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REVIEW 3 major objections 5 minor 121 references

High-pressure electride superconductor Li5N for multifunctional applications: A theoretical insight into the physical properties

T0 review · 3 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Hexagonal Li5N is predicted to remain dynamically stable from 100 to 382 GPa and to stay metallic, ductile, hard, and highly reflective while superconductivity weakens with pressure.

desk verdict Solid elastic/electronic property catalog for Li5N; the optical and superconducting claims need reframing before they can be used. read the letter →

arxiv 2608.10768 v1 pith:6I2E74VM submitted 2026-08-11 cond-mat.mtrl-sci cond-mat.supr-con

M. Abdul Hadi Shah , S.H. Naqib This is my paper · ORCID
classification cond-mat.mtrl-scicond-mat.supr-con
keywords Li5Nhigh-pressureelectridefirst-principlesDFTphononstabilityelasticpropertiessuperconductivityopticalP6/mmm
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Li5N is a predicted high-pressure electride: a crystal in which extra electrons occupy the spaces between atoms and act as anions. This paper argues that its hexagonal form is dynamically stable between 100 and 382 GPa and mechanically stable from 150 to 350 GPa, and that pressure tunes it into a ductile, hard, metallic solid with very high Debye and melting temperatures. The authors further claim that the compound should be a near-perfect infrared reflector and strong ultraviolet absorber, and that its superconductivity weakens as pressure rises because the density of states at the Fermi level drops.

What carries the argument

The central object is the one-formula-unit hexagonal cell of Li5N in space group P6/mmm, with Li at 1a and 4h sites and N at 1b; the electride's interstitial electrons give the material its metallic and optical character. The argument is carried by a consistent first-principles workflow on that same structure: finite-displacement density-functional perturbation theory phonon dispersion for dynamical stability, stress-strain elastic constants for mechanical and thermo-physical quantities, band structure and density of states for the electronic picture, and the McMillan equation with a Bennemann-Garland Coulomb pseudopotential for superconductivity. The optical response combines Kramers-Kronig interband dielectric functions with a semi-empirical Drude term whose plasma frequency is fixed at 2.0 eV and damping at 0.05 eV for every pressure; that Drude term produces the negative real dielectric function and the near-unity low-energy reflectivity.

What would settle it

Recompute the optical response with the plasma frequency and damping obtained from the band structure and electron lifetime rather than fixed values; if the low-energy reflectivity no longer reaches about 0.97 or the real dielectric function no longer stays negative in the same energy windows, the paper's optical and multifunctional conclusion is refuted.

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Extended reading notes

Core claim

On the paper's own terms, the discovery is that hexagonal P6/mmm Li5N is a pressure-stabilized multifunctional electride. Compression from 150 to 350 GPa smoothly stiffens the lattice, with the bulk modulus rising from 468 to 982 GPa and the average Vickers hardness from about 27 to 34 GPa, while the compound stays ductile (Poisson's ratio 0.29 to 0.34, Pugh's ratio below 0.57) and remains metallic with no band gap. The Debye temperature climbs from about 1764 K to 2134 K and the estimated melting temperature from about 5156 K to 9457 K. Using a previously predicted critical temperature as input to the McMillan equation, the authors find the electron-phonon coupling constant falls from 0.569 at 150 GPa to 0.118 at 350 GPa, so superconductivity is suppressed by pressure. The optical calculation yields a Drude-like negative real dielectric function at low energy, low-energy reflectivity near 0.97, and strong ultraviolet absorption around $10^{5}$ $cm^{-1}$.

Load-bearing premise

The paper's optical claims stand on a simplified free-electron model whose two main numbers, plasma frequency set to 2.0 eV and damping set to 0.05 eV at every pressure, are chosen rather than computed, and those numbers drive the predicted negative dielectric function and near-perfect low-energy reflectivity.

Editorial extensions

If this is right

  • If hexagonal Li5N is synthesized in the 150 to 350 GPa range, it should be a mechanically stable, ductile metal that becomes stiffer and harder as pressure increases.
  • The predicted Debye temperatures of 1764 to 2134 K and melting temperatures of about 5156 to 9457 K imply a very stiff, thermally conductive lattice at high pressure.
  • Because the Fermi-level density of states falls from 0.207 to 0.077 states/eV between 150 and 350 GPa, electron-phonon coupling weakens and the superconducting transition temperature should drop with pressure.
  • The optical calculations imply that, if the Drude parameters are right, Li5N would be an efficient infrared reflector and a strong ultraviolet absorber, with refractive index above 2 in the infrared.
  • The reported elastic anisotropy and direction-dependent sound velocities mean practical use of Li5N would have to account for its anisotropic mechanical and thermal response.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper: deriving the Drude plasma frequency from the calculated band structure would probably make it pressure-dependent, so the near-constant 0.97 reflectivity is a testable prediction rather than a robust first-principles result.
  • Beyond the paper: the phonon data across 100 to 382 GPa could be fed into ab initio molecular dynamics to test the superionic lithium mobility predicted for this electride by earlier work, connecting the mechanical picture to ionic transport.
  • Beyond the paper: if reflectivity near 0.97 persists only above 100 GPa, applications as an infrared mirror or optical component would require pressure-retention strategies or quenching to metastable ambient forms, which the paper does not address.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The manuscript reports a first-principles DFT (CASTEP, PBEsol) study of hexagonal Li5N (P6/mmm) under high pressure (150–350 GPa). It covers structural optimization, formation and cohesive energies, phonon dispersions, elastic constants and derived mechanical properties, elastic anisotropy, sound velocities, Debye temperature, minimum and lattice thermal conductivity, melting temperature, electronic band structure and density of states, Mulliken population analysis, charge density, superconductivity via the McMillan equation, and optical properties including a Drude intraband term. The authors claim dynamic stability from 100 to 382 GPa, mechanical stability and ductility between 150 and 350 GPa, metallic character, high hardness, high Debye temperatures, strong ultraviolet absorption, near-unity low-energy reflectivity, and pressure-tunable superconducting and optical properties. They conclude that Li5N is a multifunctional high-pressure electride with potential for optoelectronic and high-temperature applications.

