Vibrational states of atomic hydrogen in bulk and nanocrystalline palladium studied by neutron spectroscopy

The vibrational states of hydrogen atoms in bulk and nanocrystalline palladium were examined in a wide energy region $0\le \hslash \omega \le 300$ meV using neutron spectroscopy. In bulk ${\mathrm{PdH}}_{0.73}$, the vibrational excitations of H atoms were roughly reproduced by the quantum harmonic oscillator (QHO) model. In ${\mathrm{PdH}}_{0.42}$ nanocrystals with a diameter of 8 nm, however, additional vibrational excitations were found at energies above 80 meV. The energies and intensities of the additional states were not explained by the QHO but reasonably described as vibrations in a highly anharmonic trumpetlike potential. The additional excitations are attributed to the vibrations of H atoms at tetrahedral sites in the subsurface region stabilized by surface effects. Thus, this is an experimental work which clearly detects hydrogen vibration inside metal nanoparticles.

Figure 1

Locations of interstitial hydrogen atoms in an fcc Pd lattice; octahedral ($O$) and tetrahedral ($T$) sites.

Figure 2

Dynamical structure factors as functions of energy $\hslash \omega$ and momentum transfer $Q$ for bulk and nano-${\mathrm{PdH}}_x$ recorded at 10 K. The scattering contribution from nano-Pd has been subtracted from nano-${\mathrm{PdH}}_{0.42}$. The data were obtained with $E_{\mathrm{i}}=331$ meV.

Figure 3

Inelastic neutron scattering spectra of nano-${\mathrm{PdH}}_{0.42}$ and nano-Pd, recorded with $E_{\mathrm{i}}\text{"}\mathrm{s}$ of (a) 168 and (b) 331 meV at 10 K. The differences between the two spectra, (nano-${\mathrm{PdH}}_{0.42}$) $-$ (nano-Pd), are also shown.

Figure 4

Inelastic neutron scattering spectra of bulk ${\mathrm{PdH}}_{0.73}$ and nano-${\mathrm{PdH}}_{0.42}$ recorded with $E_{\mathrm{i}}\text{"}\mathrm{s}$ of (a) 168 and (b) 331 meV. The data of nano-${\mathrm{PdH}}_{0.42}$, from which the scattering contribution from nano-Pd is subtracted, are multiplied by 7.3 for a comparison purpose.

Figure 5

Inelastic neutron scattering spectrum of bulk ${\mathrm{PdH}}_{0.73}$ with $E_{\mathrm{i}}=168$ meV at 10 K. Solid curve represents the result of the fit with multiple Gaussians. The dashed curves correspond to each Gaussian function.

Figure 6

(a) Inelastic neutron scattering spectrum for bulk ${\mathrm{PdH}}_{0.73}$ at 10 K. The cyan, green, magenta, red, and orange dashed curves correspond to the $n$ = 1, 2, 3, 4, 5 excitation modes, respectively. (b) Intensity and (c) excitation energy against quantum number $n$.

Figure 7

(a) Inelastic neutron scattering spectrum for nano-${\mathrm{PdH}}_{0.42}$ at 10 K. The scattering contribution from nano-Pd is subtracted. (b) Intensity and (c) excitation energy against a quantum number $n^{\prime }$.

Figure 8

Potential energy as a function of the atomic displacements relative to the equilibrium position of the H atom. The curve is calculated using Eq. (5). The parameters ${\omega }_0$ and $c_{2i}$ used in the calculation are summarized in Table. 1. Horizontal lines represent the eigenvalues $E_{n^{\prime }}$.