J Phys Condens 365402 Y Fan et al 12 entire simulated

J phys condens 365402 y fan et al 12 entire simulated

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J. Phys.: Condens. Matter 26 ( 2014 ) 365402
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Y Fan et al 12 entire simulated temperature range, which indicates that the anisotropic effect is weak (figure 13 ( d )). On the other hand, the plot in figure  13 ( d ) shows a very interesting non-mono- tonic behavior; at the low temperature ( T  < 175 K), diffusion is more isotropic, contrary to the behavior of vacancy diffu- sion. At intermediate temperatures (175 K <  T  <600 K), the anisotropy increases as a function of temperature, with Dc/Da decreasing to 0.83.When the temperature is higher than 600 K, the anisotropy decreases as a function of temperature, with Dc/Da again increasing towards 1.00. Although all the mechanisms introduced in section  3 con- tribute to the diffusion along the <a> direction, the motion along the  <c>  direction can only arise from the O-M1-BC and O-M2-O mechanisms. Therefore, the diffusivity along the  <c>  direction, D c , is a good indicator of the diffusion mechanisms at different temperatures. In figure  14 we plot D c Figure 12. ( a ) SIA diffusion trajectories up to 100 ps at 300 K and 500 K. ( b ) The projections of the trajectories from ( a ) on the basal plane. Figure 13. ( a )–( c ) The MSD along the <a> and <c> directions at 150 K, 600 K, and 900 K. ( d ) The ratio between the diffusivities along the <c> and <a> directions at various temperatures. J. Phys.: Condens. Matter 26 ( 2014 ) 365402
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Y Fan et al 13 as a function of temperature. It can be seen that the overall behavior fits well into an Arrhenius manner, with the effective barrier around 0.1 eV, which is a reflection of the O-M1-BC and O-M2-O mechanisms. (See table  2 .) However, in the intermediate temperature regime between 400 K and 700 K, the slope of the curve is smaller (a lower barrier), which means the increase of D c is slower with temperature in this regime. The non-monotonic behavior in figure  13 ( d ) and the slow increase of D c at intermediate temperatures in figure  14 origi- nate from the temperature dependence of the stability of the SIA site, which favors the O site at the lower temperatures. As shown in table  1 , within the MA07 potential, the O state has lower formation energy than the BC state by about 0.1 eV. On the other hand, the O-M2-O mechanism has a lower migra- tion barrier than the O-M1-BC mechanism by about 0.035 eV. Therefore, at low temperatures, the system mostly stays at the O state, and the diffusion is governed by the O-M2-O mecha- nism, which displays a 3D diffusion and is more isotropic. As the temperature increases, the system has a higher probability to stay at the BC state. For the BC mechanism, as discussed above, the BC-BC glide has a lower barrier than the BC-M1-O migration. Therefore, the fraction of 1D motion, i.e. the ani- sotropy, starts to increase. This explains the reason for the slow increase of D c between 400 K and 700 K in figure  14 .
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