New Insights into Phase Separation of Cerium Hydrides under Pressure.

We report theoretical calculations of the static ground-state structures and pressure-induced phase transformations of four cerium hydrides: CeH, CeH2, CeH2.5, and CeH3. Under pressure, the experimental CaF2-type structure of CeH2 is likely to disproportionate to face-centered cubic (fcc) Ce and a cubic Pm3̅n (β-UH3 type) structure of CeH3 above 6 GPa. At further increasing pressures, fcc Ce will transform to a tetragonal I4/mmm structure above 12 GPa, while CeH3 moves through the following sequence of phases: Pm3®n (β-UH3 type) → Pm3̅n (A15 type) → R3®m; the corresponding transition pressures are calculated to be 10 and 70 GPa, respectively. The tetragonal I41/amd structure of CeH2.5 has the similar decomposition as that of CeH2. Finding this previously unreported pressure-induced decomposition of CeH2 will pave the way for investigations on the nature of hydrogen-metal interactions.

Introduction

Rare-earth metal hydrides are suitable compounds to study the hydrogen–metal interactions[1,2] since they have various electronic and structural transitions depending on hydrogen concentration, such as metal–insulator transition (MIT), lattice contraction from dihydrides to trihydrides of rare-earth metals,[3] and pressure-induced disproportionation of dihydrides.[4]

The formation of NaCl-type monohydride is likely a common behavior for the disproportionation of rare-earth metal dihydrides, as observed for LaH2, YH2, and ScH2.[4] We also found that NaCl-type monohydride of plutonium can also be formed by PuH2 above 62 GPa on the basis of first-principles density functional theory.[5] However, up to now, there is no direct study on the pressure-induced disproportionation of CeH2. In fact, even the stable phases of CeH2 and CeH3 under pressure are still not very clear. Theoretically, Priyanga et al.[6] predicted a structural phase transition from fcc (Fm3̅m, CaF2 type) to hexagonal close-packed(hcp) (P6/mmm, AlB2 type) of CeH2 at 52 GPa, while for CeH3, the phase transition pressure is about 4 GPa from fcc (Fm3̅m, BiF3 type) to hcp (P63/mmc, LaF3 type). Peng et al.[7] also think that there is a phase transition from Fm3̅m to P6/mmm for CeH2, but the transition pressure was predicted to be 33 GPa; CeH3 will transform to the R3̅m phase from the fcc phase at around 50 GPa. Recently, Salke et al.[8] found that pressurization of CeH2 in the presence of H2 up to 33 GPa did not result in any changes in the crystal structure. However, microsecond pulsed laser heating of ∼2000 K carried out at 33 GPa resulted in the formation of β-UH3-type Pm3̅n CeH3, which proved to be stable with further compression up to 80 GPa. Xin Li et al.[9] think that further hydrogenation of CeH2 to form CeH3 can easily occur when H2 is excessive in the diamond anvil cell (DAC) chamber since CeH3 has a lower calculated enthalpy value than that of CeH2. Above 33 GPa, the distorted fcc phase of CeH3 gradually transfers to another new cubic phase (Pm3̅n, A15 type), and A15 Pm3̅n CeH3 is stable up to 72 GPa in the presence of H2. Li et al.[10] predicted that CeH2 can be stable until 39 GPa; for CeH3, the A15-type Pm3̅n phase transformed into the R3̅c phase at 53 GPa.

With this under consideration, the present work was devoted to check whether there is a pressure-induced disproportionation of CeH2 by conducting a theoretical exploration of phase transformations of four cerium hydrides under pressure: CeH, CeH2, CeH2.5, and CeH3. The results may shed light on the fundamental principles for understanding the nature of hydrogen–metal interactions.

