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High-Pressure Mg–Sc–H Phase Diagram and Its Superconductivity from First-Principles Calculations

  • Peng Song*
    Peng Song
    School of Information Science, Japan Advanced Institute of Science and Technology, Asahidai 1-1, Nomi, Ishikawa 923-1292, Japan
    *Email: [email protected]
    More by Peng Song
    Orcidhttps://orcid.org/0000-0002-9918-2734
  • , 
  • Zhufeng Hou
    Zhufeng Hou
    State Key Laboratory of Structural Chemistry, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou, 350002, China
    More by Zhufeng Hou
    Orcidhttps://orcid.org/0000-0002-0069-5573
  • , 
  • Pedro Baptista de Castro
    Pedro Baptista de Castro
    National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan
    University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8577, Japan
    More by Pedro Baptista de Castro
  • , 
  • Kousuke Nakano
    Kousuke Nakano
    School of Information Science, Japan Advanced Institute of Science and Technology, Asahidai 1-1, Nomi, Ishikawa 923-1292, Japan
    International School for Advanced Studies (SISSA), Via Bonomea 265, Trieste, 34136, Italy
    More by Kousuke Nakano
    Orcidhttps://orcid.org/0000-0001-7756-4355
  • , 
  • Kenta Hongo
    Kenta Hongo
    Research Center for Advanced Computing Infrastructure, Japan Advanced Institute of Science and Technology, Asahidai 1-1, Nomi, Ishikawa 923-1292, Japan
    More by Kenta Hongo
    Orcidhttps://orcid.org/0000-0002-2580-0907
  • , 
  • Yoshihiko Takano
    Yoshihiko Takano
    National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan
    University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8577, Japan
    More by Yoshihiko Takano
  • , and 
  • Ryo Maezono*
    Ryo Maezono
    School of Information Science, Japan Advanced Institute of Science and Technology, Asahidai 1-1, Nomi, Ishikawa 923-1292, Japan
    *Email: [email protected]
    More by Ryo Maezono
    Orcidhttps://orcid.org/0000-0002-5875-971X
Cite this: J. Phys. Chem. C 2022, 126, 5, 2747–2755
Publication Date (Web):January 26, 2022
https://doi.org/10.1021/acs.jpcc.1c08743

Copyright © 2022 The Authors. Published by American Chemical Society. This publication is licensed under

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Abstract

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In this work, a global search for crystal structures of ternary Mg–Sc–H hydrides (MgxScyHz) under high pressure (100 ≤ P ≤ 200 GPa) was performed using the evolutionary algorithm and first-principles calculations. On their basis, we computed the thermodynamic convex hull and pressure-dependent phase diagram of MgxScyHz for a wide range of compositions (x + y = 2, 3, 4 and z = 2–12, 14, 16, 18). Our crystal structure search and convex hull analysis revealed no thermodynamically stable compounds in the hydrogen-rich range (z/(x + y) ⩾ 4). On the other hand, we identified the crystal structures of four thermodynamically stable compounds in the hydrogen-middle range (3 ≤ z/(x + y) < 4), that is, R3̅m-MgScH6, C2/m-Mg2ScH10, Immm-MgSc2H9, and Pm3̅m-Mg(ScH4)3. Their superconducting transition temperatures were computationally predicted by the McMillan formula combined with first-principles phonon calculations. They were found to exhibit superconductivity; among them, R3̅m-MgScH6 was predicted to have the highest Tc (i.e., 41 K) at 100 GPa.

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1. Introduction

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Hydrogen-rich hydrides of rare earth metals and alkaline earth metals are now recognized to be viable routes to realize room temperature superconductivity under high pressure. (1−4) These hydrides are usually stabilized with the clathrates consisting of H atoms, which could significantly lower the pressure–volume (PV) term of enthalpy and thus preserve the stability at low pressures. (1,5−12) In these structures, the H atoms can substantially contribute to the electronic density of states around the Fermi level and also the phonon density of states. Such a feature enables them to be the potential candidates to exhibit high-temperature superconductivity. For instance, theoretical calculations recently have predicted that YH10 with H32 cage structure might exhibit room-temperature superconductivity (Tc = 286–326 K). (9)
For binary alkaline earth and rare earth hydrides, a systematic search for their crystal structures and superconductivity has been accomplished mostly by theoretical prediction, with the exception of few magnetic rare earth hydrides. (4,13) The binary hydrides potentially with high-temperature superconductivity have attracted great attention for the experimental verification. Previous theoretical simulations have predicted that Tc values of ScH6, ScH7, ScH9, ScH10, ScH12, and MgH6 are in the range of 120–270 K above 250 GPa. (10−12,14−16) With the further increase of H content, the predicted Tc of ScH14, MgH12, MgH16, and MgH22 becomes much lower, and the H components appear mainly in the form of molecular hydrogen. (17,18) These results imply that the hydrogen-content and the corresponding structures formed by hydrogens are essential for determining Tc values. LaH10, CaH6, YH6, BaH12, and CeH9 are examples of the superconducting clathrate structures confirmed in experiments. (7,19−22) The agreement between the theoretical prediction and the experimental discovery in the superconductivity of these binary hydrides has greatly encouraged the theoretical search for metal hydrides in a more extensive range such as the ternary case.
For ternary cases, a very recent experiment on the La–Y–H system has revealed that the synthesized (La,Y)H10 at P = 180 GPa exhibits a Tc of 253 K. (23) More interestingly, the pressure required for (La,Y)H10 to achieve superconductivity is lower than that of the LaH10 high-temperature superconductor, indicating that the ternary hydride has more potential in the search for low-pressure room-temperature superconductivity. (9,19) The stability analysis and superconductivity prediction for a minor portion of ternary metal hydrides, such as La–Y–H, Ca–Y–H, Sc–Ca–H, Sc–Y–H, Y–Mg–H, and Ca–Mg–H, have been accomplished recently by theoretical calculations. (23−29) The majority of the high-temperature (high-Tc) superconducting compounds in the aforementioned systems prefer the cage-like structures. For example, -CaYH12 with cubic structure preserves the clathrate structure consisting of the H24 cages, as does CaH6 and YH6. Meanwhile, -CaYH12, as compared to CaH6 and YH6, can remain stable above 170 GPa with a Tc value of 254 K. (1,5,25) Theoretical calculations further revealed that the strong electron–phonon coupling (EPC) in these clathrate structures of ternary metal hydrides is associated strongly with the phonon mode of the H–H bond in the cage. (25) Furthermore, the characteristics of these materials look very similar, including the atomic radius, electron number (spd valence electrons), electron negativity, atomic mass of constituent elements, and so on. (4) This might prevent the H cage from collapsing and preserve the same cage structure and superconductivity in the ternary hydride with clathrate structure. ScCaH8 and ScCaH12 are two potential high-Tc superconductor compounds in the Sc–Ca–H system. The cage structure is preserved in these two compounds and the corresponding Tc values are around 212 and 182 K at 200 GPa, respectively. (26) The above-mentioned ternary compounds (La–Y–H, Ca–Y–H, Sc–Ca–H, Sc–Y–H, Y–Mg–H, and Ca–Mg–H) can be considered as combinations of different (stable) binary hydrides AHx and BHy (A and B are different metals). As we mentioned before, for instance, MgH2 and ScH2 are known to be stable phases at ambient pressure. (12,30−34) Therefore, MgH2 and ScH2 can be used to chemically synthesize the ternary Mg–Sc–H compounds (if some stable phases exist), instead of using Mg–Sc binary alloys as an intermediate medium in the reaction. This could further reduce the interference in experiment caused by the use of ammonia borane. (19,22,23,35,36) Despite these, the Mg–Sc–H system has yet to be reported not only experimentally, but also theoretically.
Motivated by the aforementioned studies, herein we concentrated our studies on the Mg–Sc–H system to explore the phase diagram and superconductivity of the associated ternary compounds under high pressure. By employing the evolutionary algorithm for crystal structure prediction, we have found the stable structures of MgScH6, Mg2ScH10, MgSc2H9, and Mg(ScH4)3 under high pressure, which are expected to have the highest hydrogen content in the ternary Mg–Sc–H compounds. In the studied pressure range (i.e., 100–200 GPa), no stable compounds beyond the hydrogen content in the aforementioned compounds were discovered in the hydrogen-rich cases of the Mg–Sc–H system, unlike the La–Y–H, Ca–Y–H, and other ternary systems. (23−29) Although some of the stable structures of ternary Mg–Sc–H compounds are predicted to exhibit superconductivity, their superconducting transition temperatures are high up to only 41 K at 100 GPa, owing to the relatively low density of states at their Fermi level and also a relatively weak electron–phonon coupling (EPC).

2. Computational Methods

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We considered the fixed compositions of ternary Mg–Sc–H compounds (MgSc3Hx, MgSc2Hx, MgScHx, Mg2ScHx, and Mg3ScHx, where x = 2–12, 14, 16, and 18) along selected lines in a ternary convex hull at a fixed pressure of 100 and 200 GPa. The crystal-structure search for the Mg–Sc–H systems was performed using the evolutionary algorithm implemented in the Universal Structure Predictor: Evolutionary Xtallography (USPEX) (37) software, together with the first-principles calculations of structural optimization based on density functional theory (DFT). The initial structures are created at random, and the subsequent structures are composed of 40% heredity, 40% random, 10% mutation, and 10% soft mutation.
Our DFT structural optimization and the enthalpies at the considered pressures were carried out using the VASP (Vienna ab initio simulation package) (38−41) code. The electron–ion interaction is described by the projector augmented wave (PAW) (42,43) method. The cutoff energy for the plane-wave basis sets was set to 600 eV. The exchange-correlation functional was treated by the Perdew–Burke–Ernzerhof (PBE) implementation (44) within the generalized gradient approximation (GGA). All structural models were drawn by using VESTA. (45)
The ternary convex hulls of MgxScyHz were constructed by calculating their formation enthalpies with respect to the enthalpies of Mg, Sc, and H single phases as defined below: (46−48)
(1)
where is the enthalpy per formula unit (f.u.) of the Mg–Sc–H compound; , , and are the reference enthalpies of Mg, Sc, and H single phases, respectively. The thermodynamic stability of the predicted phase was determined by comparing the formation enthalpies with respect to the convex hull energy:
(2)
where is a convex hull energy obtained by constraining the minimum value of the total enthalpies of a linear combination of stable phases, (49) which can be computed using the ConvexHull module in scipy. (50)Eabove_hull is energy above the convex hull. Eabove_hull = 0 means that the corresponding ternary phase is stable, namely, such a phase would not decompose into any combination of elementary, binary, or other ternary phases. The stabilities of the predicted phases at a finite temperature can be checked using the similar approach as mentioned above, and their computational details are given in the Supporting Information (SI).
The EPC and phonons of the stable ternary Mg–Sc–H phases were predicted using the QUANTUM ESPRESSO (QE) suite of programs (51−53) with the PAW method and the Perdew–Burke–Ernzerhof (PBE) (44) exchange-correlation functional. The cutoff energy for plane-wave basis sets in the QE calculations was set to 80 Ry. The q-point mesh (k-point mesh for integral of the EPC constant and Tc) in the Brillouin zone was set as follows: 4 × 4 × 4 (16 × 16 × 16) for MgScH6, 5 × 5 × 2 (20 × 20 × 8) for Mg2ScH10, 3 × 4 × 4 (12 × 16 × 16) for MgSc2H9, and 5 × 5 × 5 (20 × 20 × 20) for Mg(ScH4)3, respectively. The McMillan formula (54) and the Eliashberg function derived from the EPC calculation were used to predict the superconducting critical temperature.

3. Results and Discussion

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3.1. First-Principles Phase Diagram of the Mg–Sc–H System

To determine the ternary phase diagram of the Mg–Sc–H system under high pressure, we have taken the Mg–H and Sc–H binary systems (1,10−12,18) as well as the simple substances of constituent elements (Mg, Sc, and H) (46−48) as references in the estimation of thermodynamic stability. It is worth noting that the superconducting structures of the Mg–H and Sc–H binary hydride systems have been discovered recently. For instance, MgH6 and ScH7 were predicted to exhibit the highest Tc values of around 260 and 169 K in the Mg–H and Sc–H binary systems, respectively. (1,10−12,18) However, the pressure to stabilize these two superconducting compounds is greater than 300 GPa for both, which is far beyond the mostly focused high-pressure range (i.e., around 200 GPa) of the widely studied metal hydrides in the literature. (1,5,25,55)
To explore the most likely composition for the succeeding experimental synthesis, herein we have sampled a wide phase space of the ternary Mg–Sc–H system at fixed pressures (i.e., 100, 150, and 200 GPa). The ternary phase diagram of the Mg–Sc–H system at 200 GPa is shown in Figure 1, while the results for the pressure at 100 and 150 GPa and the associated formation energies are given in the Supporting Information. Since most high-pressure studies are carried out under laser heating (1000–2000 K), some metastable phases at 0 K can be stabilized at higher temperatures. (23,56) Therefore, we calculated the ternary phase diagram of the Mg–Sc–H system at 200 GPa mainly in three different cases: (i) formation enthalpy without considering the zero point energy (ZPE), (ii) formation enthalpy with the contribution of ZPE and without the contribution of entropy, and (iii) Gibbs free energy with the corresponding entropy contribution at 1000 K.

Figure 1

Figure 1. (a) Ternary convex hulls of the Mg–Sc–H system at a pressure of 200 GPa; (b,c) convex hulls of Gibbs free energy at 0 K and at finite temperature (1000 K), respectively. The stable and metastable phases are shown by circles and diamond, respectively.

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Looking at Figure 1, the stable compounds in the ternary convex hull of Mg–Sc–H system without ZPE at 200 GPa were found to be Pm3̅m-Mg3ScH3, Pm3̅m-Mg3ScH4, C2/m-Mg2ScH10, I41/amd-MgScH2, P63/mmc-MgScH3, -MgScH4, R3̅m-MgScH6, Immm-MgSc2H3, R3̅m-Mg(ScH2)2, P63/mmc-Mg(ScH2)3, Immm-MgSc2H9, and Pm3̅m-Mg(ScH4)3. It is to be noted that the incorporation of the ZPE contribution leads to the transition of ScH4 from a metastable state to a stable one, which is consistent with the results reported by Ye et al. (12) for the binary Sc–H system. In contrast to the Sc–H binary cases, the ternary hydrides, Pm3̅m-Mg3ScH4, P63/mmc-MgScH3, R3̅m-MgScH6, and R3̅m-Mg(ScH2)2 undergo a change from a stable state to a metastable state because of their large ZPE contributions. The four ternary compounds are located on the convex hull planes, with energy differences of 0.003, 0.032, 0.008, and 0.015 eV/atom, respectively. Furthermore, we noticed that at a high temperature of 1000 K, R3̅m-Mg(ScH2)2 can shift from a metastable state to a stable one due to the entropy contribution of lattice vibration. In the binary Mg–H and Sc–H systems, Cmcm-MgH4 and Cmcm-ScH6 are stable compounds with the greatest H content in the pressure range of 100–200 GPa. (11,12) Despite the fact that most of the existing high-Tc superconducting hydrides are hydrogen-rich compounds, no stable compounds in the extremely hydrogen-rich case have been identified in the pressure range of 100–200 GPa in our search.
We focus on the stabilities of three ternary compounds, R3̅m-MgScH6, Immm-MgSc2H9, and Pm3̅m-Mg(ScH4)3. To better understand their stabilities, we compare them with reference binary compounds, ScH3, MgH2, and MgH4. Figure 2 shows their binary convex hulls. Note that only a few high-Tc ternary compounds such as (La,Y)H6 and (La,Y)H10 have been successfully realized by chemical synthesis so far. (23,24) Their synthesis conditions are that La–Y alloy and NH3BH3 are mixed under high pressure and then heated to over 2000 K by laser. (23) For the Sc–H and Mg–H systems, the high-pressure experiments clearly showed that only ScH3 and MgH2 exist stably, (57−61) which have been extensively studied by previous theoretical simulations as well. (10−12,14−16) For the chemical synthesis of ScH3, the mixture of Sc and NH3BH3 was used as precursor and then heated by laser under high pressure so that ScH3 can be stabilized. According to the binary diagram shown in Figure 2, R3̅m-MgScH6, Immm-MgSc2H9, and Pm3̅m-Mg(ScH4)3 can be stabilized at 100 GPa regardless of ambient temperature or high temperature. Therefore, following the similar approach used for (La,Y)H6 and (La,Y)H10, it is expected that these three ternary Mg–Sc–H compounds can be realized via chemical synthesis using the Mg–Sc alloy mixed with NH3BH3 at high temperature and high pressure.

Figure 2

Figure 2. Enthalpy per atom of (MgH2 + MgH4)x as a function of x at the pressure of 100, 150, and 200 GPa, where x is defined as . The stable phase and the metastable phase are connected by solid and dashed lines, respectively.

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On the basis of the calculated formation of enthalpy without taking into account the ZPE contribution, Figure 3 summarizes the pressure-dependent phase stability of the Mg–Sc–H system. In particular, several phases including Pm3̅m-Mg(ScH4)3, Immm-MgSc2H10, -MgScH4, and P63/mmc-MgScH3 can be stable in a wide pressure range from 100 to 200 GPa. It is remarkable that the Mg-rich ternary Mg–Sc–H phases tend to be stable in the pressure range toward 200 GPa, while the Sc-rich ones except R3̅m-Mg(ScH2)2 can also be stabilized at the pressure of 100 GPa. P63/mmc-Mg(ScH2)2 can be stable only in the lower pressure range of 100–130 GPa. This trend might be attributed to the pressure range of stable Mg–H and Sc–H binary hydride systems. At the low pressure, the number of possible stable compounds in the Sc–H system are more than that of the Mg–H system. (11,12)

Figure 3

Figure 3. Phase diagram of Mg–Sc–H in the pressure range of 100–200 GPa.