Significance. The manuscript provides a reasonably well-converged set of structural, elastic, phonon, and electronic data for a candidate high-pressure electride, and the mechanical and electronic sections appear internally consistent and compatible with the limited prior data. However, the two application-oriented claims—the superconducting λep values (Table 9) and the low-energy optical response (Fig. 14)—are not predictions from first principles. The λep values are back-solved from an input Tc via the McMillan equation, and the optical spectra are dominated by an assumed Drude term with arbitrary plasma frequency and damping. These issues do not invalidate the structural/mechanical results, but they prevent the paper from supporting its 'multifunctional applications' conclusions in its present form.

major comments (3)
  1. [Section 3.7, Eq. (17), Table 9] The electron–phonon coupling constants λep are obtained by solving the McMillan equation for λep using the Tc values from Ref. [26] and the ΘD values computed here. This is an inversion rather than an ab initio calculation, so the pressure trend '0.569 → 0.227 → 0.118' is a consequence of the assumed Tc and the model, not a new prediction. The comparison with the Ref. [26] λep values in Table 9 is misleading because both sets derive from the same Tc through different approximate equations; the discrepancy mainly reflects the different phonon-frequency scales used. The section should be reframed as a consistency check, and the conclusion that 'very high Debye temperature facilitates high-temperature superconductivity' should be reconsidered: for fixed Tc, a higher ΘD lowers the inferred λep in the McMillan equation.
  2. [Section 3.8 and Fig. 14] The low-energy optical properties—negative ε1(ω), R(0)≈0.97, infrared refractive index n>2, and the low-energy loss peak—are generated by adding a semi-empirical Drude term with plasma frequency fixed at 2.0 eV and damping fixed at 0.05 eV (plus 0.5 eV Gaussian smearing) for all pressures. These parameters are not computed from the electronic structure, so the claimed 'impressive low-energy reflectivity' and 'excellent reflector in the infrared region' are not first-principles results. The choice of γ=0.05 eV in particular is critical: larger physical damping values would substantially reduce R(0) and broaden or wash out the ε1<0 window. The authors should compute the intraband dielectric response from the band structure (or from the plasma frequency and a physically justified scattering rate) and provide a sensitivity analysis; otherwise the optical 'multifunctional' claims are not supported.
  3. [Section 3.5.2 and Table 7] The melting temperatures (5156–9457 K) are estimated from the empirical relation Tm = 354 + 1.5(2C11 + C33), which was calibrated for elemental metals near ambient pressure. Applying this formula at 150–350 GPa yields values far beyond any benchmark and likely far above the actual melting curve of Li5N, especially given the superionic behavior reported in Ref. [26] at high pressures. The statement in the conclusion that 'the melting temperature of the compound is extremely high' is therefore not warranted without additional evidence, such as ab initio molecular dynamics or comparison with related nitrides at similar pressures.
minor comments (5)
  1. [Section 3.7] The text contains a typo 'Li5Ni' at the end of the superconductivity section, and 'MacMillan' should be spelled 'McMillan' in two places.
  2. [Section 3.5.2, Eq. (15)] The numerical constant in the expression for A(γa) is garbled ('4.85628 × 10଻'), and the definitions of M_av and the average atomic volume δ should be stated explicitly for reproducibility.
  3. [Fig. 14 caption] The label 'αf' in the caption should be 'α(ω)' for the absorption coefficient.
  4. [Section 3.1.1] The reported positive formation energy (0.107 eV/atom) at 100 GPa appears to contradict the thermodynamic stability predicted for Li5N at 80–100 GPa in Ref. [37]; the authors should comment on this discrepancy and justify the pressure window more carefully.
  5. [Section 2.1] The phonon methodology is described as 'DFPT based on the finite displacement supercell method'; these are two distinct approaches, and the text should clarify which one was actually used, since the cited references correspond to different methods.

Circularity Check

2 steps flagged · score 6.0 of 10

Low-energy optical 'predictions' reduce to the assumed Drude plasma frequency (2.0 eV) and damping (0.05 eV) in Sec. 3.8, while the superconducting λep in Table 9 is back-solved from the prior Tc of Ref. [26] via McMillan inversion.

  1. self definitional [Section 3.8, Optical properties (discussion of Fig. 14)]
    "Due to the metallic nature of Li5N, a semi-empirical Drude term with a Gaussian smearing of 0.5 eV is incorporated to evaluate the frequency-dependent dielectric constant. Accordingly, a uniform Drude damping parameter of 0.05 eV is applied in all cases, while the plasma frequency is set to 2.0 eV."

    The low-energy optical response—negative ε1 window (0 to ~1 eV), the IR loss peak, and the static reflectivity R(0)≈0.97—is governed almost entirely by the assumed Drude term, not by the DFT interband dielectric function. With ωp=2.0 eV and γ=0.05 eV, Drude theory gives ε1(0)=1−(ωp/γ)^2≈−1599 and a diverging ε2, forcing normal-incidence reflectivity close to 1−2γ/ωp≈0.95 before interband corrections; the reported 0.97 is therefore a direct output of the chosen γ≪ωp. The paper presents this as a 'calculated' first-principles result, but the headline optical claims are encoded in the input constants rather than derived from the electronic structure.

  2. fitted input called prediction [Section 3.7, Eq. (17), Table 9]
    "The electron–phonon coupling constant (λep) can be calculated using t he familiar McMillan equation [113] when Tc, Debye temperature and μ* are known as follows: ... We have used the theoretically predicted Tc [26] here."

