AKMC is a versatile method that can be used to simulate the evolution of materials with complex microstructure at the atomic scale by modeling the elementary atomic mechanisms. It has been used extensively to study phase transformations such as precipitation, phase separation, and/or ordering in many systems, as discussed in a recent review.92 Despite the fact that the algorithm is fairly simple, the method is most of the time nontrivial to imple­ment in the case of realistic materials (as opposed to AB alloys for instance). Indeed, the determination of the total potential energy of the system, that is, the construction of the cohesive model when the chemis­try ofthe system under study is complex and involves many species or a complex crystallographic structure, is difficult to obtain. Furthermore, the knowledge of all the possible events and the rates at which they occur, that is, the possible migration paths as well as their energies is nontrivial. On rigid lattices, the migration paths are more obvious to determine and cluster expansion type methods may be extended to determine the saddle point energies as a function of the local chemical environment. This can, however, take a very large amount of calculation time when there is a drastic difference in the local environment. Furthermore, complicated correlated motions such as the adatom diffusion on the (100) surfaces of fcc metals which occurs by a two-atom concerted dis­placement, in which the adatom replaces a surface atom, which in turn becomes an adatom, cannot be modeled within the simple scheme usually followed in AKMC of jumps to 1nn neighbor sites.

Another drawback is that to be efficient, it is tempting to use rigid lattices as a large number of KMC steps have to be performed. This can lead to an approximate (or even completely unrealistic) treat­ment of microstructure elements such as incoherent carbide precipitates, SIA clusters, or interstitial dis­location loops. Note, however, that it is possible to perform off-lattice AKMC, which will of course require more time consuming simulations, as pro­posed recently by Mason et a/.93 to investigate phase transformation in Al-Cu-Mg alloys. The authors noticed that the use of flexible lattices instead of rigid ones affected the mobility of the vacancies as well as the driving force of the reaction and therefore the rate at which phase separation took place. Fur­thermore, note that off-lattice AKMC also requires an equilibrium continuous cohesive model, which is difficult to build for multicomponent alloys.

At the moment, OKMC methods have been mostly used to investigate the annealing of the primary dam­age as in Heinisch and Singh14 or Domain eta/.28 or the effect of temperature change in the damage accumula- tion,94 but its strongest contribution in the field seems to be the study of parameters or assumptions such as the motion, 3D versus 1D motion, mobility of the SIA clusters,95-98 or corroboration of theoretical assump­tions such as the analytical description of the sink strength.99 They have been used also to model as well as reexamine simple experiments such as He desorp­tion in W1 0 or in Fe101 as well as the influence of C in isochronal annealing experiments. It can also be used to determine the production rate or source term (i. e., the ‘irradiation flux’) in mean field rate theory (MFRT) models, as discussed in the chapter on MFRT. As no spatial correlation is explicitly considered in these techniques, the source term has to take into account intracascade agglomeration and recombination. The amount of agglomeration can be obtained by annealing the cascade debris using OKMC.1

In the OKMC, the evolution of individual objects is simulated on the basis of time scales that encom­pass individual atomic diffusive jumps, dominated by the very fast events. This method is not efficient at high temperatures and/or high doses. The difficulty is the inability to model sufficiently high doses nec­essary for macroscopic materials behavior due to the focus on fast dynamics.

The time-step between events is much longer in EKMC models, which require that a reaction (e. g., clustering among like defects, annihilation among opposite defects, cluster dissolution, or new cascade introduction) occur within each Monte Carlo sweep. EKMC can therefore simulate much longer times and therefore simulate materials evolution over higher doses. It is most efficient when few objects are present in the simulation box. But questions relate to whether the time-steps are too large to reliably capture the underlying fast dynamics and whether the assumed binary interactions are sufficient to reli­ably calculate interaction probabilities. Further, EKMC models developed to date have not included all of the relevant microstructural evolution mechan­isms, but they do represent an interesting approach in the limit of long time-step Monte Carlo simulations.