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3.2. Predicted Superconductivity of the Mg–Sc–H System

Previous studies on the alkali metals and alkaline earth hydrides have shown that the superconducting properties of these hydrides are strongly dependent on the hydrogen content and that the higher Tc is more likely to appear in the hydrogen-rich cases. (1,4) Herein we pay more attention to R3̅m-MgScH6, C2/m-Mg2ScH10, Immm-MgSc2H9, and Pm3̅m-Mg(ScH4)3) for their electronic structures and superconductivity because they contain very high hydrogen content.
The crystal structures and the electron localization function (ELF) of these aforementioned four compounds are shown in Figure 4. R3̅m-MgScH6 is stable above 100 GPa and has a hexagonal crystal structure, in which each Mg and Sc atom is surrounded by 14 H atoms. The shortest H–H bond length in this structure is about 1.587 Å, and the corresponding ELF value at the H–H bond center is about 0.4, indicating a nearly metallic character. The ultrashort distance between atoms translates to a significant ELF value of around 0.7, indicating that the H–H bond in C2/m-Mg2ScH10 exhibits a strong covalent character. In Immm-MgSc2H9 and Pm3̅m-Mg(ScH4)3, the shortest H–H bond lengths are 1.628 and 1.650 Å, respectively; the corresponding ELF values at the H–H bond center are 0.3 and 0.1. However, the H lattice sites exhibit much greater ELF values. Therefore, the chemical bonding in Immm-MgSc2H9 and Pm3̅m-Mg(ScH4)3 can be regarded as being mostly ionic interaction. Furthermore, Pm3̅m-Mg(ScH4)3 can still form a clathrate structure, in which each Mg and Sc atom is surrounded by the H14 cages. This structure can be regarded as a structure formed when replacing the central Sc in Fm3̅m-ScH3 with Mg. We should point out that the Fm3̅m-ScH3 binary does not exhibit superconductivity, as reported previously by Ye et al. (12) Therefore, the partial substitution of Sc in Fm3̅m-ScH3 by Mg triggers the superconductivity in Pm3̅m-Mg(ScH4)3.

Figure 4

Figure 4. Predicted crystal structures of (a) R3̅m-MgScH6, (b) C2/m-Mg2ScH10, (c) Immm-MgSc2H9, (d) Pm3̅m-MgSc3H12 at 200 GPa. Bottom panels show the corresponding contour plots of electron localization function (ELF) in these structures.

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Figure 5 shows the calculated electronic energy band structure and atom-projected electronic density of states (eDOS) of the aforementioned four structures of great interest. All of them at 200 GPa exhibit metallic features. Among these four structures, R3̅m-MgScH6 has the most robust density of states at the Fermi level (EF), while Pm3̅m-MgSc3H12 has the least density of states at EF. The dominant contributions to the density of states at EF come from the Sc and H atoms, while the contribution from Mg atoms is negligible. The valence bands in all of these four structures are mainly ascribed to the strong hybridization between the Sc and H atoms. At the EF of R3̅m-MgScH6, there are doubly degenerated flat bands along the Γ → Z direction (i.e., parallel to the c axis of the hexagonal unit cell of R3̅m-MgScH6). Such a flat band would aid in enhancing the electron–phonon interaction, (62) thereby leading to the highest Tc of R3̅m-MgScH6 among these four structures.

Figure 5

Figure 5. Electronic band structures and atom-projected electronic density of states of (a) R3̅m-MgScH6, (b) C2/m-Mg2ScH10, (c) Immm-MgSc2H9, (d) Pm3̅m-MgSc3H12 at 200 GPa.

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Figure 6 demonstrates the phonon band structure, atom-decomposed phonon density of states (pDOS), and Eliashberg spectra of R3̅m-MgScH6, C2/m-Mg2ScH10, Immm-MgSc2H9, and Pm3̅m-Mg(ScH4)3 at 200 GPa. At first, we can see no imaginary modes appearing in all of these four structures, and hence their structures are dynamically stable. In addition, their phonons can be clearly grouped into three frequency regions. The low frequency region (i.e., below 20 THz) is dominantly ascribed to the vibration of Mg and Sc atoms because of their heavier atomic masses. The middle frequency region (i.e., centered around 40 THz) and the high frequency region (i.e., above 50 THz) are exclusively due to the vibration of the H atom.

Figure 6

Figure 6. Phonon dispersion and atom-projected phonon density of states (pDOS), and Eliashberg spectral of (a) R3̅m-MgScH6, (b) C2/m-Mg2ScH10, (c) Immm-MgSc2H9, (d) Pm3̅m-MgSc3H12 at 200 GPa.

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Table 1 lists computed Tc values and their related properties at 200 GPa. The estimated EPC constants (λ) of these four structures follow the ordering of R3̅m-MgScH6 > C2/m-Mg2ScH10 > Immm-MgSc2H9 > Pm3̅m-Mg(ScH4)3. Their Tc values exhibit the same ordering. R3̅m-MgScH6 is found to have the highest Tc (i.e., 23.3 K) among these four structures at 200 GPa. However, this superconducting temperature is much lower than the reported other metal hydrides with high hydrogen content such as LaH10 and YH10. (1,4) In general, the superconducting Tc is determined by the electron–phonon interaction. Although these four ternary Mg–Sc–H compounds possess similar logarithmic phonon average ωlog, which are also similar to those of LaH10 and YH10, they have much different EPC constants. As shown in Figure S3a, the total DOS at the Fermi level (Nt(EF)) of LaH10 and YH10 is higher than those of the above-mentioned four Mg–Sc–H compounds. More specifically, the main difference comes from the contributions of H atoms to Nt(EF), as shown in Figure S3b. According to the BCS theory, (63) the value of superconducting Tc shows a positive correlation with Nt(EF). Therefore, the contribution of H atoms to Nt(EF) of the above four compounds is too low to achieve high-Tc superconductivity.
Table 1. Tc Estimated by McMillan Formula Using First-Principles Phonon Calculations for Mg–Sc–H at Each Pressure. λ and ωlog Are the Parameters Appearing in the Formula
phasespace groupP (GPa)λωlog (K)NEF (states/eV/Å3)Tc (K) at μ = 0.1 – 0.13
MgScH6R3̅m2000.5361478.840.015 023.34–15.08
Mg2ScH10C2/m2000.5121350.170.012 517.94–11.10
MgSc2H9Immm2000.4101427.390.012 06.88–3.14
Mg(ScH4)3Pm3̅m2000.3531377.730.010 22.61–0.83
It is to be noted that YH3 and Fm3̅m-ScH3 have the same hydrogen content per metal atom with R3̅m-MgScH6, Immm-MgSc2H9, and Pm3̅m-Mg(ScH4)3. However, YH3 has a strong EPC constant of 1.6 and a Tc value of around 40 K. (64) In contrast, the EPC constant of Fm3̅m-ScH3 is about 0.23 and it hardly leads to the superconductivity. (12) The EPC constants of aforementioned four structures of Mg–Sc–H are in the range from 0.35 to 0.54, and thus their Tc values are lower than that of YH3.
In Figure 7 we present the pressure dependence of the superconducting Tc and the associated properties for R3̅m-MgScH6, C2/m-Mg2ScH10, Immm-MgSc2H9, and Pm3̅m-Mg(ScH4)3. It is clear to see that their Tc values monotonically decrease with the increase of pressure. However, the behavior of the pressure-dependence of the ωlog and λ is completely opposite to that of the Tc. As shown in Figures S4 and S5, the Nt(EF) of all four compounds decreases with the increase of pressure. The variation of the partial DOS of Mg and Sc atoms at Fermi level with respect to the pressure exhibit an opposite tendency to that of H atoms. The dominant contribution to Nt(EF) comes from H atoms, resulting in a negative pressure-dependence of the Nt(EF). Accordingly the similar trends are observed for the pressure dependence of Tc and λ for these four compounds. The phonon and EPC spectra of these four compounds at different pressures are shown in Figures S6, S7, S8, and S9. It is noticed that the λ values of the four compounds, either for the phonon frequencies of above 20 THz (dominant contribution from H atoms) or below 20 THz (dominant contribution from Mg and Sc atoms), decrease with the increase of pressure. The drop of the λ for the phonon frequencies of above 20 THz with respect to the increase of pressure is more significant than the one for the phonon frequencies of below 20 THz. In the Eliashberg spectral function, the superconducting Tc exhibits a positive correlation with both ωlog and λ. Overall, the EPC constants (λ) of R3̅m-MgScH6, C2/m-Mg2ScH10, Immm-MgSc2H9, and Pm3̅m-Mg(ScH4)3 decrease as the pressure increases and thus their Tc also decrease.

Figure 7

Figure 7. Pressure-dependent superconductivity of R3̅m-MgScH6, C2/m-Mg2ScH10, Immm-MgSc2H9, Pm3̅m-MgSc3H12. (a) Tc from the McM equation, (b) EPC constant λ, (c) logarithmic phonon average ωlog and (d)the total DOS at the Fermi level .

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Finally, we should point out that the predicted Tc value of R3̅m-MgScH6 at 100 GPa is 41 K, which is slightly higher than the McMillan limit (39 K). (54) The predicted Tc value of MgH4, which has a greater content ratio of hydrogen over metal as compared to R3̅m-MgScH6, can reach only 38 K at the same pressure (i.e., 100 GPa). (18) The EPC constant of R3̅m-MgScH6 is somewhat lower than that of MgH4, although its ωlog (1204 K) is similar to those of LaH10 and YH10. The previous calculations suggest that the Tc for ScH3 might be quite low; (12) however, the recent high-pressure experiment has revealed a Tc of roughly 20 K in the pressure range of 130–160 GPa. (59) In the present study we theoretically demonstrate that R3̅m-MgScH6 is a stable compound at 100 GPa at both room temperature and high temperature, and that the predicted Tc of R3̅m-MgScH6 is higher than those of the parent compounds (i.e., ScH3, MgH2, and MgH4). This can be a very promising candidate for high-pressure experiments of superconducting metal hydrides.

4. Conclusion

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In summary, we have employed the evolutionary algorithm in the USPEX code and the first-principles calculations to explore the ternary phase diagram of the Mg–Sc–H system under pressure from 100 to 200 GPa. Our calculations show that the Sc-rich ternary Mg–Sc–H compounds are favorable to be stable around 100 GPa, while the Mg-rich ones are more likely to stable above 180 GPa. The ternary Mg–Sc–H hydrides with the hydrogen/metal ratio around three have been predicted to exhibit superconductivity. In particular, the superconducting transition temperature of R3̅m-MgScH6 is around 41 K at 100 GPa. Although the superconducting transition temperature of Pm3̅m-Mg(ScH4)3 is relatively low, it can be stable in the low range of high pressure toward 100 GPa. Our results provide useful information for the discovery of new low-pressure superconducting hydrides.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpcc.1c08743.

  • Computational details of Gibbs free energy at finite temperature and the superconducting Tc; ternary convex hulls of Mg–Sc–H systems at 100 and 150 GPa; total electronic density of states (DOS) and the partial DOS of H atoms of some representative Mg–Sc–H compounds under high pressure; pressure-dependent phonons and electron–phonon coupling spectra for MgScH6, Mg2ScH10, MgSc2H9, and Mg(ScH4)3; Gibbs free energy (including the enthalpy, zero-point energy (ZPE) correction, and other associated terms) of the main stable and metastable phases in the Mg–Sc–H system at 100, 150, and 200 GPa; structural information of newly predicted structures of ternary Mg–Sc–H compounds (PDF)

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Author Information

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  • Corresponding Authors
  • Authors
    • Zhufeng Hou - State Key Laboratory of Structural Chemistry, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou, 350002, China;  Orcidhttps://orcid.org/0000-0002-0069-5573
    • Pedro Baptista de Castro - National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan;  University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8577, Japan
    • Kousuke Nakano - School of Information Science, Japan Advanced Institute of Science and Technology, Asahidai 1-1, Nomi, Ishikawa 923-1292, Japan;  International School for Advanced Studies (SISSA), Via Bonomea 265, Trieste, 34136, Italy;  Orcidhttps://orcid.org/0000-0001-7756-4355
    • Kenta Hongo - Research Center for Advanced Computing Infrastructure, Japan Advanced Institute of Science and Technology, Asahidai 1-1, Nomi, Ishikawa 923-1292, Japan;  Orcidhttps://orcid.org/0000-0002-2580-0907
    • Yoshihiko Takano - National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan;  University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8577, Japan
  • Notes
    The authors declare no competing financial interest.

Acknowledgments

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The computations in this work have been performed using the facilities of Research Center for Advanced Computing Infrastructure (RCACI) at JAIST. K.H. is grateful for financial support from the HPCI System Research Project (Project ID: hp190169) and MEXT-KAKENHI (JP16H06439, JP17K17762, JP19K05029, and JP19H05169) and the Air Force Office of Scientific Research (Award Nos: FA2386-20-1-4036). R.M. is grateful for financial support from MEXT-KAKENHI (19H04692 and 16KK0097), FLAGSHIP2020 (Project Nos. hp190169 and hp190167 at K-computer), Toyota Motor Corporation, I–O DATA Foundation, the Air Force Office of Scientific Research (AFOSR-AOARD/FA2386-17-1-4049;FA2386-19-1-4015), and JSPS Bilateral Joint Projects (with India DST).

