Pith. sign in

REVIEW 4 major objections 8 minor 130 references

Topological Electronic States and Phonon Mediated Superconductivity in Ru Based Ternary Pnictides: ZrRuAs and HfRuP

T0 review · 4 major / 8 minor · reviewed 2026-07-11 · grok-4.5

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read ZrRuAs and HfRuP are ductile topological semimetals with strong-coupling phonon-mediated superconductivity near 9–10 K.

desk verdict Solid multi-property DFT map of two known ~12 K TT′X superconductors; new elastic/optical/thermo/EPC numbers are useful, topology and Tc mostly reconfirm prior work with standard caveats. read the letter →

arxiv 2607.04651 v1 pith:GRYWAXZY submitted 2026-07-06 cond-mat.mtrl-sci cond-mat.supr-con

Jubair Hossan Abir , Tanvir Khan , Tauhidur Rahman , Md. Kamrul Hassan , Sraboni Saha Moly , Mst. Maskura Khatun , Raihana Shams Islam , Saleh Hasan Naqib This is my paper · ORCID
classification cond-mat.mtrl-scicond-mat.supr-con
keywords TopologicalquantummaterialssuperconductorRu-basedternarypnictidesThermophysicalpropertiesOptoelectronicElectron-phononcouplingZrRuAsHfP
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

This paper sets out a full first-principles map of two Ru-based ternary pnictides, ZrRuAs and HfRuP, that already look like topological superconductors from earlier work. It shows that both compounds are mechanically stable and ductile, with mixed metallic–covalent bonding, metallic optical reflectivity, and thermodynamic stability under pressure and temperature. Electron–phonon coupling calculations place them in the strong-coupling conventional regime, with predicted transition temperatures of 9.75 K and 9.03 K. The same electronic-structure analysis supports topological semimetallic character—consistent with a topological crystalline insulator picture for ZrRuAs and a type-II Weyl picture for HfRuP—while filling in the elastic, optical, and thermophysical properties that had not been studied in detail. A sympathetic reader cares because these materials combine processable ductility with topology and phonon-mediated superconductivity in a single family of intermetallics.

What carries the argument

Electron–phonon coupling strength λ(ω) and the Eliashberg spectral function α²F(ω) from density-functional perturbation theory, inserted into the Allen–Dynes modified McMillan formula with μ* = 0.10 to obtain Tc.

What would settle it

A measured superconducting transition temperature for single-phase ZrRuAs or HfRuP that lies well outside the 9–10 K window predicted by Allen–Dynes with λ ≈ 1.2 and μ* = 0.10, or a phonon calculation with spin–orbit coupling that substantially changes λ or the soft-mode weight.

Watch

Extended reading notes

Core claim

Density-functional calculations of structure, bands, surface spectra, elasticity, optics, thermodynamics, phonons, and electron–phonon coupling establish that ZrRuAs and HfRuP are dynamically and mechanically stable topological semimetals that are ductile and machinable, and that they are strong-coupling conventional superconductors with Tc ≈ 9.75 K (ZrRuAs) and 9.03 K (HfRuP) driven mainly by soft low-frequency Ru out-of-plane modes.

Load-bearing premise

The Coulomb repulsion parameter is fixed by hand at 0.10 and spin–orbit coupling is dropped from the phonon and coupling calculations without a material-specific check.

Editorial extensions

If this is right

  • Both compounds should remain ductile and machinable enough for wire or magnet applications typical of intermetallic superconductors.
  • Low-frequency Ru vibrations dominate pairing, so pressure or doping that hardens those modes should suppress Tc while lattice expansion should raise it.
  • Surface-sensitive probes on HfRuP should see robust gapless states near the Fermi level consistent with type-II Weyl points; ZrRuAs should show partially gapped crystalline-surface states.
  • Strong metallic reflectivity and ultraviolet absorption make the materials candidates for reflective coatings or UV optoelectronic use in the calculated energy windows.

Reading between the lines

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

  • Because experimental Tc values reported for the hexagonal family sit near 12–13 K, the calculated 9–10 K values imply that either μ* is slightly lower than 0.10 or anharmonic/pressure effects missing from the quasi-harmonic treatment raise the effective coupling.
  • The soft ductile response suggests moderate hydrostatic pressure could be used as a continuous knob on both band topology and Tc without fracturing the lattice.
  • If surface Majorana modes are later sought, HfRuP’s Weyl classification makes it the more natural platform of the pair for engineered superconducting interfaces.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 8 minor

