Proton mobility in metallic copper hydride from high-pressure nuclear magnetic resonance

The atomic and electronic structures of ${\mathrm{Cu}}_2\mathrm{H}$ and CuH have been investigated by high-pressure nuclear magnetic resonance spectroscopy up to 96 GPa, X-ray diffraction up to 160 GPa, and density functional theory-based calculations. Metallic ${\mathrm{Cu}}_2\mathrm{H}$ was synthesized at a pressure of 40 GPa, and semimetallic CuH at 90 GPa, found stable up to 160 GPa. For ${\mathrm{Cu}}_2\mathrm{H}$, experiments and computations show an anomalous increase in the electronic density of state at the Fermi level for the hydrogen $1s$ states and the formation of a hydrogen network in the pressure range 43–58 GPa, together with high ${}^1\mathrm{H}$ mobility of $\sim {10}^{-7}\mathrm{c}{\mathrm{m}}^2/\mathrm{s}$. A comparison of these observations with results on FeH suggests that they could be common features in metal hydrides.

Figure 1

(a) Examples of powder X-ray diffraction patterns of ${\mathrm{Cu}}_2\mathrm{H}$ and CuH synthesized at different pressures; yellow lines are Rietveld fits to the experimental data (blue dots); red lines denote the residuals. Indexed peaks are for the $P\overline{3}m1{\mathrm{Cu}}_2\mathrm{H}$ and $Fm\overline{3}m\mathrm{Cu}{\mathrm{H}}_x$ structures. (b) Equations-of-state of the copper hydride phases and pure Cu: the equations-of-state for pure copper [41] and $\mathrm{Cu}{\mathrm{H}}_{0.65}$ [11] are shown in purple and green, respectively. The pink dashed line denotes the equation-of-state for $P\overline{3}m1{\mathrm{Cu}}_2\mathrm{H}$ [10]. The results of a third-order Birch-Murnaghan fit to the DFT ground-state energies are shown by a blue curve for ${\mathrm{Cu}}_2\mathrm{H}$ and in red for CuH. The equation-of-state parameters can be found in Table S1 in the Supplemental Material [27]. Open orange squares ($\mathrm{Cu}{\mathrm{H}}_x$) and blue triangles (${\mathrm{Cu}}_2\mathrm{H}$) represent diffraction data, and the arrows illustrate the experimental pathways of heating (red) and compression (black).

Figure 2

Representative ${}^1\mathrm{H}-\mathrm{NMR}$ spectra of copper hydrides, CuH, ${\mathrm{Cu}}_2\mathrm{H}$, and $\mathrm{Cu}{\mathrm{H}}_{0.15}$, formed after laser heating of copper-paraffin loaded cells at 89 and 50 GPa, and on decompression at 13 GPa.

Figure 3

Comparison of experimental NMR data and DFT-based electronic structure calculations. (a) Double logarithmic power plot of relative changes in the NMR Knight shift $K_{\mathrm{H}}\left(V\right)$ and the electron density-of-states at the Fermi energy $N\left(E_{\mathrm{F}}\right)$ as a function of compression. Experimental data (blue, magenta, orange, and green) are normalized to $K_{\mathrm{H}}\left(V_0\right)$ using $V_0$ from the respective equation-of-state from Tkacz et al. [42] ($\mathrm{Cu}{\mathrm{H}}_{0.15}$) and DFT computations from this study (CuH and ${\mathrm{Cu}}_2\mathrm{H}$) (Table S1 in the Supplemental Material [27]). The blue, magenta, and orange dashed lines (splines through computed values) show the respective volume dependence of $N\left(E_{\mathrm{F}}\right)$. Diagonal color stripes are guides to the eye, representing $\mathrm{a}\propto V^{2/3}$ scaling for free-electron Fermi-gas-like behavior [18]. Black arrows denote respective pressure points. Data and results for FeH were taken from our previous work [18]. (b) Relative FWHM linewidths of ${}^1\mathrm{H}-\mathrm{NMR}$ spectra as a function of the H-H distance $r_{\mathrm{HH}}$ for CuH, ${\mathrm{Cu}}_2\mathrm{H}$, and FeH. The dotted blue line depicts the theoretical linewidth dependence for pure dipolar broadening and vertical red dashed lines show the $r_{\mathrm{HH}}$ corresponding to the pressure intervals marked by the arrows in (a).

Figure 4

Comparison of electronic structure and proton diffusivities. (a) Hydrogen 1-$s$ electron density-of-state contribution $N_{\mathrm{H}-1s}\left(E_{\mathrm{F}}\right)$ for CuH, ${\mathrm{Cu}}_2\mathrm{H}$, and FeH as a function of the H-H distance in the structures (pressure increasing to the right). (b) Proton diffusion coefficients extracted from NMR data (blue, purple, and orange circles) and computed via DFT-based molecular dynamics simulations (blue and magenta squares and lines) for metallic ${\mathrm{Cu}}_2\mathrm{H}$ and FeH, and the semimetal CuH. The values fall into two groups: (i) high $N_{\mathrm{H}-1s}\left(E_{\mathrm{F}}\right)$ values and high diffusivity for the metallic compounds and (ii) small $N_{\mathrm{H}-1s}\left(E_{\mathrm{F}}\right)$ values accompanied by a smaller diffusion coefficient in CuH.