(22d) Theoretical Predictions of Hydrogen Permeability in Pd-Based Membranes

The present work deals with the study of palladium-silver (PdAg) and palladium-gold (PdAu) binary alloys over a broad range of temperatures and alloy compositions using density functional theory (DFT) to find out possible conditions where the solubility, diffusivity, and permeability of hydrogen (H) is significantly higher than that of pure palladium (Pd). Several alloy structures, such as Pd(100-x)Ag(x) with x=14.81, 25.93, 37.04 and 48.51, Pd(100-x)Au(x) with x=14.81, 25.93, 37.04, and Pd(100-x)Cu(x) with x=25.93 and 48.51 have been considered. The lattice constants of these structures were optimized using DFT, and relaxed structures were used for the estimation of binding energy. It was found that the solubility of H in PdAg is higher than pure Pd with a maximum at approximately 30%Ag at 456K. Also, the solubility of PdAu alloys was higher than the pure Pd with a maximum at about 20%Au with solubility 12 times higher than that of pure Pd. It was found that for a 3.7% H concentration in a PdAg alloy, a cell expansion of 0.15-0.2% occurs, which if ignored may affect the individual binding energy of the O-site by approximately 3.56% and affect the predicted solubility by approximately 11.8%.

Kinetic Monte Carlo simulations (KMC) were carried out using predicted rate constants for hydrogen hopping throughout simulated Pd-based alloy lattices. DFT has been employed to obtain octahedral (O-), tetrahedral (T-) and transition state (TS-) site energetics as a function of local alloy composition for several PdAg and PdAu alloys with compositions in supercells of X=14.18, 25.93, 37.07 and 48.15% with the nearest (NN) and next-nearest neighbors (NNN) varied over the entire range of compositions. The estimates were then used to obtain a model relating O-, T-, and TS-energy of a given site with NN(X), NNN(X), and the lattice constant. The first passage approach combined with KMC simulations was used for the H diffusion coefficient predictions. It was found that the diffusion coefficient of H in PdAg alloy decreases with increasing Ag and increases with increasing temperature, matching closely with the experimental results reported in the literature. The calculated permeabilities of H in these novel binary alloys obtained from both diffusivity and solubility predictions were found to have a maximum at ~20% Ag and ~12% Au, which agree well to experimental predictions. Specifically, the permeability of H in PdAg alloy with ~20% Ag at 456K is 3-4 times that of pure Pd, while the PdAu alloy at 12% Au is 4-5 times that of pure Pd at 456 K.