Summary. This manuscript presents a broad first-principles study (Quantum ESPRESSO/CASTEP, PBE-GGA, DFPT, GIBBS2, WannierTools) of the hexagonal ZrNiAl-type compounds ZrRuAs and HfRuP. It reports optimized structures, electron-density difference maps, elastic constants and derived mechanical indices, optical spectra with a Drude term, quasi-harmonic thermodynamic quantities, bulk bands with and without SOC, Fermi surfaces, surface spectral functions, phonon dispersions, Eliashberg α²F(ω), and Allen–Dynes Tc estimates. The central claims are that both materials are mechanically stable and ductile, exhibit topological semimetallic character consistent with prior classification (ZrRuAs as a topological crystalline insulator; HfRuP as a type-II Weyl semimetal), and are conventional phonon-mediated superconductors with λ = 1.18 and 1.30 and Tc ≈ 9.75 K and 9.03 K (μ* = 0.10), driven mainly by low-frequency out-of-plane Ru modes.

Significance. ZrRuAs and HfRuP are established experimental superconductors (Tc ~12–13 K) that have been proposed as topological materials; a single study that ties elastic, optical, thermodynamic, topological, and EPC properties together is therefore of genuine interest to the topological-superconductor and intermetallic communities. Strengths include Born-stable elastic constants, dynamically stable phonons, explicit mode-resolved PhDOS and EPC weighting showing that phonons below ~100 cm⁻¹ supply ~68–78% of λ, and surface spectral functions that qualitatively track the prior topological assignments of Qian et al. If the superconducting and topological conclusions hold under tighter checks, the work usefully closes documented gaps on machinability, optical response, and thermophysical behavior for these Ru-based ternary pnictides.

major comments (4)
  1. §3.5, Eq. (14) and Table 4: Tc is obtained with a fixed Coulomb pseudopotential μ* = 0.10 and no material-specific estimate or sensitivity scan. Because Tc depends exponentially on [λ − μ*(1 + 0.62λ)], shifting μ* over the conventional 0.10–0.15 window changes Tc by several kelvin and can move the results relative to the experimental ~12–13 K values. A short μ* scan (or a Morel–Anderson-style estimate) is needed to show that the strong-coupling classification and the reported Tc ordering (ZrRuAs > HfRuP) are robust.
  2. §2 and §3.5: Phonon and EPC spectra are computed without SOC, justified only by the statement that the effect is “considered insignificant” and by citations to other systems. For HfRuP the heavy Hf atom makes this assumption least secure; the same low-frequency Ru modes that dominate λ (~68% of the total) could soften or harden under SOC, shifting both λ and ωlog. At minimum the manuscript should either (i) report a SOC phonon check at selected q-points for HfRuP or (ii) quantify the expected error and temper the strong-coupling claim accordingly.
  3. §3.5 and Conclusions vs. experimental literature cited in the Introduction: Calculated Tc values (9.75 K / 9.03 K) systematically underestimate the reported experimental Tc (~12 K for ZrRuAs; ~12.7 K for HfRuP). The text asserts consistency with prior experimental reports without discussing the discrepancy, the role of μ*, mesh convergence of α²F(ω), or possible pressure/stoichiometry effects. A quantitative comparison and an explicit discussion of why theory sits ~3 K below experiment are load-bearing for the superconducting claim.
  4. §3.2.1 (band structure / surface states) and Abstract/Conclusions: Topological assignments (TCI for ZrRuAs; type-II Weyl for HfRuP) rest largely on qualitative band crossings, SOC gap openings, and surface spectral intensity near K, together with citation of Ref. [58]. The manuscript does not report computed topological invariants (mirror Chern numbers, Weyl-node chirality/locations, or Z2) for the present DFT setup. Either compute the relevant invariants with the same Wannier model used for Fig. 5, or clearly reframe the topological section as a consistency check with prior theory rather than an independent classification.
minor comments (8)
  1. Abstract vs. §3.5/Conclusions: coupling strength is called “strong” in places and “medium-coupling” in the abstract body; with λ = 1.18–1.30 the language should be unified (intermediate-to-strong is conventional).
  2. §3.3.2 Reflectivity paragraph: compound names are swapped (“HfRuAs”, “ZrRuP”); correct to ZrRuAs and HfRuP.
  3. Figure 8 panel labels in the text (e.g. refractive index referred to as 8(e), absorption as 8(c)) do not match the figure caption ordering; renumber or re-letter for consistency.
  4. Table 1: experimental lattice parameters are listed under a blank “Functionals” row with Ref. [58]; clarify whether those are experimental or previously calculated values.
  5. Optical Drude parameters (plasma energy 10 eV vs 5 eV, damping 0.05 eV) are stated without justification or sensitivity; a brief note on how they were chosen would help reproducibility.
  6. §3.2 Mechanical section is numbered “3.2” and electronic band structure is also under “3.2.1”; renumber subsections for a clean hierarchy.
  7. Several typographical issues: “machinability”/“machinability index” spelling varies; “Pugh’s ratio k (G/B)” in Table 3 header is inverted relative to the G/B values discussed as ductile when G/B < 0.57; “Hf RuP” spacing; “zero photon energy” phrasing.
  8. Conclusions speculate that moderate pressure will substantially change Tc without presenting pressure-dependent EPC; either add a short calculation or mark the statement as a suggestion for future work.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: superconducting Tc and topological classifications follow from independent DFPT/EPC spectra plus a conventional external μ* and from prior non-overlapping theory, with no equation reducing the headline results to their own inputs.

