Unique Phase Diagram and Superconductivity of Calcium Hydrides at

Feb 7, 2019 - Synopsis. For the alkaline earth hydrides, no stoichiometry with an odd H content is thermodynamically stable under pressures via DFT ...
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Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

Unique Phase Diagram and Superconductivity of Calcium Hydrides at High Pressures Ziji Shao,† Defang Duan,*,† Yanbin Ma,‡ Hongyu Yu,† Hao Song,† Hui Xie,† Da Li,† Fubo Tian,† Bingbing Liu,† and Tian Cui*,† †

State Key Laboratory of Superhard Materials, College of Physics, Jilin University, Changchun 130012, P. R. China College of Physics, Harbin University of Science and Technology, Harbin 150080, P. R. China

‡

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S Supporting Information *

ABSTRACT: Structure prediction studies on Ca−H binary systems under high pressures were carried out, and the structures of calcium hydrides in earlier works were reproduced. The previously unreported composition of CaH9 was found to be stable and experienced the phase transition series Cm → P21/m → C2/m from 100 to 400 GPa. To the best of our knowledge, CaH9 may be the only alkaline earth hydride with an odd H content. At 400 GPa, the metastable R3̅m-CaH10 phase shares the same space group with the R3̅m-SrH10 phase with puckered honeycomb H layers. The C2/m phase of CaH9 and the R3̅m phase of CaH10 are excellent superconductors with Tc values of about 240−266 and 157−175 K at 300 and 400 GPa, respectively. The high contributions of H-derived states at the Fermi level play an important role in the superconductivity of calcium hydrides. = Mg, Ca, Sr) is always the first stable stoichiometry under pressure with respect to XH2 and H2; MgH4 possesses Cmcm22 symmetry, while CaH4 and SrH4 demonstrate the same phase transition from I4/mmm to Cmcm.5,17,21 All of the above XH4 phases consist of H+ and H2 units. As pressure increases, phases containing numerous H atoms, such as MgH12,16, CaH6,12, SrH6,10,12, and BaH6,8,12, gradually become more stable with a variety of H sublattices, such as H3 units, helical H chains, puckered honeycomb H layers, and even sodalite H cages.5,17,21−23 The superconductivities of alkaline hydrides with metallic characteristics have been systematically investigated. In general, the values of Tc for the majority of the phases with H+, H2, and H3 units are under 70 K. However, the polyhydrides R3̅m-SrH6, R3̅m-SrH10, and Im3̅m-CaH6 with 1D helical H chains, 2D puckered hexagonal H layers, and 3D sodalite-like H frameworks are noteworthy due to their respective high Tc of about 108−156, 259, and 235 K under high pressure.5,17,25 Pressure can considerably enrich the phase diagrams and formation strategies of H atoms of all alkaline earth polyhydrides. In addition, with the realization of high Tc in H3S and LaH10, calcium hydrides have once again become a major focus in the quest for room-temperature superconductors. I4/mmm-CaH4 and the new stoichiometry C2/ m-Ca 2 H5 with H+ and H2 units were experimentally synthesized at 116 GPa and 1600 K and 22 GPa and 780 K,

I. INTRODUCTION The high superconducting transition temperature (Tc) of 200 K, which was determined in sulfur hydride Im3̅m-H3S under high pressure1−3 via both theoretical prediction and experimental measurement, is a record-high critical temperature. Numerous high-Tc superconductors have also been theoretically found in other systems, such as P6/mmm-TeH44 with Tc of about 104 K at 170 GPa, Im3̅m-CaH65 with Tc of about 235 K at 150 GPa, Im3̅m-YH66 with Tc of about 264 K at 120 GPa, I41md-ScH97 with Tc of about 233 K at 300 GPa, P63/mmcYH98 with Tc of about 276 K at 150 GPa, Fm-3m-YH108,9 with Tc of about 326 K at 250 GPa, and Fm-3m-LaH108,9 with Tc of about 288 K at 200 GPa. Notably, superconductivity has been measured in a hydride of lanthanum whose properties are in line with theoretical predictions for LaH10. The measured Tc is 260 K at 180−200 GPa,10,11 and 215 K at about 170 GPa,12 and then it improved to 250 K.13 These significant discoveries of high-Tc hydride superconductors under high pressures are the motivation behind research on the high-pressure phase diagrams and unusual properties of new high-pressure hydrides. Alkaline earth hydrides have been intensively explored5,14−24 in previous investigations on H-rich compounds. Traditional alkaline hydrides possess the stoichiometry of XH2 (X = Be, Mg, Ca, Sr, Ba) at ambient pressure. Except for BeH2, which has the only stable H stoichiometry determined thus far,19−21 other alkaline earth hydrides are theoretically predicted to form nontraditional stoichiometries of a H-rich phase XHn (X = Mg, Ca, Sr, Ba) where n can be 4, 6, 8, 10, 12, and even 16. XH4 (X © XXXX American Chemical Society

