The emission or dissociation rate is usually the sum of the binding energy of the emitted particle and its migration energy. As in the case of migration energy, the binding energies can be obtained using either experimental studies, ab initio calculations, or MD.

As stated previously, three kinds of KMC techni­ques (AKMC, OKMC, and EKMC) have been used so far to model microstructural evolutions during radia­tion damage. In atomistic KMC, the evolution of a complex microstructure is modeled at the atomic scale, taking into account elementary atomic mech­anisms. In the case of diffusion, the elementary mech­anisms leading to possible state changes are the diffusive jumps of mobile point defect species, includ­ing point defect clusters. Typically, vacancies and SIAs can jump from one lattice site to another lattice site (in general first nearest neighbor sites). If foreign interstitial atoms such as C atoms or He atoms are included in the model as in Hin et a/.,70,71 they lie on an interstitial sublattice and jump on this sublattice.

In OKMC, the microstructure consists of objects which are the intrinsic defects (vacancies, SIAs, dis­locations, grain boundaries) and their clusters (‘pure’ clusters, such as voids, SIA clusters, He or C clus­ters), as well as mixed clusters such as clusters con­taining both He atoms, solute/impurity atoms, and
interstitials, or vacancies. These objects are located at known (and traced) positions in a simulation volume on a lattice as in LAKIMOCA or a known spatial position as in BIGMAC and migrate according to their migration barriers.

In the EKMC approach,72,73 the microstructure also consists of objects. The crystal lattice is ignored and objects’ coordinates can change continuously. The only events considered are those which lead to a change in the defect population, namely clustering of objects, emission of mobile species, elimination of objects on fixed sinks (surface, dislocation), or the recombination between vacancy and interstitial defect species. The migration of an object in its own right is considered an event only if it ends up with a reaction that changes the defect population. In this case, the migration step and the reaction are processed as a single event; otherwise, the migration is performed only once at the end of the EKMC time interval At. In contrast to the RTA, in which all rates are lumped into one total rate to obtain the time increment, in an EKMC scheme the time delays of all possible events are calculated separately and sorted by increasing order in a list. The event corresponding to the shortest delay, ts, is processed first, and the remaining list of delay times for other events is modified accordingly by eliminating the delay time associated with the particle that just disappeared, adding delay times for a new mobile object, etc.

To illustrate the power of KMC for modeling radi­ation effects in structural materials and nuclear fuels, this chapter next considers two examples, namely the use of AKMC simulations to predict the coupled evo­lution of vacancy clusters and copper precipitates dur­ing low dose rate neutron irradiation of Fe-Cu alloys and the use of an OKMC model to predict the trans­port and diffusional release of fission product, silver, in tri-isotropic (TRISO) nuclear fuel. These two examples will provide more details about the possible implementations of AKMC and OKMC models.