full rationale

The load-bearing superconducting chain (phonon dispersions via DFPT → Eliashberg α^{2}F(ω) and λ(ω) → Allen–Dynes Tc with fixed μ*=0.10) is a standard first-principles workflow. λ and ω_log are computed from electronic matrix elements and phonon linewidths (Eqs. 16–18); they are not fitted to the experimental ~12 K values, nor is Tc defined in terms of itself. The choice μ*=0.10 is the conventional external range (0.10–0.16) and is not tuned to force agreement. Topology is read from bulk bands + MLWF surface spectral functions and is explicitly stated to be consistent with the independent classification of Qian et al. [58] (Weyl for HfRuP, TCI for ZrRuAs); that reference has no author overlap with the present work. Elastic, optical and thermodynamic quantities are obtained from standard stress–strain, dielectric-function and quasi-harmonic Debye formulae applied to the same DFT ground state; none of them redefine the target observables. Occasional self-citations (e.g., prior Naqib-group hardness or anisotropy papers) supply only auxiliary formulae and are not load-bearing for the central claims. The derivation is therefore self-contained against external benchmarks and exhibits no self-definitional, fitted-as-prediction, or uniqueness-imported circularity.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central SC claim rests on standard DFT/DFPT plus the Allen–Dynes formula with a hand-chosen μ*. Optical spectra add ad-hoc Drude plasma energies. Topological interpretation imports prior classification rather than inventing new entities. No new particles or forces are postulated; free parameters are the usual computational knobs that control quantitative Tc and optics.

free parameters (3)
  • Coulomb pseudopotential μ* = 0.10
    Fixed at 0.10 in Eq. 14 without material-specific calculation; Tc depends exponentially on μ*.
  • Drude plasma energy and damping (optical) = 10 eV / 5 eV; damping 0.05 eV
    Plasma energies 10 eV (ZrRuAs) and 5 eV (HfRuP) with 0.05 eV damping are inserted by hand for metallic dielectric response.
  • Plane-wave cutoffs and k/q meshes = 60 Ry; 400 eV; meshes as stated
    60 Ry (QE), 400 eV (CASTEP), 12×12×12 / 24×24×24 k-meshes and 4×4×4 / 3×3×3 q-meshes are author-chosen convergence settings that affect quantitative EPC and elastic numbers.
assumptions (5)
  • domain assumption PBE-GGA DFT adequately describes bands, topology-relevant crossings, and EPC for these metallic pnictides.
    Used throughout electronic, phonon, and optical sections; authors note DFT band-overlap issues for TI classification but still rely on it.
  • domain assumption Allen–Dynes modified McMillan equation with isotropic EPC gives a reliable Tc for these compounds.
    Section 3.5, Eqs. 14–18; no anisotropic Eliashberg solution or experimental μ* constraint.
  • ad hoc to paper Spin–orbit coupling may be omitted from phonon and EPC calculations because its effect is insignificant.
    Stated in Computational Methodology with citations to other systems; not verified for ZrRuAs/HfRuP despite heavy Hf.
  • domain assumption Quasi-harmonic Debye model (GIBBS2) captures thermodynamic response from E–V curves.
    Section 3.4; standard but approximate for anisotropic metals.
  • standard math Born mechanical stability criteria and Hill averaging correctly classify ductility/machinability from Cij.
    Section 3.2 elastic analysis.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Topological Electronic States and Phonon Mediated Superconductivity in Ru Based Ternary Pnictides: ZrRuAs and HfRuP." pith.science (2026). https://pith.science/paper/GRYWAXZY

@misc{pith2026260704651,
  author       = {Pith},
  title        = {Pith review of: Topological Electronic States and Phonon Mediated Superconductivity in Ru Based Ternary Pnictides: ZrRuAs and HfRuP},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GRYWAXZY}},
  note         = {Machine review of arXiv:2607.04651}
}
read the original abstract