Received: November 11, 2018

A

DOI: 10.1021/acs.inorgchem.8b03165 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry respectively.26 Both phases were determined to be insulating below 120 GPa. With a summary of the results of the previous theoretical works on alkaline earth hydrides under pressure, a phenomenon is revealed that no stoichiometry with an odd ratio of H/metal atoms has been predicted to be thermodynamically stable via DFT calculations. However, the synthesis of Ca2H5 in a high-pressure experiment with nonintegral H contents may indicate a diverse phase diagram of the Ca−H system under pressure. The phase stability of the Ca−H system above 200 GPa has not been explored. This knowledge gap has led us to investigate the stabilities of other new phases of CaHn under high pressure and the existence of high Tc in these phases. The present work reports the phase stabilities and structures of calcium hydrides in the high-pressure range 50−400 GPa. An unexpected phase of CaH9 that appears to be stable over the entire investigated pressure range was found. The phase transition Cm → P21/m → C2/m occurs at 167 and 235 GPa, respectively, and CaH9 may be the only stoichiometry with an odd H content among the alkaline earth hydrides. We also found a metastable phase R3̅m-CaH10 at 400 GPa; this phase is isostructural with R3̅ m-SrH10 at 300 GPa. The superconductivities of CaH9 and CaH10 under pressure were finally calculated.

ω log =

f2 = 1 +

ÄÅ Å2 ω2 = ÅÅÅÅ ÅÅÇ λ

(4)

(5)

(ω2 /⟨ω⟩log − 1)λ 2 2

λ + [1.82(1 + 6.3μ*)(ω2 /⟨ω⟩log )]2

(6)

∫

∫0

∞

ÉÑ1/2 Ñ ωα 2F(ω) dωÑÑÑÑ ÑÑÖ

(8)

III. RESULTS AND DISCUSSION Formation enthalpies (ΔHf) of the most stable candidate structures for each stoichiometry relative to CaH2 and solid H2 were calculated in the pressure range 50−400 GPa, as depicted in the convex hull (Figure 1). The stable structures of H2 were taken from the work of Pickard et al.,36 and those of CaH2 were taken from the work5 of Wang et al. The compounds located on the hull are thermodynamically stable. At 50 GPa, only CaH4 is stable which is in agreement with previous work.5 In the pressure range 100−400 GPa, the stable stoichiometries are CaH4, CaH6, CaH9, and CaH12. To the best of our knowledge, odd H stoichiometries (n = 3, 5, 7, 9) in alkaline earth hydrides MHn (M = Be, Mg, Ca, Sr, Ba)5,14−23,37,38 have not been reported. Thus, CaH9 may be the only alkaline earth hydride with an odd H content, and the stable phase diagrams of Ca−H systems under high pressures are different from those of other alkaline earth hydrides. The pressure−composition phase diagram of the Ca−H system is illustrated in Figure 1b. As mentioned before,5 from 100 to 400 GPa, CaH4 and CaH12 experienced phase transitions I4/mmm → Cmcm and R3̅ → C2/c, respectively. CaH6 is stable with the Im3̅m structure. The most stable structure of CaH9 has Cm symmetry from 100 to 167 GPa, and then the compound converts to the P21/m space group; at 235 GPa, the C2/m phase replaces the P21/m phase and keeps its stability until 400 GPa. Zero-point energy (ZPE) always plays an important role in the total energy of hydrogen-rich materials. Thus, we estimated the ZPE of calcium hydrides using the quasiharmonic model at 400 GPa (Figure S1). The ΔHf of CaHn at 400 GPa is lowered by the inclusion of ZPE, but the overall phase stabilities are not changed. Results indicate that ZPE will not change the topology of the highpressure phase diagram of calcium hydrides. The presence of this unexpected stoichiometry can also presumably be explained by the diagonal relationship,39 which suggests that some chemical properties between diagonally adjacent elements may be similar. This kind of similarity has been found between the Sc−H system and the Mg−H system40 at high pressure, since MgH6 and ScH6 have the same two crystal structures P63/mmc and Im3̅m and even the same