Results and Discussion

Stabilities for Different Stoichiometries under Pressure

To predict stable phases in the Ce-H system, the enthalpies of candidate structures of CeH (n = 1, 2, 2.5, 3) found by us are plotted in a typical convex hull diagram, indicating compositions relative to Ce + solid H2 at selected pressures, in Figure ; this can be also seen in Figure S1 in the Supporting Information. We plotted previously predicted Ce polyhydrides[8] in the diagram: CeH4-I4/mmm, CeH6-P63mc, CeH8-P63mc, CeH9-P63/mmc, and CeH10-Fm3®m. It is important to consider the zero-point energies (ZPEs) when determining the energetics of systems containing light atoms, and the enthalpies plotted in Figure also include ZPEs. The detailed enthalpy curves of CeH (n = 1, 2, 2.5, 3) are listed in Figures S2–S5 in the Supporting Information.

Figure 1

Convex hulls of the Ce-H system at selected pressures with ZPE included. The stoichiometric index n (in CeH) is indicated at the top. The compositions on the solid lines are stable at the corresponding pressure, while those on the dashed lines are unstable with respect to decomposition or disproportionation into other hydrides and potentially molecular hydrogen. The reference phases of solid hydrogen are from Labet’s work.[11]

As can be seen in Figure , CeH, CeH2, CeH2.5, and CeH3 are very stable with respect to decomposition into the elements. Indeed, CeH2, CeH2.5, and CeH3 are known experimentally, and as expected, they are all stable at 1 atm. CeH2 is the global thermodynamic minimum at 1 atm, while CeH3 achieves a global thermodynamic minimum above 6 GPa. This is consistent with the experimental observation.[12] Similar to the monohydride of La,Y, and Sc being stable at high pressures,[4] CeH is stable but in a very narrow pressure range near 6 GPa.

Interestingly, CeH, CeH2, and CeH2.5 will decompose into Ce and CeH3 above 6 GPa through disproportionation reactions. Pure Ce can be obtained by squeezing cerium hydrides, which has not been reported before to the best of our knowledge. On the other hand, it also indicates that CeH2 will decompose before undergoing any crystal structural changes above 10 GPa, not like the previous suggestions that CeH2 is stable up to 33 GPa.[6−8]Figure shows, in another way, the range of stabilities of different stoichiometries of cerium hydrides. All the thermodynamically stable phases are also dynamically stable (see Figures S9–S12). Interestingly, we found that Fm3̅m CeH2 is not dynamically stable above 20 GPa (see Figure S10a), which also indicates that CeH2 may undergo pressure-induced phase transitions or disproportionation reactions.

Figure 2

Pressure–composition phase diagram of theoretically predicted stable phases in the Ce-H system from 1 atm to 50 GPa with inclusion of ZPEs.

We will return to the interconversions between the various structures after presenting initial discussion of the calculated structural types.

Predicted CeHn (n = 1,2,2.5,3) Structures

CeH2, CeH2.5, and CeH3 are the experimentally known cerium hydrides. The structure search readily reproduced the observed structure of CeH2 and CeH2.5 at 1 atm. At 1 atm, CeH2 adopts the CaF2-type crystal structure (Fm3̅m, Z = 4, Figure a). All hydrogens occupy the tetrahedral holes of the fcc lattice. The calculated Ce-H separations of 2.35 Å match the experimental crystallographic values at P = 1 atm.[12] CeH2.5 adopts the tetragonal I41/amd structure (Z = 8, Figure b). This structure is similar to an alternative combination of fcc CeH2 and fcc CeH3. Hydrogens occupy the tetrahedral (T) and octahedral (O) holes of the lattice with Ce-H separations between 2.32 and 2.71 Å at 1 atm. This is in accordance with the trend that extra H atoms enter into the octahedral interstices during the formation of continuous solid solution CeH (2.0 < x < 3.0).[12]

Figure 3

Predicted ground-state static structures of CeH2, CeH2.5, and CeH3 at 1 atm. (a) Fm3̅m CeH2, (b) I41/amd CeH2.5, (c) Fm3̅m CeH3, and (d) Pm3̅n (β-UH3 type) CeH3. Large balls are Ce, and small balls are hydrogen. Lines are drawn for Ce-H separations shorter than 2.71 Å.

