Hydrogen-rich hydrides attract great attention due to recent theoretical ( 1 ) and then experimental discovery of record high-temperature superconductivity in H 3 S [T c = 203 K at 155 GPa ( 2 )]. Here we search for stable uranium hydrides at pressures up to 500 GPa using ab initio evolutionary crystal structure prediction. Chemistry of the U-H system turned out to be extremely rich, with 14 new compounds, including hydrogen-rich UH 5 , UH 6 , U 2 H 13 , UH 7 , UH 8 , U 2 H 17 , and UH 9 . Their crystal structures are based on either common face-centered cubic or hexagonal close-packed uranium sublattice and unusual H 8 cubic clusters. Our high-pressure experiments at 1 to 103 GPa confirm the predicted UH 7 , UH 8 , and three different phases of UH 5 , raising confidence about predictions of the other phases. Many of the newly predicted phases are expected to be high-temperature superconductors. The highest-T c superconductor is UH 7 , predicted to be thermodynamically stable at pressures above 22 GPa (with T c = 44 to 54 K), and this phase remains dynamically stable upon decompression to zero pressure (where it has T c = 57 to 66 K).

Uranium hydride is a highly toxic compound that spontaneously ignites in the air ( 3 ) and reacts with water ( 4 ). It is used mainly for separation of hydrogen isotopes ( 5 ), but it can also be a component of explosives. It was first synthesized by F. Driggs during heating of metallic uranium in hydrogen atmosphere, and it was initially the assigned the composition UH 4 . Later, the composition was determined as UH 3 ( 6 ): this phase is known as β-UH 3 . When bulk uranium was heated in hydrogen atmosphere at lower temperature ( 7 ), a metastable α-UH 3 phase appeared, and transformation to β-UH 3 occurred above 523 K. The crystal structure of α-UH 3 is of Cr 3 Si-type (also known as A15 or β-W); U atoms have icosahedral coordination and form a body-centered cubic sublattice. Many superconductors belong to the Cr 3 Si structure type (for example, Nb 3 Sn). The structure of β-UH 3 is more complex and based on a β-W–like uranium sublattice containing hydrogen atoms in distorted tetrahedral voids ( 8 , 9 ). UH 3 is the only known uranium hydride found to be stable at ambient conditions [although there is evidence of isolated molecules of UH, UH 2 , UH 4 , UH 3 , U 2 H 2 , and U 2 H 4 ( 10 )]. Hydrogen, being a molecular solid, has large atomic volume in the elemental form—volume reduction, favorable under pressure, can be achieved through compound formation, and one expects polyhydrides to form under pressure. Another motivation was that some uranium compounds were shown to have peculiar (and previously inconceivable) coexistence of superconductivity and ferromagnetism ( 11 – 13 ), and (nonmagnetic) polyhydrides are prime candidates for high-temperature superconductivity.

RESULTS AND DISCUSSION

To predict stable phases in the U-H system at pressures of 0, 5, 25, 50, 100, 200, 300, 400, and 500 GPa, we performed variable-composition evolutionary structure/compound searches using the Universal Structure Predictor: Evolutionary Xtallography (USPEX) algorithm (14–16). By definition, a thermodynamically stable phase has lower Gibbs free energy (or, at 0 K, lower enthalpy) than any phase or phase assemblage of the same composition. Having predicted stable compounds and their structures at different pressures (Fig. 1), we built the composition-pressure phase diagram (Fig. 2), which shows pressure ranges of stability (with an estimated numerical error of approximately 1 to 2 GPa) for all the phases found (for convex hull diagrams at the selected pressures, see fig. S1). As shown in Fig. 2, our calculations correctly reproduce stability of both phases of UH 3 and predict 12 new stable phases corresponding to 14 new compounds (Cmcm-UH and P6 3 /mmc-UH, Ibam-U 2 H 3 , Pbcm-UH 2 , C2/c-U 2 H 5 , α-UH 3 and β-UH 3 , Immm-U 3 H 10 , P6 3 mc-UH 5 , P6 3 /mmc-UH 6 , -U 2 H 13 , P6 3 /mmc-UH 7 , -UH 8 , -U 2 H 17 , P6 3 /mmc-UH 9 , and metastable -UH 9 ). Detailed information on crystal structures of the predicted phases can be found in table S1 and fig. S2. Phonon calculations confirmed that none of the newly predicted phases have imaginary phonon frequencies in their predicted ranges of thermodynamic stability (see phonon dispersion curves and densities of states in the supplementary materials). The only uranium hydride phase remains stable at zero pressure is β-UH 3 , which transforms into α-phase above 5.5 GPa (fig. S3).