Here, the EPC parameter λ and logarithmic average frequency ωlog are, respectively, calculated as follows: α 2F(ω) dω ω

α 2F(ω)ln(ω) dω ω

⟨ω⟩log and ω2, which are the logarithmically averaged phonon frequency and second moment of the normalized weight function, respectively, are defined as É ÅÄÅ 2 ∞ dω ÑÑÑÑ ⟨ω⟩log = expÅÅÅÅ α 2F(ω)log ω Ñ ÅÅÇ λ 0 (7) ω ÑÑÑÖ

The Allen−Dynes-modified McMillan formula is as follows:35 ÄÅ ÑÉÑ ÅÅ ω log 1.04(1 + λ) ÑÑ ÑÑ Tc = expÅÅÅÅ− ÅÅÇ λ − μ*(1 + 0.62λ) ÑÑÑÖ 1.2 (2)

∞

∞

1/3 ÄÅ ÉÑ3/2 o l o ÅÅ ÑÑ | o o λ o o Å Ñ Å Ñ f1 = o m1 + ÅÅ Ñ } o o ÅÅÇ 2.46(1 + 3.8μ*) ÑÑÑÖ o o o n ~

We carried out an extensive search for stable CaHn (n = 3−10) compounds within 2−4 formula units and CaH12 with 2 formula units between 50 and 400 GPa using the evolutionary algorithm USPEX.27−29 Structural relaxations, electronic properties, and total energies were determined in the framework of density functional theory with Perdew−Burke−Ernzerhof parametrization of the generalized gradient approximation30 as implemented in the Vienna ab initio simulation package (VASP).31 Ion−electron interactions were described using the all-electron projector augmented wave32 method with 1s1 and 3p64s2 as valence electrons for H and Ca, respectively. A plane-wave energy cutoff of 800 eV was used. Monkhorst−Pack meshes for Brillion zone sampling with resolutions of 2π × 0.03 Å−1 and 2π × 0.02 Å−1 were employed for thermodynamic calculations and electronic property determination, respectively. Phonon dispersion and electron−phonon coupling (EPC) were carried out using density functional perturbation theory as implemented in the Quantum-ESPRESSO package.33 A kinetic energy cutoff of 80 Ry and ultrasoft pseudopotentials for H and Ca were adopted. The numbers of k-points and q-points were 20 × 20 × 12 and 5 × 5 × 3 for Cmcm-CaH4, 20 × 20 × 12 and 5 × 5 × 3 for the monoclinic phase CaH9, and 20 × 20 × 20 and 5 × 5 × 5 for the rhombohedral phase CaH10. Zero-point energies (ZPE) were calculated using VASP combined with the phonopy code.34 Tc was estimated using the Allen−Dynes-modified McMillan formula with correction as follows:35 ÉÑ ÄÅ ÅÅ ÑÑ ω log 1.04(1 + λ) ÑÑ Tc = f1 f2 expÅÅÅÅ− Ñ ÅÅÇ λ − μ*(1 + 0.62λ) ÑÑÑÖ 1.2 (1)

∫0

∫0

Here, f1 and f 2 are the strong coupling and shape correction factors, respectively, and μ* is the effective Coulomb repulsion. f1 and f 2 are, respectively, defined as

