32 SIA migration pathways The migration of a SIA in Zr is much more complicated

32 sia migration pathways the migration of a sia in

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3.2. SIA migration pathways The migration of a SIA in Zr is much more complicated than that of a vacancy since the SIA can exist at different interstitial sites. Here we consider six possible interstitial sites based on the geometry of hcp crystals. These are the octahedral (O), basal octahedral (BO), tetrahedral (T), basal tetrahedral (BT), crowdion (C), and basal crowdion (BC), as shown in figure  5 . According to previously reported DFT calculations [ 50 , 51 ], the split (S) configuration is another candidate site for the interstitial. However, these S structures are very unstable [ 49 ] and can exist in multiple slightly different configurations, which makes the assessment uncertain [ 49 , 52 ]. Therefore, we did not consider the S site in the analysis. To check the stabilities based on formation energies for an SIA at these interstitial sites, we insert an extra atom into each interstitial site (one at a time) and then relax the system by the steepest descent algorithm. It can be seen in figure  6 that, among the six interstitial sites, only three stable struc- tures arise. Both the perfect O and C sites decay to a distorted O site with the degeneracy of six. Both the T and BT sites are unstable and decay to the BC site. The BO site is energeti- cally stable. The energetics for these sites with the MA07 potential are summarized in table  1 below. We define the formation energy of an SIA at different sites as: = - + uni22C5 + E E N N E 1 , f SIA tot N perfect N 1 where + E tot N 1 represents the total potential energy of the system, including the SIA, while E perfect N is the potential energy of a perfect hcp Zr system containing N atoms. The distorted O site is relatively more stable, with the for- mation energy of 2.74 eV. The formation energies for the BC and BO sites are 2.83 eV and 2.86 eV, respectively. The rela- tive stability of the O site is consistent with previous works using the same potential [ 40 , 53 ] and several DFT calculations [ 50 , 51 ]. However, the quantitative results differ, and the dis- crepancies might arise from the size of simulation cells used in various reports [ 50 , 51 , 53 , 54 ]. It is notable that all three Figure 4. The in-plane (M1) and out-of-plane (M2) migration paths for a Zr vacancy in the hcp crystal. Both of these paths are captured by the ABC-E algorithm sequentially. The red spheres represent the atoms on the lattice points, while the blue square represents the missing atom—i.e. the vacancy. Figure 5. Six possible interstitial sites in a hcp crystal, shown by green spheres. The red spheres represent the atoms on the lattice points. J. Phys.: Condens. Matter 26 ( 2014 ) 365402
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Y Fan et al 8 SIA sites have comparable energies, and therefore SIAs are expected to be present comparably at all of these three sites at elevated temperatures. We identified the migration mechanisms and the cor- responding activation energies of SIA diffusion in hcp Zr using the ABC-E method. Two key mechanisms describe the migration of SIA: the O-mechanism and the BC-mechanism, respectively.
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