also possi­ble to obtain quantitative results on the Peierls poten­tial; namely, the 2D energy landscape seen by a straight screw dislocation as it moves perpendicular to the Burgers vector. This is exemplified in the following Figure 10(a), where a high symmetry direc­tion of the Peierls potential is sampled: the line going between two easy core positions along the glide direc­tion, that is, the Peierls barrier. These calculations

were performed by simultaneously displacing the two dislocations constituting the dislocation dipole in the same direction and by using a constrained relaxation method. In the same work, the behavior of the Ackland-Mendelev potential for iron,45 which gives the correct nondegenerate core structure unlike most other potentials, has been tested against the obtained DFT results. It appears that it compares well with the DFT results for the g-surfaces, but discrepancies exist on the deviation from anisotropic elasticity of both edge and screw components and on the Peierls potential. Indeed, the empirical potential results do not predict any dilatation elastic field exerted by the core. Besides, the Peierls barrier dis­played by the Ackland-Mendelev potential yields a camel hump shape, as illustrated in Figure 10(a), and at the halfway position, the core spreads between

two easy core positions, whereas it exhibits a single hump barrier within DFT and a nearly hard-core structure at halfway position. The effect of the exchange-correlation functional within DFT appears to be significant.87

More insight into the stability of the core structure can be gained by looking at the response of the polarization of the core, as represented in Figure 10(b). In the Ackland-Mendelev and DFT cases, these calculations confirm that the stable core is completely unpolarized, and they prove that there is no metastable polarized core.95

Finally, the methodology exists for calculating the structure and formation and migration energies of single kinks, but using it with DFT96 remains chal­lenging because cells with about 1000 atoms are needed, together with a high accuracy.