Fig. 1 Crystal structures of the predicted phases. (A) -UH 8 , (B) P6 3 /mmc-UH 7 , and (C) P6 3 /mmc-UH 9 . (D and E) Basic hydrogen motifs. U atoms are shown by large orange balls, and hydrogens are shown by small blue balls.

Fig. 2 Pressure-composition phase diagram of the U-H system.

Among the numerous predicted stable U-H phases, below, we focus on hydrogen-rich (H/U > 3) polyhydrides as potential high-temperature superconductors. All these hydrogen-rich phases are metallic, and their crystal structures feature very notable building blocks—H 8 cubes (Fig. 1, D and E). Lattice dynamics calculations show a big gap between phonon contributions from uranium and hydrogen atoms due to their large mass difference: Low-frequency modes mostly belong to uranium atoms, while high-frequency modes belong to hydrogen (fig. S4).

The first hydrogen-rich compound, U 3 H 10 , is predicted to become stable at 6 GPa. This structure is a derivative of α-UH 3 with one additional hydrogen atom and a tripled lattice parameter along the c direction. At pressures above 7 GPa, a family of UH 5–7 hydrides becomes stable with the same hexagonal close-packed (hcp) sublattice of U atoms. The P6 3 /mmc-UH 7 structure (Fig. 1B) is a derivative of the anti-NiAs structure, where all octahedral voids of U sublattice are filled by H 8 cubes (occupying the same positions as nickel atoms in the NiAs structure), forming infinite one-dimensional (1D) chains that run along the c axis, with each H 8 cube sharing a corner with neighboring two cubes in the chain (Fig. 1E). At 20 GPa, the shortest H-H distance is 1.56 Å, and the U-H distances vary from 2.12 to 2.25 Å. -U 2 H 13 is a derivative of the UH 7 structure, with a doubled unit cell along the c direction: U atoms still form an hcp sublattice, but half of linkages between H 8 cubes are deleted. As a result, instead of infinite 1D chains of corner-sharing H 8 cubes, we have isolated (“0D”) corner-sharing pairs of incomplete H 7 cubes and the composition changes from UH 7 = U 2 H 14 to U 2 H 14–1 = U 2 H 13 . At 20 GPa, the H-H distance is 1.55 Å, and the U-H distances vary from 2.09 to 2.13 Å. Derivatives of U 2 H 13 , the UH 6 and UH 5 structures, form after deletion of corner-sharing H atoms in the pair of H 7 -cubes and another hydrogen atom from the chain, respectively. Evolution of the hydrogen chains in the octahedral channels is presented in Fig. 3. The only magnetic phase among UH 5–7 hydrides is UH 5 (fig. S4). Notably, lattice dynamics calculations indicate that all these phases are dynamically stable even at zero pressure, that is, they may exist as metastable materials at atmospheric pressure (fig. S5).

Fig. 3 Evolution of hydrogen sublattice in hcp UH 5–7 structures.