Interestingly, at 1 atm, we find several new structures that are calculated to be more stable enthalpically than the suggested Fm3̅m CeH3 (Z = 4, Figure c), and Fm3̅m CeH3 is also dynamically unstable under atmospheric pressure (see Figure S12a). The most stable phase we calculate is the cubic Pm3̅n (β-UH3 type) structure (Z = 8, Figure d), in which hydrogen atoms are tetrahedrally coordinated by Ce, with Ce-H separations between 2.32 and 2.39 Å at 1 atm. β-UH3-type CeH3 was also found recently in the experiment of Salke.[8] However, compared with Pm3̅n CeH3, Fm3̅m CeH3 can be easily synthesized by the reaction of cerium and hydrogen at normal pressure. We doubt that there may be a kinetic barrier to the transition between Pm3̅n CeH3 and Fm3̅m CeH3. This requires further research. As we know, one of the attractive structural properties exists in the Ce-H system is the lattice contraction from CeH2 to CeH3.[3] The predicted structures of CeH2, CeH2.5, and CeH3 reproduce this experimental observation well.

Above 10 GPa, the β-UH3-type Pm3®n structure transformed to the A15 type Pm3̅n structure (Z = 2, Figure a), in which hydrogen atoms are also tetrahedrally coordinated by Ce, with Ce-H separations of 2.13 Å at 50 GPa. The hexagonal R3̅m structure (Figure b) becomes thermodynamically stable relative to the A15-type Pm3̅n structure at 70 GPa, in which hydrogen atoms are tetrahedrally and octahedrally coordinated by Ce, with Ce-H separations between 2.03 and 2.27 Å at 100 GPa. The evolution of H coordination in CeH3 with increasing pressure, from tetrahedral to octahedral, is consistent with the anticipated generalization that the number of neighbors of a hydrogen-occupied site is likely to increase with increasing pressure. Note that especially, the hexagonal R3̅c (Z = 6, Figure c) structure reported by Li et al[10] is the metastable phase, and depending on the tolerance used in the automated symmetry assignment (CASTEP with tolerance larger than 0.01), the program assigns the R3̅c structure to the A15-type Pm3̅n symmetry below 80 GPa.

Figure 4

Predicted ground-state static structures of CeH3. (a) A15 Pm3̅n CeH3 at 50 GPa, (b) R3̅m CeH3 at 100 GPa, and (c) R3̅c CeH3 at 50 GPa. Large balls are Ce, and small balls are hydrogen. Lines are drawn for Ce-H separations shorter than 2.30 Å.

The ground-state static phase transition sequence of CeH2 during the pressure increase to 100 GPa is Fm3̅m → P4/nmm (tetragonal, Z = 2, Figure a) → C2/m (monoclinic, Z = 4, Figure b) → P6/mmm (MgB2-type, Z = 1, Figure c); the corresponding transition pressures are 10, 24, and 95 GPa with ZPEs included, respectively (see Figure S3). These similar high pressure phases of CeH2 also emerged in ScH2.[13]

Figure 5

Predicted ground-state static structures of CeH2. (a) P4/nmm CeH2 at 20 GPa, (b) C2/m CeH2 at 50 GPa, (c) P6/mmm CeH2 at 100 GPa. Large balls are Ce, and small balls are hydrogen. Lines are drawn for Ce-H separations shorter than 2.30 Å.

As expected, we reproduced the previously suggested rock-salt structure for CeH at 1 atm (Z = 4, Figure b) with hydrogen atoms octahedrally coordinated by Ce. At 15 GPa, a new static structure emerges. This is a hexagonal P63/mmc structure (Z = 2, Figure c), in which hydrogen atoms are also octahedrally coordinated by Ce, with Ce-H separations of 2.32 Å at 20 GPa. Above ∼50 GPa, the cubic Pm3̅m structure (Z = 1, Figure d) becomes thermodynamically stable relative to the P63/mmc structure, in which hydrogen atoms are body-centered by Ce, with Ce-H separations of 2.33 Å at 50 GPa.

Figure 6

Predicted ground-state static structures of Ce and CeH. (a) Fm3̅m Ce at 0 GPa, (b) Fm3̅m CeH at 0 GPa, (c) P63/mmc CeH at 20 GPa, and (d) Pm3̅m CeH at 50 GPa. Large balls are Ce, and small balls are hydrogen. Lines are drawn for Ce-H separations shorter than 2.51 Å.

