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

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 (ΔHₛₒₗ), the activation energy for C diffusion (Eₐ), 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 (Eₐ=1.62eV), 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≈0eV) in the ferromagnetic state, but repulsive in the paramagnetic state (B=-0.2eV). These results are consistent with anelastic relaxation experiments, which find B<0.1eV in the FM state. The calculated heat of solution in the paramagnetic Ni state (ΔHₛₒₗᵖᵃʳᵃ=0.2--0.35eV) is in reasonable agreement with high-temperature experimental values of ~0.4eV, and the magnitude of ΔHₛₒₗ 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.