II. COMPUTATIONAL METHODS AND DETAILS

λ=2

2 λ

(3)

and B

DOI: 10.1021/acs.inorgchem.8b03165 Inorg. Chem. XXXX, XXX, XXX−XXX

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known stable phases, similar to CaH4 and CaH6.6,8,9 I4/mmmYH4 and Im3̅m-YH6, which are stable above 128 and 122 GPa,6 are isostructural with I4/mmm-CaH4 and Im3̅m-CaH6, respectively. YH9 begins to emerge on the convex hull at 100 GPa and maintains its stability until 400 GPa;8 by comparison, CaH9 consistently stays on the convex hull from 100 to 400 GPa in our investigation. However, different from the stable compounds in Ca−H and Y−H systems with 1:4 and 1:6 stoichiometries, which share the same symmetries,5,6 respectively, the structure of stable CaH9 is C2/m, slightly different from that of YH9 (P63/mmc). We substituted the Y atoms in P63/mmc-YH9 with Ca atoms, relaxed the substituted P63/mmc-CaH9, and calculated the enthalpies of the resulting hydride from 200 to 300 GPa to compare the stabilities of the P63/mmc structure, which widely exists in rare earth hydrides (ScH9, YH9, and CeH9)8 and our newfound P21/m and C2/m structures in CaH9. The enthalpy differences ΔHf under different pressure points of C2/m-CaH9 and P21/m-CaH9 compared with that of P63/mmc-CaH9 are shown in Figure S2. Compared with those of other phases, P63/mmc-CaH9 has higher enthalpies, thereby suggesting its energetic instability. The emergence of imaginary frequencies in the phonon band structure of P63/mmc-CaH9 at 300 GPa (Figure S3) also indicates its dynamic instability. The distinctive features of the predicted structures are depicted in Figure 2, and the detailed crystallographic data are listed in the table in the Supporting Information. Cm-CaH9 consists of H atoms and H2 units messily distributing around Ca atoms. At 100 GPa, the H−H distances of Cm-CaH9 in H2 units are 0.800, 0.77, and 0.783 Å. P21/m-CaH9 has a stacked layer structure in which the first layer consists of Ca atoms, monatomic H, and H2 units, and the second layer consists only of H2 units with orientations different from those in the first layer. The H−H distance of H2 units in the first layer is 0.812 Å, while that in the second layer is 0.906 Å at 200 GPa. Further compression causes the formation of bent H3 units and the rotation of H2 units. In C2/m-CaH9, one Ca atom is surrounded by 29 H atoms with three different moieties at 300 GPa: H2 units (0.888 and 0.928 Å), monatomic H, and bent H3 units (0.977 Å). The existence of these H units can be

Figure 1. (a) Enthalpies of formation of CaHn (n = 3−10 and 12) with respect to CaH2 and H2 at 50−400 GPa. (b) The phase transition series of stable compounds CaH4, CaH6, CaH9, and CaH12.

phase transition P63/mmc → Im3̅m. Obviously, Y and Ca are diagonally adjacent, and some similarities exist between Y−H and Ca−H systems in terms of phase stabilities under high pressure. For the Y−H system, YH4 and YH6 are also well-

Figure 2. Crystal structures of (a) P21/m-CaH9, (b) C2/m-CaH9, (c) R3̅m-CaH10, and (d) Cm-CaH9. Calcium atoms are colored dusty blue, and hydrogen atoms are pink. C

