KMC models are now widely used for simulating radi­ation effects on materials.21- 0 Advantages of KMC models include the ability to capture spatial correla­tions in a full 3D simulation with atomic resolution, while ignoring the atomic vibration time scales cap­tured by MD models. In KMC, individual point defects, point defect clusters, solutes, and impurities are treated as objects, either on or off an underlying crystallo­graphic lattice, and the evolution of these objects is modeled over time. Two general approaches have been used in KMC simulations, object KMC (OKMC) and event KMC (EKMC),35,36 which differ in the treatment of time scales or step between individual events. Within the OKMC designation, it is also possi­ble to further subdivide the techniques into those that explicitly treat atoms and atomic interactions, which are often denoted as atomic KMC (AKMC), or lattice KMC (LKMC), and which were recently reviewed by Becquart and Domain,45 and those that track the defects on a lattice, but without complete resolution of the atomic arrangement. This later technique is predomi­nately referred to as object Monte Carlo and used in such codes as BIGMAC27 or LAKIMOCA.28 More recently, several algorithmic ideas have been identified that, in combination, promise to deliver breakthrough KMC simulations for materials computations by making their performance essentially independent of the particle density and the diffusion rate disparity, and these will be further discussed as outstanding areas for future research at the end of the chapter.

KMC modeling of radiation damage involves tracking the location and fate of all defects, impurities, and solutes as a function oftime to predict microstruc­tural evolution. The starting point in these simulations is often the primary damage state, that is, the spa­tially correlated locations of vacancy, self-interstitials, and transmutants produced in displacement cascades resulting from irradiation and obtained from MD simulations, along with the displacement or damage rate which sets the time scale for defect introduction. The rates of all reaction-diffusion events then control the subsequent evolution or progression in time and are determined from appropriate activation energies for diffusion and dissociation; moreover, the reactions and rates of these reactions that occur between species are key inputs, which are assumed to be known. The defects execute random diffusion jumps (in one, two, or three dimensions depending on the nature of the defect) with a probability (rate) proportional to their diffusivity. Similarly, cluster dissociation rates are gov­erned by a dissociation probability that is proportional to the binding energy of a particle to the cluster. The events to be performed and the associated time-step of each Monte Carlo sweep are chosen from the RTA.17,18 In these simulations, the events which are considered to take place are thus diffusion, emission, irradiation, and possibly transmutation, and their corresponding occurrence rates are described below.