References

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    Ye, Xiaoqiu; Hoffmann, Roald; Ashcroft, N. W.
    Journal of Physical Chemistry C (2015), 119 (10), 5614-5625CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
    The authors report theor. calcns. of the static ground-state structures and pressure-induced phase transformations of three scandium hydrides: ScH, ScH2, and ScH3. For the monohydride, ScH, we predict several phases to be more stable at 1 atm than the previously suggested rock-salt structure, in particular one of P42/mmc symmetry. The NaCl-type structure for ScH takes over at 10 GPa and dominates over a wide pressure range until it is replaced by a Cmcm structure around 265 GPa. Under pressure, the exptl. P = 1 atm CaF2-type structure of ScH2 should transform to a C2/m structure around 65 GPa, which then is likely to disproportionate to NaCl-type ScH and face-centered cubic ScH3 above 72 GPa. According to theory, as the pressure is elevated, ScH3 moves through the following sequence of phases: P63 → Fm‾3m → P63/mmc(YH3-type) → Cmcm; the corresponding transition pressures are calcd. to be 29, 360, and 483 GPa, resp. The predicted disproportionation tendencies of ScH2 are fascinating: stable to decompn. to ScH and ScH3 at low pressures, it should begin to disproportionate near 72 GPa. However, the process is predicted to reverse at still higher pressures (above 300 GPa). They also find ScH to be stable to disproportionation to Sc and ScH2 above ∼25 GPa. The three hydrides are metallic, except for (at low pressures) ScH3.
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  15. 15
    Abe, K. Hydrogen-rich scandium compounds at high pressures. Phys. Rev. B 2017, 96, 144108,  DOI: 10.1103/PhysRevB.96.144108
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    15
    Hydrogen-rich scandium compounds at high pressures
    Abe, Kazutaka
    Physical Review B (2017), 96 (14), 144108/1-144108/7CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)
    Scandium hydrides at high pressures have been investigated by using ab initio d. functional calcns. Although the stable scandium hydride so far known to have the highest content rate of hydrogen is ScH3, other more hydrogen-rich compds. are found to be possible at high pressures. These are ScH4 in the I4/mmm structure above 160 GPa, ScH6 in the P63/mmc structure from 135 to 265 GPa, and ScH6 in the Im3m structure above 265 GPa. The three phases are all metallic, and the superconducting transition temps. estd. from the extended McMillan equation are 67 K in the I4/mmm ScH4 at 195 GPa, 63 K in the P63/mmc ScH6 at 145 GPa, and 130 K in the Im3m ScH6 at 285 GPa. While the I4/mmm tetrahydride and the Im3m hexahydride were similarly predicted for yttrium (another group-3 element), the P63/mmc hexahydride is possible only for scandium. The smaller at. size of scandium stabilizes the P63/mmc structure, and other nearby d-block elements, whose at. sizes are smaller or comparable, might be likewise capable of forming such polyhydrides.
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  16. 16
    Wei, Y.-K.; Yuan, J.-N.; Khan, F. I.; Ji, G.-F.; Gu, Z.-W.; Wei, D.-Q. Pressure induced superconductivity and electronic structure properties of scandium hydrides using first principles calculations. RSC Adv. 2016, 6, 81534– 81541,  DOI: 10.1039/C6RA11862C
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    16
    Pressure induced superconductivity and electronic structure properties of scandium hydrides using first principles calculations
    Wei, Yong-Kai; Yuan, Jiao-Nan; Khan, Faez Iqbal; Ji, Guang-Fu; Gu, Zhuo-Wei; Wei, Dong-Qing
    RSC Advances (2016), 6 (85), 81534-81541CODEN: RSCACL; ISSN:2046-2069. (Royal Society of Chemistry)
    The electronic, vibrational and superconducting properties of scandium hydrides (ScH2 and ScH3) under pressure were studied using first-principles calcns. The results indicate that ScH2 and ScH3 are dynamically stable in the pressure ranges of 0-85 GPa and 46-80 GPa, resp. The superconducting properties of ScH2 and ScH3 were investigated by employing BCS (BCS) theory, and this shows that the superconducting temp. of ScH2 initially increases exponentially and then reaches a max. value of about 38.11 K at 30 GPa, while it remains const. under further compression. However, the superconducting behavior of ScH3 is not obvious under low pressure (P < 46 GPa), and it almost disappears under higher pressure, in agreement with exptl. observations. Anal. of the energy band structures demonstrates that the distinct superconducting behaviors of ScH2 and ScH3 are related to the hybridization between the s-state of the H atom and the d-state of the Sc atom. The superconducting behavior of ScH2 follows the variation of the hybridization between the HO-s state and Sc-d state, while for ScH3, it is found that there is no d. of states obsd. for HT or HO when the pressure is above 46 GPa. Anal. of the electronic structure of ScH2 was also performed to allow for further comprehension of the metallic behavior of ScH2 under pressure. This work may offer help to understand the mechanism of pressure-induced supercond. in metal-hydride systems.
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  17. 17
    Shipley, A. M.; Hutcheon, M. J.; Needs, R. J.; Pickard, C. J. High-throughput discovery of high-temperature conventional superconductors. arXiv (Condensed Matter, Superconductivity) 2105.02296, ver. 3, May 5, 2021, https://arxiv.org/abs/2105.02296.
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    Lonie, D. C.; Hooper, J.; Altintas, B.; Zurek, E. Metallization of magnesium polyhydrides under pressure. Phys. Rev. B 2013, 87, 054107,  DOI: 10.1103/PhysRevB.87.054107
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    18
    Metallization of magnesium polyhydrides under pressure
    Lonie, David C.; Hooper, James; Altintas, Bahadir; Zurek, Eva
    Physical Review B: Condensed Matter and Materials Physics (2013), 87 (5), 054107/1-054107/8CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
    Evolutionary structure searches are used to predict stable phases with unique stoichiometries in the hydrogen-rich region of the magnesium/hydrogen phase diagram under pressure. MgH4, MgH12, and MgH16 are found to be thermodynamically stable with respect to decompn. into MgH2 and H2 near 100 GPa, and all lie on the convex hull by 200 GPa. MgH4 contains two H- anions and one H2 mol. per Mg2+ cation, whereas the hydrogenic sublattices of MgH12 and MgH16 are composed solely of Hδ-2 mols. The high-hydrogen content stoichiometries have a large d. of states at the Fermi level, and the Tc of MgH12 at 140 GPa is calcd. to be nearly three times greater than that of the classic hydride, MgH2, at 180 GPa.
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  19. 19
    Drozdov, A. P.; Kong, P. P.; Minkov, V. S.; Besedin, S. P.; Kuzovnikov, M. A.; Mozaffari, S.; Balicas, L.; Balakirev, F. F.; Graf, D. E.; Prakapenka, V. B. Superconductivity at 250 K in lanthanum hydride under high pressures. Nature 2019, 569, 528– 531,  DOI: 10.1038/s41586-019-1201-8
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    19
    Superconductivity at 250 K in lanthanum hydride under high pressures
    Drozdov, A. P.; Kong, P. P.; Minkov, V. S.; Besedin, S. P.; Kuzovnikov, M. A.; Mozaffari, S.; Balicas, L.; Balakirev, F. F.; Graf, D. E.; Prakapenka, V. B.; Greenberg, E.; Knyazev, D. A.; Tkacz, M.; Eremets, M. I.
    Nature (London, United Kingdom) (2019), 569 (7757), 528-531CODEN: NATUAS; ISSN:0028-0836. (Nature Research)
    With the discovery1 of supercond. at 203 K in H3S, attention returned to conventional superconductors with properties that can be described by the BCS and the Migdal-Eliashberg theories. Although these theories predict the possibility of room-temp. supercond. in metals that have certain favorable properties-such as lattice vibrations at high frequencies-they are not sufficient to guide the design or predict the properties of new superconducting materials. First-principles calcns. based on d. functional theory have enabled such predictions, and have suggested a new family of superconducting hydrides that possess a clathrate-like structure in which the host atom (calcium, yttrium, lanthanum) is at the center of a cage formed by hydrogen atoms2-4. For LaH10 and YH10, the onset of supercond. is predicted to occur at crit. temps. between 240 and 320 K at megabar pressures3-6. Here we report supercond. with a crit. temp. of around 250 K within the Fm‾3m structure of LaH10 at a pressure of about 170 gigapascals. This is, to our knowledge, the highest crit. temp. that has been confirmed so far in a superconducting material. Supercond. was evidenced by the observation of zero resistance, an isotope effect, and a decrease in crit. temp. under an external magnetic field, which suggested an upper crit. magnetic field of about 136 T at zero temp. The increase of around 50 K compared with the previous highest crit. temp.1 is an encouraging step towards the goal of achieving room-temp. supercond. in the near future.
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  20. 20
    Troyan, I. A.; Semenok, D. V.; Kvashnin, A. G.; Sadakov, A. V.; Sobolevskiy, O. A.; Pudalov, V. M.; Ivanova, A. G.; Prakapenka, V. B.; Greenberg, E.; Gavriliuk, A. G. Anomalous High-Temperature Superconductivity in YH6. Adv. Mater. 2021, 33, 2006832,  DOI: 10.1002/adma.202006832
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    20
    Anomalous High-Temperature Superconductivity in YH6
    Troyan, Ivan A.; Semenok, Dmitrii V.; Kvashnin, Alexander G.; Sadakov, Andrey V.; Sobolevskiy, Oleg A.; Pudalov, Vladimir M.; Ivanova, Anna G.; Prakapenka, Vitali B.; Greenberg, Eran; Gavriliuk, Alexander G.; Lyubutin, Igor S.; Struzhkin, Viktor V.; Bergara, Aitor; Errea, Ion; Bianco, Raffaello; Calandra, Matteo; Mauri, Francesco; Monacelli, Lorenzo; Akashi, Ryosuke; Oganov, Artem R.
    Advanced Materials (Weinheim, Germany) (2021), 33 (15), 2006832CODEN: ADVMEW; ISSN:0935-9648. (Wiley-VCH Verlag GmbH & Co. KGaA)
    Pressure-stabilized hydrides are a new rapidly growing class of high-temp. superconductors, which is believed to be described within the conventional phonon-mediated mechanism of coupling. Here, the synthesis of one of the best-known high-TC superconductors-yttrium hexahydride Im3m-YH6 is reported, which displays a superconducting transition at ≈224 K at 166 GPa. The extrapolated upper crit. magnetic field Bc2(0) of YH6 is surprisingly high: 116-158 T, which is 2-2.5 times larger than the calcd. value. A pronounced shift of TC in yttrium deuteride YD6 with the isotope coeff. 0.4 supports the phonon-assisted supercond. Current-voltage measurements show that the crit. current IC and its d. JC may exceed 1.75 A and 3500 A mm-2 at 4 K, resp., which is higher than that of the com. superconductors, such as NbTi and YBCO. The results of superconducting d. functional theory (SCDFT) and anharmonic calcns., together with anomalously high crit. magnetic field, suggest notable departures of the superconducting properties from the conventional Migdal-Eliashberg and BCS theories, and presence of an addnl. mechanism of supercond.
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  21. 21
    Ma, L.; Wang, K.; Xie, Y.; Yang, X.; Wang, Y.; Zhou, M.; Liu, H.; Liu, G.; Wang, H.; Ma, Y. Experimental observation of superconductivity at 215 K in calcium superhydride under high pressures. arXiv (Condensed Matter, Superconductivity) 2103.16282 ver. 3, March 30, 2021, https://arxiv.org/abs/2103.16282.
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    Salke, N. P.; Esfahani, M. M. D.; Zhang, Y.; Kruglov, I. A.; Zhou, J.; Wang, Y.; Greenberg, E.; Prakapenka, V. B.; Liu, J.; Oganov, A. R. Synthesis of clathrate cerium superhydride CeH9 at 80–100 GPa with atomic hydrogen sublattice. Nat. Commun. 2019, 10, 1– 10,  DOI: 10.1038/s41467-019-12326-y
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    22
    Synthesis of clathrate cerium superhydride CeH9 at 80-100 GPa with atomic hydrogen sublattice
    Salke, Nilesh P.; Davari Esfahani, M. Mahdi; Zhang, Youjun; Kruglov, Ivan A.; Zhou, Jianshi; Wang, Yaguo; Greenberg, Eran; Prakapenka, Vitali B.; Liu, Jin; Oganov, Artem R.; Lin, Jung-Fu
    Nature Communications (2019), 10 (1), 1-10CODEN: NCAOBW; ISSN:2041-1723. (Nature Research)
    Hydrogen-rich superhydrides are believed to be very promising high-Tc superconductors. Recent expts. discovered superhydrides at very high pressures, e.g. FeH5 at 130 GPa and LaH10 at 170 GPa. With the motivation of discovering new hydrogen-rich high-Tc superconductors at lowest possible pressure, here we report the prediction and exptl. synthesis of cerium superhydride CeH9 at 80-100 GPa in the laser-heated diamond anvil cell coupled with synchrotron X-ray diffraction. Ab initio calcns. were carried out to evaluate the detailed chem. of the Ce-H system and to understand the structure, stability and supercond. of CeH9. CeH9 crystallizes in a P63/mmc clathrate structure with a very dense 3-dimensional at. hydrogen sublattice at 100 GPa. These findings shed a significant light on the search for superhydrides in close similarity with at. hydrogen within a feasible pressure range. Discovery of superhydride CeH9 provides a practical platform to further investigate and understand conventional supercond. in hydrogen rich superhydrides.
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  23. 23
    Semenok, D. V.; Troyan, I. A.; Ivanova, A. G.; Kvashnin, A. G.; Kruglov, I. A.; Hanfland, M.; Sadakov, A. V.; Sobolevskiy, O. A.; Pervakov, K. S.; Lyubutin, I. S. Superconductivity at 253 K in lanthanum–yttrium ternary hydrides. Mater. Today 2021, 48, 1369– 7021,  DOI: 10.1016/j.mattod.2021.03.025
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    Song, P.; Hou, Z.; de Castro, P. B.; Nakano, K.; Hongo, K.; Takano, Y.; Maezono, R. High-Tc Superconducting Hydrides Formed by LaH24 and YH24 Cage Structures as Basic Blocks. Chem. Mater. 2021, 33, 9501– 9507,  DOI: 10.1021/acs.chemmater.1c02371
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    24
    High-Tc superconducting hydrides formed by LaH24 and YH24 cage structures as basic blocks
    Song, Peng; Hou, Zhufeng; Castro, Pedro Baptista de; Nakano, Kousuke; Hongo, Kenta; Takano, Yoshihiko; Maezono, Ryo
    Chemistry of Materials (2021), 33 (24), 9501-9507CODEN: CMATEX; ISSN:0897-4756. (American Chemical Society)
    Based on recent studies regarding high-temp. (high-Tc) La-Y ternary hydrides (e.g., P‾1-La2YH12, Pm‾3m-LaYH12, and Pm‾3m-(La,Y)H10 with a max. Tc ∼253 K), we examd. the phase and structural stabilities of the (LaH6)(YH6)y series as high-Tc ternary hydride compns. using a genetic algorithm and ab initio calcns. Our evaluation showed that Pm‾3m-LaYH12 reported in the previous study was unstable during decompn. into R‾3c-LaH6 + Im‾3m-YH6. We also discovered new crystal structures, namely, Cmmm-LaYH12 (y = 1), R‾3c-LaYH12 (y = 1), Cmmm-LaY3H24 (y = 3), and R‾3-LaY3H24 (y = 3), showing stability against such decompn. While R‾3c (y = 1) and R‾3 (y = 3) did not exhibit supercond. owing to the extremely low d. of states at the Fermi level, Cmmm phases exhibited a Tc of approx. 140 K at around 200 GPa owing to the extremely high electron-phonon coupling const. (λ = 1.876 for LaYH12). By the twice longer stacking for Cmmm-LaY3H24, the coupling const. increased owing to the chem. pressure of Y, leading to a slightly increased Tc.
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    Liang, X.; Bergara, A.; Wang, L.; Wen, B.; Zhao, Z.; Zhou, X.-F.; He, J.; Gao, G.; Tian, Y. Potential high-Tc superconductivity in CaYH12 under pressure. Phys. Rev. B 2019, 99, 100505,  DOI: 10.1103/PhysRevB.99.100505
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    25
    Potential high-Tc superconductivity in CaYH12 under pressure
    Liang, Xiaowei; Bergara, Aitor; Wang, Linyan; Wen, Bin; Zhao, Zhisheng; Zhou, Xiang-Feng; He, Julong; Gao, Guoying; Tian, Yongjun
    Physical Review B (2019), 99 (10), 100505CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)
    The high-pressure phases and supercond. of CaYH12 have been explored by using a particle swarm optimization structure prediction methodol. in combination with first-principles calcns. Our results show that CaYH12 becomes stable with a cubic Fd3‾ m structure above 170 GPa, where metal atoms form body-centered-cubic (bcc) lattices and hydrogens occupy all the tetrahedral interstices of these bcc lattices, completing sodalitelike cages. The electron-phonon coupling calcns. indicate that the Fd3‾ m structure is a potential high-temp. superconductor, with a calcd. Tc of 258 K at 200 GPa. Our current study provides a possibility for searching new high-Tc superconductors in ternary hydrides.
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  26. 26
    Shi, L.-T.; Wei, Y.-K.; Liang, A.-K.; Turnbull, R.; Cheng, C.; Chen, X.-R.; Ji, G.-F. Prediction of pressure-induced superconductivity in the novel ternary system ScCaH2n (n = 1–6). J. Mater. Chem. C 2021, 9, 7284– 7291,  DOI: 10.1039/D1TC00634G
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    26
    Prediction of pressure-induced superconductivity in the novel ternary system ScCaH2n (n = 1-6)
    Shi, Lan-Ting; Wei, Yong-Kai; Liang, A-Kun; Turnbull, Robin; Cheng, Cai; Chen, Xiang-Rong; Ji, Guang-Fu
    Journal of Materials Chemistry C: Materials for Optical and Electronic Devices (2021), 9 (23), 7284-7291CODEN: JMCCCX; ISSN:2050-7534. (Royal Society of Chemistry)
    Hydrogen-rich systems are currently thought to constitute the most promising potential high-temp. superconductor materials. Here, the high-pressure structure and supercond. of the ternary hydrogen-rich system ScCaH2n (n = 1-6) are systematically investigated by using the prediction method of particle swarm optimization structure combined with first-principles calcns. As n increases, the electron local function (ELF) indicates that the hydrogen atoms in this system exhibit different behaviors corresponding to single H atoms, H2 mols., graphene-like layers and, ultimately, H clathrate cages. The electron phonon coupling (EPC) calcn. shows that the superconducting transition temp. for the hydrogen cage structures is much higher than that of other structures, which is mainly attributed to the increasing contribution of H in the cage structure to the d. of states (DOS) at the Fermi level. With the ScCaH2n system we have found two potential high temp. superconductor structures: ScCaH8 and ScCaH12. For these two compds., the corresponding Tc values reach around 212 K and 182 K, resp., at 200 GPa. The ScCaH8 structure exhibits an H18-cage in which the length of four hydrogen bonds increases abnormally with increasing pressure, leading to a decrease in the Tc value after 200 GPa. The present work therefore demonstrates an unusual pressure-induced behavior and provides new ideas to guide the search for new high temp. superconductors in ternary hydrides.
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    Wei, Y. K.; Jia, L. Q.; Fang, Y. Y.; Wang, L. J.; Qian, Z. X.; Yuan, J. N.; Selvaraj, G.; Ji, G. F.; Wei, D. Q. Formation and superconducting properties of predicted ternary hydride ScYH6 under pressures. Int. J. Quantum Chem. 2021, 121, e26459  DOI: 10.1002/qua.26459
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    27
    Formation and superconducting properties of predicted ternary hydride ScYH6 under pressures
    Wei, Yong Kai; Jia, Liang Quan; Fang, Yan Yan; Wang, Long Jun; Qian, Zhi Xiu; Yuan, Jiao Nan; Selvaraj, Gurudeeban; Ji, Guang Fu; Wei, Dong Qing
    International Journal of Quantum Chemistry (2021), 121 (4), e26459CODEN: IJQCB2; ISSN:0020-7608. (John Wiley & Sons, Inc.)
    Ternary metal hydrides play an essential role in the search for conventional high-temp. superconductors because they can be synthesized under mild conditions and recovered at ambient pressure. It has been widely accepted that the electronic structure, metalization pressure, and superconducting behavior of binary hydrides can be adjusted effectively by doping, replacing, or introducing a new element. In this work, yttrium hydrides were chosen as parent hydrides, while scandium was considered the doping element to perform systematical crystal structure searches on the Sc-Y-H system under pressure. A new ternary hydride ScYH6 with a Pm-3 structure (cP8) was found below 150 GPa according to Particle Swarm Optimization calcns., and then, a P4/mmm phase (tP8) becomes favorable from 150 GPa. Importantly, cP8-ScYH6 is dynamically stable under pressure as low as 0.01 GPa with a superconducting temp. (Tc) of 32.110 K for Coulomb pseudopotential μ* = 0.13, indicating that ternary hydrides are promising candidates in the search for superconductors that can be synthesized under mild conditions in hydrogen-rich materials. The anal. using the "triangle straight-line method", compared with enthalpy difference calcns., showed that the most reasonable synthesis pathway of ScYH6 is ScH3 + YH3 → ScYH6 in the whole pressure regime studied in this work. The Tc of ScYH6 has a linear relationship with pressure up to 52.907 K under 200 GPa. The lattice dynamical calcns. demonstrate that the H atoms in both cP8 and tP8 structures make crucial contributions to the superconducting behavior of ScYH6. These findings can further reveal the influence of doping, replacing, and introducing element on the superconducting behavior of binary hydrides.
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    Song, P.; Hou, Z.; de Castro, P. B.; Nakano, K.; Takano, Y.; Maezono, R.; Hongo, K. The systematic study on the stability and superconductivity of Y-Mg-H compounds under high pressure. Adv. Theory Simul. 2022 2100364. DOI: 10.1002/adts.202100364
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    Sukmas, W.; Tsuppayakorn-aek, P.; Pinsook, U.; Bovornratanaraks, T. Near-room-temperature superconductivity of Mg/Ca substituted metal hexahydride under pressure. J. Alloys Compd. 2020, 849, 156434,  DOI: 10.1016/j.jallcom.2020.156434
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    29
    Near-room-temperature superconductivity of Mg/Ca substituted metal hexahydride under pressure
    Sukmas, Wiwittawin; Tsuppayakorn-aek, Prutthipong; Pinsook, Udomsilp; Bovornratanaraks, Thiti
    Journal of Alloys and Compounds (2020), 849 (), 156434CODEN: JALCEU; ISSN:0925-8388. (Elsevier B.V.)
    A quest for room-temp. superconductors is undergoing rapid innovation due to the continuing proliferation of exptl. and theor. researches on high-pressure physics. Hydrogen-caged metal compds. have been proposed to promote high crit. temp. supercond. at pressures, providing a decent opportunity to investigate related phenomena at exptl. attainable pressures. This breakthrough is attributable to the uplifting key parameters, such as electron-phonon interaction and max. phonon frequency, once thought to be limited, by utilizing high pressures. A large class of metal polyhydrides has been theor. proposed and exptl. realized to promote near-room-temp. supercond. under high pressures. In this work, the authors theor. reported the near-room-temp. supercond. in a sym. Mg/Ca substituted hexahydride, i.e. Mg0.5Ca0.5H6. We showed that this ternary Mg0.5Ca0.5H6 compd. adopts an Im3m structure, wherein a metal atom is embedded in a H24 cage, is thermodynamically and dynamically stable at pressures ranging from 200 to 400 GPa. The analyses of the electronic band structure, Fermi surface topologies, phonon dispersion, and spectral function manifest strong support for supercond. We obtained λ = 2.53 and ωlog = 1,400K for our Mg/Ca substituted hexahydride at 200 GPa, exhibiting a near-room-temp. Tc of 288 K, which completely exceeds the calcd. Tc of its parent compds., i.e. MgH6 and CaH6.