    Eq. (17) is solved for λep using ΘD and μ* from this work together with the transition temperature Tc taken from Ref. [26]. Consequently, the λep values in Table 9 (0.569, 0.227, 0.118) are not independent predictions; they are the coupling constants required to reproduce the input Tc within the McMillan formula. The comparison with λep[Ref**] merely reflects the difference between the McMillan and Allen-Dynes expressions for the same input Tc, adding no new superconducting evidence. The paper's conclusion that pressure suppresses superconductivity is thus inherited from the prior Tc input rather than derived from a self-contained first-principles calculation.

full rationale

The paper contains substantial independent first-principles content: structural relaxation, phonon stability between 100 and 382 GPa, elastic constants and derived mechanical/thermal quantities, electronic band structure, and DOS are all genuine DFT results computed in this work rather than imported from the prior study. Those parts are not circular and would stand on their own. However, two load-bearing 'predictions' reduce by construction to their own inputs. First, the multifunctional-application claims centered on near-unity low-energy reflectivity, high infrared refractive index, and plasma-resonance behavior are produced in Sec. 3.8 by adding a semi-empirical Drude term with the plasma frequency fixed at 2.0 eV and damping fixed at 0.05 eV for all pressures; the low-energy spectra and R(0)≈0.97 are mathematically forced by these choices, so the first-principles framing is not justified for those quantities. Second, the superconducting analysis in Sec. 3.7 inserts the previously predicted Tc of Ref. [26] into the McMillan equation and solves for λep, making the resulting coupling constants and the pressure trend of superconductivity a restatement of the input Tc under a different model formula. No load-bearing self-citation or imported uniqueness theorem is present; the authors' several self-citations are routine methodological references. Because the central optical and superconducting conclusions are construction-level while the structural, elastic, and electronic core remains independent, the appropriate circularity score is 6 rather than 0 or 10.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central property predictions rest mainly on standard DFT assumptions and the prior identification of the P6/mmm phase. The only clearly ad hoc inputs are the Drude parameters governing the optical response, and the superconducting analysis borrows Tc from ref [26] rather than deriving it. No new physical entities are introduced.

free parameters (3)
  • Drude plasma frequency = 2.0 eV
    Set to a constant for all pressures to model intraband optical transitions (Section 3.8).
  • Drude damping constant = 0.05 eV
    Applied uniformly to all calculations (Section 3.8).
  • Gaussian smearing for optical spectra = 0.5 eV
    Used in the Drude term and optical response calculation (Section 3.8).
assumptions (4)
  • domain assumption DFT with the PBEsol functional accurately predicts the physical properties of Li5N under high pressure.
    The entire property set is computed within DFT; the authors chose PBEsol based on volume agreement but no experimental data exist to validate most properties.
  • domain assumption Li5N adopts the P6/mmm structure throughout 150-350 GPa.
    The structure is taken from prior computational studies [26,37]; the paper does not perform a new structure search. If another phase were stable, the results would change.
  • domain assumption The McMillan equation with Debye temperature and the Tc from ref [26] are valid for estimating lambda_ep.
    Used to invert lambda_ep; the paper acknowledges it cannot compute the Eliashberg spectral function with CASTEP.
  • domain assumption Mulliken population analysis gives chemically meaningful charges for this metallic system.
    The method is basis-dependent; the paper reports unusual charge values (e.g., Li(1) with -2.98 e) without discussion.

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Pith. "Pith review of High-pressure electride superconductor Li5N for multifunctional applications: A theoretical insight into the physical properties." pith.science (2026). https://pith.science/paper/6I2E74VM

@misc{pith2026260810768,
  author       = {Pith},
  title        = {Pith review of: High-pressure electride superconductor Li5N for multifunctional applications: A theoretical insight into the physical properties},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6I2E74VM}},
  note         = {Machine review of arXiv:2608.10768}
}
read the original abstract

This study aims to unveil the physical properties of multifunctional Li5N electride under high pressure in the range of 150-350 GPa through first principles analysis within the density functional theory.

Discussion (0). Continue with ORCID to comment.

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Works this paper leans on

121 extracted references · 67 canonical work pages

  1. [26]

    Z. Wan, C. Zhang, T. Yang, W. Xu, and R. Zhang, Predicted superconductivity and superionic state in the electride Li5N under high pressure, New J. Phys. 24, 113012 (2022)

    2022

  2. [1]

    D. J. Singh, H. Krakauer, C. Haas, and W. E. Pickett, Theoretical determination that electrons act as anions in the electride Cs+ (15-crown-5)2·e-, Nature 365, 39 (1993)

    1993

  3. [2]

    K. Lee, S. W. Kim, Y. Toda, S. Matsuishi, and H. Hosono, Dicalcium nitride as a two-dimensional electride with an anionic electron layer, Nature 494, 336 (2013)

    2013

  4. [3]

    Matsuishi, Y

    S. Matsuishi, Y. Toda, M. Miyakawa, K. Hayashi, T. Kamiya, M. Hirano, I. Tanaka, and H. Hosono, High-Density Electron Anions in a Nanoporous Single Crystal: [Ca24Al28O64]4+(4e-), Science (80-. ). 301, 626 (2003)

    2003

  5. [4]

    Y. Toda, H. Yanagi, E. Ikenaga, J. J. Kim, M. Kobata, S. Ueda, T. Kamiya, M. Hirano, K. Kobayashi, and H. Hosono, Work Function of a Room‐Temperature, Stable Electride [Ca24Al28O64]4+(e –)4, Adv. Mater. 19, 3564 (2007)

    2007

  6. [5]

    Xu, Z.-R

    H.-L. Xu, Z.-R. Li, D. Wu, B.-Q. Wang, Y. Li, F. L. Gu, and Y. Aoki, Structures and Large NLO Responses of New Electrides: Li-Doped Fluorocarbon Chain, J. Am. Chem. Soc. 129, 2967 (2007)

    2007

  7. [6]

