2c BC BO BC migration As shown in figure 10 below the middle atom in the

2c bc bo bc migration as shown in figure 10 below the

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(2.c) BC-BO-BC migration . As shown in figure  10 below, the middle atom in the crowdion migrates to the BO site in the basal plane. The BO site is not stable since the outgoing barrier is only 0.011 eV. Then the BO state migrates to the BC state, with a degeneracy of three. The corresponding migration barriers are also marked in the figure. The effective barrier for such BC rotation is about 0.03 eV. All the SIA migration mechanisms that were found by ABC-E in hcp Zr are summarized in table  2 . We compare the results to Subramanian et al ’s recent calculations [ 49 ] by the TAD method, and most of the mechanisms are found consist- ently by both the ABC-E and TAD methods, except for the S structure (and its migration paths) which was not consid- ered in this work. The quantitative differences are small, in the range of error tolerance. In general, all the SIA migration barriers were found to be small (0.011–0.131 eV); therefore, SIAs in hcp Zr are expected to exhibit fast diffusion. In summary, the SIA diffusion in hcp Zr is governed by a mix of 1D and 3D migration mechanisms comprising the fol- lowing: the O state prefers to hop among the six degenerate neighboring sites in the basal plane with the lowest migration Figure 7. Direct O-O hopping mechanism. O state can migrate to either the 1st NN O state or the 2nd NN O state, as shown in ( a ) and ( b ), respectively. Figure 8. O-M1-BC migration pathway and associated barriers for an SIA from the O state to the BC state. Notice that O-M1 transition actually has a degeneracy of two, although the figure above only shows one of them. J. Phys.: Condens. Matter 26 ( 2014 ) 365402
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Y Fan et al 10 barrier. The O state also has some probability to migrate to the O site in a neighboring basal plane via the O-M2-O mecha- nism, and thus overall would exhibit a 3D migration com- bining in-plane and out-of plane diffusion. In addition, the O state has a chance to evolve into the BC state via the O-M1-BC mechanism. Once the SIA transits to the BC state, the SIA migration will be mainly governed by the 1D glide motion in the basal plane with the smallest barrier. The BC state also has a probability to transform to another BC state along another direction in the same basal plane, via the BC-BO-BC mechanism. The BC state can jump back to the O state via the BC-M1-O mechanism. Overall, the O-M2-O mechanism pro- vides a 3D motion, while the BC glide provides a 1D motion in the basal plane. The fraction of the 1D and 3D motion can change as a function of temperature because of the different activation energies of these mechanisms. Finally, we would like to note that the activation energies for the BC and BO mechanisms are very small (equivalent to less than 400 K). As a result, at temperatures higher than 400 K, the BC and BO mechanisms can be washed out by thermal fluctuation, and it would not be possible to resolve the different pathways. In the following part of this paper, when discussing the kinetics, we first assume the transition state theory is valid through
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  • Summer '19
  • Transition state, KMC

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