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  30. 30
    Jain, A.; Ong, S. P.; Hautier, G.; Chen, W.; Richards, W. D.; Dacek, S.; Cholia, S.; Gunter, D.; Skinner, D.; Ceder, G. Commentary: The Materials Project: A materials genome approach to accelerating materials innovation. APL Mater. 2013, 1, 011002,  DOI: 10.1063/1.4812323
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    30
    Commentary: The Materials Project: A materials genome approach to accelerating materials innovation
    Jain, Anubhav; Ong, Shyue Ping; Hautier, Geoffroy; Chen, Wei; Richards, William Davidson; Dacek, Stephen; Cholia, Shreyas; Gunter, Dan; Skinner, David; Ceder, Gerbrand; Persson, Kristin A.
    APL Materials (2013), 1 (1), 011002/1-011002/11CODEN: AMPADS; ISSN:2166-532X. (American Institute of Physics)
    Accelerating the discovery of advanced materials is essential for human welfare and sustainable, clean energy. In this paper, we introduce the Materials Project (www.materialsproject.org), a core program of the Materials Genome Initiative that uses high-throughput computing to uncover the properties of all known inorg. materials. This open dataset can be accessed through multiple channels for both interactive exploration and data mining. The Materials Project also seeks to create open-source platforms for developing robust, sophisticated materials analyses. Future efforts will enable users to perform rapid-prototyping'' of new materials in silico, and provide researchers with new avenues for cost-effective, data-driven materials design. (c) 2013 American Institute of Physics.
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    Yu, R.; Lam, P. K. Electronic and structural properties of MgH2. Phys. Rev. B 1988, 37, 8730– 8737,  DOI: 10.1103/PhysRevB.37.8730
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    Electronic and structural properties of magnesium hydride
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    Physical Review B: Condensed Matter and Materials Physics (1988), 37 (15), 8730-7CODEN: PRBMDO; ISSN:0163-1829.
    The electronic and structural properties of MgH2 were calcd. using an ab initio pseudopotential method. The calcd. quantities are the equil. structural parameters, the cohesive energy, a few selected elastic consts., the bulk modulus, the phonon frequency of a zone-center optical mode involving H vibration, the energy-band structure, the d. of states, and the electronic charge distributions. The structural parameters and the cohesive energy agree with expts. The bonding nature of MgH2 is interpreted in terms of the band structure and the charge distribution. Covalent bonding was not found. Based on the band-structure and charge-d. results, MgH2 doped with a monovalent element could be a superconductor.
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    Vajeeston, P.; Ravindran, P.; Kjekshus, A.; Fjellvåg, H. Pressure-Induced Structural Transitions in MgH2. Phys. Rev. Lett. 2002, 89, 175506,  DOI: 10.1103/PhysRevLett.89.175506
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    Pressure-Induced Structural Transitions in MgH2
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    Physical Review Letters (2002), 89 (17), 175506/1-175506/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    The stability of MgH2 was studied up to 20 GPa using d.-functional total-energy calcns. At ambient pressure α-MgH2 takes a TiO2-rutile-type structure. α-MgH2 is predicted to transform into γ-MgH2 at 0.39 GPa. The calcd. structural data for α- and γ-MgH2 are in very good agreement with exptl. values. At equil. the energy difference between these modifications is very small, and as a result both phases coexist in a certain vol. and pressure field. Above 3.84 GPa γ-MgH2 transforms into β-MgH2, consistent with exptl. findings. Two further transformations were identified at still higher pressure: (i) β- to δ-MgH2 at 6.73 GPa and (ii) δ- to ε-MgH2 at 10.26 GPa.
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    Galakhov, A. V.; Finkelstein, L. D.; Kurmaev, E. Z.; Wilks, R. G.; Moewes, A.; Fedotov, V. K. X-ray spectra and electronic structure of Sc and Ti dihydrides. J. Condens. Matter Phys. 2008, 20, 335224,  DOI: 10.1088/0953-8984/20/33/335224
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    X-ray spectra and electronic structure of Sc and Ti dihydrides
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    A possible phase transition in a hydride of Sc0.995Gd0.005H1.9 was indicated by ESR and x-ray diffraction studies. This transition apparently occurs below 140 K. Possible mechanisms are discussed.
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    Frueh, S.; Kellett, R.; Mallery, C.; Molter, T.; Willis, W. S.; King’ondu, C.; Suib, S. L. Pyrolytic Decomposition of Ammonia Borane to Boron Nitride. Inorg. Chem. 2011, 50, 783– 792,  DOI: 10.1021/ic101020k
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    Pyrolytic Decomposition of Ammonia Borane to Boron Nitride
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    Inorganic Chemistry (2011), 50 (3), 783-792CODEN: INOCAJ; ISSN:0020-1669. (American Chemical Society)
    The thermal decompn. of ammonia borane was studied using a variety of methods to qual. identify gas and remnant solid phase species after thermal treatments up to 1500 °C. At about 110 °C, ammonia borane begins to decomp. yielding H2 as the major gas phase product. A two step decompn. process leading to a polymeric -[NH=BH]n- species above 130 °C is generally accepted. In this comprehensive study of decompn. pathways, we confirm the first two decompn. steps and identify a third process initiating at 1170 °C which leads to a semicryst. hexagonal phase boron nitride. Thermogravimetric anal. (TGA) was used to identify the onset of the third step. Temp. programmed desorption-mass spectroscopy (TPD-MS) and vacuum line methods identify mol. aminoborane (H2N=BH2) as a species that can be released in appreciable quantities with the other major impurity, borazine. Attenuated total reflectance Fourier transform IR spectroscopy (ATR-FTIR) was used to identify the chem. states present in the solid phase material after each stage of decompn. The boron nitride product was examd. for compn., structure, and morphol. using scanning Auger microscopy (SAM), powder X-ray diffraction (XRD), and field emission SEM (FESEM). Thermogravimetric Anal.-Mass Spectroscopy (TGA-MS) and Differential Scanning Calorimetry (DSC) were used to identify the onset temp. of the first two mass loss events.
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    Computer Physics Communications (2006), 175 (11-12), 713-720CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier B.V.)
    The authors approach the problem of computational crystal structure prediction, implementing an evolutionary algorithm-USPEX (Universal Structure Predictor: Evolutionary Xtallog.). Starting from chem. compn. the authors have tested USPEX on numerous systems (with ≤80 atoms in the unit cell) for which the stable structure is known and obsd. a success rate of nearly 100%, simultaneously finding large sets of competitive metastable structures. The focus is on implementation and discussion of the method.
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    The authors present ab initio quantum-mech. mol.-dynamics calcns. based on the calcn. of the electronic ground state and of the Hellmann-Feynman forces in the local-d. approxn. at each mol.-dynamics step. This is possible using conjugate-gradient techniques for energy minimization, and predicting the wave functions for new ionic positions using sub-space alignment. This approach avoids the instabilities inherent in quantum-mech. mol.-dynamics calcns. for metals based on the use of a factitious Newtonian dynamics for the electronic degrees of freedom. This method gives perfect control of the adiabaticity and allows one to perform simulations over several picoseconds.
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    Kresse, G.; Hafner, J. Ab initio molecular-dynamics simulation of the liquid-metal–amorphous-semiconductor transition in germanium. Phys. Rev. B 1994, 49, 14251– 14269,  DOI: 10.1103/PhysRevB.49.14251
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    Ab initio molecular-dynamics simulation of the liquid-metal-amorphous-semiconductor transition in germanium
    Kresse, G.; Hafner, J.
    Physical Review B: Condensed Matter and Materials Physics (1994), 49 (20), 14251-69CODEN: PRBMDO; ISSN:0163-1829.
    The authors present ab initio quantum-mech. mol.-dynamics simulations of the liq.-metal-amorphous-semiconductor transition in Ge. The simulations are based on (a) finite-temp. d.-functional theory of the 1-electron states, (b) exact energy minimization and hence calcn. of the exact Hellmann-Feynman forces after each mol.-dynamics step using preconditioned conjugate-gradient techniques, (c) accurate nonlocal pseudopotentials, and (d) Nose' dynamics for generating a canonical ensemble. This method gives perfect control of the adiabaticity of the electron-ion ensemble and allows the authors to perform simulations over >30 ps. The computer-generated ensemble describes the structural, dynamic, and electronic properties of liq. and amorphous Ge in very good agreement with expt.. The simulation allows the authors to study in detail the changes in the structure-property relation through the metal-semiconductor transition. The authors report a detailed anal. of the local structural properties and their changes induced by an annealing process. The geometrical, bounding, and spectral properties of defects in the disordered tetrahedral network are studied and compared with expt.
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    Kresse, G.; Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 1996, 6, 15– 50,  DOI: 10.1016/0927-0256(96)00008-0
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    Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set
    Kresse, G.; Furthmuller, J.
    Computational Materials Science (1996), 6 (1), 15-50CODEN: CMMSEM; ISSN:0927-0256. (Elsevier)
    The authors present a detailed description and comparison of algorithms for performing ab-initio quantum-mech. calcns. using pseudopotentials and a plane-wave basis set. The authors will discuss: (a) partial occupancies within the framework of the linear tetrahedron method and the finite temp. d.-functional theory, (b) iterative methods for the diagonalization of the Kohn-Sham Hamiltonian and a discussion of an efficient iterative method based on the ideas of Pulay's residual minimization, which is close to an order N2atoms scaling even for relatively large systems, (c) efficient Broyden-like and Pulay-like mixing methods for the charge d. including a new special preconditioning optimized for a plane-wave basis set, (d) conjugate gradient methods for minimizing the electronic free energy with respect to all degrees of freedom simultaneously. The authors have implemented these algorithms within a powerful package called VAMP (Vienna ab-initio mol.-dynamics package). The program and the techniques have been used successfully for a large no. of different systems (liq. and amorphous semiconductors, liq. simple and transition metals, metallic and semi-conducting surfaces, phonons in simple metals, transition metals and semiconductors) and turned out to be very reliable.
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    Kresse, G.; Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 1996, 54, 11169– 11186,  DOI: 10.1103/PhysRevB.54.11169
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    Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set
    Kresse, G.; Furthmueller, J.
    Physical Review B: Condensed Matter (1996), 54 (16), 11169-11186CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
    The authors present an efficient scheme for calcg. the Kohn-Sham ground state of metallic systems using pseudopotentials and a plane-wave basis set. In the first part the application of Pulay's DIIS method (direct inversion in the iterative subspace) to the iterative diagonalization of large matrixes will be discussed. This approach is stable, reliable, and minimizes the no. of order Natoms3 operations. In the second part, we will discuss an efficient mixing scheme also based on Pulay's scheme. A special "metric" and a special "preconditioning" optimized for a plane-wave basis set will be introduced. Scaling of the method will be discussed in detail for non-self-consistent and self-consistent calcns. It will be shown that the no. of iterations required to obtain a specific precision is almost independent of the system size. Altogether an order Natoms2 scaling is found for systems contg. up to 1000 electrons. If we take into account that the no. of k points can be decreased linearly with the system size, the overall scaling can approach Natoms. They have implemented these algorithms within a powerful package called VASP (Vienna ab initio simulation package). The program and the techniques have been used successfully for a large no. of different systems (liq. and amorphous semiconductors, liq. simple and transition metals, metallic and semiconducting surfaces, phonons in simple metals, transition metals, and semiconductors) and turned out to be very reliable.
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    Projector augmented-wave method
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    There is no expanded citation for this reference.
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    Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method. Phys. Rev. B 1999, 59, 1758– 1775,  DOI: 10.1103/PhysRevB.59.1758
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    From ultrasoft pseudopotentials to the projector augmented-wave method
    Kresse, G.; Joubert, D.
    Physical Review B: Condensed Matter and Materials Physics (1999), 59 (3), 1758-1775CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
    The formal relationship between ultrasoft (US) Vanderbilt-type pseudopotentials and Blochl's projector augmented wave (PAW) method is derived. The total energy functional for US pseudopotentials can be obtained by linearization of two terms in a slightly modified PAW total energy functional. The Hamilton operator, the forces, and the stress tensor are derived for this modified PAW functional. A simple way to implement the PAW method in existing plane-wave codes supporting US pseudopotentials is pointed out. In addn., crit. tests are presented to compare the accuracy and efficiency of the PAW and the US pseudopotential method with relaxed-core all-electron methods. These tests include small mols. (H2, H2O, Li2, N2, F2, BF3, SiF4) and several bulk systems (diamond, Si, V, Li, Ca, CaF2, Fe, Co, Ni). Particular attention is paid to the bulk properties and magnetic energies of Fe, Co, and Ni.
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    Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865– 3868,  DOI: 10.1103/PhysRevLett.77.3865
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    Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
    Physical Review Letters (1996), 77 (18), 3865-3868CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    Generalized gradient approxns. (GGA's) for the exchange-correlation energy improve upon the local spin d. (LSD) description of atoms, mols., and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental consts. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential.
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    Momma, K.; Izumi, F. VESTA3 for three-dimensional visualization of crystal, volumetric and morphology data. J. Appl. Crystallogr. 2011, 44, 1272– 1276,  DOI: 10.1107/S0021889811038970
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    VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data
    Momma, Koichi; Izumi, Fujio
    Journal of Applied Crystallography (2011), 44 (6), 1272-1276CODEN: JACGAR; ISSN:0021-8898. (International Union of Crystallography)
    VESTA is a 3D visualization system for crystallog. studies and electronic state calcns. It was upgraded to the latest version, VESTA 3, implementing new features including drawing the external morphpol. of crysals; superimposing multiple structural models, volumetric data and crystal faces; calcn. of electron and nuclear densities from structure parameters; calcn. of Patterson functions from the structure parameters or volumetric data; integration of electron and nuclear densities by Voronoi tessellation; visualization of isosurfaces with multiple levels, detn. of the best plane for selected atoms; an extended bond-search algorithm to enable more sophisticated searches in complex mols. and cage-like structures; undo and redo is graphical user interface operations; and significant performance improvements in rendering isosurfaces and calcg. slices.
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    Liu, Q.; Fan, C.; Zhang, R. First-principles study of high-pressure structural phase transitions of magnesium. J. Appl. Phys. 2009, 105, 123505,  DOI: 10.1063/1.3151687
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    First-principles study of high-pressure structural phase transitions of magnesium
    Liu, Qiuxiang; Fan, Changzeng; Zhang, Ruijun
    Journal of Applied Physics (2009), 105 (12), 123505/1-123505/4CODEN: JAPIAU; ISSN:0021-8979. (American Institute of Physics)
    The structural phase transitions for the hcp., bcc., dhcp., and fcc. of magnesium at hydrostatic pressures larger than ∼200 GPa at zero temp. are studied by first-principles total energy calcns. The plane-wave basis pseudopotential method was adopted, in which the generalized gradient approxn. implanted in the CASTEP code is employed. By comparing the enthalpy differences of the hcp. structure with other three structures under different pressures, it can be seen that when the pressure becomes higher than ∼65, 130, and 190 GPa, the bcc., dhcp., and fcc. structures become more stable relative to the hcp. structure, resp. Due to the lowest enthalpy value of the bcc. structure above 65 GPa, it can be deduced that magnesium may transform to the bcc. structure from the ground state hcp. structure around 65 GPa, but no further phase transitions occur without addnl. applying high temp. In addn., the equation of state of magnesium is calcd., indicating that bcc. structure is the softest phase. (c) 2009 American Institute of Physics.
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    Akahama, Y.; Fujihisa, H.; Kawamura, H. New Helical Chain Structure for Scandium at 240 GPa. Phys. Rev. Lett. 2005, 94, 195503,  DOI: 10.1103/PhysRevLett.94.195503
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    Physical Review Letters (2005), 94 (19), 195503/1-195503/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    X-ray diffraction expts. were carried out at 297 K to study structural-phase transitions of the trivalent rare-earth metal Sc at pressures of up to 297 GPa. Four stages of structural transition were obsd. around 23, 104, 140, and 240 GPa. The crystal structure of the highest-pressure phase, Sc-V, is a hexagonal lattice (S.G.: P6122 or P6522) consisting of 6-screw helical chains. The lattice can be derived from modulations of the interplane stacking of the (111) planes in an fcc. arrangement. The occurrence of an anisotropic structure suggests the importance of interactions between 3d orbitals with their nearest-neighbor atoms.
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    Structure of phase III of solid hydrogen
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    Nature Physics (2007), 3 (7), 473-476CODEN: NPAHAX; ISSN:1745-2473. (Nature Publishing Group)
    Hydrogen, being the first element in the periodic table, has the simplest electronic structure of any atom, and the hydrogen mol. contains the simplest covalent chem. bond. Nevertheless, the phase diagram of hydrogen is poorly understood. Detg. the stable structures of solid hydrogen is a tremendous exptl. challenge, because hydrogen atoms scatter X-rays only weakly, leading to low-resoln. diffraction patterns. Theor. studies encounter major difficulties owing to the small energy differences between structures and the importance of the zero-point motion of the protons. We have systematically investigated the zero-temp. phase diagram of solid hydrogen using first-principles d. functional theory (DFT) electronic-structure methods, including the proton zero-point motion at the harmonic level. Our study leads to a radical revision of the DFT phase diagram of hydrogen up to nearly 400 GPa. That the most stable phases remain insulating to very high pressures eliminates a major discrepancy between theory and expt. One of our new phases is calcd. to be stable over a wide range of pressures, and its vibrational properties agree with the available exptl. data for phase III.
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    Akbarzadeh, A. R.; Ozoliņš, V.; Wolverton, C. First-Principles Determination of Multicomponent Hydride Phase Diagrams: Application to the Li-Mg-N-H System. Adv. Mater. 2007, 19, 3233– 3239,  DOI: 10.1002/adma.200700843
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    First-principles determination of multicomponent hydride phase diagrams: application to the Li-Mg-N-H system
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    QUANTUM ESPRESSO is an integrated suite of computer codes for electronic-structure calculations and materials modeling, based on density-functional theory, plane waves, and pseudopotentials (norm-conserving, ultrasoft, and projector-augmented wave). The acronym ESPRESSO stands for opEn Source Package for Research in Electronic Structure, Simulation, and Optimization. It is freely available to researchers around the world under the terms of the GNU General Public License. QUANTUM ESPRESSO builds upon newly-restructured electronic-structure codes that have been developed and tested by some of the original authors of novel electronic-structure algorithms and applied in the last twenty years by some of the leading materials modeling groups worldwide. Innovation and efficiency are still its main focus, with special attention paid to massively parallel architectures, and a great effort being devoted to user friendliness. QUANTUM ESPRESSO is evolving towards a distribution of independent and interoperable codes in the spirit of an open-source project, where researchers active in the field of electronic-structure calculations are encouraged to participate in the project by contributing their own codes or by implementing their own ideas into existing codes.
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    Figure 1

