First-principles study of diffusion and interactions of hydrogen with silicon, phosphorus, and sulfur impurities in nickel

Abstract

Using density functional theory (DFT), we systematically study the effect of Si, P, and S impurities on the diffusion and binding of an H atom in a face-centered-cubic (FCC) Ni lattice. First, we quantify binding energies of an H atom to a vacancy, an impurity atom, and a vacancyimpurity atom defect pair. The energetics of H interactions show that a vacancy-impurity atom defect pair with larger binding energy traps the H atom more strongly and correlates with electronic bonding. Next, we study how the impurities influence diffusion of an H atom by using the Climbing Image Nudged Elastic band method to evaluate the Minimum Energy Path and the energy barrier for diffusion. The H atom preferentially diffuses between tetrahedral to octahedral (T-O) interstitial positions in pure Ni and when impurities are present. However, the activation energy significantly decreases from 0.95 eV in pure Ni to 0.47 eV, 0.52 eV, and 0.46 eV, respectively, in the presence of Si, P, and S impurities, which speeds up H diffusion. We rationalize this by comparing the bonding character of the saddle point configuration and changes in the electronic structure of Ni for each system. Notably, these analyses correlate the lower values of the activation energies to a local atomic strain in a Ni lattice. Our DFT study also validates the hypothesis of Berkowitz and Kane that P increases the H diffusion and, thereby, significantly increases H embrittlement susceptibility of Ni. We report a similar effect for Si and S impurities in Ni.

Correlation between bonding, vacancy migration mechanisms, and creep in model binary and ternary hcp-Mg solid solutions

“…Subscript "S" denotes a substitutional site. We use literature convention of positive binding energy 31,32 where larger E B corresponds to stronger solute-vacancy binding.…”

“…Finally, we have analyzed these computed energy values in terms of charge density distributions using an iso-surface level of 0.015 e/Å 3 to visualize bonding between the atoms. In the density of states calculations, we have evaluated and compared occupancy number 32,37 of Mg atom in terms of s, p, and d orbitals. The electron occupation numbers are obtained by integrating partial density of states (PDOS) of the Mg atom up to Fermi energy.…”

“…This localization of charge density points to an increased local directional bonding or bonds with greater degree of covalent character. 32,43 Similarly, the bond length between an alloying atom and Mg-1 atom marginally decreases in the presence of a Zn atom when compared to corresponding bond lengths in binary systems. For example, in the presence of Zn atom, the Mg (−1)-Ca bond length reduces from 3.29 Å to 3.26 Å.…”

“…Such elevated Δρ indicates stronger and stiffer bonds between Zn and solutes (Ca, Y, and Gd). 32,43 This enhancement in bond strength is reflected in shorter bond lengths. For example, in Fig.…”

“…5) using the NEB method in 96 atom supercells of binary Mg-X (Ca, Y, and Gd) and ternary Mg-X-Zn systems. Activation energy of diffusion, which is the sum of vacancy formation energy and migration energy barrier, 32 is shown in Table IV. We find that the activation energies are roughly inversely proportional to the binding energies of X and X-Zn (see Fig.…”