Disproportionations

With the phase transition sequences of CeH, CeH2, CeH2.5, and CeH3 in hand (see Figures S2–S5), we can approach the pressure dependence of the CeH2 disproportionation reaction. Figure compares the enthalpies of the reactionswith and without ZPEs. Positive enthalpies mark a region of stability of CeH2, and negative ones mark that of CeH + CeH3 or Ce + CeH3.

Figure 7

Static ground-state enthalpy curves per formula unit (magenta and black curves) as a function of pressure with respect to CeH2. We also move beyond the static approximation by estimating the contribution of ZPEs (dashed lines). We have considered the most stable structures for Ce, CeH, CeH2, and CeH3 found in this work at the specified pressure ranges. The ZPE differences are taken to be approximately pressure-independent. (a) Enthalpy curves between 0 and 100 GPa. (b) Enthalpy curves between 3 and 12 GPa.

Figure shows that CeH2 is enthalpically stable below 5 GPa but becomes unstable compared to Ce, CeH, and CeH3 at higher pressure. Pure Ce can be formed by the pressure-induced disproportionation of CeH2 above 6 GPa. This is different from the case of MH2 (M = Sc, Y, and La),[4] in which MH2 decomposed to MH and MH3 under high pressure; no pure metal was found. Note that especially, Salke et al.[8] found that pressurization of CeH2 in a H2 atmosphere up to 33 GPa did not result in any changes in the crystal structure. This is not in accordance with our results and the phenomenon of disproportionation reactions of MH2 (M = Sc, Y, and La).[4] In the case of excessive H2, CeH2 can easily react with H2 to form CeH3, which was also confirmed by the experiment of Li.[9] Salke[8] found that the mixture of CeH2 and H2 up to 33 GPa did not result in any changes in X-ray diffraction (XRD) spectra, which may be due to the difficulty in distinguishing the XRD peaks between CeH2 and CeH3. In this work, CeH2 was pressurized alone in the absence of H2, and it is found that when the pressure reaches a certain value, CeH2 will decompose to form Ce and CeH3.

Interestingly, CeH2.5 also has a similar disproportionation trend as that of CeH2 (see Figure S7). Our results confirmed that the disproportionation reactions of MH2+ (M = rare-earth metals, 0 ≤ x < 1) under high pressure are likely common behaviors. However, for CeH2+ (0 ≤ x < 1), pure Ce can be formed under high pressure due to the disproportionation reaction. Indeed, CeH is stable but in a very narrow pressure range near 6 GPa (see Figures and S6), which is to say that CeH2 or CeH2.5 is likely to disproportionate to CeH and CeH3, and then, CeH continues to disproportionate to Ce and CeH3, as shown in Figure S6.

To elucidate the mechanisms for the pressure-induced disproportionation of CeH2 leading to the formation of Ce and CeH3, we examined the evolution of the internal energy (U) and the product of pressure and volume (PV), which contribute to the enthalpy (H = U + PV) of the pertinent material systems and phases in response to pressure change. We show in Figure the pressure dependence of ΔU, Δ(PV), and ΔH, defined as the values for the mixture of 1/3 Ce + 2/3 CeH3 relative to that for CeH2, which are set to zero. It is seen clearly that the transition from CeH2 to the 1/3 Ce + 2/3 CeH3 mixture is caused by the decrease in the internal energy of the latter; meanwhile, the PV term rises with increasing pressure, although its large negative magnitude is still the main contributor to the overall negative relative enthalpy around the phase transition pressure. Bettween 10 and 30 GPa, both the U and PV terms make similar contributions to lowering the enthalpy. After 35 GPa, the large negative magnitude of U overcompensates for the increasing PV term, resulting in the stabilization of the 1/3 Ce + 2/3 CeH3 mixture relative to CeH2.

Figure 8

Calculated ΔH, ΔU, and Δ(PV) versus pressure for the predicted phase transitions: CeH2 → 1/3 Ce + 2/3 CeH3, where CeH2 is chosen as the reference phase. We have considered the most stable structures for Ce, CeH2, and CeH3 found in this work at the specified pressure ranges.