DOI: 10.1021/acs.inorgchem.8b03165 Inorg. Chem. XXXX, XXX, XXX−XXX

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of P63/mmc-CaH9 (Chex) at 300 GPa and the corresponding H−H distances are shown in Figure 3. The squares and hexagons of Chex are both symmetrical about mirror planes (perpendicular to the c axis for squares and perpendicular to the c and b axes for hexagons) with two groups of equal lengths (1.118 and 1.186 Å for squares; 1.118 and 1.039 Å for hexagons). However, the formation of H2 units in Cmon shortens one length (0.928 Å for squares and 0.888 Å for hexagons), and the adjacent edges (1.222 and 1.205 Å for squares; 1.126 and 1.222 Å for hexagons) are stretched. Hence, the squares and hexagons in Cmon are irregular. The formation of H3 units in pentagons shortens the upper sides of the two connected pentagons. The bend angle ∠H−H−H of H3 units is 126.40°, which is larger than the corresponding angle in Chex (114.93°). Thus, the adjacent H−H distances of H3 units are not extended but slightly shortened (1.168 Å) compared with those in Chex (1.186 Å). Below the pentagons, the formation of H2 units (0.928 Å) lengthens the two lower edges (1.126 Å) of the connected pentagons, resulting in unequal lengths of the lower edges compared with those in the upper ones (H3 units). Therefore, the complete pentagons in Cmon are distorted compared with those in Chex. The unequal H−H distances described above induce the distortion of these polygons in the pseudocages, and the whole cages are distorted, which reduces the symmetry of CaH9. We further calculated the Bader43,44 charge of the stable C2/ m-CaH9 and the stable P63/mmc-YH9 at 300 GPa to determine the reasons behind the observed distortions. The charge transfer can also explain why P63/mmc-CaH9 is unstable. For C2/m-CaH9 and P63/mmc-CaH9, every Ca atom donates 0.896 and 0.883 e to H, respectively, while for P63/mmc-YH9, every Y atom donates about 1.378 e. Molecular H2 has a filled covalent bond, and the electrons donated by Ca or Y atoms must reside in the antibonding orbitals, which lengthens or even breaks the H−H bonds. Compared with that of P63/mmc-YH9, the Ca atom fails to provide enough electrons to stabilize the H29 cage in P63/mmc-CaH9. The pseudocage in C2/m-CaH9 does not receive enough electrons to occupy all H−H antibonds and form a cage with uniform H−H bonds. Thus, the formation of H2 and H3 units in C2/m-CaH9 may be energetically and dynamically favorable. In analogous isoelectric systems, such as Sr−H17,21 and Ba− H,23 the compositions SrH10 and BaH10 are predicted to be stable under high pressures in contrast to that in the Ca−H system. The composition CaH10 deviates from the hull and is metastable under high pressure. In this study, a predicted trigonal R3̅m-CaH10 at 400 GPa has the same type of structure as R3̅m-SrH10, which is predicted to exist at 300 GPa.17 For R3̅m-CaH10, the layers of Ca atoms insert into two staggered and puckered H layers. The H layers are puckered honeycomb H layers with H−H distances alternating between 0.945 and 0.959 Å with the values of ICOHP being about −3.36 and −1.38 eV at 400 GPa, respectively (Figure S6). The ELF of R3̅m-CaH10 (Figure S4) illustrates that the electrons uniformly stay around 2D H layers, and large electron densities are found in the two H−H distances, thereby indicating the tendency of covalent interactions between each H atom. Since Ca is the neighboring element of Sc, the Ca−H system also shares some similarities with the Sc−H system. For example, the ScH9 stoichiometry is also found to be thermodynamically stable at 285−325 GPa.7 In addition, a layer hydrogen structure is also found in ScH10 with Cmcm symmetry. However, in Cmcm-ScH10, the Sc and H atoms are

illustrated using the electron localization function (ELF) (Figure S4). The COHP and ICOHP of all the H units in C2/ m-CaH9 are calculated41,42 (Figure S5). All the ICOHP values of these H−H distances are negative which means that they all have bonding interactions. For C2/m-CaH9, the ICOHP values of those short H−H distances like 0.888, 0.928, and 0.977 Å in H2 units and H3 units are −5.68, −2.81, and −4.88 eV, which indicate strong bonding interactions. In addition, the 2D ELF shows large electron densities among these H atoms. Then, the covalent bonds are confirmed in these H2 and H3 units. For the other long H−H distances, though their ICOHP values are negative in the range −1.59 to −3.63 eV, the 2D ELF shows that low electron densities are found between them. Thus, we can say that there are bonding interactions between these H atoms. H atoms may fail to form the perfect covalent cages, such as those in P63/mmc-YH9,8 but the complete shape formed by these 29 H atoms can be regarded as a distorted pseudopolyhedral (Figure 3). Compared with that of P63/ mmc-YH9, the distorted pseudopolyhedral of C2/m-CaH9 also consists of six irregular squares, six irregular pentagons, and six irregular hexagons. To compare the geometric distortion of the C2/m structure with that of the P63/mmc structure, detailed configurations of the pseudopolyhedral cage of C2/m-CaH9 (Cmon) and the cage

Figure 3. (a) Pseudopolyhedral of C2/m-CaH9 at 300 GPa with a Ca atom and 29 H atoms. (b) The polyhedral of P63/mmc-CaH9 at 300 GPa with a Ca atom and 29 H atoms. (c, d) The square units in C2/ m-CaH9 and P63/mmc-CaH9. (e, f) The pentagon units in C2/mCaH9 and P63/mmc-CaH9. (g, h) The hexagon units in C2/m-CaH9 and P63/mmc-CaH9. D