This study investigates the structural, electronic, mechanical, optical, thermodynamic, and superconducting properties of ZrRuAs and HfRuP. Electronic band structure calculations reveal topological semimetallic behavior in both compounds with several bands crossing the Fermi level. The inclusion of spin orbit coupling lifts band degeneracies in both compounds. The Fermi surface shows both electron and hole segments. The estimated Pugh ratio, Poisson ratio and machinability index indicate that both compounds are ductile in nature and exhibit excellent machinability. Optical results show metallic reflectivity and notable absorption in the ultraviolet region. Thermodynamic analysis indicates stable behavior. The estimated superconducting transition temperatures are 9.75 K for ZrRuAs and 9.03 K for HfRuP that indicates strong coupling conventional superconductivity. The results provide a detailed view of the physical and superconducting properties of ZrRuAs and HfRuP and help to close the existing research gaps in these topological superconducting materials.

Figures

Figures reproduced from arXiv: 2607.04651 by the authors.

Figure 1
Figure 1. Schematic 3D representation of layered Crystal structures of ZrRuAs and HfRuP [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

130 extracted references · 66 canonical work pages

  1. [58]

    https://doi.org/10.1088/0305-4608/15/4/009

    doi:10.1088/0305-4608/15/4/009

  2. [1]

    Beenakker, Search for Majorana fermions in superconductors, Annual Review of Condensed Matter Physics, 4 (2013) 113 –136

    C.W.J. Beenakker, Search for Majorana fermions in superconductors, Annual Review of Condensed Matter Physics, 4 (2013) 113 –136. https://doi.org/10.1146/annurev -conmatphys- 030212-184337

    doi:10.1146/annurev 2013

  3. [2]

    Hasan, C.L

    M.Z. Hasan, C.L. Kane, Colloquium: Topological insulators, Reviews of Modern Physics, 82 (2010) 3045–3067. https://doi.org/10.1103/RevModPhys.82.3045

    doi:10.1103/revmodphys.82.3045 2010

  4. [3]

    M. Sato, Y. Ando, Topological superconductors: a review, Reports on Progress in Physics, 80 (2017) 076501. https://doi.org/10.1088/1361-6633/aa6ac7

    doi:10.1088/1361-6633/aa6ac7 2017

  5. [4]

    Kitaev, Unpaired Majorana fermions in quantum wires, Physics-Uspekhi, 44 (2001) 131

    A.Y. Kitaev, Unpaired Majorana fermions in quantum wires, Physics-Uspekhi, 44 (2001) 131. https://doi.org/10.1070/1063-7869/44/10S/S29

    doi:10.1070/1063-7869/44/10s/s29 2001

  6. [5]

    Y. Ando, L. Fu, Topological Crystalline Insulators and Topological Superconductors: From Concepts to Materials, arXiv.org. Accessed: May 13, 2026. [Online]. Available: https://arxiv.org/abs/1501.00531v1

    arXiv 2026

  7. [6]

    X. -L. Qi, S. -C. Zhang, Topological insulators and superconductors, Reviews of Modern Physics, 83 (2011) 1057–1110. https://doi.org/10.1103/RevModPhys.83.1057

    doi:10.1103/revmodphys.83.1057 2011

  8. [7]

    G.M. Luke, Y. Fudamoto, K.M. Kojima, M.I. Larkin, J. Merrin, B. Nachumi, Y.J. Uemura, Y. Maeno, Z.Q. Mao, Y. Mori, H. Nakamura, M. Sigrist, Time -Reversal Symmetry Breaking Superconductivity in Sr2RuO4, Nature, 394 (1998) 558–561. https://doi.org/10.1038/29038

    doi:10.1038/29038 1998

Show all 130 references
  1. [8]

    Guguchia, F

    Z. Guguchia, F. von Rohr, Z. Shermadini, A.T. Lee, S. Banerjee, A.R. Wieteska, C.A. Marianetti, B.A. Frandsen, H. Luetkens, Z. Gong, S.C. Cheung, C. Baines, A. Shengelaya, G. Taniashvili, A.N. Pasupathy, E. Morenzoni, S.J.L. Billinge, A. Amato, R.J. Ca va, R. Khasanov, Y.J. Ue...

    2017 doi

  2. [9]

    Liu, C.-S

    C. Liu, C.-S. Lian, M.-H. Liao, Y. Wang, Y. Zhong, C. Ding, W. Li, C.-L. Song, K. He, X.-C. Ma, W. Duan, D. Zhang, Y. Xu, L. Wang, Q. -K. Xue, Two -dimensional superconductivity and topological states in PdTe 2 thin films, Physical Review Materials, 2 (2018) 094001. https://do...