    Kitano, Y

    M. Kitano, Y. Inoue, Y. Yamazaki, F. Hayashi, S. Kanbara, S. Matsuishi, T. Yokoyama, S.-W. Kim, M. Hara, and H. Hosono, Ammonia synthesis using a stable electride as an electron donor and reversible hydrogen store, Nat. Chem. 4, 934 (2012)

    2012

  8. [7]

    Ellaboudy, J

    A. Ellaboudy, J. L. Dye, and P. B. Smith, Cesium 18-crown-6 compounds. A crystalline ceside and a crystalline electride, J. Am. Chem. Soc. 105, 6490 (1983)

    1983

Show all 121 references
  1. [8]

    M. Y. Redko, J. E. Jackson, R. H. Huang, and J. L. Dye, Design and Synthesis of a Thermally Stable Organic Electride, J. Am. Chem. Soc. 127, 12416 (2005)

    2005

  2. [9]

    J. L. Dye, Electrides: Ionic Salts with Electrons as the Anions, Science (80-. ). 247, 663 (1990)

    1990

  3. [10]

    M. J. Wagner, R. H. Huang, J. L. Eglin, and J. L. Dye, An electride with a large six-electron ring, Nature 368, 726 (1994)

    1994

  4. [11]

    T. J. Kim, H. Yoon, and M. J. Han, Calculating magnetic interactions in organic electrides, Phys. Rev. B 97, 214431 (2018)

    2018

  5. [12]

    R. C. Phillips, W. P. Pratt, and J. L. Dye, Thermionic Emission from Cold Electride Films, Chem. Mater. 12, 3642 (2000). 32

    2000

  6. [13]

    Zhang, H

    Y. Zhang, H. Wang, Y. Wang, L. Zhang, and Y. Ma, Computer-Assisted Inverse Design of Inorganic Electrides, Phys. Rev. X 7, 011017 (2017)

    2017

  7. [14]

    S. Zhao, E. Kan, and Z. Li, Electride: from computational characterization to theoretical design, WIREs Comput. Mol. Sci. 6, 430 (2016)

    2016

  8. [15]

    Hosono and M

    H. Hosono and M. Kitano, Advances in Materials and Applications of Inorganic Electrides, Chem. Rev. 121, 3121−3185 (2021)

    2021

  9. [16]

    Zhang and G

    X. Zhang and G. Yang, Recent Advances and Applications of Inorganic Electrides, J. Phys. Chem. Lett. 11, 3841−3852 (2020)

    2020

  10. [17]

    J. Wang, Q. Zhu, Z. Wang, and H. Hosono, Ternary inorganic electrides with mixed bonding, Phys. Rev. B 99, 064104 (2019)

    2019

  11. [18]

    A. S. Ichimura, J. L. Dye, M. A. Camblor, and L. A. Villaescusa, Toward Inorganic Electrides, J. Am. Chem. Soc. 124, 1170 (2002)

    2002

  12. [19]

    W. Meng, J. Wang, X. Wang, W. Wang, X. Zhang, Y. Bando, and Z. Cheng, Multi-dimensional inorganic electrides for energy conversion and storage, J. Mater. Chem. A 12, 2583 (2024)

    2024

  13. [20]

    Y. Toda, S. Matsuishi, K. Hayashi, K. Ueda, T. Kamiya, M. Hirano, and H. Hosono, Field Emission of Electron Anions Clathrated in Subnanometer‐Sized Cages in [Ca24Al28O64]4+ (4e–), Adv. Mater. 16, 685 (2004)

    2004

  14. [21]

    Yanagi, K.-B

    H. Yanagi, K.-B. Kim, I. Koizumi, M. Kikuchi, H. Hiramatsu, M. Miyakawa, T. Kamiya, M. Hirano, and H. Hosono, Low Threshold Voltage and Carrier Injection Properties of Inverted Organic Light- Emitting Diodes with [Ca24Al28O64]4+(4e−) Cathode and Cu2−xSe Anode, J. Phys. Chem. C...

    2009

  15. [22]

    Wan et al., Identifying quasi-2D and 1D electrides in yttrium and scandium chlorides via geometrical identification, Npj Comput

    B. Wan et al., Identifying quasi-2D and 1D electrides in yttrium and scandium chlorides via geometrical identification, Npj Comput. Mater. 4, 77 (2018)

    2018

  16. [23]

    Zhang, Z

    X. Zhang, Z. Xiao, H. Lei, Y. Toda, S. Matsuishi, T. Kamiya, S. Ueda, and H. Hosono, Two- Dimensional Transition-Metal Electride Y2C, Chem. Mater. 26, 6638 (2014)

    2014

  17. [24]

    B. Wan, J. Zhang, L. Wu, and H. Gou, High-pressure electrides: From design to synthesis, Chinese Phys. B 28, 106201 (2019)

    2019

  18. [25]

    Tsuji, P

    Y. Tsuji, P. L. V. K. Dasari, S. F. Elatresh, R. Hoffmann, and N. W. Ashcroft, Structural Diversity and Electron Confinement in Li4N: Potential for 0-D, 2-D, and 3-D Electrides, J. Am. Chem. Soc. 138, 14108 (2016)

    2016

  19. [27]

    Z. S. Pereira, G. M. Faccin, and E. Z. da Silva, Predicted superconductivity in the electride Li5C, J. Phys. Chem. C 125, 8899 (2021)

    2021

  20. [28]

    Yang et al., Superconductivity in Nb5Ir3N: a nitrogen-filled electride, Supercond

    Q.-S. Yang et al., Superconductivity in Nb5Ir3N: a nitrogen-filled electride, Supercond. Sci. Technol. 37, 075003 (2024)

    2024

  21. [29]

    Huang and G

    B. Huang and G. Frapper, Barium–Nitrogen Phases Under Pressure: Emergence of Structural Diversity and Nitrogen-Rich Compounds, Chem. Mater. 30, 7623 (2018)

    2018

  22. [30]

