Praseodymium polyhydrides synthesized at high temperatures and pressures

Rare earth element polyhydrides have been predicted to exhibit high-$T_c$ superconductivity at extreme compressions. Through a series of in situ high-pressure high-temperature x-ray powder diffraction experiments combined with density functional theory calculations, we report the emergence of polyhydride species in the praseodymium-hydrogen system. We initially observe the formation of ${\mathrm{PrH}}_3$, which continuously increases in hydrogen content on compression towards ${\mathrm{PrH}}_4$. Laser heating ${\mathrm{PrH}}_4$ in a hydrogen medium at pressures of 85 GPa leads to the synthesis of both ${\mathrm{PrH}}_9$ and ${\mathrm{PrH}}_7$. Both structures are characterized by hexagonal arrays of praseodymium atoms surrounded by hydrogen clathrate cages.

Figure 1

(a) Representative Le Bail refinement of high-pressure x-ray diffraction data of ${\mathrm{PrH}}_7/{\mathrm{PrH}}_9$ mixture at 91.4 GPa. Tick marks indicate the calculated peak positions, the difference between observed and calculated profiles is shown below, $w{R}_p=0.82\%$. Inset shows an image of the sample chamber at 20 GPa. Culet size is $50\mu \mathrm{m}$; (b) High-pressure x-ray diffraction patterns ($\lambda =0.4115\AA$) taken on compression showing the continuous transition from cubic ($Fm\overline{3}m$) ${\mathrm{PrH}}_3$ to tetragonal ($I4/mmm$) ${\mathrm{PrH}}_4$. Subsequent laser heating above 90 GPa leads to the synthesis of new praseodymium hydrides ${\mathrm{PrH}}_9$ ($P{6}_3/mmc$) and ${\mathrm{PrH}}_7$ ($P{6}_3/mmc$) as a minor phase; (c) X-ray diffraction patterns before and after laser heating; (d) Diffraction patterns taken on decompression showing the transition of ${\mathrm{PrH}}_9$ from a hexagonal to a complex unknown structure below 82.5 GPa followed by its decomposition to ${\mathrm{PrH}}_4$ below 59 GPa. ${\mathrm{PrH}}_7$ remains stable down to 54 GPa. Both polyhydrides eventually decompose to ${\mathrm{PrH}}_4$ with further decompression.

Figure 2

(a) Volume per Pr atom for praseodymium hydrides. Empty circles correspond to the cubic phase of ${\mathrm{PrH}}_3$. Filled blue circles correspond to high-pressure tetragonal ${\mathrm{PrH}}_{4+x}$ polymorph ($I4/mmm$). Solid line indicates volume derived from the atomic volumes of the elements [27, 28, 29], while dashed lines refer to volumes derived from our DFT calculations. (b) Unit cell parameters for ${\mathrm{PrH}}_7$ (green) and ${\mathrm{PrH}}_9$ (red). Dashed lines correspond to the DFT predicted values. (c) Crystal structures of Pr polyhydrides, ${\mathrm{PrH}}_7$ ($P{6}_3/mmc$) and ${\mathrm{PrH}}_9$ ($P{6}_3/mmc$); Pr atoms are yellow, H are white.

Figure 3

(a) Convex hull construction for ${\mathrm{PrH}}_n$ phases relative to PrH and 1/2 ${\mathrm{H}}_2$, at a sequence of pressures. Empty (filled) symbols denote metastable (stable) phases, the latter form the convex hull at each pressure. The stoichiometries considered are indicated. (b) Stability ranges of Pr-hydrides from spin-orbit coupling DFT calculations. Compositions and space groups/prototypes are indicated. Thin lines denote pressure ranges where the phases are metastable, defined as up to 10 meV/atom above the convex hull.

Figure 4

Electronic densities of state (DOS) for ${\mathrm{PrH}}_4, {\mathrm{PrH}}_7, {\mathrm{PrH}}_9$ ($F\overline{4}3m$), and ${\mathrm{PrH}}_9$ ($P{6}_3/mmc$) from spin-orbit coupling calculations, all at 80 GPa.