    Figure 1. (a) Ternary convex hulls of the Mg–Sc–H system at a pressure of 200 GPa; (b,c) convex hulls of Gibbs free energy at 0 K and at finite temperature (1000 K), respectively. The stable and metastable phases are shown by circles and diamond, respectively.

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    Figure 2

    Figure 2. Enthalpy per atom of (MgH2 + MgH4)x as a function of x at the pressure of 100, 150, and 200 GPa, where x is defined as . The stable phase and the metastable phase are connected by solid and dashed lines, respectively.

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    Figure 3

    Figure 3. Phase diagram of Mg–Sc–H in the pressure range of 100–200 GPa.

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    Figure 4

    Figure 4. Predicted crystal structures of (a) R3̅m-MgScH6, (b) C2/m-Mg2ScH10, (c) Immm-MgSc2H9, (d) Pm3̅m-MgSc3H12 at 200 GPa. Bottom panels show the corresponding contour plots of electron localization function (ELF) in these structures.

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    Figure 5

    Figure 5. Electronic band structures and atom-projected electronic density of states of (a) R3̅m-MgScH6, (b) C2/m-Mg2ScH10, (c) Immm-MgSc2H9, (d) Pm3̅m-MgSc3H12 at 200 GPa.

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    Figure 6

    Figure 6. Phonon dispersion and atom-projected phonon density of states (pDOS), and Eliashberg spectral of (a) R3̅m-MgScH6, (b) C2/m-Mg2ScH10, (c) Immm-MgSc2H9, (d) Pm3̅m-MgSc3H12 at 200 GPa.

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    Figure 7

    Figure 7. Pressure-dependent superconductivity of R3̅m-MgScH6, C2/m-Mg2ScH10, Immm-MgSc2H9, Pm3̅m-MgSc3H12. (a) Tc from the McM equation, (b) EPC constant λ, (c) logarithmic phonon average ωlog and (d)the total DOS at the Fermi level .

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    This article references 64 other publications.

