First-principles study of the solubility, diffusion, and clustering of C in Ni

Abstract

Within the framework of density functional theory, we investigate three key properties of a C interstitial solid solution in crystalline Ni: the heat of solution $(\ensuremath{\Delta}{H}_{\mathrm{sol}}),$ the activation energy for C diffusion ${(E}_{a}),$ and the C-C pair binding energy $(B).$ In addition, we assess the impact of Ni magnetism upon each property. The most energetically favorable lattice site for C is the interstitial octahedral site $(O$ site), which is 1.59 eV lower in energy than the tetrahedral site $(T$ site). Using the nudged elastic band method, we determine that diffusion between O sites proceeds via a T-site intermediate. The calculated activation energy ${(E}_{a}=1.62\mathrm{eV}),$ is in good agreement with experimental data from the literature (1.54--1.71 eV). The binding of C pairs is sensitive to magnetization effects, and is negligible $(B\ensuremath{\approx}0\mathrm{eV})$ in the ferromagnetic state, but repulsive in the paramagnetic state $(B=\ensuremath{-}0.2\mathrm{eV}).$ These results are consistent with anelastic relaxation experiments, which find $Bl0.1\mathrm{eV}$ in the FM state. The calculated heat of solution in the paramagnetic Ni state $(\ensuremath{\Delta}{H}_{\mathrm{sol}}^{\mathrm{para}}=0.2--0.35\mathrm{eV})$ is in reasonable agreement with high-temperature experimental values of $\ensuremath{\sim}0.4\mathrm{eV},$ and the magnitude of $\ensuremath{\Delta}{H}_{\mathrm{sol}}$ in the ferromagnetic state is found to be about 0.4 eV greater than in the paramagnetic state. Lastly, we briefly assess the effect of pseudopotential choice and exchange-correlation functionals upon the accuracy of the results.