    Y. Yin, F. Chen, G. Hu, X. Zhao, X. Yuan, and J. Ren, Ambient pressure superconductivity mediated by vanadium d electrons in electride 2H − VN2, Phys. Rev. B 111, 064519 (2025)

    2025

  23. [31]

    Y. Zhao, J. Gao, X. Zhang, S. Ding, Y. Liu, and G. Yang, Superconducting Li11Sb2 electride at ambient pressure, J. Mater. Chem. C 11, 17087 (2023)

    2023

  24. [32]

    Miao and R

    M. Miao and R. Hoffmann, High Pressure Electrides: A Predictive Chemical and Physical Theory, Acc. Chem. Res. 47, 1311−1317 (2014)

    2014

  25. [33]

    Zhang, Y

    L. Zhang, Y. Wang, J. Lv, and Y. Ma, Materials discovery at high pressures, Nat. Rev. Mater. 2, 17005 (2017)

    2017

  26. [34]

    Racioppi and E

    S. Racioppi and E. Zurek, High-Pressure Electrides: A Quantum Chemical Perspective, Annu. Rev. Mater. Res. 55, 421 (2025)

    2025

  27. [35]

    M. Miao, Y. Sun, E. Zurek, and H. Lin, Chemistry under high pressure, Nat. Rev. Chem. 4, 508 (2020)

    2020

  28. [36]

    Horvath-Bordon, R

    E. Horvath-Bordon, R. Riedel, A. Zerr, P. F. McMillan, G. Auffermann, Y. Prots, W. Bronger, R. Kniep, and P. Kroll, High-pressure chemistry of nitride-based materials, Chem. Soc. Rev. 35, 987 (2006)

    2006

  29. [37]

    Y. Shen, A. R. Oganov, G. Qian, J. Zhang, H. Dong, Q. Zhu, and Z. Zhou, Novel lithium-nitrogen compounds at ambient and high pressures, Sci. Rep. 5, 14204 (2015). 33

    2015

  30. [38]

    X. Wang, B. Cao, W. Tang, M. Yang, J. Chen, S. Chen, M. Zhang, F. Tian, and L. Li, Superconductivity and superionic behaviors of Kagome lattices in Li–Si compounds under high pressure, J. Mater. Chem. C 12, 8461 (2024)

    2024

  31. [39]

    Zhang, B

    Y. Zhang, B. Wang, Z. Xiao, Y. Lu, T. Kamiya, Y. Uwatoko, H. Kageyama, and H. Hosono, Electride and superconductivity behaviors in Mn5Si3-type intermetallics, Npj Quantum Mater. 2, 45 (2017)

    2017

  32. [40]

    Z. Zhao, S. Zhang, T. Yu, H. Xu, A. Bergara, and G. Yang, Predicted Pressure-Induced Superconducting Transition in Electride Li6P, Phys. Rev. Lett. 122, 097002 (2019)

    2019

  33. [41]

    Y. Ge, S. Guan, and Y. Liu, Two dimensional superconductors in electrides, New J. Phys. 19, 123020 (2017)

    2017

  34. [42]

    Hosono, S.-W

    H. Hosono, S.-W. Kim, S. Matsuishi, S. Tanaka, A. Miyake, T. Kagayama, and K. Shimizu, Superconductivity in room-temperature stable electride and high-pressure phases of alkali metals, Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. 373, 20140450 (2015)

    2015

  35. [43]

    Z. Zhao, L. Liu, T. Yu, G. Yang, and A. Bergara, Pressure-Induced Stable Li5P for High-Performance Lithium-Ion Batteries, J. Phys. Chem. C 121, 21199 (2017)

    2017

  36. [44]

    P. Chen, Z. Xiong, J. Luo, J. Lin, and K. L. Tan, Interaction of hydrogen with metal nitrides and imides, Nature 420, 302 (2002)

    2002

  37. [45]

    Y. H. Hu and E. Ruckenstein, Ultrafast Reaction between Li3N and LiNH2 To Prepare the Effective Hydrogen Storage Material Li2NH, Ind. Eng. Chem. Res. 45, 4993 (2006)

    2006

  38. [46]

    Bhattacharya and S

    A. Bhattacharya and S. Bhattacharya, Exploring N-Rich Phases in LixNy Clusters for Hydrogen Storage at Nanoscale, J. Phys. Chem. Lett. 6, 3726 (2015)

    2015

  39. [47]

    F. Peng, Y. Yao, H. Liu, and Y. Ma, Crystalline LiN5 Predicted from First-Principles as a Possible High-Energy Material, J. Phys. Chem. Lett. 6, 2363 (2015)

    2015

  40. [48]

    Laniel, G

    D. Laniel, G. Weck, and P. Loubeyre, Direct Reaction of Nitrogen and Lithium up to 75 GPa: Synthesis of the Li3N, LiN, LiN2, and LiN5 Compounds, Inorg. Chem. 57, 10685 (2018)

    2018

  41. [49]

    S. Wang, X. Wang, L. Yuan, G. Ma, J. Zhang, Y. Zhang, X. Cui, X. Wu, and D. Lu, Shape Controllable Synthesis of Bi-Based Perovskite Superconductor Microcrystals via a Mild Hydrothermal Method, Cryst. Growth Des. 20, 2123 (2020)

    2020

  42. [50]

    M. D. Segall, P. J. Lindan, M. A. Probert, C. J. Pickard, P. J. Hasnip, S. J. Clark, and M. C. Payne, First- principles simulation: ideas, illustrations and the CASTEP code, J. Phys. Condens. Matter 14, 2717 (2002)

    2002

  43. [51]

    J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized Gradient Approximation Made Simple, Phys. Rev. Lett. 77, 3865 (1996)

    1996

  44. [52]

    J. P. Perdew, A. Ruzsinszky, G. I. Csonka, O. A. Vydrov, G. E. Scuseria, L. A. Constantin, X. Zhou, and K. Burke, Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces, Phys. Rev. Lett. 100, 136406 (2008)