At a higher pressure of 52 GPa, a new stable hydrogen-rich phase is predicted—UH 8 (Fig. 1A). At pressures between 100 and 280 GPa, UH 8 is the only stable hydrogen-rich uranium hydride. Its structure is a derivative of the rocksalt structure, where U atoms occupy Na sites and isolated H 8 cubes occupy Cl sites. At 50 GPa, the H-H distances are 1.38 Å and the U-H distances are 2.13 Å. The coordination number of uranium atoms in this remarkable structure is equal to 24. At 280 GPa, another stable compound appears—UH 9 (Fig. 1C). It is structurally similar to UH 7 : Just like UH 7 , it has an hcp sublattice of uranium atoms and infinite 1D chains of corner-sharing H 8 cubes running along the c axis, but in addition, it has single H atoms located within close-packed uranium layers (Fig. 1C). At 300 GPa, the shortest H-H distances are 1.13 Å within H 8 cubes and 1.09 and 1.23 Å between the cubes. Besides the above-mentioned stable phase of UH 9 , our calculations uncovered a low-enthalpy metastable (by only 18 meV/atom) polymorph with a space group . This metastable structure (fig. S2J) is based on the face-centered cubic (fcc) sublattice of uranium atoms, all the octahedral voids of which are occupied by isolated H 8 cubes, and half of the tetrahedral voids are occupied by single H atoms. This structure can be described as a half-Heusler alloy. USPEX found a stable U 2 H 17 (fig. S2I) whose structure is a derivative of the cubic UH 9 , with half of single H atom positions vacant in the alternating layer, which lowers symmetry to tetragonal .

We have successfully synthesized the predicted uranium hydrides in a diamond anvil cell (DAC) at various pressures (1 to 103 GPa) on loading and unloading cycles, applying moderate laser heating (up to 2000 K) in the loading cycles. Three experiments examined the reaction pathways of U and H 2 . In one control experiment, U was loaded in Ar medium, and in the other two, naturally oxidized uranium samples were studied in H 2 medium (these latter ones will not be considered here). Experiments with the Ar medium revealed the presence of metallic U and a small amount (<5%) of fcc UO 2 [for example, ref. (17)]. In the experiments with H 2 medium, UO 2 was not detected. Shortly after H 2 loading to an initial pressure (0.1 to 2 GPa), the U sample swells and changes appearance, and x-ray diffraction (XRD) shows the formation of coexisting α-UH 3 and β-UH 3 (Fig. 4A). At the lowest pressures, the amount of α-UH 3 is approximately 30%. As the pressure increases, the share dwindles until this phase becomes undetectable above 5 GPa (or 7.5 GPa if not heated).

Fig. 4 Experimental data on U-H compounds. XRD patterns of synthesized U-H phases: α-UH 3 and β-UH 3 (A), fcc UH 5 (B), hcp UH 7 and fcc UH 8+δ (C), hcp UH 5 (D), and Cmcm-UH 5 (E).

In contrast, β-UH 3 remains metastable up to 69 GPa (if not heated). The experimental unit cell volumes of these UH 3 phases are slightly larger (within 3%) compared to our theoretical predictions (Fig. 5). Above 5 GPa, a new phase starts to appear after laser heating. It becomes a dominant phase at 8 GPa (Fig. 4B) and remains detectable at up to 36 GPa. It is fcc-based, and the hydrogen content can be evaluated using the measured and calculated unit cell volumes (Fig. 5). If we assume x = 5, the experimental volumes are again slightly larger than the theoretically calculated ones. Other predicted UH 5 structures (with very similar volumes) are hcp-like and orthorhombic, and these will be discussed below. The structure of fcc UH 5 is similar to the predicted UH 8 , but instead of H 8 cubes, it has alternating H 4 tetrahedra and single H atoms (fig. S6B). At 31 GPa, another hydride starts to appear; it matches well with the predicted hcp UH 7 phase. This polyhydride can be observed at up to 103 GPa, which is the highest pressure in this study, and can be present as a single phase. However, above 45 GPa, weak peaks of yet another fcc structure appear (Fig. 4C), which remains stable up to 103 GPa. Volume of this phase is close to the theoretically found -UH 9 structure (metastable above 280 GPa) (see Fig. 5), but its formation pressure is close to the UH 8 phase (52 GPa). Thus, we believe that this experimental phase is an intermediate structure between fcc UH 8 and UH 9 phases, and later in the text, we will denote it as UH 8+δ .

Fig. 5 Volumes per formula unit as a function of pressure for the polyhydrides synthesized in this work in comparison to theoretical predictions. The combined literature volumes of U metal and solid molecular hcp H 2 in different proportions are also shown to illustrate the stability of polyhydrides at high pressures. f.u., formula unit.