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      A review. Room-temp. supercond. has been a long-held dream and an area of intensive research. Recent exptl. findings of supercond. at 200 K in highly compressed hydrogen (H) sulfides have demonstrated the potential for achieving room-temp. supercond. in compressed H-rich materials. We report first-principles structure searches for stable H-rich clathrate structures in rare earth hydrides at high pressures. The peculiarity of these structures lies in the emergence of unusual H cages with stoichiometries H24, H29, and H32, in which H atoms are weakly covalently bonded to one another, with rare earth atoms occupying the centers of the cages. We have found that high-temp. supercond. is closely assocd. with H clathrate structures, with large H-derived electronic densities of states at the Fermi level and strong electron-phonon coupling related to the stretching and rocking motions of H atoms within the cages. Strikingly, a yttrium (Y) H32 clathrate structure of stoichiometry YH10 is predicted to be a potential room-temp. superconductor with an estd. Tc of up to 303 K at 400 GPa, as derived by direct soln. of the Eliashberg equation.
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      First-principles calcns. coupled with evolutionary algorithms have been employed to predict the structures of hydrides of the alkali metals and alk. earth metals under pressure. A plethora of novel phases with MH and M=Li, Na, K, Rb, Cs, and MH and M=Mg, Ca, Sr, Ba have been predicted to be stable at pressures that can be achieved in a diamond anvil cell. A no. of structural motifs, including H H H one-dimensional hydrogenic chains or three-dimensional sodalite-like lattices of hydrogen atoms, are found in the stable phases. The electronic structure and mechanism of metalization under pressure turn out to depend on the hydrogenic motifs that are present. Phases with 1D or 3D hydrogenic lattices are predicted to be the best candidates for high-temp. supercond., with those contg. H mols. following suit. Structures with H- or H are not predicted to be good superconductors. Chem. trends regarding the pressure required for stabilization of the polyhydrides are discussed. Exptl. studies that have successfully synthesized the polyhydrides of lithium and sodium are described. Lithium subhydrides, Li with , are also predicted to be stable between 50-100 GPa.
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      Journal of Chemical Physics (2019), 150 (5), 050901/1-050901/13CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      The theor. exploration of the phase diagrams of binary hydrides under pressure using ab initio crystal structure prediction techniques coupled with first principles calcns. has led to the in silico discovery of numerous novel superconducting materials. This Perspective focuses on the alk. earth and rare earth polyhydrides whose superconducting crit. temp., Tc, was predicted to be above the b.p. of liq. nitrogen. After providing a brief overview of the computational protocol used to predict the structures of stable and metastable hydrides under pressure, we outline the equations that can be employed to est. Tc. The systems with a high Tc can be classified according to the motifs found in their hydrogenic lattices. The highest Tcs are found for cages that are reminiscent of clathrates and the lowest for systems that contain at. and mol. hydrogen. A wide variety of hydrogenic motifs including 1- and 2-dimensional lattices, as well as Hδ-10 mol. units comprising fused Hδ-5 pentagons, are present in phases with intermediate Tcs. Some of these phases are predicted to be superconducting at room temp. Some may have recently been synthesized in diamond anvil cells. (c) 2019 American Institute of Physics.
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      Using the data on the superconducting crit. temp. (TC) for a no. of metal hydrides, we found a rule that makes it possible to predict the max. TC based only on the information about the electronic structure of metal atoms. Using this guiding principle, we explored the hydride systems for which no reliable information existed, predicted new higher hydrides in the K-H, Zr-H, Hf-H, Ti-H, Mg-H, Sr-H, Ba-H, Cs-H, and Rb-H systems at high pressures, and calcd. their TC. The highest-temp. superconducting hydrides are formed by metals in the "lability belt" roughly between 2nd and 3rd groups of the Periodic Table. Results of the study of actinoids and lanthanoids show that they form highly sym. superhydrides XH7-XH9, but the increasing no. of d- and esp. f-electrons affects superconducitivity adversely. Hydrides of late transition metals (e.g. platinoids) and all but early lanthanoids and actinoids are not promising for high-Tc supercond. Designed neural network allowing the prediction of TC of various hydrides shows high accuracy and was used to est. upper limit for TC of hydrides for which no date are available. The developed rule, based on regular behavior of the max. achievable crit. temp. as a function of no. of d + f electrons, enables targeted predictions about the existence of new high-TC superconductors.
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      Hydrogen-rich compds. hold promise as high-temp. superconductors under high pressures. Recent theor. hydride structures on achieving high-pressure supercond. are composed mainly of H2 fragments. Through a systematic investigation of Ca hydrides with different hydrogen contents using particle-swam optimization structural search, we show that in the stoichiometry CaH6 a body-centered cubic structure with hydrogen that forms unusual "sodalite" cages contg. enclathrated Ca stabilizes above pressure 150 GPa. The stability of this structure is derived from the acceptance by two H2 of electrons donated by Ca forming an "H4" unit as the building block in the construction of the three-dimensional sodalite cage. This unique structure has a partial occupation of the degenerated orbitals at the zone center. The resultant dynamic Jahn-Teller effect helps to enhance electron-phonon coupling and leads to supercond. of CaH6. A superconducting crit. temp. (Tc) of 220-235 K at 150 GPa obtained from the soln. of the Eliashberg equations is the highest among all hydrides studied thus far.
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      The structures of the strontium polyhydrides, SrHn with n > 2, under pressure are studied using evolutionary algorithms coupled with d. functional theory calcns. A no. of phases with even n are found to be thermodynamically stable below 150 GPa. Particularly interesting is the SrH4 stoichiometry, which comprises the convex hull at 50, 100, and 150 GPa. Its hydrogenic sublattice contains H2 and H- units, and throughout the pressure range considered, it adopts one of two configurations which were previously predicted for CaH4 under pressure. At 150 GPa, the SrH6 stoichiometry has the lowest enthalpy of formation. The most stable configuration assumes P‾3 symmetry, and its lattice consists of one-dimensional H2···H- hydrogenic chains. Symmetrization of these chains results in the formation of 1∞[Hδ-] helixes, which are reminiscent of the trigonal phase of sulfur. The R‾3m-SrH6 phase, which is comprised of these helixes, becomes dynamically stable by 250 GPa and has a high d. of states at the Fermi level. We explore the geometric relationships between R‾3m-SrH6 and the Im‾3m-CaH6 and Imm2-BaH6 structures found in prior investigations.
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      Chen, W.; Semenok, D. V.; Kvashnin, A. G.; Huang, X.; Kruglov, I. A.; Galasso, M.; Song, H.; Duan, D.; Goncharov, A. F.; Prakapenka, V. B. Synthesis of molecular metallic barium superhydride: pseudocubic BaH12. Nat. Commun. 2021, 12, 1– 9,  DOI: 10.1038/s41467-020-20103-5
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      Kruglov, I. A.; Semenok, D. V.; Song, H.; Szczesniak, R.; Wrona, I. A.; Akashi, R.; Esfahani, M. M. D.; Duan, D.; Cui, T.; Kvashnin, A. G. Superconductivity of LaH10 and LaH16 polyhydrides. Phys. Rev. B 2020, 101, 024508,  DOI: 10.1103/PhysRevB.101.024508
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      Superconductivity of LaH10 and LaH16 polyhydrides
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      Physical Review B (2020), 101 (2), 024508CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)
      Recent expts. have established previously predicted LaH10 as the highest-temp. superconductor, with TC up to 250-260 K [Drozdov, Nature (London)569, 528 (2019)10.1038/s41586-019-1201-8; Somayazulu, Phys.Rev.Lett.122, 027001 (2019)10.1103/PhysRevLett.122.027001]. In this work we explore the high-pressure phase stability and supercond. of lanthanum hydrides LaHm. We predict the stability of the hitherto unreported polyhydride P6/mmm-LaH16 at pressures above 150 GPa; at 200 GPa, its predicted superconducting TC is 156 K, the crit. field μ0HC(0) is approx. 35 T, and the superconducting gap is up to 35 meV. We revisit the superconducting of LaH10 and find its TC to be up to 259 K at 170 GPa from solving the Eliashberg equation and 271 K from solving the gap equation within the superconducting d. functional theory, which also allows us to compute the Coulomb pseudopotential μ* for LaH10 and LaH16.
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      Potential high-Tc superconducting lanthanum and yttrium hydrides at high pressure
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      A systematic structure search in the La-H and Y-H systems under pressure reveals some hydrogen-rich structures with intriguing electronic properties. For example, LaH10 is found to adopt a sodalite-like fcc. structure, stable >200 GPa, and LaH8 a C2/m space group structure. Phonon calcns. indicate both are dynamically stable; electron phonon calcns. coupled to BCS arguments indicate they might be high-Tc superconductors. In particular, the superconducting transition temp. Tc calcd. for LaH10 is 274-286 K at 210 GPa. Similar calcns. for the Y-H system predict stability of the sodalite-like fcc. YH10 and a Tc above room temp., reaching 305-326 K at 250 GPa. Probably dense hydrides consisting of these and related hydrogen polyhedral networks may represent new classes of potential very high-temp. superconductors.
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      The synthesis of hydrogen sulfides, with the potential of high-temp. supercond., was recently proposed at high Tc =203 K. It motivated us to employ an ab initio approach for the predictions of crystal structures to find the stable scandium hydrides. In addn. to the earlier predicted three stoichiometries of ScH, ScH2, and ScH3, we identify three other metallic stoichiometries of ScH4, ScH6, and ScH8, which show supercond. at significantly higher temps. The phases of ScH4 and ScH6, whose stability does not require extremely high pressures (<150 GPa with ZPE), are primarily ionic compds. contg. exotic quasimol. H2 arrangements. The present electron-phonon calcns. revealed the superconductive potential of ScH4 and ScH6 with estd. Tc of 98 K and 129 K at 200 GPa and 130 GPa, resp. The supercond. of ScHn stems from the large electron-phonon coupling assocd. with the wagging, bending, and intermediate-frequency modes attributed mainly to the hydrogen atoms.
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      Recently, an exptl. work reported a very high Tc of ∼190 K in hydrogen sulfide (H2S) at 200 GPa. The search for new superconductors with high superconducting crit. temps. in hydrogen-dominated materials has attracted significant attention. Here we predict a candidate phase of MgH6 with a sodalite-like framework in conjunction with first-principles electronic structure calcns. The calcd. formation enthalpy suggests that it is thermodynamically stable above 263 GPa relative to MgH2 and solid hydrogen (H2). Moreover, the absence of imaginary frequency in phonon calcns. implies that this MgH6 structure is dynamically stable. Furthermore, our electron-phonon coupling calcn. based on BCS theory indicates that this MgH6 phase is a conventional superconductor with a high superconducting crit. temp. of ∼260 K under high pressure, which is even higher than that of the recently reported compressed H2S. The present results offer insight in understanding and designing new high-temp. superconductors.
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      High hydrides of scandium under pressure: Potential superconductors
      Ye, Xiaoqiu; Zarifi, Niloofar; Zurek, Eva; Hoffmann, Roald; Ashcroft, N. W.
      Journal of Physical Chemistry C (2018), 122 (11), 6298-6309CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
      In a systematic investigation of scandium hydrides with high hydrogen content we predict seven phases of scandium hydrides (ScH4, ScH6, ScH7, ScH8, ScH9, ScH10, and ScH12), which are stable above 150 GPa. Zero point energies are essential in detg. the phases and pressure ranges within which they are stable. The interconversion of the various hydrides is intriguing; in one case there is a "return" to a lower hydrogen content hydride with increasing pressure. We argue that these hydrides may be synthesized by compressing mixts. of ScH3 and H2 above 150 GPa. New H bonding motifs are uncovered, including "H5" pentagons or "H8" octagons in ScH9, ScH10, and ScH12. High Tcs are predicted for ScH6, ScH7, ScH9, ScH10, and ScH12, with superconducting transition temps. (Tcs) of 120-169 K above 250 GPa, as estd. by the Allen-Dynes modified McMillan equation.
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      Flores-Livas, J. A.; Boeri, L.; Sanna, A.; Profeta, G.; Arita, R.; Eremets, M. A perspective on conventional high-temperature superconductors at high pressure: Methods and materials. Phys. Rep. 2020, 856, 1– 78,  DOI: 10.1016/j.physrep.2020.02.003
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      A perspective on conventional high-temperature superconductors at high pressure: Methods and materials
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      Physics Reports (2020), 856 (), 1-78CODEN: PRPLCM; ISSN:0370-1573. (Elsevier B.V.)
      A review. Two hydrogen-rich materials, H3S and LaH10, synthesized at megabar pressures, have revolutionized the field of condensed matter physics providing the first glimpse to the soln. of the hundred-year-old problem of room temp. supercond. The mechanism underlying supercond. in these exceptional compds. is the conventional electron-phonon coupling. Here we describe recent advances in exptl. techniques, supercond. theory and first-principles computational methods which have made possible these discoveries. This work aims to provide an up-to-date compendium of the available results on superconducting hydrides and explain how the synergy of different methodologies led to extraordinary discoveries in the field. Besides, in an attempt to evidence empirical rules governing supercond. in binary hydrides under pressure, we discuss general trends in the electronic structure and chem. bonding. The last part of the Review introduces possible strategies to optimize pressure and transition temps. in conventional superconducting materials as well as future directions in theor., computational and exptl. research.
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      Theoretical Study of Phase Separation of Scandium Hydrides under High Pressure
      Ye, Xiaoqiu; Hoffmann, Roald; Ashcroft, N. W.
      Journal of Physical Chemistry C (2015), 119 (10), 5614-5625CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
      The authors report theor. calcns. of the static ground-state structures and pressure-induced phase transformations of three scandium hydrides: ScH, ScH2, and ScH3. For the monohydride, ScH, we predict several phases to be more stable at 1 atm than the previously suggested rock-salt structure, in particular one of P42/mmc symmetry. The NaCl-type structure for ScH takes over at 10 GPa and dominates over a wide pressure range until it is replaced by a Cmcm structure around 265 GPa. Under pressure, the exptl. P = 1 atm CaF2-type structure of ScH2 should transform to a C2/m structure around 65 GPa, which then is likely to disproportionate to NaCl-type ScH and face-centered cubic ScH3 above 72 GPa. According to theory, as the pressure is elevated, ScH3 moves through the following sequence of phases: P63 → Fm‾3m → P63/mmc(YH3-type) → Cmcm; the corresponding transition pressures are calcd. to be 29, 360, and 483 GPa, resp. The predicted disproportionation tendencies of ScH2 are fascinating: stable to decompn. to ScH and ScH3 at low pressures, it should begin to disproportionate near 72 GPa. However, the process is predicted to reverse at still higher pressures (above 300 GPa). They also find ScH to be stable to disproportionation to Sc and ScH2 above ∼25 GPa. The three hydrides are metallic, except for (at low pressures) ScH3.
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      Abe, Kazutaka
      Physical Review B (2017), 96 (14), 144108/1-144108/7CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)
      Scandium hydrides at high pressures have been investigated by using ab initio d. functional calcns. Although the stable scandium hydride so far known to have the highest content rate of hydrogen is ScH3, other more hydrogen-rich compds. are found to be possible at high pressures. These are ScH4 in the I4/mmm structure above 160 GPa, ScH6 in the P63/mmc structure from 135 to 265 GPa, and ScH6 in the Im3m structure above 265 GPa. The three phases are all metallic, and the superconducting transition temps. estd. from the extended McMillan equation are 67 K in the I4/mmm ScH4 at 195 GPa, 63 K in the P63/mmc ScH6 at 145 GPa, and 130 K in the Im3m ScH6 at 285 GPa. While the I4/mmm tetrahydride and the Im3m hexahydride were similarly predicted for yttrium (another group-3 element), the P63/mmc hexahydride is possible only for scandium. The smaller at. size of scandium stabilizes the P63/mmc structure, and other nearby d-block elements, whose at. sizes are smaller or comparable, might be likewise capable of forming such polyhydrides.
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    16. 16
      Wei, Y.-K.; Yuan, J.-N.; Khan, F. I.; Ji, G.-F.; Gu, Z.-W.; Wei, D.-Q. Pressure induced superconductivity and electronic structure properties of scandium hydrides using first principles calculations. RSC Adv. 2016, 6, 81534– 81541,  DOI: 10.1039/C6RA11862C
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      16
      Pressure induced superconductivity and electronic structure properties of scandium hydrides using first principles calculations
      Wei, Yong-Kai; Yuan, Jiao-Nan; Khan, Faez Iqbal; Ji, Guang-Fu; Gu, Zhuo-Wei; Wei, Dong-Qing
      RSC Advances (2016), 6 (85), 81534-81541CODEN: RSCACL; ISSN:2046-2069. (Royal Society of Chemistry)
      The electronic, vibrational and superconducting properties of scandium hydrides (ScH2 and ScH3) under pressure were studied using first-principles calcns. The results indicate that ScH2 and ScH3 are dynamically stable in the pressure ranges of 0-85 GPa and 46-80 GPa, resp. The superconducting properties of ScH2 and ScH3 were investigated by employing BCS (BCS) theory, and this shows that the superconducting temp. of ScH2 initially increases exponentially and then reaches a max. value of about 38.11 K at 30 GPa, while it remains const. under further compression. However, the superconducting behavior of ScH3 is not obvious under low pressure (P < 46 GPa), and it almost disappears under higher pressure, in agreement with exptl. observations. Anal. of the energy band structures demonstrates that the distinct superconducting behaviors of ScH2 and ScH3 are related to the hybridization between the s-state of the H atom and the d-state of the Sc atom. The superconducting behavior of ScH2 follows the variation of the hybridization between the HO-s state and Sc-d state, while for ScH3, it is found that there is no d. of states obsd. for HT or HO when the pressure is above 46 GPa. Anal. of the electronic structure of ScH2 was also performed to allow for further comprehension of the metallic behavior of ScH2 under pressure. This work may offer help to understand the mechanism of pressure-induced supercond. in metal-hydride systems.
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    17. 17
      Shipley, A. M.; Hutcheon, M. J.; Needs, R. J.; Pickard, C. J. High-throughput discovery of high-temperature conventional superconductors. arXiv (Condensed Matter, Superconductivity) 2105.02296, ver. 3, May 5, 2021, https://arxiv.org/abs/2105.02296.
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      Lonie, D. C.; Hooper, J.; Altintas, B.; Zurek, E. Metallization of magnesium polyhydrides under pressure. Phys. Rev. B 2013, 87, 054107,  DOI: 10.1103/PhysRevB.87.054107
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      18
      Metallization of magnesium polyhydrides under pressure
      Lonie, David C.; Hooper, James; Altintas, Bahadir; Zurek, Eva
      Physical Review B: Condensed Matter and Materials Physics (2013), 87 (5), 054107/1-054107/8CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
      Evolutionary structure searches are used to predict stable phases with unique stoichiometries in the hydrogen-rich region of the magnesium/hydrogen phase diagram under pressure. MgH4, MgH12, and MgH16 are found to be thermodynamically stable with respect to decompn. into MgH2 and H2 near 100 GPa, and all lie on the convex hull by 200 GPa. MgH4 contains two H- anions and one H2 mol. per Mg2+ cation, whereas the hydrogenic sublattices of MgH12 and MgH16 are composed solely of Hδ-2 mols. The high-hydrogen content stoichiometries have a large d. of states at the Fermi level, and the Tc of MgH12 at 140 GPa is calcd. to be nearly three times greater than that of the classic hydride, MgH2, at 180 GPa.
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    19. 19
      Drozdov, A. P.; Kong, P. P.; Minkov, V. S.; Besedin, S. P.; Kuzovnikov, M. A.; Mozaffari, S.; Balicas, L.; Balakirev, F. F.; Graf, D. E.; Prakapenka, V. B. Superconductivity at 250 K in lanthanum hydride under high pressures. Nature 2019, 569, 528– 531,  DOI: 10.1038/s41586-019-1201-8
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      19
      Superconductivity at 250 K in lanthanum hydride under high pressures
      Drozdov, A. P.; Kong, P. P.; Minkov, V. S.; Besedin, S. P.; Kuzovnikov, M. A.; Mozaffari, S.; Balicas, L.; Balakirev, F. F.; Graf, D. E.; Prakapenka, V. B.; Greenberg, E.; Knyazev, D. A.; Tkacz, M.; Eremets, M. I.
      Nature (London, United Kingdom) (2019), 569 (7757), 528-531CODEN: NATUAS; ISSN:0028-0836. (Nature Research)
      With the discovery1 of supercond. at 203 K in H3S, attention returned to conventional superconductors with properties that can be described by the BCS and the Migdal-Eliashberg theories. Although these theories predict the possibility of room-temp. supercond. in metals that have certain favorable properties-such as lattice vibrations at high frequencies-they are not sufficient to guide the design or predict the properties of new superconducting materials. First-principles calcns. based on d. functional theory have enabled such predictions, and have suggested a new family of superconducting hydrides that possess a clathrate-like structure in which the host atom (calcium, yttrium, lanthanum) is at the center of a cage formed by hydrogen atoms2-4. For LaH10 and YH10, the onset of supercond. is predicted to occur at crit. temps. between 240 and 320 K at megabar pressures3-6. Here we report supercond. with a crit. temp. of around 250 K within the Fm‾3m structure of LaH10 at a pressure of about 170 gigapascals. This is, to our knowledge, the highest crit. temp. that has been confirmed so far in a superconducting material. Supercond. was evidenced by the observation of zero resistance, an isotope effect, and a decrease in crit. temp. under an external magnetic field, which suggested an upper crit. magnetic field of about 136 T at zero temp. The increase of around 50 K compared with the previous highest crit. temp.1 is an encouraging step towards the goal of achieving room-temp. supercond. in the near future.
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    20. 20
      Troyan, I. A.; Semenok, D. V.; Kvashnin, A. G.; Sadakov, A. V.; Sobolevskiy, O. A.; Pudalov, V. M.; Ivanova, A. G.; Prakapenka, V. B.; Greenberg, E.; Gavriliuk, A. G. Anomalous High-Temperature Superconductivity in YH6. Adv. Mater. 2021, 33, 2006832,  DOI: 10.1002/adma.202006832
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      20
      Anomalous High-Temperature Superconductivity in YH6
      Troyan, Ivan A.; Semenok, Dmitrii V.; Kvashnin, Alexander G.; Sadakov, Andrey V.; Sobolevskiy, Oleg A.; Pudalov, Vladimir M.; Ivanova, Anna G.; Prakapenka, Vitali B.; Greenberg, Eran; Gavriliuk, Alexander G.; Lyubutin, Igor S.; Struzhkin, Viktor V.; Bergara, Aitor; Errea, Ion; Bianco, Raffaello; Calandra, Matteo; Mauri, Francesco; Monacelli, Lorenzo; Akashi, Ryosuke; Oganov, Artem R.
      Advanced Materials (Weinheim, Germany) (2021), 33 (15), 2006832CODEN: ADVMEW; ISSN:0935-9648. (Wiley-VCH Verlag GmbH & Co. KGaA)
      Pressure-stabilized hydrides are a new rapidly growing class of high-temp. superconductors, which is believed to be described within the conventional phonon-mediated mechanism of coupling. Here, the synthesis of one of the best-known high-TC superconductors-yttrium hexahydride Im3m-YH6 is reported, which displays a superconducting transition at ≈224 K at 166 GPa. The extrapolated upper crit. magnetic field Bc2(0) of YH6 is surprisingly high: 116-158 T, which is 2-2.5 times larger than the calcd. value. A pronounced shift of TC in yttrium deuteride YD6 with the isotope coeff. 0.4 supports the phonon-assisted supercond. Current-voltage measurements show that the crit. current IC and its d. JC may exceed 1.75 A and 3500 A mm-2 at 4 K, resp., which is higher than that of the com. superconductors, such as NbTi and YBCO. The results of superconducting d. functional theory (SCDFT) and anharmonic calcns., together with anomalously high crit. magnetic field, suggest notable departures of the superconducting properties from the conventional Migdal-Eliashberg and BCS theories, and presence of an addnl. mechanism of supercond.