    2008

  45. [53]

    T. H. Fischer and J. Almlof, General methods for geometry and wave function optimization, J. Phys. Chem. 96, 9768 (1992)

    1992

  46. [54]

    Baroni, S

    S. Baroni, S. de Gironcoli, A. Dal Corso, and P. Giannozzi, Phonons and related crystal properties from density-functional perturbation theory, Rev. Mod. Phys. 73, 515 (2001)

    2001

  47. [55]

    Parlinski, Z

    K. Parlinski, Z. Q. Li, and Y. Kawazoe, First-principles determination of the soft mode in cubic ZrO2, Phys. Rev. Lett. 78, 4063 (1997)

    1997

  48. [56]

    J. Wang, J. Li, S. Yip, S. Phillpot, and D. Wolf, Mechanical instabilities of homogeneous crystals, Phys. Rev. B 52, 12627 (1995)

    1995

  49. [57]

    D. Qu, L. Bao, Z. Kong, and Y. Duan, First-principles predictions of electronic, elastic, and optical properties of ScBC and YBC ternary cermet phases, Vacuum 179, 109488 (2020)

    2020

  50. [58]

    J. P. Watt and L. Peselnick, Clarification of the Hashin‐Shtrikman bounds on the effective elastic moduli of polycrystals with hexagonal, trigonal, and tetragonal symmetries, J. Appl. Phys. 51, 1525 (1980)

    1980

  51. [59]

    Zhang, P

    R. Zhang, P. Gao, X. Wang, and Y. Zhou, First-principles study on elastic and superconducting properties of Nb3Sn and Nb3Al under hydrostatic pressure, AIP Adv. 5, 107233 (2015)

    2015

  52. [60]

    Y. Ding, M. Chen, and W. Wu, Mechanical properties, hardness and electronic structures of new post- cotunnite phase (Fe2P-type) of TiO2, Phys. B Condens. Matter 433, 48 (2014)

    2014

  53. [61]

    M. A. H. Shah, M. Nuruzzaman, A. Hossain, M. Jubair, and M. A. K. Zilani, A DFT insight into structural, mechanical, elasto-acoustic, and anisotropic properties of AePdH3 (Ae = Ca, Sr, Ba) 34 perovskites under pressure, Comput. Condens. Matter 34, e00774 (2023)

    2023

  54. [62]

    Rameshe, R

    B. Rameshe, R. Murugan, and B. Palanivel, First principle study on electronic structure, structural phase stability, optical and vibrational properties of Ba2ScMO6 (M = Nb, Ta), Int. J. Mod. Phys. B 30, 1550246 (2016)

    2016

  55. [63]

    Marius, Kramers-Kronig Relations (The Physics of Semiconductors) (Springer US, Berlin Heidelberg, 2010)

    G. Marius, Kramers-Kronig Relations (The Physics of Semiconductors) (Springer US, Berlin Heidelberg, 2010)

    2010

  56. [64]

    Hassan, I

    M. Hassan, I. Arshad, and Q. Mahmood, Computational study of electronic, optical and thermoelectric properties of X3PbO (X = Ca, Sr, Ba) anti-perovskites, Semicond. Sci. Technol. 32, 115002 (2017)

    2017

  57. [65]

    Omata, N

    T. Omata, N. Ueda, N. Hikuma, K. Ueda, H. Mizoguchi, T. Hashimoto, and H. Kawazoe, New oxide phase with wide band gap and high electroconductivity CdGa2O4 spinel, Appl. Phys. Lett. 62, 499 (1993)

    1993

  58. [66]

    Naderizadeh, S

    S. Naderizadeh, S. M. Elahi, M. R. Abolhassani, F. Kanjouri, N. Rahimi, and J. Jalilian, Electronic and optical properties of Full-Heusler alloy Fe3−xMnxSi, Eur. Phys. J. B 85, 144 (2012)

    2012

  59. [67]

    T. Yang, L. Hao, R. Khenata, and X. Wang, Strain Conditions for the Inverse Heusler Type Fully Compensated Spin-Gapless Semiconductor Ti2MnAl: A First-Principles Study, Materials (Basel). 11, 2091 (2018)

    2018

  60. [68]

    M. A. H. Shah, M. I. Naher, and S. H. Naqib, First-principles exploration of the pressure dependent physical properties of Sn4Au: A superconducting topological semimetal, Phys. B Condens. Matter 700, 416939 (2025)

    2025

  61. [69]

    X. Wang, Z. Cheng, J. Wang, and G. Liu, A full spectrum of spintronic properties demonstrated by a C1b-type Heusler compound Mn2Sn subjected to strain engineering, J. Mater. Chem. C 4, 8535 (2016)

    2016

  62. [70]

    M. A. H. Shah, M. A. Alam, A. Hossain, M. F. Hossain, M. Nuruzzaman, F. Parvin, and M. A. K. Zilani, Hydrostatic pressure on XLiH3 (X = Ba, Sr, Ca) perovskite hydrides: An insight into structural, thermo-elastic and ultrasonic properties through first-principles investigation,...