We also looked at potential metastability of phases synthesized under extreme conditions and also at possible appearance of some other metastable phases, which can be realized because of kinetic reasons. No laser heating was applied in unloading cycles from 60, 45, and 38 GPa. A uniquely identified hexagonal UH 7 phase remains metastable down to at least 29 GPa. At this pressure, we could have been able to identify a hexagonal UH 5 phase which was theoretically predicted (Fig. 4D). However, at lower pressure, the diffraction patterns become very complex, possibly representing a mixture of several phases that could not be uniquely identified and also remnants of unreacted β-UH 3 . After unloading under nearly-ambient conditions (near 1 GPa), a single phase appeared to have been formed, which we were able to index in an orthorhombic lattice with a = 3.438 Å, b = 7.15 Å, and c = 6.20 Å and the space group Cmma (Fig. 4E). The unit cell volume suggests the UH 5 composition (Fig. 5), although UH 4 could also be possible. The best match from among the theoretically predicted structures is Cmcm-UH 5 , which is above the convex hull by 5 meV/atom at 5 GPa. This structure describes well most of the observed peaks, although there are some discrepancies too (Fig. 4E). The volume-pressure data for the newly synthesized α-UH 3 and β-UH 3 , orthorhombic UH 5 , hcp UH 5 and UH 7 , and fcc UH 5 and UH 8 are compared in Fig. 5 to the calculations and combinations of the experimental equations of state of hcp H 2 and metallic U (18). The latter comparison shows that the polyhydrides are stable when their volumes are lower than the sum of volumes of the elements. As one can see in Fig. 5, the polyhydrides with higher H content require higher pressures for their stability; this trend emerges both from our experiments and structure predictions. More detailed XRD patterns can be found in figs. S7 to S11.

The calculated electronic band structures of the predicted stable U-H phases are shown in fig. S4. All these phases are metallic and feature numerous flat bands near the Fermi level. Only UH 3 and UH 5 phases are magnetic (below 100 and 170 GPa, respectively). Their ferromagnetism can also be seen from the band structures shown in fig. S4 (A to C), where contributions of U atoms to the spin-up and spin-down states are shown in red and blue, respectively.

While for UH 3 , the bands near the Fermi level come mainly from uranium orbitals, in uranium polyhydrides, contributions of both uranium and hydrogen atoms are large. Geometric similarities (for example, between P6 3 /mmc-UH 7 and -U 2 H 13 ) result in similar densities of states and electronic properties (see fig. S4, E and F). Likewise, stable P6 3 /mmc and metastable polymorphs of UH 9 (actually, these can even be described as polytypes) have similar electronic density of states due to geometric similarities of their crystal structures. As we will see below, similarities are observed also for electron-phonon coupling (EPC) coefficients and superconducting T c .

In the Migdal-Eliashberg theory of superconductivity, the central quantity is the EPC coefficient λ. The superconducting transition temperature (T c ) can be calculated using the Allen-Dynes–modified McMillan formula (Eq. 1) or directly solving the Eliashberg equation (for details, see Materials and methods and supplementary materials), where for the Coulomb pseudopotential μ*, we use the commonly accepted bracketing values of 0.10 and 0.15. All T c values were calculated using the Eliashberg equation (which is more accurate by definition), but the critical temperature values calculated using the Allen-Dynes–modified McMillan formula (table S2) are in agreement with the data presented below. Detailed information on the calculated superconducting properties of uranium hydrides is given in Table 1, and spectral function α2F(ω) and the integrated EPC coefficient λ for UH 7–9 are presented on fig. S12. For UH 7 at 20 GPa, we find an EPC coefficient of 0.83 resulting in T c in the range of 44 to 54 K (57 to 66 K at 0 GPa; see Table 1). The structurally related U 2 H 13 should display similar EPC coefficient and T c values. For UH 8 at 50 GPa, we predict λ = 0.73 and T c in the range of 23 to 33 K (46 to 55 K at 0 GPa). P6 3 /mmc-UH 9 at 300 GPa has the lowest T c among the above considered hydrides (20 to 31 K at 300 GPa).