All models use periodic boundary conditions in the direction of the dislocation line so that the dislocation is effectively infinite in length. If the model contains one obstacle, the length, L, of the model in the periodic direction represents the center-to-center obstacle spacing along an infinite row of obstacles. It is the treatment of the boundaries in the other two directions that distinguishes one method from another. A versatile atomic-scale model should allow for the following.10

1. Reproduction of the correct atomic configuration of the dislocation core and its movement under the action of stress.

2. Application of external effects such as applied stress or strain, and calculation of the resultant response such as strain (elastic and plastic) or stress and crystal energy.

3. Possibility of moving the dislocation over a long distance under applied stress or strain without hindrance from the model boundaries.

4. Simulation of either zero or non-zero temperatures.

5. Possibility of simulating a realistic dislocation density and spacing between obstacles.

6. Sufficiently fast computing speed to allow simula­tion of crystallites in the sizes range where size effects are insignificant.

A comprehensive review ofmodels developed so far is to be found in Bacon et at.? and so here we merely present a short summary of the pros and cons of some models used most commonly. Historically, the earliest models consisted of a small region of mobile atoms surrounded in the directions perpendicular to the dislocation direction by a shell of atoms fixed in the positions obtained by either isotropic or anisotropic elasticity for displacements around the dislocation of interest.11 This model was used successfully to inves­tigate dislocation core structure and, being simple and computationally efficient, can use a mobile region large enough to simulate interaction between static dislocations and defects and small defect clusters. Its main deficiencies are its inability to model dislocation motion beyond a few atomic spacings because of the rigid boundaries (condition 3) and its restriction to temperature T = 0 K (condition 4).

The desirability of allowing for elastic response of the boundary atoms due to atomic relaxation in the inner region, for example, when a dislocation moves, has led to the development ofseveral quasicontinuum models. The elastic response can be accounted for by using either a surrounding FE mesh or an elastic Green’s function to calculate the response of bound­ary atoms to forces generated by the inner region. Such models are accurate but computationally
inefficient and have not found wide application so far.4 Furthermore, their use for simulation of T> 0K (condition 4) is still under development.12 Nevertheless, quasicontinuum models, especially those based on Green’s function solutions, can be employed in applications where calculation of forces on atoms is computationally expensive and a signifi­cant reduction in the number of mobile atoms is desirable.13

The models now most widely applied to simulate dislocation behavior in metals are based on the peri­odic array of dislocations (PAD) scheme first intro­duced for simulating edge dislocations.14,15 In this, periodic boundary conditions are applied in the direction of dislocation glide as well as along the dislocation line, that is, the glide plane is periodic. This means that the dislocation is one of a periodic, 2D array of identical dislocations. The success of PAD models is because of their simplicity and good computational efficiency when applied with modern empirical IAPs, for example, embedded atom model (EAM) type. They can be used to simulate screw, edge, and mixed dislocations.4,10,16 With a PAD model containing ^106-107 mobile atoms, essentially all con­ditions 1-6 can be satisfied. Their ability to simulate interactions with strong obstacles of size up to at least ~10 nm makes PAD models efficient for investi­gating dislocation-obstacle interactions relevant to a radiation damage environment. Practically all impor­tant radiation-induced obstacles can be simulated on modern computers using parallelized codes and most can even be treated by sequential codes.

Details of model construction for different dislo­cations can be found elsewhere.4,10,16 Here we just present an example of system setup for screw or edge dislocations in bcc and fcc metals interacting with dislocations loops and SFTs, as presented in Figure 1.

There are two types of DL in an fcc metal: glissile perfect loops with bL = 1/2(110) and sessile Frank loops with bL = 1/3(111). There are two types of glissile loop with Burgers vectors 1/2(111) and (100) in a body-centered cubic (bcc) metal.

Visualizing interaction mechanisms is a strong feature of atomic scale modeling. The main idea is to extract atoms involved in an interaction and visua­lize them to understand the mechanism. Usually these atoms are characterized by high energy, local stresses, and lattice deformation. The techniques used are based on analysis of nearest neighbors,17 central symmetry parameter,18 energy,19 stress,20 dis­placements,10 and Voronoi polyhedra.21 A relatively simple and fast technique, for example, was suggested for an fcc lattice.16 It is based on comparison of position of atoms in the first coordination of an atom with that of a perfect fcc lattice. If all 12 neigh­bors of the analyzed atom are close to that position, it is assigned to be fcc. If only nine neighbors corre­spond to perfect fcc coordination, the atom is taken to be on a stacking fault. Other numbers of neighbors can be attributed to different dislocations. Modifica­tions of this method have been successfully applied in hexagonal close-packed (hcp)22 and bcc23 crystals. Another improvement of this method for MD simu­lation at T> 0 K was introduced24 in which the above analysis was applied periodically (every 10-50 time — steps depending on strain rate e) and over a certain time period (100-1000 steps). A probability of an atom to be in different environment was estimated and the final state was assigned to the maximum over the analyzed period. Such a probability analysis can be applied to other characteristics such as energy or stress excess over the perfect state and it provides a clear picture when the majority of thermal fluctua­tions are omitted.