    2018 doi

  3. [10]

    Kohmoto, Topological invariant and the quantization of the Hall conductance, Annals of Physics, 160 (1985) 343–354

    M. Kohmoto, Topological invariant and the quantization of the Hall conductance, Annals of Physics, 160 (1985) 343–354. https://doi.org/10.1016/0003-4916(85)90148-4. 27 | P a g e

    1985 doi

  4. [11]

    Thouless, M

    D.J. Thouless, M. Kohmoto, M.P. Nightingale, M. den Nijs, Quantized Hall Conductance in a Two -Dimensional Periodic Potential, Physical Review Letters, 49 (1982) 405 –408. https://doi.org/10.1103/PhysRevLett.49.405

    1982 doi

  5. [12]

    Kane, E.J

    C.L. Kane, E.J. Mele, Quantum Spin Hall Effect in Graphene, Physical Review Letters, 95 (2005) 226801. https://doi.org/10.1103/PhysRevLett.95.226801

    2005 doi

  6. [13]

    Kane, E.J

    C.L. Kane, E.J. Mele, Z 2 Topological Order and the Quantum Spin Hall Effect, Physical Review Letters, 95 (2005) 146802. https://doi.org/10.1103/PhysRevLett.95.146802

    2005 doi

  7. [14]

    Moore, L

    J.E. Moore, L. Balents, Topological invariants of time -reversal-invariant band structures, Physical Review B, 75 (2007) 121306. https://doi.org/10.1103/PhysRevB.75.121306

    2007 doi

  8. [15]

    L. Fu, C.L. Kane, E.J. Mele, Topological Insulators in Three Dimensions, Physical Review Letters, 98 (2007) 106803. https://doi.org/10.1103/PhysRevLett.98.106803

    2007 doi

  9. [16]

    Roy, Topological phases and the quantum spin Hall effect in three dimensions, Physical Review B, 79 (2009) 195322

    R. Roy, Topological phases and the quantum spin Hall effect in three dimensions, Physical Review B, 79 (2009) 195322. https://doi.org/10.1103/PhysRevB.79.195322

    2009 doi

  10. [17]

    Ando, Topological Insulator Materials, Journal of the Physical Society of Japan, 82 (2013) 102001

    Y. Ando, Topological Insulator Materials, Journal of the Physical Society of Japan, 82 (2013) 102001. https://doi.org/10.7566/JPSJ.82.102001

    2013 doi

  11. [18]

    Schnyder, S

    A.P. Schnyder, S. Ryu, A. Furusaki, A.W.W. Ludwig, Classification of topological insulators and superconductors in three spatial dimensions, Physical Review B, 78 (2008) 195125. https://doi.org/10.1103/PhysRevB.78.195125

    2008 doi

  12. [19]

    Schaak, R.J

    R.E. Schaak, R.J. Cava, Boron substitution in ternary metal phosphide superconductors, Materials Research Bulletin, 39 (2004) 1231 –1235. https://doi.org/10.1016/j.materresbull.2004.04.011

    2004 doi

  13. [20]

    R.J. Cava, H. Takagi, H.W. Zandbergen, J.J. Krajewski, W.F. Peck Jr, T. Siegrist, B. Batlogg, R.B. van Dover, R.J. Felder, K. Mizuhashi, J.O. Lee, H. Eisaki , S. Uchida, Superconductivity in the quaternary intermetallic compounds LnNi 2B2C, Nature, 367 (1994) 252 -253. https:/...

    1994 doi

  14. [21]

    Schilling, M

    A. Schilling, M. Cantoni, J. Guo, H. Ott, Superconductivity above 130 K in the Hg -Ba-Ca- Cu-O system, Nature, 363 (1993) 56–58. https://doi.org/10.1038/363056a0

    1993 doi

  15. [22]

    Meisner, Superconductivity and structural transformation in HfRuAs, Physics Letters A, 96 (1983) 483–486

    G.P. Meisner, Superconductivity and structural transformation in HfRuAs, Physics Letters A, 96 (1983) 483–486. https://doi.org/10.1016/0375-9601(83)90171-8

    1983 doi

  16. [23]

    B. -B. Ruan, X. -C. Wang, J. Yu, B. -J. Pan, Q. -G. Mu, T. Liu, G. -F. Chen, Z. -A. Ren, Superconductivity at 3.1 K in the orthorhombic ternary silicide ScRuSi, Superconductor Science and Technology, 30 (2016) 025008. https://doi.org/10.1088/1361-6668/30/2/025008

    2016 doi

  17. [24]

    Inohara, Y

    T. Inohara, Y. Okamoto, Y. Yamakawa, K. Takenaka, Synthesis and Superconducting Properties of a Hexagonal Phosphide ScRhP, Journal of the Physical Society of Japan, 85 (2016) 094706. https://doi.org/10.7566/JPSJ.85.094706

    2016 doi

  18. [25]