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    21. 21
      Ma, L.; Wang, K.; Xie, Y.; Yang, X.; Wang, Y.; Zhou, M.; Liu, H.; Liu, G.; Wang, H.; Ma, Y. Experimental observation of superconductivity at 215 K in calcium superhydride under high pressures. arXiv (Condensed Matter, Superconductivity) 2103.16282 ver. 3, March 30, 2021, https://arxiv.org/abs/2103.16282.
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      Salke, N. P.; Esfahani, M. M. D.; Zhang, Y.; Kruglov, I. A.; Zhou, J.; Wang, Y.; Greenberg, E.; Prakapenka, V. B.; Liu, J.; Oganov, A. R. Synthesis of clathrate cerium superhydride CeH9 at 80–100 GPa with atomic hydrogen sublattice. Nat. Commun. 2019, 10, 1– 10,  DOI: 10.1038/s41467-019-12326-y
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      22
      Synthesis of clathrate cerium superhydride CeH9 at 80-100 GPa with atomic hydrogen sublattice
      Salke, Nilesh P.; Davari Esfahani, M. Mahdi; Zhang, Youjun; Kruglov, Ivan A.; Zhou, Jianshi; Wang, Yaguo; Greenberg, Eran; Prakapenka, Vitali B.; Liu, Jin; Oganov, Artem R.; Lin, Jung-Fu
      Nature Communications (2019), 10 (1), 1-10CODEN: NCAOBW; ISSN:2041-1723. (Nature Research)
      Hydrogen-rich superhydrides are believed to be very promising high-Tc superconductors. Recent expts. discovered superhydrides at very high pressures, e.g. FeH5 at 130 GPa and LaH10 at 170 GPa. With the motivation of discovering new hydrogen-rich high-Tc superconductors at lowest possible pressure, here we report the prediction and exptl. synthesis of cerium superhydride CeH9 at 80-100 GPa in the laser-heated diamond anvil cell coupled with synchrotron X-ray diffraction. Ab initio calcns. were carried out to evaluate the detailed chem. of the Ce-H system and to understand the structure, stability and supercond. of CeH9. CeH9 crystallizes in a P63/mmc clathrate structure with a very dense 3-dimensional at. hydrogen sublattice at 100 GPa. These findings shed a significant light on the search for superhydrides in close similarity with at. hydrogen within a feasible pressure range. Discovery of superhydride CeH9 provides a practical platform to further investigate and understand conventional supercond. in hydrogen rich superhydrides.
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    23. 23
      Semenok, D. V.; Troyan, I. A.; Ivanova, A. G.; Kvashnin, A. G.; Kruglov, I. A.; Hanfland, M.; Sadakov, A. V.; Sobolevskiy, O. A.; Pervakov, K. S.; Lyubutin, I. S. Superconductivity at 253 K in lanthanum–yttrium ternary hydrides. Mater. Today 2021, 48, 1369– 7021,  DOI: 10.1016/j.mattod.2021.03.025
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      Song, P.; Hou, Z.; de Castro, P. B.; Nakano, K.; Hongo, K.; Takano, Y.; Maezono, R. High-Tc Superconducting Hydrides Formed by LaH24 and YH24 Cage Structures as Basic Blocks. Chem. Mater. 2021, 33, 9501– 9507,  DOI: 10.1021/acs.chemmater.1c02371
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      24
      High-Tc superconducting hydrides formed by LaH24 and YH24 cage structures as basic blocks
      Song, Peng; Hou, Zhufeng; Castro, Pedro Baptista de; Nakano, Kousuke; Hongo, Kenta; Takano, Yoshihiko; Maezono, Ryo
      Chemistry of Materials (2021), 33 (24), 9501-9507CODEN: CMATEX; ISSN:0897-4756. (American Chemical Society)
      Based on recent studies regarding high-temp. (high-Tc) La-Y ternary hydrides (e.g., P‾1-La2YH12, Pm‾3m-LaYH12, and Pm‾3m-(La,Y)H10 with a max. Tc ∼253 K), we examd. the phase and structural stabilities of the (LaH6)(YH6)y series as high-Tc ternary hydride compns. using a genetic algorithm and ab initio calcns. Our evaluation showed that Pm‾3m-LaYH12 reported in the previous study was unstable during decompn. into R‾3c-LaH6 + Im‾3m-YH6. We also discovered new crystal structures, namely, Cmmm-LaYH12 (y = 1), R‾3c-LaYH12 (y = 1), Cmmm-LaY3H24 (y = 3), and R‾3-LaY3H24 (y = 3), showing stability against such decompn. While R‾3c (y = 1) and R‾3 (y = 3) did not exhibit supercond. owing to the extremely low d. of states at the Fermi level, Cmmm phases exhibited a Tc of approx. 140 K at around 200 GPa owing to the extremely high electron-phonon coupling const. (λ = 1.876 for LaYH12). By the twice longer stacking for Cmmm-LaY3H24, the coupling const. increased owing to the chem. pressure of Y, leading to a slightly increased Tc.
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    25. 25
      Liang, X.; Bergara, A.; Wang, L.; Wen, B.; Zhao, Z.; Zhou, X.-F.; He, J.; Gao, G.; Tian, Y. Potential high-Tc superconductivity in CaYH12 under pressure. Phys. Rev. B 2019, 99, 100505,  DOI: 10.1103/PhysRevB.99.100505
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      25
      Potential high-Tc superconductivity in CaYH12 under pressure
      Liang, Xiaowei; Bergara, Aitor; Wang, Linyan; Wen, Bin; Zhao, Zhisheng; Zhou, Xiang-Feng; He, Julong; Gao, Guoying; Tian, Yongjun
      Physical Review B (2019), 99 (10), 100505CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)
      The high-pressure phases and supercond. of CaYH12 have been explored by using a particle swarm optimization structure prediction methodol. in combination with first-principles calcns. Our results show that CaYH12 becomes stable with a cubic Fd3‾ m structure above 170 GPa, where metal atoms form body-centered-cubic (bcc) lattices and hydrogens occupy all the tetrahedral interstices of these bcc lattices, completing sodalitelike cages. The electron-phonon coupling calcns. indicate that the Fd3‾ m structure is a potential high-temp. superconductor, with a calcd. Tc of 258 K at 200 GPa. Our current study provides a possibility for searching new high-Tc superconductors in ternary hydrides.
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    26. 26
      Shi, L.-T.; Wei, Y.-K.; Liang, A.-K.; Turnbull, R.; Cheng, C.; Chen, X.-R.; Ji, G.-F. Prediction of pressure-induced superconductivity in the novel ternary system ScCaH2n (n = 1–6). J. Mater. Chem. C 2021, 9, 7284– 7291,  DOI: 10.1039/D1TC00634G
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      26
      Prediction of pressure-induced superconductivity in the novel ternary system ScCaH2n (n = 1-6)
      Shi, Lan-Ting; Wei, Yong-Kai; Liang, A-Kun; Turnbull, Robin; Cheng, Cai; Chen, Xiang-Rong; Ji, Guang-Fu
      Journal of Materials Chemistry C: Materials for Optical and Electronic Devices (2021), 9 (23), 7284-7291CODEN: JMCCCX; ISSN:2050-7534. (Royal Society of Chemistry)
      Hydrogen-rich systems are currently thought to constitute the most promising potential high-temp. superconductor materials. Here, the high-pressure structure and supercond. of the ternary hydrogen-rich system ScCaH2n (n = 1-6) are systematically investigated by using the prediction method of particle swarm optimization structure combined with first-principles calcns. As n increases, the electron local function (ELF) indicates that the hydrogen atoms in this system exhibit different behaviors corresponding to single H atoms, H2 mols., graphene-like layers and, ultimately, H clathrate cages. The electron phonon coupling (EPC) calcn. shows that the superconducting transition temp. for the hydrogen cage structures is much higher than that of other structures, which is mainly attributed to the increasing contribution of H in the cage structure to the d. of states (DOS) at the Fermi level. With the ScCaH2n system we have found two potential high temp. superconductor structures: ScCaH8 and ScCaH12. For these two compds., the corresponding Tc values reach around 212 K and 182 K, resp., at 200 GPa. The ScCaH8 structure exhibits an H18-cage in which the length of four hydrogen bonds increases abnormally with increasing pressure, leading to a decrease in the Tc value after 200 GPa. The present work therefore demonstrates an unusual pressure-induced behavior and provides new ideas to guide the search for new high temp. superconductors in ternary hydrides.
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    27. 27
      Wei, Y. K.; Jia, L. Q.; Fang, Y. Y.; Wang, L. J.; Qian, Z. X.; Yuan, J. N.; Selvaraj, G.; Ji, G. F.; Wei, D. Q. Formation and superconducting properties of predicted ternary hydride ScYH6 under pressures. Int. J. Quantum Chem. 2021, 121, e26459  DOI: 10.1002/qua.26459
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      Formation and superconducting properties of predicted ternary hydride ScYH6 under pressures
      Wei, Yong Kai; Jia, Liang Quan; Fang, Yan Yan; Wang, Long Jun; Qian, Zhi Xiu; Yuan, Jiao Nan; Selvaraj, Gurudeeban; Ji, Guang Fu; Wei, Dong Qing
      International Journal of Quantum Chemistry (2021), 121 (4), e26459CODEN: IJQCB2; ISSN:0020-7608. (John Wiley & Sons, Inc.)
      Ternary metal hydrides play an essential role in the search for conventional high-temp. superconductors because they can be synthesized under mild conditions and recovered at ambient pressure. It has been widely accepted that the electronic structure, metalization pressure, and superconducting behavior of binary hydrides can be adjusted effectively by doping, replacing, or introducing a new element. In this work, yttrium hydrides were chosen as parent hydrides, while scandium was considered the doping element to perform systematical crystal structure searches on the Sc-Y-H system under pressure. A new ternary hydride ScYH6 with a Pm-3 structure (cP8) was found below 150 GPa according to Particle Swarm Optimization calcns., and then, a P4/mmm phase (tP8) becomes favorable from 150 GPa. Importantly, cP8-ScYH6 is dynamically stable under pressure as low as 0.01 GPa with a superconducting temp. (Tc) of 32.110 K for Coulomb pseudopotential μ* = 0.13, indicating that ternary hydrides are promising candidates in the search for superconductors that can be synthesized under mild conditions in hydrogen-rich materials. The anal. using the "triangle straight-line method", compared with enthalpy difference calcns., showed that the most reasonable synthesis pathway of ScYH6 is ScH3 + YH3 → ScYH6 in the whole pressure regime studied in this work. The Tc of ScYH6 has a linear relationship with pressure up to 52.907 K under 200 GPa. The lattice dynamical calcns. demonstrate that the H atoms in both cP8 and tP8 structures make crucial contributions to the superconducting behavior of ScYH6. These findings can further reveal the influence of doping, replacing, and introducing element on the superconducting behavior of binary hydrides.
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    28. 28
      Song, P.; Hou, Z.; de Castro, P. B.; Nakano, K.; Takano, Y.; Maezono, R.; Hongo, K. The systematic study on the stability and superconductivity of Y-Mg-H compounds under high pressure. Adv. Theory Simul. 2022 2100364. DOI: 10.1002/adts.202100364
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      Sukmas, W.; Tsuppayakorn-aek, P.; Pinsook, U.; Bovornratanaraks, T. Near-room-temperature superconductivity of Mg/Ca substituted metal hexahydride under pressure. J. Alloys Compd. 2020, 849, 156434,  DOI: 10.1016/j.jallcom.2020.156434
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      29
      Near-room-temperature superconductivity of Mg/Ca substituted metal hexahydride under pressure
      Sukmas, Wiwittawin; Tsuppayakorn-aek, Prutthipong; Pinsook, Udomsilp; Bovornratanaraks, Thiti
      Journal of Alloys and Compounds (2020), 849 (), 156434CODEN: JALCEU; ISSN:0925-8388. (Elsevier B.V.)
      A quest for room-temp. superconductors is undergoing rapid innovation due to the continuing proliferation of exptl. and theor. researches on high-pressure physics. Hydrogen-caged metal compds. have been proposed to promote high crit. temp. supercond. at pressures, providing a decent opportunity to investigate related phenomena at exptl. attainable pressures. This breakthrough is attributable to the uplifting key parameters, such as electron-phonon interaction and max. phonon frequency, once thought to be limited, by utilizing high pressures. A large class of metal polyhydrides has been theor. proposed and exptl. realized to promote near-room-temp. supercond. under high pressures. In this work, the authors theor. reported the near-room-temp. supercond. in a sym. Mg/Ca substituted hexahydride, i.e. Mg0.5Ca0.5H6. We showed that this ternary Mg0.5Ca0.5H6 compd. adopts an Im3m structure, wherein a metal atom is embedded in a H24 cage, is thermodynamically and dynamically stable at pressures ranging from 200 to 400 GPa. The analyses of the electronic band structure, Fermi surface topologies, phonon dispersion, and spectral function manifest strong support for supercond. We obtained λ = 2.53 and ωlog = 1,400K for our Mg/Ca substituted hexahydride at 200 GPa, exhibiting a near-room-temp. Tc of 288 K, which completely exceeds the calcd. Tc of its parent compds., i.e. MgH6 and CaH6.
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    30. 30
      Jain, A.; Ong, S. P.; Hautier, G.; Chen, W.; Richards, W. D.; Dacek, S.; Cholia, S.; Gunter, D.; Skinner, D.; Ceder, G. Commentary: The Materials Project: A materials genome approach to accelerating materials innovation. APL Mater. 2013, 1, 011002,  DOI: 10.1063/1.4812323
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      Commentary: The Materials Project: A materials genome approach to accelerating materials innovation
      Jain, Anubhav; Ong, Shyue Ping; Hautier, Geoffroy; Chen, Wei; Richards, William Davidson; Dacek, Stephen; Cholia, Shreyas; Gunter, Dan; Skinner, David; Ceder, Gerbrand; Persson, Kristin A.
      APL Materials (2013), 1 (1), 011002/1-011002/11CODEN: AMPADS; ISSN:2166-532X. (American Institute of Physics)
      Accelerating the discovery of advanced materials is essential for human welfare and sustainable, clean energy. In this paper, we introduce the Materials Project (www.materialsproject.org), a core program of the Materials Genome Initiative that uses high-throughput computing to uncover the properties of all known inorg. materials. This open dataset can be accessed through multiple channels for both interactive exploration and data mining. The Materials Project also seeks to create open-source platforms for developing robust, sophisticated materials analyses. Future efforts will enable users to perform rapid-prototyping'' of new materials in silico, and provide researchers with new avenues for cost-effective, data-driven materials design. (c) 2013 American Institute of Physics.
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      Yu, R.; Lam, P. K. Electronic and structural properties of MgH2. Phys. Rev. B 1988, 37, 8730– 8737,  DOI: 10.1103/PhysRevB.37.8730
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      Electronic and structural properties of magnesium hydride
      Yu, Rici; Lam, Pui K.
      Physical Review B: Condensed Matter and Materials Physics (1988), 37 (15), 8730-7CODEN: PRBMDO; ISSN:0163-1829.
      The electronic and structural properties of MgH2 were calcd. using an ab initio pseudopotential method. The calcd. quantities are the equil. structural parameters, the cohesive energy, a few selected elastic consts., the bulk modulus, the phonon frequency of a zone-center optical mode involving H vibration, the energy-band structure, the d. of states, and the electronic charge distributions. The structural parameters and the cohesive energy agree with expts. The bonding nature of MgH2 is interpreted in terms of the band structure and the charge distribution. Covalent bonding was not found. Based on the band-structure and charge-d. results, MgH2 doped with a monovalent element could be a superconductor.
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      Pressure-Induced Structural Transitions in MgH2
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      The stability of MgH2 was studied up to 20 GPa using d.-functional total-energy calcns. At ambient pressure α-MgH2 takes a TiO2-rutile-type structure. α-MgH2 is predicted to transform into γ-MgH2 at 0.39 GPa. The calcd. structural data for α- and γ-MgH2 are in very good agreement with exptl. values. At equil. the energy difference between these modifications is very small, and as a result both phases coexist in a certain vol. and pressure field. Above 3.84 GPa γ-MgH2 transforms into β-MgH2, consistent with exptl. findings. Two further transformations were identified at still higher pressure: (i) β- to δ-MgH2 at 6.73 GPa and (ii) δ- to ε-MgH2 at 10.26 GPa.
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      X-ray spectra and electronic structure of Sc and Ti dihydrides
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      Pyrolytic Decomposition of Ammonia Borane to Boron Nitride
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      Inorganic Chemistry (2011), 50 (3), 783-792CODEN: INOCAJ; ISSN:0020-1669. (American Chemical Society)
      The thermal decompn. of ammonia borane was studied using a variety of methods to qual. identify gas and remnant solid phase species after thermal treatments up to 1500 °C. At about 110 °C, ammonia borane begins to decomp. yielding H2 as the major gas phase product. A two step decompn. process leading to a polymeric -[NH=BH]n- species above 130 °C is generally accepted. In this comprehensive study of decompn. pathways, we confirm the first two decompn. steps and identify a third process initiating at 1170 °C which leads to a semicryst. hexagonal phase boron nitride. Thermogravimetric anal. (TGA) was used to identify the onset of the third step. Temp. programmed desorption-mass spectroscopy (TPD-MS) and vacuum line methods identify mol. aminoborane (H2N=BH2) as a species that can be released in appreciable quantities with the other major impurity, borazine. Attenuated total reflectance Fourier transform IR spectroscopy (ATR-FTIR) was used to identify the chem. states present in the solid phase material after each stage of decompn. The boron nitride product was examd. for compn., structure, and morphol. using scanning Auger microscopy (SAM), powder X-ray diffraction (XRD), and field emission SEM (FESEM). Thermogravimetric Anal.-Mass Spectroscopy (TGA-MS) and Differential Scanning Calorimetry (DSC) were used to identify the onset temp. of the first two mass loss events.
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      The authors approach the problem of computational crystal structure prediction, implementing an evolutionary algorithm-USPEX (Universal Structure Predictor: Evolutionary Xtallog.). Starting from chem. compn. the authors have tested USPEX on numerous systems (with ≤80 atoms in the unit cell) for which the stable structure is known and obsd. a success rate of nearly 100%, simultaneously finding large sets of competitive metastable structures. The focus is on implementation and discussion of the method.
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      The authors present ab initio quantum-mech. mol.-dynamics calcns. based on the calcn. of the electronic ground state and of the Hellmann-Feynman forces in the local-d. approxn. at each mol.-dynamics step. This is possible using conjugate-gradient techniques for energy minimization, and predicting the wave functions for new ionic positions using sub-space alignment. This approach avoids the instabilities inherent in quantum-mech. mol.-dynamics calcns. for metals based on the use of a factitious Newtonian dynamics for the electronic degrees of freedom. This method gives perfect control of the adiabaticity and allows one to perform simulations over several picoseconds.
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      Kresse, G.; Hafner, J. Ab initio molecular-dynamics simulation of the liquid-metal–amorphous-semiconductor transition in germanium. Phys. Rev. B 1994, 49, 14251– 14269,  DOI: 10.1103/PhysRevB.49.14251
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      Ab initio molecular-dynamics simulation of the liquid-metal-amorphous-semiconductor transition in germanium
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      The authors present ab initio quantum-mech. mol.-dynamics simulations of the liq.-metal-amorphous-semiconductor transition in Ge. The simulations are based on (a) finite-temp. d.-functional theory of the 1-electron states, (b) exact energy minimization and hence calcn. of the exact Hellmann-Feynman forces after each mol.-dynamics step using preconditioned conjugate-gradient techniques, (c) accurate nonlocal pseudopotentials, and (d) Nose' dynamics for generating a canonical ensemble. This method gives perfect control of the adiabaticity of the electron-ion ensemble and allows the authors to perform simulations over >30 ps. The computer-generated ensemble describes the structural, dynamic, and electronic properties of liq. and amorphous Ge in very good agreement with expt.. The simulation allows the authors to study in detail the changes in the structure-property relation through the metal-semiconductor transition. The authors report a detailed anal. of the local structural properties and their changes induced by an annealing process. The geometrical, bounding, and spectral properties of defects in the disordered tetrahedral network are studied and compared with expt.
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      Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set
      Kresse, G.; Furthmuller, J.
      Computational Materials Science (1996), 6 (1), 15-50CODEN: CMMSEM; ISSN:0927-0256. (Elsevier)
      The authors present a detailed description and comparison of algorithms for performing ab-initio quantum-mech. calcns. using pseudopotentials and a plane-wave basis set. The authors will discuss: (a) partial occupancies within the framework of the linear tetrahedron method and the finite temp. d.-functional theory, (b) iterative methods for the diagonalization of the Kohn-Sham Hamiltonian and a discussion of an efficient iterative method based on the ideas of Pulay's residual minimization, which is close to an order N2atoms scaling even for relatively large systems, (c) efficient Broyden-like and Pulay-like mixing methods for the charge d. including a new special preconditioning optimized for a plane-wave basis set, (d) conjugate gradient methods for minimizing the electronic free energy with respect to all degrees of freedom simultaneously. The authors have implemented these algorithms within a powerful package called VAMP (Vienna ab-initio mol.-dynamics package). The program and the techniques have been used successfully for a large no. of different systems (liq. and amorphous semiconductors, liq. simple and transition metals, metallic and semi-conducting surfaces, phonons in simple metals, transition metals and semiconductors) and turned out to be very reliable.
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      Kresse, G.; Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 1996, 54, 11169– 11186,  DOI: 10.1103/PhysRevB.54.11169
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      Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set
      Kresse, G.; Furthmueller, J.
      Physical Review B: Condensed Matter (1996), 54 (16), 11169-11186CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
      The authors present an efficient scheme for calcg. the Kohn-Sham ground state of metallic systems using pseudopotentials and a plane-wave basis set. In the first part the application of Pulay's DIIS method (direct inversion in the iterative subspace) to the iterative diagonalization of large matrixes will be discussed. This approach is stable, reliable, and minimizes the no. of order Natoms3 operations. In the second part, we will discuss an efficient mixing scheme also based on Pulay's scheme. A special "metric" and a special "preconditioning" optimized for a plane-wave basis set will be introduced. Scaling of the method will be discussed in detail for non-self-consistent and self-consistent calcns. It will be shown that the no. of iterations required to obtain a specific precision is almost independent of the system size. Altogether an order Natoms2 scaling is found for systems contg. up to 1000 electrons. If we take into account that the no. of k points can be decreased linearly with the system size, the overall scaling can approach Natoms. They have implemented these algorithms within a powerful package called VASP (Vienna ab initio simulation package). The program and the techniques have been used successfully for a large no. of different systems (liq. and amorphous semiconductors, liq. simple and transition metals, metallic and semiconducting surfaces, phonons in simple metals, transition metals, and semiconductors) and turned out to be very reliable.
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      Projector augmented-wave method
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      There is no expanded citation for this reference.
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      Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method. Phys. Rev. B 1999, 59, 1758– 1775,  DOI: 10.1103/PhysRevB.59.1758
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      Kresse, G.; Joubert, D.
      Physical Review B: Condensed Matter and Materials Physics (1999), 59 (3), 1758-1775CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
