Temperature-dependent diffusion coefficients fromab initiocomputations: Hydrogen, deuterium, and tritium in nickel

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Abstract

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., $D={D}_{0}\phantom{\rule{0.2em}{0ex}}\mathrm{exp}[\ensuremath{-}Q∕(RT)]$, with $Q=45.72$, 44.09, and $43.04\phantom{\rule{0.3em}{0ex}}\mathrm{kJ}∕\mathrm{mol}$ and ${D}_{0}=3.84\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$, $2.40\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$, $1.77\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}\phantom{\rule{0.3em}{0ex}}{\mathrm{m}}^{2}\phantom{\rule{0.2em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$ 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 $400\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. 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.

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