DOI: 10.1021/acs.inorgchem.8b03165 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry coplanar, and the H atoms prefer to form three connected pentagons, which is different from those in metastable R3̅mCaH10. The electron band structures and partial electronic density of states (PDOS) of C2/m-CaH9 at 300 GPa and R3̅m-CaH10 at 400 GPa are shown in Figure 4. C2/m-CaH9 and R3̅m-

Figure 5. Phonon band structure (left), PHDOS (middle), and Eliashberg spectral function α2F(ω) (right) for (a) C2/m-CaH9 at 300 GPa and (b) R3̅m-CaH10 400 GPa. Red solid circles indicate the phonon line width with a radius proportional to the EPC strength. The integral EPC parameter λ as a function of frequency is calculated and shown in red solid lines. The contributions of the low-frequency region and high-frequency region are also illustrated in percentages.

cm−1, which mainly correspond to the vibrations of Ca atoms for C2/m-CaH9 and R3̅m-CaH10, respectively, and the highfrequency ranges occur at 500−3000 and 750−3320 cm−1, which are mainly related to H atoms for C2/m-CaH9 and R3̅mCaH10, respectively. Employing the Allen−Dynes-modified McMillan eq 1, the values of Tc were calculated with the commonly accepted values of Coulomb pseudopotential parameters μ* = 0.1 and 0.13 (Table 1). The relatively large values of λ for C2/m-CaH9 and R3̅m-CaH10, which are 2.93 and 1.67, respectively, reveal the presence of strong electron− phonon coupling (EPC). As shown in the integral of the Eliashberg spectral function α2F(ω), the low-frequency regions of C2/m-CaH9 and R3̅m-CaH10 contribute about 28.52% and 29.33% to the EPC, and their high-frequency regions donate about 71.48% and 70.67%, respectively. In both phases, the high-frequency regions related to H atom vibrations contribute greatly to the EPC, which may explain their large coupling constants. The calculated Tc are adjusted using the shape correction factors f1 and f 2 and estimated through eqs 5 and 6 because both values of λ of C2/m-CaH9 and R3̅m-CaH10 are larger than 1.5. The final values of Tc are about 239−266 and 157−175 K for C2/m-CaH9 and R3̅m-CaH10 at 300 and 400 GPa, respectively. For the stable compounds C2/m-CaH9, the Tc is about 256.6−274.7 and 260.6−285.2 K at 350 and 400 GPa with λ 2.29 and 2.28, ωlog 1355.5, and 1404.1 K, respectively. We can see that, as pressure increases, through λ is reduced, the Tc is increased by the increase of ωlog. While the CaH10 phase has a larger H content than the CaH9 phase, the small λ causes a low Tc. This phenomenon suggests that a high H content may not always cause a high Tc, and the entire crystal structures of the H-rich compounds may influence the electronic and superconductive properties of the related phases. For example, the quasilayered structure of R3̅m-

Figure 4. Band structure (left) and PDOS (right) of (a) C2/m-CaH9 at 300 GPa and (b) R3̅m-CaH10 at 400 GPa. The red dashed lines represent the Fermi level.

CaH10 are good metal materials with highly dispersive bands crossing the Fermi level. The total DOS values at the Fermi level N(εf) of C2/m-CaH9 and R3̅m-CaH10 are 0.54 and 0.48 states/eV/f.u, respectively. These N(εf) values are comparable with that of the high-Tc superconductor H3S (0.54 states/eV/ f.u.).1 The determined PDOS shows that the contribution of N(εf) mainly comes from H atoms with about 0.40 and 0.38 states/eV/f.u. in C2/m-CaH9 and R3̅m-CaH10, respectively. The large electronic states projected onto H atoms at the Fermi level suggest the possibility of large electron−phonon coupling between H phonons and electrons close to the Fermi level, 45 and promising superconductive properties are expected. The phonon band structures, partial phonon density of states (PHDOS), corresponding Eliashberg spectral functions α2F(ω), and integral EPC parameters λ as a function of frequency of C2/m-CaH9 and R3̅m-CaH10 at 300 and 400 GPa are calculated and shown in Figure 5. In terms of PHDOS, the phonon dispersions of these two structures consist of two parts: the low-frequency ranges occur below 500 and 750 E