      The formal relationship between ultrasoft (US) Vanderbilt-type pseudopotentials and Blochl's projector augmented wave (PAW) method is derived. The total energy functional for US pseudopotentials can be obtained by linearization of two terms in a slightly modified PAW total energy functional. The Hamilton operator, the forces, and the stress tensor are derived for this modified PAW functional. A simple way to implement the PAW method in existing plane-wave codes supporting US pseudopotentials is pointed out. In addn., crit. tests are presented to compare the accuracy and efficiency of the PAW and the US pseudopotential method with relaxed-core all-electron methods. These tests include small mols. (H2, H2O, Li2, N2, F2, BF3, SiF4) and several bulk systems (diamond, Si, V, Li, Ca, CaF2, Fe, Co, Ni). Particular attention is paid to the bulk properties and magnetic energies of Fe, Co, and Ni.
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      Physical Review Letters (1996), 77 (18), 3865-3868CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      Generalized gradient approxns. (GGA's) for the exchange-correlation energy improve upon the local spin d. (LSD) description of atoms, mols., and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental consts. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential.
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      Momma, K.; Izumi, F. VESTA3 for three-dimensional visualization of crystal, volumetric and morphology data. J. Appl. Crystallogr. 2011, 44, 1272– 1276,  DOI: 10.1107/S0021889811038970
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      VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data
      Momma, Koichi; Izumi, Fujio
      Journal of Applied Crystallography (2011), 44 (6), 1272-1276CODEN: JACGAR; ISSN:0021-8898. (International Union of Crystallography)
      VESTA is a 3D visualization system for crystallog. studies and electronic state calcns. It was upgraded to the latest version, VESTA 3, implementing new features including drawing the external morphpol. of crysals; superimposing multiple structural models, volumetric data and crystal faces; calcn. of electron and nuclear densities from structure parameters; calcn. of Patterson functions from the structure parameters or volumetric data; integration of electron and nuclear densities by Voronoi tessellation; visualization of isosurfaces with multiple levels, detn. of the best plane for selected atoms; an extended bond-search algorithm to enable more sophisticated searches in complex mols. and cage-like structures; undo and redo is graphical user interface operations; and significant performance improvements in rendering isosurfaces and calcg. slices.
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      Liu, Q.; Fan, C.; Zhang, R. First-principles study of high-pressure structural phase transitions of magnesium. J. Appl. Phys. 2009, 105, 123505,  DOI: 10.1063/1.3151687
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      First-principles study of high-pressure structural phase transitions of magnesium
      Liu, Qiuxiang; Fan, Changzeng; Zhang, Ruijun
      Journal of Applied Physics (2009), 105 (12), 123505/1-123505/4CODEN: JAPIAU; ISSN:0021-8979. (American Institute of Physics)
      The structural phase transitions for the hcp., bcc., dhcp., and fcc. of magnesium at hydrostatic pressures larger than ∼200 GPa at zero temp. are studied by first-principles total energy calcns. The plane-wave basis pseudopotential method was adopted, in which the generalized gradient approxn. implanted in the CASTEP code is employed. By comparing the enthalpy differences of the hcp. structure with other three structures under different pressures, it can be seen that when the pressure becomes higher than ∼65, 130, and 190 GPa, the bcc., dhcp., and fcc. structures become more stable relative to the hcp. structure, resp. Due to the lowest enthalpy value of the bcc. structure above 65 GPa, it can be deduced that magnesium may transform to the bcc. structure from the ground state hcp. structure around 65 GPa, but no further phase transitions occur without addnl. applying high temp. In addn., the equation of state of magnesium is calcd., indicating that bcc. structure is the softest phase. (c) 2009 American Institute of Physics.
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      Akahama, Y.; Fujihisa, H.; Kawamura, H. New Helical Chain Structure for Scandium at 240 GPa. Phys. Rev. Lett. 2005, 94, 195503,  DOI: 10.1103/PhysRevLett.94.195503
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      Physical Review Letters (2005), 94 (19), 195503/1-195503/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      X-ray diffraction expts. were carried out at 297 K to study structural-phase transitions of the trivalent rare-earth metal Sc at pressures of up to 297 GPa. Four stages of structural transition were obsd. around 23, 104, 140, and 240 GPa. The crystal structure of the highest-pressure phase, Sc-V, is a hexagonal lattice (S.G.: P6122 or P6522) consisting of 6-screw helical chains. The lattice can be derived from modulations of the interplane stacking of the (111) planes in an fcc. arrangement. The occurrence of an anisotropic structure suggests the importance of interactions between 3d orbitals with their nearest-neighbor atoms.
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      Nature Physics (2007), 3 (7), 473-476CODEN: NPAHAX; ISSN:1745-2473. (Nature Publishing Group)
      Hydrogen, being the first element in the periodic table, has the simplest electronic structure of any atom, and the hydrogen mol. contains the simplest covalent chem. bond. Nevertheless, the phase diagram of hydrogen is poorly understood. Detg. the stable structures of solid hydrogen is a tremendous exptl. challenge, because hydrogen atoms scatter X-rays only weakly, leading to low-resoln. diffraction patterns. Theor. studies encounter major difficulties owing to the small energy differences between structures and the importance of the zero-point motion of the protons. We have systematically investigated the zero-temp. phase diagram of solid hydrogen using first-principles d. functional theory (DFT) electronic-structure methods, including the proton zero-point motion at the harmonic level. Our study leads to a radical revision of the DFT phase diagram of hydrogen up to nearly 400 GPa. That the most stable phases remain insulating to very high pressures eliminates a major discrepancy between theory and expt. One of our new phases is calcd. to be stable over a wide range of pressures, and its vibrational properties agree with the available exptl. data for phase III.
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      Akbarzadeh, A. R.; Ozoliņš, V.; Wolverton, C. First-Principles Determination of Multicomponent Hydride Phase Diagrams: Application to the Li-Mg-N-H System. Adv. Mater. 2007, 19, 3233– 3239,  DOI: 10.1002/adma.200700843
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      First-principles determination of multicomponent hydride phase diagrams: application to the Li-Mg-N-H system
      Akbarzadeh, Alireza R.; Ozolins, Vidvuds; Wolverton, Christopher
      Advanced Materials (Weinheim, Germany) (2007), 19 (20), 3233-3239CODEN: ADVMEW; ISSN:0935-9648. (Wiley-VCH Verlag GmbH & Co. KGaA)
      Complex solid-state hydrides can store hydrogen at very high volumetric and gravimetric densities. We present a theor. framework, which automatically dets. phase diagrams and thermodynamically favored hydrogen storage reactions in complex multicomponent systems, such as Li-Mg-N-H (see figure). This method can be used to efficiently scan the phase space and pinpoint those compns., which have the greatest potential for thermodynamically reversible H2 storage.
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      Virtanen, P.; Gommers, R.; Oliphant, T. E.; Haberland, M.; Reddy, T.; Cournapeau, D.; Burovski, E.; Peterson, P.; Weckesser, W. Author Correction: SciPy 1.0: fundamental algorithms for scientific computing in Python. Nat. Methods 2020, 17, 352– 352,  DOI: 10.1038/s41592-020-0772-5
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      Author Correction: SciPy 1.0: fundamental algorithms for scientific computing in Python
      Virtanen, Pauli; Gommers, Ralf; Oliphant, Travis E.; Haberland, Matt; Reddy, Tyler; Cournapeau, David; Burovski, Evgeni; Peterson, Pearu; Weckesser, Warren; Bright, Jonathan; van der Walt, Stefan J.; Brett, Matthew; Wilson, Joshua; Millman, K. Jarrod; Mayorov, Nikolay; Nelson, Andrew R. J.; Jones, Eric; Kern, Robert; Larson, Eric; Carey, C. J.; Polat, Ilhan; Feng, Yu; Moore, Eric W.; Vander Plas, Jake; Laxalde, Denis; Perktold, Josef; Cimrman, Robert; Henriksen, Ian; Quintero, E. A.; Harris, Charles R.; Archibald, Anne M.; Ribeiro, Antonio H.; Pedregosa, Fabian; van Mulbregt, Paul
      Nature Methods (2020), 17 (3), 352CODEN: NMAEA3; ISSN:1548-7091. (Nature Research)
      An amendment to this paper has been published and can be accessed via a link at the top of the paper.
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      Giannozzi, P.; Baroni, S.; Bonini, N.; Calandra, M.; Car, R.; Cavazzoni, C.; Ceresoli, D.; Chiarotti, G. L.; Cococcioni, M.; Dabo, I. QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. J. Phys.: Condens. Matter 2009, 21, 395502,  DOI: 10.1088/0953-8984/21/39/395502
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      QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials
      Giannozzi Paolo; Baroni Stefano; Bonini Nicola; Calandra Matteo; Car Roberto; Cavazzoni Carlo; Ceresoli Davide; Chiarotti Guido L; Cococcioni Matteo; Dabo Ismaila; Dal Corso Andrea; de Gironcoli Stefano; Fabris Stefano; Fratesi Guido; Gebauer Ralph; Gerstmann Uwe; Gougoussis Christos; Kokalj Anton; Lazzeri Michele; Martin-Samos Layla; Marzari Nicola; Mauri Francesco; Mazzarello Riccardo; Paolini Stefano; Pasquarello Alfredo; Paulatto Lorenzo; Sbraccia Carlo; Scandolo Sandro; Sclauzero Gabriele; Seitsonen Ari P; Smogunov Alexander; Umari Paolo; Wentzcovitch Renata M
      Journal of physics. Condensed matter : an Institute of Physics journal (2009), 21 (39), 395502 ISSN:.
      QUANTUM ESPRESSO is an integrated suite of computer codes for electronic-structure calculations and materials modeling, based on density-functional theory, plane waves, and pseudopotentials (norm-conserving, ultrasoft, and projector-augmented wave). The acronym ESPRESSO stands for opEn Source Package for Research in Electronic Structure, Simulation, and Optimization. It is freely available to researchers around the world under the terms of the GNU General Public License. QUANTUM ESPRESSO builds upon newly-restructured electronic-structure codes that have been developed and tested by some of the original authors of novel electronic-structure algorithms and applied in the last twenty years by some of the leading materials modeling groups worldwide. Innovation and efficiency are still its main focus, with special attention paid to massively parallel architectures, and a great effort being devoted to user friendliness. QUANTUM ESPRESSO is evolving towards a distribution of independent and interoperable codes in the spirit of an open-source project, where researchers active in the field of electronic-structure calculations are encouraged to participate in the project by contributing their own codes or by implementing their own ideas into existing codes.
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      Giannozzi, P.; Andreussi, O.; Brumme, T.; Bunau, O.; Nardelli, M. B.; Calandra, M.; Car, R.; Cavazzoni, C.; Ceresoli, D.; Cococcioni, M. Advanced capabilities for materials modelling with Quantum ESPRESSO. J. Phys.: Condens. Matter 2017, 29, 465901,  DOI: 10.1088/1361-648X/aa8f79
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      Advanced capabilities for materials modelling with QUANTUM ESPRESSO
      Giannozzi, P.; Andreussi, O.; Brumme, T.; Bunau, O.; Buongiorno Nardelli, M.; Calandra, M.; Car, R.; Cavazzoni, C.; Ceresoli, D.; Cococcioni, M.; Colonna, N.; Carnimeo, I.; Dal Corso, A.; de Gironcoli, S.; Delugas, P.; Di Stasio, R. A., Jr.; Ferretti, A.; Floris, A.; Fratesi, G.; Fugallo, G.; Gebauer, R.; Gerstmann, U.; Giustino, F.; Gorni, T.; Jia, J.; Kawamura, M.; Ko, H.-Y.; Kokalj, A.; Kucukbenli, E.; Lazzeri, M.; Marsili, M.; Marzari, N.; Mauri, F.; Nguyen, N. L.; Nguyen, H.-V.; Otero-de-la-Roza, A.; Paulatto, L.; Ponce, S.; Rocca, D.; Sabatini, R.; Santra, B.; Schlipf, M.; Seitsonen, A. P.; Smogunov, A.; Timrov, I.; Thonhauser, T.; Umari, P.; Vast, N.; Wu, X.; Baroni, S.
      Journal of Physics: Condensed Matter (2017), 29 (46), 465901/1-465901/30CODEN: JCOMEL; ISSN:0953-8984. (IOP Publishing Ltd.)
      QUANTUM ESPRESSO is an integrated suite of open-source computer codes for quantum simulations of materials using state-of-the-art electronic-structure techniques, based on d.-functional theory, d.-functional perturbation theory, and many-body perturbation theory, within the plane-wave pseudopotential and projector-augmented-wave approaches. QUANTUM ESPRESSO owes its popularity to the wide variety of properties and processes it allows to simulate, to its performance on an increasingly broad array of hardware architectures, and to a community of researchers that rely on its capabilities as a core open-source development platform to implement their ideas. In this paper we describe recent extensions and improvements, covering new methodologies and property calculators, improved parallelization, code modularization, and extended interoperability both within the distribution and with external software.
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      Giannozzi, P.; Baseggio, O.; Bonfà, P.; Brunato, D.; Car, R.; Carnimeo, I.; Cavazzoni, C.; de Gironcoli, S.; Delugas, P.; Ruffino, F. F. QuantumESPRESSO toward the exascale. J. Chem. Phys. 2020, 152, 154105,  DOI: 10.1063/5.0005082
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      QUANTUM ESPRESSO toward the exascale
      Giannozzi, Paolo; Baseggio, Oscar; Bonfa, Pietro; Brunato, Davide; Car, Roberto; Carnimeo, Ivan; Cavazzoni, Carlo; de Gironcoli, Stefano; Delugas, Pietro; Ferrari Ruffino, Fabrizio; Ferretti, Andrea; Marzari, Nicola; Timrov, Iurii; Urru, Andrea; Baroni, Stefano
      Journal of Chemical Physics (2020), 152 (15), 154105CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      A review. QUANTUM ESPRESSO is an open-source distribution of computer codes for quantum-mech. materials modeling, based on d.-functional theory, pseudopotentials, and plane waves, and renowned for its performance on a wide range of hardware architectures, from laptops to massively parallel computers, as well as for the breadth of its applications. In this paper, we present a motivation and brief review of the ongoing effort to port QUANTUM ESPRESSO onto heterogeneous architectures based on hardware accelerators, which will overcome the energy constraints that are currently hindering the way toward exascale computing. (c) 2020 American Institute of Physics.
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      The superconducting transition temp. is calcd. as a function of the electronphonon and electron-electron coupling consts. within the framework of the strong-coupling theory. By using this theoretical result, empirical values are found of the coupling consts. and the "band-structure" d. of states for a no. of metals and alloys. The electron-phonon coupling const. depends primarily on the phonon frequencies rather than on the electronic properties of the metal. By using these results, one can predict a max. super-conducting transition temp.
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      Einaga, M.; Sakata, M.; Ishikawa, T.; Shimizu, K.; Eremets, M. I.; Drozdov, A. P.; Troyan, I. A.; Hirao, N.; Ohishi, Y. Crystal structure of the superconducting phase of sulfur hydride. Nat. Phys. 2016, 12, 835– 838,  DOI: 10.1038/nphys3760
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      Nature Physics (2016), 12 (9), 835-838CODEN: NPAHAX; ISSN:1745-2473. (Nature Publishing Group)
      A superconducting crit. temp. above 200 K has recently been discovered in H2S (or D2S) under high hydrostatic pressure. These measurements were interpreted in terms of a decompn. of these materials into elemental sulfur and a hydrogen-rich hydride that is responsible for the supercond., although direct exptl. evidence for this mechanism has so far been lacking. Here we report the crystal structure of the superconducting phase of hydrogen sulfide (and deuterium sulfide) in the normal and superconducting states obtained by means of synchrotron X-ray diffraction measurements, combined with elec. resistance measurements at both room and low temps. We find that the superconducting phase is mostly in good agreement with the theor. predicted body-centered cubic (bcc) structure for H3S. The presence of elemental sulfur is also manifest in the X-ray diffraction patterns, thus proving the decompn. mechanism of H2S to H3S + S under pressure.
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      A review with 179 refs. of the use of diamond anvil cells for ultrahigh-pressure generation (a few hundred GPa) and the various techniques used in studying the high-pressure behavior of solids.
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      Ohmura, A.; Machida, A.; Watanuki, T.; Aoki, K.; Nakano, S.; Takemura, K. Pressure-induced structural change from hexagonal to fcc metal lattice in scandium trihydride. J. Alloys Compd. 2007, 446–447, 598– 602,  DOI: 10.1016/j.jallcom.2007.04.018
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      Pressure-induced structural change from hexagonal to fcc metal lattice in scandium trihydride
      Ohmura, A.; Machida, A.; Watanuki, T.; Aoki, K.; Nakano, S.; Takemura, K.
      Journal of Alloys and Compounds (2007), 446-447 (), 598-602CODEN: JALCEU; ISSN:0925-8388. (Elsevier B.V.)
      We synthesized Sc hydrides by hydrogenation of a Sc foil with H2 fluid under high pressure at ambient temp. ScH2 and ScH3 were prepd. near 4 and 5 GPa, resp. The hydrogenation process and pressure-induced structural changes in ScH3 were investigated by synchrotron radiation x-ray diffraction measurements ≤54.7 GPa. A structural transition from hexagonal to the fcc. lattice began at 30 GPa and was completed at 46 GPa via an intermediate state similar to those reported for other hexagonal trihydrides. The intermediate state was not interpreted in terms of a coexisting state for the low-pressure hexagonal and the high-pressure fcc. structures. The onset transition pressure of ScH3 supported the previously proposed relation that the hexagonal-fcc. transition pressure is inversely proportional to the ionic radius of the trihydride.
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      Kume, T.; Ohura, H.; Takeichi, T.; Ohmura, A.; Machida, A.; Watanuki, T.; Aoki, K.; Sasaki, S.; Shimizu, H.; Takemura, K. High-pressure study of ScH3: Raman, infrared, and visible absorption spectroscopy. Phys. Rev. B 2011, 84, 064132,  DOI: 10.1103/PhysRevB.84.064132
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      Physical Review B: Condensed Matter and Materials Physics (2011), 84 (6), 064132/1-064132/7CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
      Raman, IR, and visible absorption spectra of Sc trihydride (ScH3) were measured at high pressures up to 50 GPa, to study the structural and electronic phase transitions. Successive hcp.-intermediate-fcc. phase transitions were obsd. at 25 and 46 GPa by Raman and IR measurements. Probably the intermediate phase of ScH3 takes the same structure as that of YH3 with a long periodicity of the stacking of the metal planes. The visible absorption spectra allowed one to det. that the energy gap of ScH3 is 1.7 eV at the ambient condition and is closed around 50 GPa, at which the crystal structure transforms to fcc.
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      Shao, M.; Chen, S.; Chen, W.; Zhang, K.; Huang, X.; Cui, T. Superconducting ScH3 and LuH3 at Megabar Pressures. Inorg. Chem. 2021, 60, 15330– 15335,  DOI: 10.1021/acs.inorgchem.1c01960
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      Superconducting ScH3 and LuH3 at Megabar Pressures
      Shao, Mengyao; Chen, Su; Chen, Wuhao; Zhang, Kexin; Huang, Xiaoli; Cui, Tian
      Inorganic Chemistry (2021), 60 (20), 15330-15335CODEN: INOCAJ; ISSN:0020-1669. (American Chemical Society)
      Rare-earth (RE) superhydrides have great potential as high-temp. superconductors, with recent discoveries almost achieving room-temp. supercond. in compressed LaH10 and YH9. Here, we continue to study the rare-earth hydrides by focusing on the new hydrides that the lightest element Sc and the heaviest element Lu formed under pressure. Two new superconducting hydrides ScH3 (Tc ∼ 18.5 K at 131 GPa) and LuH3 (Tc ∼ 12.4 K at 122 GPa) have been identified both with cubic structure by combining X-ray diffraction and elec. resistance techniques. Among all of the REH3, only the superconducting properties of ScH3 and LuH3 have been exptl. confirmed. Our current results may offer guidance to other REH3, which were predicted to be superconductors but have not been exptl. confirmed.
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      Bortz, M.; Bertheville, B.; Böttger, G.; Yvon, K. Structure of the High Pressure Phase Γ-MgH2 by Neutron Powder Diffraction. J. Alloys Compd. 1999, 287, L4– L6,  DOI: 10.1016/S0925-8388(99)00028-6
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      The high-pressure phase γ-MgH2 was formed by heating the low-pressure phase α-MgH2 in a multianvil press at 2 GPa pressure to 1070 K for 120 min and successive rapid quenching. Study by x-ray and neutron powder diffraction on the deuteride at ambient conditions revealed that it crystallizes with the orthorhombic α-PbO2 type structure (space group Pbcn, Z = 4, a 4.5213(3), b 5.4382(3), c 4.9337(3) Å (hydride); a 4.5056(3), b 5.4212(3), c 4.9183(3) Å (deuteride) at T = 295 K). The D atoms surround Mg in a distorted octahedral configuration with bond distances Mg-D 1.915(3), 1.943(3) and 2.004(3) Å. The rutile structure of α-MgH2 was reevaluated.
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      The structural stability of MgH2 was studied up to 16 GPa using a high-pressure synchrotron x-ray diffraction technique. Several pressure-induced phase transitions were identified in this pressure range. Owing to the close structural similarity between the α and γ modifications the high-pressure γ form can be stabilized as a metastable phase after pressure release. The exptl. obsd. structural transition sequence and the vol. changes at the transition points as well as bulk modulii are in good agreement with theor. calcd. data. The bonding nature of MgH2 is analyzed with the help of charge-d., charge-transfer, electron-localization-function, and Mulliken-population analyses which clearly show that all polymorphs of MgH2 are to be classified as ionic materials with Mg and H in nearly 2+ and 1- states, resp.
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      A theory simple enough possibly to yield calcns. of thermal, transport, and electromagnetic properties is based on the dominance of neg. phonon interaction over Coulomb interaction in supercond. The theory seems to give a natural indication of the fraction of electrons above the Fermi surface in virtual pair states. An exponential factor in the energy may account for kTc <<< hω/2π (C.A. 49, 15461h). The theory leads to an energy gap in terms of electron-hole pair creation that may account for electromagnetic properties (C.A. 49, 8643g). The gap predicted for Sn is 13.8°K.; exptl. value is 11.2°K. The theory gives the isotope effect (cf. Fr.ovrddot.ohlich, C.A. 44, 10420i).
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      Kim, D. Y.; Scheicher, R. H.; Ahuja, R. Predicted High-Temperature Superconducting State in the Hydrogen-Dense Transition-Metal Hydride YH3 at 40 K and 17.7 GPa. Phys. Rev. Lett. 2009, 103, 077002,  DOI: 10.1103/PhysRevLett.103.077002
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      Predicted High-Temperature Superconducting State in the Hydrogen-Dense Transition-Metal Hydride YH3 at 40 K and 17.7 GPa
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      Physical Review Letters (2009), 103 (7), 077002/1-077002/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      Metalization in pure hydrogen has been proposed to give rise to high-temp. supercond. at pressures which still lie beyond the reach of contemporary exptl. techniques. Hydrogen-dense materials offer an opportunity to study related phenomena at exptl. achievable pressures. Here we report the prediction of high-temp. supercond. in yttrium hydride (YH3), with a Tc of 40 K at 17.7 GPa, the lowest reported pressure for hydrogen-dense materials to date. Specifically, we find that the face-centered cubic structure of YH3 exhibits supercond. of different origins in two pressure regions. The evolution of Tc with pressure follows the corresponding change of s-d hybridization between H and Y, due to an enhancement of the electron-phonon coupling by a matching of the energy level from Y-H vibrations with the peak of the s electrons from the octahedrally coordinated hydrogen atoms.
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    The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpcc.1c08743.

    • Computational details of Gibbs free energy at finite temperature and the superconducting Tc; ternary convex hulls of Mg–Sc–H systems at 100 and 150 GPa; total electronic density of states (DOS) and the partial DOS of H atoms of some representative Mg–Sc–H compounds under high pressure; pressure-dependent phonons and electron–phonon coupling spectra for MgScH6, Mg2ScH10, MgSc2H9, and Mg(ScH4)3; Gibbs free energy (including the enthalpy, zero-point energy (ZPE) correction, and other associated terms) of the main stable and metastable phases in the Mg–Sc–H system at 100, 150, and 200 GPa; structural information of newly predicted structures of ternary Mg–Sc–H compounds (PDF)


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