Molecular dynamics simulations are conducted to study self-interstitial migration in zirconium. By defining crystal lattice points where more than one atom is present in corresponding Wigner-Seitz cells, as the locations of self-interstitial atoms (LSIAs), three types of events are identified as LSIA migrations: the jump remaining in one 11 20 direction (ILJ), the jump from one 11 20 to another 11 20 direction in the same basal plane (OLJ), and the jump from one basal plane to an adjacent basal plane (OPJ). The occurrence frequencies of the three types are calculated. ILJ is found to be a dominant event in a temperature range from 300 K to 1200 K, but the occurrence frequencies of OLJ and OPJ increase with temperature increasing. The total occurrence frequency of all jump types has a good linear dependence on temperature. Moreover, the migration trajectories of LSIAs in the hcp basal-plane is not what is observed if only conventional one-or two-dimensional migrations exists; rather, they exhibit the feature that we call fraction-dimensional. Using Monte Carlo simulations, the potential kinetic effects of fraction-dimensional migration, which is measured by the average number of lattice sites visited per jump event (denoted by n SPE ), are analysed. The significant differences between the n SPE value of the fraction-dimensional migration and those of conventional one-and two-dimensional migrations suggest that the conventional diffusion coefficient cannot give an accurate description of the underlying kinetics of SIAs in Zr. This conclusion could be generally meaningful for the cases where the low-dimensional migration of defects are observed.

Tungsten, due to its desirable properties (high melting point, low sputtering coefficient, good irradiation resistance etc.), is considered as a promising candidate for the plasma facing materials in future nuclear fusion reactors. Therefore, it will work in extremely harsh environments because it is subjected to the bombadement of high-flux plasma particles and the irradiation of high energy neutrons, resulting in vacancies and interstitials. The migration behavior of self-interstitial atoms is one of the most important factors determining the microstructure evolution in irradiated metals because it will greatly affect the mechanical properties of materials. The study of the diffusion behavior of di-interstitials with different configurations contributes to a better understanding of the self-interstitial atom behavior in tungsten. Despite the inherent difficulty in experimental approaches, atomistic simulation provides an effective means of investigating the defect evolution in materials. In this paper, based on the newly developed interatomic potential for W-W interaction, the diffusion behavior of self-interstitial atoms in tungsten is studied by molecular dynamics simulation. This work focuses on the investigation of the diffusion behavior of di-interstitials with different configurations at different temperatures. The obtained results show that the di-interstitials with the first nearest neighbor configuration presents the one-dimensional migration in the <inline-formula><tex-math id="Z-20190530101816-19">\begin{document}$\left\langle 111 \right\rangle $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20190310_Z-20190530101816-19.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20190310_Z-20190530101816-19.png"/></alternatives></inline-formula> direction at temperatures below 1400 K. As the temperature increases, it makes rotations from one <inline-formula><tex-math id="Z-20190530101818-20">\begin{document}$ \left\langle 111 \right\rangle$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20190310_Z-20190530101818-20.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20190310_Z-20190530101818-20.png"/></alternatives></inline-formula>- to other <inline-formula><tex-math id="Z-20190530101823-21">\begin{document}$\left\langle 111 \right\rangle $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20190310_Z-20190530101823-21.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20190310_Z-20190530101823-21.png"/></alternatives></inline-formula>-directions. Thus migration of di-interstitial atoms with the first nearest neighbor configuration exhibits a change in mechanism from one-dimensional to three-dimensional migration, keeping the stable <inline-formula><tex-math id="Z-20190530101828-22">\begin{document}$\left\langle 111 \right\rangle $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20190310_Z-20190530101828-22.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20190310_Z-20190530101828-22.png"/></alternatives></inline-formula> configuration in the whole investigated temperature range. The migration of di-interstitial atoms with the second nearest neighbor configuration is one-dimensional along the <inline-formula><tex-math id="Z-20190530102029-23">\begin{document}$\left\langle 111 \right\rangle$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20190310_Z-20190530102029-23.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20190310_Z-20190530102029-23.png"/></alternatives></inline-formula> direction within a certain temperature range. When the temperature is above 600 K, the di-interstitial atoms will dissociate into two individual self-interstitial atoms and move independently. However, the migration of di-interstitial atoms with the third nearest neighbor configuration dissociates at a temperature just above 300 K. The non-parallel self-interstitial atoms form a sessile configuration within a certain temperature range. Once the sessile cluster is formed it can hardly move. Interestingly, it will transform into mobile defect when the temperature is higher than 1000 K. By comparing the migration energy values of these configurations obtained by nudged elastic band method with those of the Arrhenius fits, we find that the diffusivity for each of single- and di-interstitial atoms in tungsten is a linear function of temperature rather than Arrhenius as usually assumed.

Molecular dynamic simulations were conducted to study the self-interstitial migration in zirconium. By defining the crystal lattice point, at which more than one atom fall in the Wigner-Seitz cell of the lattice point, for the location of interstitial atoms (LSIA), three types of events were identified for LSIA migration: the jump remaining in one 1120 direction (ILJ), the jump from one 1120 to another 1120 direction in the same basal plane (OLJ) and the jump from one basal plane to an adjacent basal plane (OPJ). The occurrence frequencies of the three types were calculated. ILJ was found to be the dominant event in the temperature range (300K to 1200K), but the occurrence frequencies of OLJ and OPJ increased with increasing temperature. Although the three types of jumps may not follow Brownian and Arrhenius behavior, on the whole, the migration of the LSIAs tend to be Brownian-like. Moreover, the migration trajectories of LSAs in the hcp basal-plane are not what are observed if only conventional one-or two-dimensional migrations exist; rather, they exhibit the feature we call fraction-dimensional. Namely, the trajectories are composed of line segments in 1120 directions with the average length of the line segments varying with the temperature. Using Monte Carlo simulations, the potential kinetic impacts of the fraction-dimensional migration, which is measured by the average number of lattice sites visited per jump event (denoted by nSP E ), was analyzed. The significant differences between the nSP E value of the fraction-dimensional migration and those of the conventional one-and two-dimensional migrations suggest that the conventional diffusion coefficient, which cannot reflect the feature of fraction-dimensional migration, cannot give an accurate description of the underlying kinetics of SIAs in Zr. This conclusion may not be limited to the SIA migration in Zr and could be more generally meaningful for situations in which the low dimensional migration of defects has been observed.