    2021

  63. [71]

    P. Li, G. Gao, Y. Wang, and Y. Ma, Crystal Structures and Exotic Behavior of Magnesium under Pressure, J. Phys. Chem. C 114, 21745 (2010)

    2010

  64. [72]

    M. A. Hadi, N. Kelaidis, S. H. Naqib, A. Chroneos, and A. K. M. A. Islam, Mechanical behaviors, lattice thermal conductivity and vibrational properties of a new MAX phase Lu2SnC, J. Phys. Chem. Solids 129, 162 (2019)

    2019

  65. [73]

    M. I. Naher and S. H. Naqib, Possible applications of Mo2C in the orthorhombic and hexagonal phases explored via ab-initio investigations of elastic, bonding, optoelectronic and thermophysical properties, Results Phys. 37, 105505 (2022)

    2022

  66. [74]

    G. V. Sin’ko and N. A. Smirnov, Ab initio calculations of elastic constants and thermodynamic properties of bcc, fcc, and hcp Al crystals under pressure, J. Phys. Condens. Matter 14, 6989 (2002)

    2002

  67. [75]

    B. Kong, X. R. Chen, L. C. Cai, and G. F. Ji, Structural, electronic, elastic properties and stabilities of hexagonal ZrNiAl alloy and its hydride ZrNiAlH0.67, Comput. Mater. Sci. 50, 105 (2010)

    2010

  68. [76]

    Ozisik, E

    H. Ozisik, E. Deligoz, K. Colakoglu, and G. Surucu, Structural and mechanical stability of rare-earth diborides, Chin. Phys. B 22, 046202 (2013)

    2013

  69. [77]

    H. Li, Z. Luo, Z. Liu, G. Sun, and Z. Wang, A first-principles high-pressure study of Hf2PX (X=B, C, N), Solid State Commun. 259, 45 (2017)

    2017

  70. [78]

    K. Das, M. A. Ali, M. M. Hossain, S. H. Naqib, A. K. M. A. Islam, and M. M. Uddin, Dynamical stability, vibrational, and optical properties of anti-perovskite A3BX (Ti3TlN, Ni3SnN, and Co3AlC) phases: A first principles study, AIP Adv. 10, 095226 (2020)

    2020

  71. [79]

    A. Yang, L. Bao, M. Peng, and Y. Duan, Explorations of elastic anisotropies and thermal properties of the hexagonal TMSi2 (TM = Cr, Mo, W) silicides from first-principles calculations, Mater. Today Commun. 27, 102474 (2021)

    2021

  72. [80]

    M. A. Hadi, S.-R. G. Christopoulos, A. Chroneos, S. H. Naqib, and A. K. M. A. Islam, Elastic behaviour and radiation tolerance in Nb-based 211 MAX phases, Mater. Today Commun. 25, 101499 (2020)

    2020

  73. [81]

    Haines, J

    J. Haines, J. Léger, and G. Bocquillon, Synthesis and Design of Superhard Materials, Annu. Rev. Mater. Res. 31, 1 (2001)

    2001

  74. [82]

    S. F. Pugh, XCII. Relations between the elastic moduli and the plastic properties of polycrystalline pure metals, Philos. Mag. 45, 823 (1954)

    1954

  75. [83]

    M. A. Sarker, M. M. Hasan, M. Al Momin, A. Irfan, M. R. Islam, and A. Sharif, Band gap engineering 35 in lead free halide cubic perovskites GaGeX3 (X = Cl, Br, and I) based on first-principles calculations, RSC Adv. 14, 9805 (2024)

    2024

  76. [84]

    Erum and M

    N. Erum and M. A. Iqbal, First Principles Investigation of Fluorine Based Strontium Series of Perovskites, Commun. Theor. Phys. 66, 571 (2016)

    2016

  77. [85]

    Ghebouli, M

    B. Ghebouli, M. A. Ghebouli, and M. Fatmi, First-principles study of structural, elastic, electronic and optical properties of perovskites hydrides XLiH3 (X = Ba and Sr) under pressure, Eur. Phys. J. Appl. Phys. 51, 20302 (2010)

    2010

  78. [86]

    Ghebouli, M

    B. Ghebouli, M. A. Ghebouli, A. Bouhemadou, M. Fatmi, R. Khenata, D. Rached, T. Ouahrani, and S. Bin-Omran, Theoretical prediction of the structural, elastic, electronic, optical and thermal properties of the cubic perovskites CsXF3 (X = Ca, Sr and Hg) under pressure effect, S...

    2012

  79. [87]

    Jamal, S

    M. Jamal, S. Jalali Asadabadi, I. Ahmad, and H. A. Rahnamaye Aliabad, Elastic constants of cubic crystals, Comput. Mater. Sci. 95, 592 (2014)

    2014

  80. [88]

    Y. X. Wang, Elastic and electronic properties of TcB2 and superhard ReB2: First-principles calculations, Appl. Phys. Lett. 91, (2007)

    2007

  81. [89]

    A. L. Ivanovskii, Hardness of hexagonal AlB2-like diborides of s, p and d metals from semi-empirical estimations, Int. J. Refract. Met. Hard Mater. 36, 179 (2013)

    2013

  82. [90]

    X.-Q. Chen, H. Niu, D. Li, and Y. Li, Modeling hardness of polycrystalline materials and bulk metallic glasses, Intermetallics 19, 1275 (2011)

    2011

  83. [91]

    Y. Tian, B. Xu, and Z. Zhao, Microscopic theory of hardness and design of novel superhard crystals, Int. J. Refract. Hard Met. 33, 93 (2012)

    2012

  84. [92]

    N. Miao, B. Sa, J. Zhou, and Z. Sun, Theoretical investigation on the transition-metal borides with Ta3B4-type structure: A class of hard and refractory materials, Comput. Mater. Sci. 50, 1559 (2011)

    2011

  85. [93]

    D. M. Teter, Computational Alchemy: The Search for New Superhard Materials, MRS Bull. 23, 22 (1998)

    1998

  86. [94]

    A. Zerr, R. Riedel, T. Sekine, J. E. Lowther, W. Y. Ching, and I. Tanaka, Recent Advances in New Hard High-Pressure Nitrides, Adv. Mater. 18, 2933 (2006)

    2006

  87. [95]

    Tvergaard and J

    V. Tvergaard and J. W. Hutchinson, Microcracking in Ceramics Induced by Thermal Expansion or Elastic Anisotropy, J. Am. Ceram. Soc. 71, 157 (1988)

    1988

  88. [96]

    S. I. Ranganathan and M. Ostoja-Starzewski, Universal Elastic Anisotropy Index, Phys. Rev. Lett. 101, 055504 (2008)

    2008

  89. [97]