DOI: 10.1021/acs.inorgchem.8b03165 Inorg. Chem. XXXX, XXX, XXX−XXX

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Table 1. Calculated EPC Parameter (λ), Logarithmic Average Phonon Frequency (ωlog), Critical Temperature (Tc), and the Corrected Critical Temperature (f1 f 2Tc) (with μ* = 0.10 and 0.13) for Cmcm-CaH4, C2/m-CaH9, and R3̅m-CaH10 at Given Pressures structure

pressure (GPa)

λ

ωlog (K)

Tc (K) (μ*= 0.13−0.1)

f1 f 2Tc (K) (μ*= 0.13−0.1)

Cmcm-CaH4 Cmcm-CaH4 Cmcm-CaH4 C2/m-CaH9 C2/m-CaH9 C2/m-CaH9 R3̅m-CaH10

200 300 400 300 350 400 400

0.46 0.64 0.64 2.93 2.29 2.27 1.67

1398.0 1441.1 1587.5 1060.3 1355.5 1404.1 1166.4

6.3−11.6 29.0−39.6 32.3−44.1 179.5−188.9 203.8−212.2 206.1−219.2 137.9−146.5

239.3−266.4 256.6−274.7 260.6−285.2 156.9−175.3

ORCID

CaH10 determines its quasi-2D electronic structure indicated in ELF, which reduces N(εf) and weakens its metallic characteristics to a certain extent. Thus, electrons that can form Cooper pairs46 connected by phonons may not be adequate to provide larger λ47 in layered R3̅m-CaH10 compared with C2/m-CaH9 due to the smaller value of N(εf). In addition, the Tc values of Cmcm-CaH4 are increasing with the pressure and are calculated to be 11.6, 39.6, and 44.1 K at 200, 300, and 400 GPa, respectively.

Da Li: 0000-0002-0041-9181 Tian Cui: 0000-0002-9664-848X Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Key R&D Program of China (2018YFA0305900), National Natural Science Foundation of China (51632002, 11674122, 51572108, 11634004, 11504127, 11574109, 11704143, 11404134), Program for Changjiang Scholars and Innovative Research Team in University (IRT_15R23), the 111 Project (B12011), Jilin Provincial Science and Technology Development Project of China (20170520116JH), and National Found for Fostering Talents of Basic Science (J1103202). Parts of calculations were performed in the High Performance Computing Center (HPCC) of Jilin University and TianHe-1(A) at the National Supercomputer Center in Tianjin.

IV. CONCLUSION We studied the stable phases and structures of calcium hydrides in the pressure range 50−400 GPa. Under the influence of the diagonal relationship between Ca and Y, we found an unpredicted composition of CaH9. The stable highpressure CaH9 phase is no longer isostructural with P63/mmcYH9 with H29 cages but possesses a C2/m space group with the formation of H2 and H3 units due to the lack of charge transfer. The CaH9 stoichiometry may be the only alkaline earth hydride with an odd H content, and stabilization of this phase may provide some suggestions for future Ca−H experiments under high pressure. We also predicted a metastable phase R3̅m-CaH10, which is isomorphic with R3̅ m-SrH10 with puckered honeycomb H layers. The unusual C2/m-CaH9 stoichiometry and the metastable R3̅m-CaH10 are promising high-Tc superconductors with Tc of approximately 266 and 175 K at 300 and 400 GPa, respectively; these properties are due to the extensive contributions of H atoms to the electronic density of states at the Fermi level.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.8b03165.

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REFERENCES

Structure prediction method details; crystal structural parameters of CaH9 and CaH10; formation enthalpies of CaHn (n = 3−10, 12) with and without zero-point energies at 400 GPa; enthalpy difference of C2/m, P21/ m, and P63/mmc in CaH9 from 200 to 400 GPa; phonon band structure of P63/mmc-CaH9 at 300 GPa; and calculated ELF, COHPs, and ICOHPs of C2/m-CaH9 at 300 GPa and R3̅m-CaH10 at 400 GPa (PDF)

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DOI: 10.1021/acs.inorgchem.8b03165 Inorg. Chem. XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.inorgchem.8b03165 Inorg. Chem. XXXX, XXX, XXX−XXX