    Naqib, R.A

    S.H. Naqib, R.A. Chakalov, J.R. Cooper, Structural and electrical properties of c-axis oriented Y1−xCaxBa2(Cu1−yZny)3O7−δ thin films grown by pulsed laser deposition, Physica C, 407 (2004) 73 - 81. DOI 10.1016/j.physc.2004.03.249. 28 | P a g e

    2004 doi

  19. [26]

    Islam, S.H

    R.S. Islam, S.H. Naqib, Effects of Zn substitution in La 2−xSrxCu1−yZnyO4: interplay among superconductivity, pseudogap, and stripe order , Superconductor Science and Technology, 21 (2008) 125020. DOI 10.1088/0953-2048/21/12/125020

    2008 doi

  20. [27]

    H. He, M. Wang, Improving Arc Joining of Aluminum to Stainless Steel with Pure Al and Al–Cu Twin Hot Filler Wires, Metallography, Microstructure, and Analysis, 8 (2019) 329 –335. https://doi.org/10.1007/s13632-019-00539-y

    2019 doi

  21. [28]

    https://doi.org/10.1016/J.JMAPRO.2019.01.012

    Gang Mou, Xueming Hua, Min Wang, Fang Li, Effects of Ni addition on removing Fe -Ti intermetallic compounds in cold metal transfer arc -brazed TC4/304L dissimilar joints, Journal of Manufacturing Processes, 38 (2019) 104–112. https://doi.org/10.1016/J.JMAPRO.2019.01.012

    2019 doi

  22. [29]

    J. Wang, Z. Pan, L. Wei, S. He, D. Cuiuri, H. Li, Introduction of ternary alloying element in wire arc additive manufacturing of titanium aluminide intermetallic, Additive Manufacturing, 27 (2019). https://doi.org/10.1016/j.addma.2019.03.014

    2019 doi

  23. [30]

    Moisy, A

    F. Moisy, A. Gueydan, X. Sauvage, A. Guillet, C. Keller, E. Guilmeau, E. Hug, Influence of intermetallic compounds on the electrical resistivity of architectured copper clad aluminum composites elaborated by a restacking drawing method, Materials & Design, 155 (2018) 366–374. ...

    2018 doi

  24. [31]

    Gueydan, E

    A. Gueydan, E. Hug, Secondary creep stage behavior of copper -clad aluminum thin wires submitted to a moderate temperature level, Materials Science and Engineering: A, 709 (2018) 134–

    2018

  25. [32]

    https://doi.org/10.1016/j.msea.2017.10.044

    2017 doi

  26. [33]

    Pong, S.C

    I. Pong, S.C. Hopkins, B.A. Glowacki, A. Baldini, Non-Uniform Bronze Formation in Internal Tin Nb 3Sn Wire, IEEE Transactions on Applied Superconductivity, 19 (2009) 2593 –2597. https://doi.org/10.1109/TASC.2009.2018500

    2009 doi

  27. [34]

    Pong, S.C

    I. Pong, S.C. Hopkins, X. Fu, B.A. Glowacki, J.A. Elliott, A. Baldini, Microstructure development in Nb 3Sn(Ti) internal tin superconducting wire, Journal of Materials Science, 43 (2008) 3522–3530. https://doi.org/10.1007/s10853-008-2522-4

    2008 doi

  28. [35]

    Buschow, Concise Encyclopedia of Magnetic and Superconducting Materials

    K.H.J. Buschow, Concise Encyclopedia of Magnetic and Superconducting Materials. Elsevier, 2005

    2005

  29. [36]

    Meisner, H.C

    G.P. Meisner, H.C. Ku, The superconductivity and structure of equiatomic ternary transition metal pnictides, Applied Physics A, 31 (1983) 201–212. https://doi.org/10.1007/BF00614955

    1983 doi

  30. [37]

    Tütüncü, B

    H.M. Tütüncü, B. Taşlıpınar, H.Y. Uzunok, E. Karaca, S. Ba ǧcı, Probing the physical and superconducting properties of hexagonal ZrRuAs: A first -principles calculation, Physica C: Superconductivity and its Applications, 577 (2020) 1353715. https://doi.org/10.1016/j.physc.2020.1353715

    2020 doi

  31. [38]

    Shirotani, Superconductivity of Ternary Metal Compounds Prepared at High Pressures, Bulletin of the Chemical Society of Japan, 76 (2003) 1291 –1307

    I. Shirotani, Superconductivity of Ternary Metal Compounds Prepared at High Pressures, Bulletin of the Chemical Society of Japan, 76 (2003) 1291 –1307. https://doi.org/10.1246/bcsj.76.1291

    2003 doi

  32. [39]

