Understanding Deviations in Hydrogen Solubility Predictions in Transition Metals through First-Principles Calculations

Hydrogen solubility in ten transition metals (V, Nb, Ta, W, Ni, Pd, Pt, Cu, Ag, and Au) has been predicted by first-principles based on density functional theory (DFT) combined with chemical potential equilibrium between hydrogen in the gas and solid-solution phases. Binding energies and vibrational frequencies of dissolved hydrogen in metals are obtained from DFT calculations, and the sensitivity of solubility predictions with respect to the DFT-calculated variables has been analyzed. In general, the solubility increases with increasing binding strength and decreasing vibrational frequencies of hydrogen. The solubility predictions match experimental data within a factor of 2 in the cases of V, Nb, Ta, and W and within a factor of 3 in the cases of Ni, Cu, and Ag. In Pd, the deviation in solubility predictions is mainly attributed to the errors involved in the calculated vibrational frequencies of dissolved hydrogen. In Pt and Au, hydrogen in the octahedral interstitial site is less stable than in the tetrahedral site, contradicting the predictions based on the hard-sphere model. Potential energy surface analysis reveals a slightly downward concavity near the center of the octahedral sites in Pt and Au, which may explain the calculated imaginary vibrational frequencies in these sites and lead to unreliable solubility predictions.