6929 depending on the parameters used in ART In the ABC E method since the

6929 depending on the parameters used in art in the

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dancy probability is about 68.6%–92.9%, depending on the parameters used in ART. In the ABC-E method, since the observed saddle points are blocked by the penalty function, the redundancy rate is much lower. We would like to stress that the efficiencies of different methods largely depend on the parameters used and the system at hand, and that different modeling techniques have their own advantages for different types of problems. A more thorough comparison between dif- ferent techniques is warranted in the future. 3. Migration mechanisms of point defects in hcp Zr Hcp Zr is an anisotropic material, and there are multiple inequivalent transition pathways on which the point defects can migrate. For example, there are two migration paths for vacancy diffusion, one on the basal plane and one out of the basal plane. Self-interstitial atom (SIA) migration has many more pathways in hcp Zr compared to vacancy migration. It is impossible for the original ABC method to capture all pos- sible migration mechanisms because it can only provide the lowest-barrier mechanism and would inaccurately estimate the diffusion kinetics of point defects in Zr. In this section, we employ ABC-E to simulate the anisotropic diffusivities of vacancy and SIA in Zr. The migration mechanisms and the corresponding activation energy barriers of point defects J. Phys.: Condens. Matter 26 ( 2014 ) 365402
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Y Fan et al 7 are identified by ABC-E, and they are, in part, benchmarked consistently with other methods reported in literature. The transition pathways and energy barriers are then input into on-the-fly kMC simulations to study the anisotropic diffusion kinetics of point defects in Zr. An interesting behavior for the SIA diffusion was found: specifically, a non-linear isotropic- anisotropic-isotropic transition in diffusivities with increasing temperature has been observed, arising from the temperature dependence of the stable SIA structure. The dimension of the simulation cell is 38.8A*39.2A*41.3A, containing 2688 Zr atoms. To simulate the vacancy, an atom is extracted from the bulk, while for SIA an extra atom is inserted into the system. Periodic boundary conditions are applied for all directions. A recent embedded atom method (EAM) potential developed by Mendelev et al [ 40 ] (MA07) is employed. For vacancy migrations, penalty parameters of 0.5 eV, 0.25 A 2 (for both the regular bias filling function and the blocking function) are employed in ABC-E. For SIA migrations, penalty parameters of 0.01 eV and 0.05 A 2 are employed in ABC-E. 3.1. Vacancy migration pathways By employing the ABC-E method, we observed two migra- tion mechanisms for vacancy diffusion—i.e. in the basal plane and out of the basal plane. The in-plane migration (M1) had a lower barrier 0.68 eV compared to the out-of-plane migra- tion (M2), which had a 0.76 eV barrier. Both migration paths had a degeneracy of six. The derived mechanisms and barriers are consistent with other results reported independently by Subramanian et al using TAD simulations [ 49 ].
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