    Shirotani, D

    I. Shirotani, D. Kato, A. Nishimoto, T. Yagi, Superconductivity and crystal structure of ZrRu1- xRhxP alloys prepared at high pressure, Journal of Physics: Condensed Matter, 13 (2001) 9393. https://doi.org/10.1088/0953-8984/13/41/324. 29 | P a g e

    2001 doi

  33. [40]

    Shirotani, Y

    I. Shirotani, Y. Konno, D. Kato, C. Sekine, S. Todo, T. Yaagi, Superconductivity of ternary equiatomic compounds with T c of above 10 K, Japanese Journal of Applied Physics, 39 (2000)

    2000

  34. [41]

    https://doi.org/10.7567/JJAPS.39S1.525

    doi

  35. [42]

    Shirotani, K

    I. Shirotani, K. Tachi, Y. Konno, S. Todo, T. Yagi, Superconductivity of the ternary ruthenium compounds HfRuP and ZrRuX (X = P, As, Si or Ge) prepared at a high pressure, Philosophical Magazine B, 79 (1999) 767–776. https://doi.org/10.1080/13642819908205748

    1999 doi

  36. [43]

    Giannozzi, O

    P. Giannozzi, O. Andreussi, T. Brumme, O. Bunau, M.B. Nardelli, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, M. Cococcioni, N. Colonna, I. Carnimeo, A.D. Corso, S. de Gironcoli, P. Delugas, R.A. DiStasio, A. Ferretti, A. Floris, G. Fratesi, G. Fugallo, R. Gebauer, U. Gerstm...

    2017 doi

  37. [44]

    Giannozzi, S

    P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G.L. Chiarotti, M. Cococcioni, I. Dabo, A. Dal Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mau...

    2009 doi

  38. [45]

    Perdew, K

    J.P. Perdew, K. Burke, M. Ernzerhof, Generalized Gradient Approximation Made Simple, Physical Review Letters, 77 (1996) 3865–3868. https://doi.org/10.1103/PhysRevLett.77.3865

    1996 doi

  39. [46]

    Gonze, P

    X. Gonze, P. Käckell, M. Scheffler, Ghost states for separable, norm -conserving, Iab initioP pseudopotentials, Physical Review B, 41 (1990) 12264 –12267. https://doi.org/10.1103/PhysRevB.41.12264

    1990 doi

  40. [47]

    Clark, M

    S. Clark, M. Segall, C. Pickard, P. Hasnip, M. Probert, K. Refson, M. Payne, First principles methods using CASTEP, Zeitschrift für Kristallographie, 220 (2005). https://doi.org/10.1524/zkri.220.5.567.65075

    2005 doi

  41. [48]

    Nielsen, R.M

    O.H. Nielsen, R.M. Martin, First -Principles Calculation of Stress, Physical Review Letters, 50 (1983) 697–700. https://doi.org/10.1103/PhysRevLett.50.697

    1983 doi

  42. [49]

    Fox, Optical Properties of Solids

    M. Fox, Optical Properties of Solids. Oxford University Press, 2010

    2010

  43. [50]

    Wooten, Optical properties of solids

    F. Wooten, Optical properties of solids. Academic Press, 1972

    1972

  44. [51]

    Katsura, Y

    T. Katsura, Y. Tange, A Simple Derivation of the Birch –Murnaghan Equations of State (EOSs) and Comparison with EOSs Derived from Other Definitions of Finite Strain, Minerals, 9 (2019) 745. https://doi.org/10.3390/min9120745

    2019 doi

  45. [52]

    Otero-de-la-Roza, V

    A. Otero-de-la-Roza, V. Luaña, Gibbs2: A new version of the quasi-harmonic model code. I. Robust treatment of the static data, Computer Physics Communications, 182 (2011) 1708 –1720. https://doi.org/10.1016/j.cpc.2011.04.016. 30 | P a g e

    2011 doi

  46. [53]

    Baroni, S

    S. Baroni, S. de Gironcoli, A. Dal Corso, P. Giannozzi, Phonons and related crystal properties from density -functional perturbation theory, Reviews of Modern Physics, 73 (2001) 515 –562. https://doi.org/10.1103/RevModPhys.73.515

    2001 doi

  47. [54]

    Verstraete, M

    M.J. Verstraete, M. Torrent, F. Jollet, G. Zérah, X. Gonze, Density functional perturbation theory with spin -orbit coupling: Phonon band structure of lead, Physical Review B, 78 (2008) 045119. https://doi.org/10.1103/PhysRevB.78.045119

    2008 doi

  48. [55]