For Ce–Ce separations, the number of nearest neighbors in Ce (I4/mmm, Z = 2) is larger than that of CeH2 (C2/m, Z = 4) at 50 GPa, as shown in Figure S13a, while for Ce-H, the number of nearest neighbors in CeH3 (A15 type Pm3®n, Z = 2) is larger than that of CeH2 (C2/m, Z = 4) at 50 GPa (see Figure S13b). It indicates that compared with CeH2, the Ce–Ce bonding in the I4/mmm phase of Ce and the Ce–H bonding in the Pm3̅n phase of CeH3 may increase as well. We then calculated the projected crystal orbital Hamilton population (pCOHP)[14] between Ce–Ce, Ce–H, and H–H pairs in Ce, CeH2, and CeH3 all at 50 GPa, as shown in Figure S14. Compared with CeH2, the Ce–Ce bonding in the I4/mmm phase of Ce and the Ce–H bonding in the Pm3̅n phase (A15 type) of CeH3 are strengthened. It suggests that the increasing Ce–Ce bonding in the I4/mmm phase of Ce and the increasing Ce–H bonding in the Pm3®n phase of CeH3 may play an important role in the phase transition and stabilization. The calculated electronic structures show that each phase of CeH (n = 1, 2, 2.5, 3) is metallic. Hydrogen in CeH (n = 1, 2, 2.5, 3) has the form of Hδ− (δ = 0.55–0.72), as can be seen in Table S1. Histograms (Figure S13) also show that the nearest distance of H–H in CeH (n = 1, 2, 2.5, 3) is around 2 Å. Thus, no cage-like structure of hydrogen is formed as repored in cerium polyhydrides.

Conclusions

In summary, we have explored pressure-induced phase transformations of four cerium hydrides: CeH, CeH2, CeH2.5, and CeH3. We find an unusual circumstance; CeH, CeH2, and CeH2.5 will decompose into Ce and CeH3 above 6 GPa through disproportionation reactions. Pure Ce can be obtained by squeezing cerium hydrides, which is different from the case of MH2 (M = Sc,Y, and La), in which MH2 decomposed to MH and MH3 under high pressure; no pure metal was found. Indeed, CeH2 or CeH2.5 is also likely to disproportionate to CeH and CeH3, and then, CeH continues to disproportionate to Ce and CeH3 since CeH is only stable in a very narrow pressure range near 6 GPa. The increasing Ce–Ce bonding in pure Ce and the increasing Ce–H bonding in CeH3 may play an important role in the disproportionation reactions of CeH, CeH2, and CeH2.5. The theoretical work indicates that pure metal and its higher hyrides may also be obtained in other metal–hydrogen system.

Methods and Computational Details

We searched extensively for CeH (n = 1, 2, 2.5, 3) ground-state structures at 0 K using the particle swarm optimization methodology implemented in the CALYPSO code.[15] This method has been applied successfully to a wide range of crystalline systems ranging from elemental solids to binary and ternary compounds.[15] Our structure searches with system sizes containing up to 6 formula units (fu) per simulation cell were performed at pressures of 0–100 GPa. Each generation contains 30 structures. We usually follow 50 generations to achieve a converged structure.

The underlying structural relaxations were carried out at 0 K using density functional theory using the Perdew–Burke–Ernzerhof (PBE) exchange–correlation functional[16] as implemented in the VASP code.[17] The projector-augmented wave method[18] was adopted, with 1s1 (cutoff radius of 1.1a0) and 5s25p64f15d16s2 (cutoff radius of 2.7a0) treated as valence electrons for H and Ce, respectively. An energy cutoff of 800 eV and dense Monkhorst–Pack[19]k-meshes with a grid spacing of 2π × 0.03 Å–1 gave good convergence of the structural relaxations (see Figure S16). Phonon calculations were carried out using VASP in conjunction with the PHONOPY code.[20] Given the light hydrogens in the structure, vibrational contributions to the relative enthalpy were considered.