the entire temperature regime and then comment on how the kinetics would differ

The entire temperature regime and then comment on how

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the entire temperature regime, and then comment on how the kinetics would differ if the thermal fluctuations were to erase the mechanistic details. 4. Anisotropic point defect diffusion kinetics in hcp Zr 4.1. Vacancy diffusion kinetics The derived mechanisms and barriers and the hcp geom- etry for the vacancy migration are fed into the kMC model to simulate the diffusion kinetics. In the kMC simulation, we trace the coordinate of the vacancy as a function of the hops it makes in and out of the basal plane. Following the Arrhenius law, the vacancy migration rates in-plane and out- of-plane can be expressed as = - k k E k T exp[ ] a a M B 0 1 and Table 2. The summary on the SIA migration mechanisms in hcp Zr modeled by the ABC-E method. Migration mechanism Governing barrier (eV) O site O-O (1NN) 0.028 O-O (2NN) 0.062 O-M2-O 0.095 O-M1-BC 0.131 BC site BC-BC (glide) 0.013 BC-BO-BC 0.031 BC-M1-O 0.037 BO site BO-BC 0.011 Figure 9. The O-M2-O migration pathway and the associated barriers. O-M2 transition has actually the degeneracy of two, although the figure above only shows one of the transitions. Figure 10. The BC-BO-BC migration pathway and associated barriers for the SIA. BO-BC transition has a degeneracy of three, although the figure above only shows one of them. J. Phys.: Condens. Matter 26 ( 2014 ) 365402
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Y Fan et al 11 = - k k E k T exp[ / ] c c M B 0 2 , respectively. With the assumption that both migration paths have the same pre-exponential factor, i.e. = k k a c 0 0 , we then calculate the mean square displacement (MSD) of the vacancy, including the total MSD, <a> MSD (in- plane) and <c> (out-of-plane) MSD. The total MSD is defined as = + + MSD r t r t r t ( ) ( ) ( ) tot x y z 2 2 2 , where x - y plane rep- resents the basal plane and z represents the  <c>  direction. The MSD in <a> direction is therefore calculated as r t ( ) x 2 , and the MSD in <c> direction is calculated as r t ( ) z 2 . The unit of MSD is the square of the lattice parameter on the basal plane,  a 2 . Figure  11 ( a ) shows a typical MSD plot at 1000 K. It can be seen in figure  11 ( a ) that uni2248 + < > < > MSD MSD MSD 2 tot a c . Furthermore, the slope of  <a>  MSD is steeper than that of <c> MSD, which indicates an anisotropically favored dif- fusion kinetics on the basal plane compared to out-of-plane. The ratio between the c -axis and a -axis diffusivities, Dc/Da (which is equivalent to the ratio of the slope of the <c> MSD to the slope of the <a> MSD) as a function of temperature is shown in figure  11 ( b ). The Dc/Da being significantly less than unity indicates a significant anisotropy in the dif- fusion kinetics in the entire temperature range, with the higher temperatures leading to a less anisotropic behavior, as expected. This behavior is qualitatively consistent with Osetsky et al ’s previous work [ 41 ], which used a different EAM potential [ 55 ].
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  • Summer '19
  • Transition state, KMC

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