    Z. Ran, C. Zou, Z. Wei, and H. Wang, VELAS: An open-source toolbox for visualization and analysis of elastic anisotropy, Comput. Phys. Commun. 283, 108540 (2023)

    2023

  90. [98]

    O. L. Anderson, A simplified method for calculating the debye temperature from elastic constants, J. Phys. Chem. Solids 24, 909 (1963)

    1963

  91. [99]

    Schreiber, O

    E. Schreiber, O. L. Anderson, and N. Soga, Elastic Constants and Their Measurements (McGraw-Hill, New York, 1973)

    1973

  92. [100]

    B. B. Karki, L. Stixrude, S. J. Clark, M. C. Warren, G. J. Ackland, and J. Crain, Structure and elasticity of MgO at high pressure, Am. Miner. 82, 51 (1997)

    1997

  93. [101]

    Guechi, A

    A. Guechi, A. Merabet, M. Chegaar, A. Bouhemadou, and N. Guechi, Pressure effect on the structural, elastic, electronic and optical properties of the Zintl phase KAsSn, first principles study, J. Alloy. Compd. 623, 219 (2015)

    2015

  94. [102]

    Guechi, A

    N. Guechi, A. Bouhemadou, A. Guechi, M. Reffas, L. Louail, A. Bourzami, M. Chegaar, and S. Bin- Omran, First-principles prediction of the structural, elastic, electronic and optical properties of the Zintl phases MIn2P2 (M = Ca, Sr), J. Alloy. Compd. 277, 587 (2013)

    2013

  95. [103]

    D. G. Cahill and R. O. Pohl, Lattice Vibrations and Heat Transport in Crystals and Glasses, Annu. Rev. Phys. Chem. 39, 93 (1988)

    1988

  96. [104]

    D. R. Clarke, Materials selection guidelines for low thermal conductivity thermal barrier coatings, Surf. Coat. Int. 163–164, 67 (2003)

    2003

  97. [105]

    G. A. Slack, The thermal conductivity of nonmetallic crystals, Solid State Phys. 34, 1 (1979)

    1979

  98. [106]

    C. L. Julian, Theory of heat conduction in rare-gas crystals, Phys. Rev. 137, 128 (1965)

    1965

  99. [107]

    M. E. Fine, L. D. Brown, and H. L. Marcus, Elastic constants versus melting temperature in metals, Scr. Met. 18, 951 (1984)

    1984

  100. [108]

    P. B. Allen and R. C. Dynes, Transition temperature of strong-coupled superconductors reanalyzed, Phys. Rev. B 12, 905 (1975). 36

    1975

  101. [109]

    A. A. Chowdhury, M. A. Ali, M. M. Hossain, M. M. Uddin, S. H. Naqib, and A. K. M. A. Islam, Predicted MAX Phase Sc2InC: Dynamical Stability, Vibrational and Optical Properties, Phys. Status Solidi B 255, 1700235 (2018)

    2018

  102. [110]

    Sanchez-Portal, E

    D. Sanchez-Portal, E. Artacho, and J. M. Soler, Projection of plane-wave calculations into atomic orbitals, Solid State Commun. 95, 685 (1995)

    1995

  103. [111]

    Wang, The investigation of dependences of mechanical and electronic properties of TiB2 on pressure using the first-principles method, Phys

    M. Wang, The investigation of dependences of mechanical and electronic properties of TiB2 on pressure using the first-principles method, Phys. Scr. 89, 115702 (2014)

    2014

  104. [112]

    K. H. Bennemann, J. W. Garland, H. C. Wolfe, and D. H. Douglass, Theory for Superconductivity in D- Band Metals, in (1972), pp. 103–137

    1972

  105. [113]

    W. L. McMillan, Transition Temperature of Strong-Coupled Superconductors, Phys. Rev. 167, 331 (1968)

    1968

  106. [114]

    K. Sano, M. Seo, and K. Nakamura, Plasmon Effect on the Coulomb Pseudopotential μ* in the McMillan Equation, J. Phys. Soc. Japan 88, 093703 (2019)

    2019

  107. [115]

    P. B. Allen and R. C. Dynes, Transition temperature of strong-coupled superconductors reanalyzed, Phys. Rev. B 12, 905 (1975)

    1975

  108. [116]

    Harl and G

    J. Harl and G. Kresse, Ab initio reflectance difference spectra of the bare and adsorbate covered Cu(110) surfaces, Phys. Rev. B 76, 035436 (2007)

    2007

  109. [117]

    D. Y. Smith and B. Segall, Intraband and interband processes in the infrared spectrum of metallic aluminum, Phys. Rev. B 34, 5191 (1986)

    1986

  110. [118]

    Xiang, S

    X. Xiang, S. Wang, Y. Du, Y. Chen, S. Chen, S. Li, W. Zhang, Z. Yin, and H. Hou, Theoretical prediction of physical properties of Alkaline-earth metals AeSc3H8 hydrides for hydrogen storage applications, Vacuum 250, 115329 (2026)

    2026

  111. [119]

    M. I. Naher and S. H. Naqib, Structural, elastic, electronic, bonding, and optical properties of topological CaSn3 semimetal, J. Alloys Compd. 829, 154509 (2020)

    2020

  112. [120]

    Chakraborty, M

    A. Chakraborty, M. N. H. Liton, M. S. I. Sarker, M. M. Rahman, and M. K. R. Khan, Exploration of the structural, vibrational, electronic, mechanical and thermal properties of Ru4Al3B2 and Ru9Al3B8: a DFT study, RSC Adv. 13, 28912 (2023)

    2023

  113. [121]

    Z. Yu, H. Y. Geng, Y. Sun, and Y. Chen, Optical properties of dense lithium in electride phases by first- principles calculations, Sci. Rep. 8, 3868 (2018)

    2018

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