Temperature-Dependent Diffusion Coefficients From Ab Initio Computations: Hydrogen, Deuterium, and Tritium in Nickel
Erich Wimmer, Walter Wolf, Jürgen Sticht, Paul Saxe, Reza Najafabadi, George A Young
Physical Review B Condensed Matter 77, 134305 (2008)
The temperature-dependent diffusion coefﬁcients of interstitial hydrogen, deuterium, and tritium in nickel are computed using transition state theory. The coefﬁcient of thermal expansion, the enthalpy and entropy of activation, and the pre-exponential factor of the diffusion coefﬁcient are obtained from ab initio total energy and phonon calculations including the vibrations of all atoms. Numerical results reveal that diffusion between octahedral interstitial sites occurs along an indirect path via the metastable tetrahedral site and that both the migration enthalpy and entropy are strongly temperature dependent. However, the migration enthalpy and entropy are coupled so that the diffusion coefﬁcient is well described by a constant activation energy, i.e., D = D₀ exp(−Q/(RT)), with Q = 45.72, 44.09, and 43.04 kJ/mol and D₀ = 3.84×10⁻⁶, 2.40×10⁻⁶, 1.77×10⁻⁶ m² s⁻¹ for H, D, and T, respectively. The diffusion of deuterium and tritium is computed to be slower than that of hydrogen only at temperatures above 400 K. At lower temperatures, the order is reversed in excellent agreement with experiment. The present approach is applicable to atoms of any mass as it includes the full coupling between the vibrational modes of the diffusing atom with the host lattice.