Neutron spectroscopy of H impurities in PdD: Covibrations of the H and D atoms

Three powder samples of solid isotopic solutions ${\text{PdD}}_{1-x}{\text{H}}_x$ with $x=0.050$, 0.072, and 0.091 are prepared under high pressure, and the spectra of their optical vibrations are studied by inelastic neutron scattering at ambient pressure and 5 K using the high-luminosity IN1-BeF spectrometer at ILL, Grenoble. These spectra are shown to be well represented by a linear combination of a contribution from the undisturbed matrix of stoichiometric PdD and a contribution due to the H impurity. The optical spectrum of PdD consists of a strong peak at 37 meV with a shoulder extending to 65 meV. The spectrum due to the H impurity is composed of a broad peak of defect H modes centered at 68 meV and superimposed on a broad N-shaped feature with a range of negative intensity near 36 meV and a shallow maximum at 45 meV. Simulations using the Born-von Kármán model show that this unusual feature is a result of the formation of a band of optical vibrations of the D and H atoms with equal frequencies (covibrations) caused by H-D interactions.

Figure 1

(Color online) The dynamical structure factor $S\left(Q,E\right)$ of three powder ${\text{PdD}}_{1-x}{\text{H}}_x$ samples as a function of the energy loss $E$ of the inelastically scattered neutrons. $Q$ is the neutron momentum transfer and its dependence on $E$ is a characteristic of the spectrometer used. The horizontal bars at the bottom of the figure show the energy resolution. The spurious intensity at energies below 30 meV results from one- and two-phonon scattering of admixed neutrons of half the wavelength in the incoming monochromated beam.

Figure 2

(Color online) Two INS spectra $S_{\text{PdD}}$ for the defect-free PdD (top) and two spectra $S_{\text{H}}$ due to the H impurity in PdD (bottom) extracted from two different pairs of experimental ${\text{PdD}}_{1-x}{\text{H}}_x$ spectra.

Figure 3

(Color online) The $S_{\text{PdD}}$ spectrum for PdD extracted from a pair of experimental $S\left(Q,E\right)$ spectra of the ${\text{PdD}}_{1-x}{\text{H}}_x$ samples with $x=0.050$ and 0.091 (open circles connected with a thick line) and the experimental $S\left(Q,E\right)$ spectrum of PdH (Ref. 11) compressed by a factor of 1.51 along the energy scale (thin solid line without circles). The scaling factor 1.51 was chosen to reproduce the energy position of 37 meV of the maximum of the main optical peak in the spectrum of PdD. The INS spectrum of PdH was measured in Ref. 11 at 25 K using the TFXA spectrometer at ISIS, U.K., and had a better energy resolution of $\Delta E/E\approx 1.5\%$ and a lower statistical accuracy than the $S_{\text{PdD}}$ spectrum.

Figure 4

(Color online) The open circles connected with a dashed line represent the dynamical structure factor $S\left(Q,E\right)$ of (a) PdD and (b) PdH (Ref. 11). The spectrum of PdD is a combination of the optical part $\left(E>30\text{meV}\right)$ determined from the INS measurements of this work and the acoustic part $\left(E<30\text{meV}\right)$ produced by rescaling the experimental spectrum of PdH (see text). The vertical bars indicate the peak positions in the first and second optical bands. The solid curves in (a) and (b) show multiphonon contributions calculated in a harmonic isotropic approximation.

Figure 5

(Color online) The PDOS $g\left(E\right)$ of PdD calculated using 32,000 sampling points in the irreducible part of the BZ (solid curve) and the one-phonon spectrum $S_{1\text{ph}}\left(Q,E\right)$ produced by subtracting the multiphonon spectrum from the $S\left(Q,E\right)$ spectrum of PdD in Fig. 4a (dashed curve).

Figure 6

(Color online) Contributions $S_{\text{H}}\left(Q,E\right)$ to the total dynamical structure factor of the solid ${\text{PdD}}_{1-x}{\text{H}}_x$ solutions due to the presence of H impurity. The dashed curves represent the experimental $S_{\text{H}}$ from Fig. 2. The solid curves are results of the model calculations.

Figure 7

(Color online) The dashed curve shows the $S_{\text{H}}\left(Q,E\right)$ spectrum calculated for the ${\text{Pd}}_{16}{\text{D}}_{15}\text{H}$ crystal $\left(x=0.0625\right)$. The solid curves represent the contributions to this spectrum from neutron scattering on the H atoms (a) and due to changes in the vibrational spectrum of the D atoms (b).

Figure 8

(Color online) The solid line shows the $S_{\text{H}}$ spectrum calculated by applying Eq. (1) to a pair of experimental $S\left(Q,E\right)$ spectra of the ${\text{PdD}}_{1-x}{\text{H}}_x$ samples with $x=0.050$ and 0.091. The circles connected with a dashed line show the one-phonon spectra $S_{1\text{ph}}\left(Q,E\right)$ of (a) PdD and (b) PdH produced by subtracting the multiphonon contributions from the corresponding $S\left(Q,E\right)$ spectra in Fig. 4.