Nanoscale hydride formation at dislocations in palladium: Ab initio theory and inelastic neutron scattering measurements

Hydrogen arranges at dislocations in palladium to form nanoscale hydrides, changing the vibrational spectra. An ab initio hydrogen potential energy model versus Pd neighbor distances allows us to predict the vibrational excitations for H from absolute zero up to room temperature adjacent to a partial dislocation and with strain. Using the equilibrium distribution of hydrogen with temperature, we predict excitation spectra to explain new incoherent inelastic neutron-scattering measurements. At 0 K, dislocation cores trap H to form nanometer-sized hydrides, while increased temperature dissolves the hydrides and disperses H throughout bulk Pd.

Figure 1

Integrated occupancy of hydrogen around dislocations in Pd with temperature for $\Delta E=23\hspace{0.5em}\mathrm{meV}$ (solid) and $\Delta E=0$ (dashed). The integrated occupied density of sites goes from the most favored sites (dislocation cores) through the range of volumetric strain around the dislocation core; all hydrogen solutes are accounted for at the saturation concentration of $x_{\mathrm{H}}=1.3\times {10}^{-3}$. The occupancy follows a Fermi function for $\Delta E=0$, and the effect of H-H coupling is to maintain the nanoscale hydride to slightly higher temperatures. At 0 K, the Cottrell atmosphere has a sharp boundary at $r=4b=7.9\hspace{0.5em}\AA$. At 100 K, the atmosphere shows only small spreading away from the core, while at 200 K there is an increasing occupancy for H at 0 strain. At 300 K, the atmosphere is dissolving, with decreased occupancy in the core as well as around the dislocation.

Figure 2

Calculated vibrational density of states for hydrogen in Pd with temperature. Increasing temperature produces larger displacements of Pd beyond the zero-point motion at 0 K; this increases the spread in the vibrational excitations. The central peaks for the three sites are temperature independent. Peak broadening smears the low and high excitations in the dislocation core at room temperature.

Figure 3

The predicted vibrational density of states and inelastic neutron scattering intensity for 0.13 at. % H in Pd as a function of temperature. The temperature determines both the occupancy of states for H (see Fig. 1) and the vibrational spectra for all states (see Fig. 2); taken together, we predict the density of states in the top figure. To compare with IINS measurements, we scale intensity by $1/\sqrt{h\nu }$, equalize amplitudes, and scale energy by 7/8 (DFT/experimental discrepancy). The agreement in line shape at 300 K confirms that the main cause of peak broadening is Pd vibration. At lower temperatures, the formation of a Cottrell atmosphere creates nanoscale regions with high hydrogen concentration. The scattering signal from $\beta$-PdH has a width similar to the experimentally measured spectrum at 0 K (Ref. 18); the difference from the ab initio prediction is due to the dispersion of a hydride which is missing in our calculation of isolated hydrogen vibrations. The computed PdH${}_{0.63}$ spectra (dashed lines) has dispersion but is a harmonic approximation for hydrogen. The signal change can estimate the fraction of nanoscale hydrides at dislocation cores.