Development of Stochastic Perturbation Algorithm for Object Kinetic Monte Carlo

Abstract

Object kinetic Monte Carlo (OKMC) is one of the popular methods adopted in irradiation damage calculation on structural material. In the calculation of the damage process, the primary defects are calculated by a short term calculation tools such as Molecular Dynamics where the time scale is order of picoseconds. Then, OKMC extends its time scale up to days, months or years. The results of OKMC such as the average size of defect clusters or the population of object can be used to estimate the macroscopic material property change such as irradiation hardening.

On the other hand, ab initio is considered as the most reliable method in constructing input parameter set of OKMC. However, it's known that it costs very expensive in terms of the time and computational resources. To reduce the computational burden of input parameter generation, sensitivity analysis can be used to quantify the importance of input parameters. For more efficient sensitivity analysis of OKMC, a stochastic perturbation algorithm is developed based on the correlated sampling method. To develop this method, the mathematical formulation of OKMC is performed from the master equation of dynamic Monte Carlo. Since the solution to this master equation is given explicitly in Neumann series, the algorithm of OKMC can be expressed by using integration of response function.

Once the OKMC algorithm is formulated mathematically in integration form, the correlated sampling method can be applied to develop the perturbation algorithm. On the other hand, the calculation of event kernel ratio is far from straightforward because it is assumed that there is no underlying lattice structure. So the approximation based on rate theory is introduced to calculate the event kernel ratio. To verify if the developed method works properly, the algorithm is applied to the electron irradiation problem by assuming that the target is pure BCC iron. And the perturbation is introduced to the migration energy of object. As a result, it shows that algorithm works successfully.