First-principles calculations of solute transport in zirconium: Vacancy-mediated diffusion with metastable states and interstitial diffusion
Zirconium alloys are the most widely used nuclear fuel cladding materials for light water power reactors where irradiation damage causes solute redistribution, leading to degradation of alloy properties such as corrosion resistance. Designing radiation-tolerant zirconium alloys requires a thorough understanding of the atomic-scale transport behavior of the alloying elements in Zr. In this work, we perform density function theory calculations to investigate the diffusion of Sn, Cr, Fe, Be, Al, and Ni in the hexagonal close-packed (HCP) Zr matrix. We develop a methodology to accurately model the metastable vacancy states along the basal migration path, known to occur in group IV metals. We compute the vacancy-mediated solute diffusion coefficients and drag ratios using the kinetic Monte Carlo method and an analytic Green's function method—the agreement between the two validates our methodology. The computed diffusion coefficients of Sn and Al show good agreement with the experimental data and we expect these solutes to diffuse via the vacancy-mediated mechanism. We use a Green's function approach, parameterized with data from density functional theory calculations, to compute the interstitial diffusion coefficients of Cr, Fe, Be, and Ni in the HCP Zr lattice. The computed diffusion coefficients of Cr, Ni, and Be agree with the experimental measurements within one order of magnitude, while those of Fe are within two orders of magnitude of the experimental measurements. The drag ratios for Cr, Fe, Be, and Ni are positive up to 1235 K, which suggests that nonequilibrium vacancy fluxes could drag these solutes toward sinks such as dislocation loops and grain boundaries. We also compute the transport coefficients without including the metastable states, and using the eight- and thirteen-frequency model. Our results show significant differences in drag ratio for the eight- and thirteen-frequency model predictions compared with the Green's function methodology, but smaller errors in the solute diffusivity. Combining interstitial and vacancy-mediated diffusivities, we predict the unusual result that increased vacancy concentration slows down solute diffusivity, while a sufficiently high vacancy concentration can change the dominant mechanism to an accelerated vacancy-mediated diffusion.