6 Conclusions Here we presented an extension of the ABC algorithm called ABC E

6 conclusions here we presented an extension of the

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useful for the computational materials community. 6. Conclusions Here we presented an extension of the ABC algorithm, called ABC-E, to improve accuracy in predicting the kinetics of com- plex system evolution while retaining efficiency. Specifically, the ABC-E algorithm permits the sampling of multiple tran- sition pathways from a given minimum energy state on the potential energy landscape, contrary to the 1D system evolu- tion exhibited by the original ABC algorithm. When a tran- sition pathway is found using the original ABC algorithm, a blocking penalty function is added onto the saddle point, and the system is set back to the original given basin. By per- forming this procedure iteratively and choosing the blocking and search criterion carefully, a series of transition path- ways associated with the given basin can be identified. We demonstrated on a hypothetical PES that the combination of ABC-E and on-the-fly kMC calculations allows a signifi- cantly more accurate description of the kinetics of system evolution, matching that of the full catalogue kMC results. By comparing ABC-E and the ART method in the simulation of vacancy migration in hcp Zr, we have also demonstrated the prioritization of sampled paths in the order of increasing acti- vation energies. This feature of ABC-E enables computation- ally efficient importance sampling. This ABC-E algorithm, in combination with other coarse graining methods, can provide an opportunity to accurately, and relatively efficiently, describe materials’ macroscopic behavior in a multi-scale sense. For example, recent related works [ 29 , 58 ] demonstrate a multi-scale framework for stud- ying the materials’ mechanical response to the surrounding environments. Such frameworks require the atomistic mech- anisms as input, which were provided by the original ABC algorithm. In the latter part of this paper, we employed ABC-E to simulate the diffusion of point defects in an anisotropic mate- rial, the hcp Zr. This problem makes an ideal physical test bed for ABC-E because point defect diffusion is associated with multiple migration mechanisms that could not be captured by the original ABC algorithm, and because an accurate descrip- tion of point defect diffusion is important for predicting microstructure evolution in materials of importance to nuclear systems. We demonstrated that the ABC-E method could cap- ture all the multiple migration mechanisms of vacancies and self-interstitial atoms in hcp Zr, consistent with other available results from literature. Combining the mechanisms and bar- riers identified from ABC-E with on-the-fly kMC simulations, we assessed the temperature dependence of the vacancy dif- fusion and SIA diffusion kinetics. An interesting, non-linear isotropic-anisotropic-isotropic transition with increasing temperature was found for the SIA diffusion. This behavior originates from the temperature dependence of the stability of the SIA site. The SIA stability favors the O-site at the lower temperatures, and the BC-site competes with the O-site with
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  • Summer '19
  • Transition state, KMC

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