ABC E and kMC calculations are employed to simulate the point defect diffusion

Abc e and kmc calculations are employed to simulate

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ABC-E and kMC calculations are employed to simulate the point defect diffusion in an anisotropic material, hcp Zr. Point defect diffusion is important in governing the evolution of microstructure in Zr alloys, which are widely used as cladding materials of nuclear fuel in light water reactors (LWR [ 33 ]). For safety and operational purposes, it is important to be able to predict the mechanical properties of Zr, which are largely dependent on the defect evolutions [ 34 39 ]. Furthermore, the point defect diffusion in hcp Zr is an ideal problem to test the accuracy of the new algorithm, ABC-E, because the diffu- sion of vacancies and interstitials can take place via dissimilar migration paths and sites in this structure. The results show that ABC-E samples effectively multiple inequivalent transi- tion pathways for the migration of point defects in hcp Zr. The extent of anisotropy in the diffusivity of point defects is assessed as a function of temperature. We find that the SIA diffusion exhibits a non-monotonic behavior of isotropic- anisotropic-isotropic transitions with increasing temperature. This behavior originates from different stabilities and migra- tion mechanisms associated with different SIA sites when using the MA07 interatomic potential [ 40 ]. This result is in contrast to previous findings using a different potential [ 41 ], because the two potentials provide different relative stabilities of the SIA sites. 2. Methodology As noted above, it is possible that the original ABC method can overestimate the system evolution time scale in the case J. Phys.: Condens. Matter 26 ( 2014 ) 365402
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Y Fan et al 3 of multiple competitive processes [ 30 32 ]. In this section we introduce the underlying reason for the time overestimation by comparing the ABC method with analytical TST and kMC results. Then we modify the ABC algorithm to ABC-E to cap- ture multiple transition pathways from an individual basin on the PES. This extension significantly improves the accuracy of the calculated time of evolution. A very brief summary of the result of ABC-E in comparison to ABC and analytical TST was recently reported [ 32 ]. Here we provide the description of the new algorithm and its comparison to TST in detail. 2.1. Transition state theory and full catalogue kinetic monte carlo method For a given transition network, according to TST, the evo- lution time from the initial (‘ i ’ in figure 1 ) to the final state (‘ f ’ in figure 1 ) can be calculated as the following: If state p and q are connected with each other, following TST, the jump frequency from p to q can be derived by: uni23A1 uni23A3 uni23A2 uni23A4 uni23A6 uni23A5 = - k k E k T exp , p q p q B , 0 , (1) where the prefactor k 0 is the attempt frequency, and E p,q is the activation energy from state p to q . The residence time from state p is given by: uni03C4 = + + uni22EF + k k k 1 , p p p p n p ,1 ,2 , ( ) (2) where n p ( ) is the number of neighboring nodes connected with state p .
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  • Summer '19
  • Transition state, KMC

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