Studying the correlations and solubility of hydrogen in niobium using Density Functional Theory calculations

In this work, we present a Density Functional Theory (DFT) study of hydrogen correlations and solubility in niobium. Finding the preferred interstitial site for single hydrogen atoms, calculating the pair-wise hydrogen correlations, and the treatment of many hydrogen atoms in a niobium cell are parts of this work. By studying how the pair-wise hydrogen-hydrogen interaction energy varies as a function of their distance, we develop the theoretical counterpart of the empirical Westlake criterion, a rule that states that hydrogen atoms cannot simultaneously occupy pairs of interstitial sites closer than 0.21 nm. Based on this inference, we provide a systematic way of populating many (>3) hydrogens in the niobium lattice. Using the differential binding energies and vibrational frequencies of dissolved hydrogens at varying hydrogen concentrations, we estimate the solubility of hydrogen in niobium. Apart from the conventional way of calculating the entropy of interstitial hydrogens under the harmonic oscillator approximation, this work includes a new approximation that treats the hydrogens as a monatomic ideal gas. The solubility predictions are in good agreement with experimental data.