    Yan, B.-T

    L. Yan, B.-T. Wang, X. Huang, Q. Li, K. Xue, J. Zhang, W. Ren, L. Zhou, Surface passivation induced a significant enhancement of superconductivity in layered two-dimensional MSi2N4 (M = Ta and Nb) materials, Nanoscale, 13 (2021) 18947–18954. https://doi.org/10.1039/D1NR05560G

    2021 doi

  49. [56]

    Q. Wu, S. Zhang, H. -F. Song, M. Troyer, A.A. Soluyanov, WannierTools: An open -source software package for novel topological materials, Computer Physics Communications, 224 (2018) 405–416. https://doi.org/10.1016/j.cpc.2017.09.033

    2018 doi

  50. [57]

    Sancho, J.M.L

    M.P.L. Sancho, J.M.L. Sancho, J.M.L. Sancho, J. Rubio, Highly convergent schemes for the calculation of bulk and surface Green functions, Journal of Physics F: Metal Physics, 15 (1985)

    1985

  51. [59]

    Souza, N

    I. Souza, N. Marzari, D. Vanderbilt, Maximally localized Wannier functions for entangled energy bands, Physical Review B, 65 (2001) 035109. https://doi.org/10.1103/PhysRevB.65.035109

    2001 doi

  52. [60]

    Marzari, A.A

    N. Marzari, A.A. Mostofi, J.R. Yates, I. Souza, D. Vanderbilt, Maximally localized Wannier functions: Theory and applications, Reviews of Modern Physics, 84 (2012) 1419 –1475. https://doi.org/10.1103/RevModPhys.84.1419

    2012 doi

  53. [61]

    Y. Qian, S. Nie, C. Yi, L. Kong, C. Fang, T. Qian, H. Ding, Y. Shi, Z. Wang, H. Weng, Z. Fang, Topological electronic states in HfRuP family superconductors, npj Computational Materials, 5 (2019) 121. https://doi.org/10.1038/s41524-019-0260-6

    2019 doi

  54. [62]

    Félix Mouhat, François-Xavier Coudert, Necessary and sufficient elastic stability conditions in various crystal systems , Phys. Rev. B, 90 (2014) 224104. DOI: https://doi.org/10.1103/PhysRevB.90.224104

    2014 doi

  55. [63]

    Pokluda, M

    J. Pokluda, M. Černý, M. Šob, Y. Umeno, Ab initio calculations of mechanical properties: Methods and applications, Progress in Materials Science, 73 (2015) 127 –158. https://doi.org/10.1016/j.pmatsci.2015.04.001

    2015 doi

  56. [64]

    Pettifor, Theoretical predictions of structure and related properties of intermetallics, Materials Science and Technology, 8 (1992) 345–349

    D.G. Pettifor, Theoretical predictions of structure and related properties of intermetallics, Materials Science and Technology, 8 (1992) 345–349. https://doi.org/10.1179/mst.1992.8.4.345

    1992 doi

  57. [65]

    Y. Wu, Y. Duan, X. Wang, M. Peng, L. Shen, H. Qi, Elastic anisotropy and thermal properties of Zr-Al-N ternary nitrides using first-principles explorations, Materials Today Communications, 33 (2022) 104651. https://doi.org/10.1016/j.mtcomm.2022.104651

    2022 doi

  58. [66]

    D. Qu, C. Li, L. Bao, Z. Kong, Y. Duan, Structural, electronic, and elastic properties of orthorhombic, hexagonal, and cubic Cu 3Sn intermetallic compounds in Sn –Cu lead-free solder, Journal of Physics and Chemistry of Solids, 138 (2020) 109253. https://doi.org/10.1016/j.jpcs...

    2020 doi

  59. [67]

    Kleinman, Deformation Potentials in Silicon

    L. Kleinman, Deformation Potentials in Silicon. I. Uniaxial Strain, Physical Review, 128 (1962) 2614–2621. https://doi.org/10.1103/PhysRev.128.2614. 31 | P a g e

    1962 doi

  60. [68]

    Hill, The Elastic Behaviour of a Crystalline Aggregate, Proceedings of the Physical Society

    R. Hill, The Elastic Behaviour of a Crystalline Aggregate, Proceedings of the Physical Society. Section A, 65 (1952) 349. https://doi.org/10.1088/0370-1298/65/5/307

    1952 doi

  61. [69]

    Reuss, Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle

    A. Reuss, Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle . https://doi.org/10.1002/zamm.19290090104

    doi

  62. [70]

    Amamou, B

    H. Amamou, B. Ferhat, A. Bois, Calculation of the Voigt Function in the Region of Very Small Values of the Parameter a Where the Calculation Is Notoriously Difficult, American Journal of Analytical Chemistry, 04 (2013) 725–731. https://doi.org/10.4236/ajac.2013.412087

    2013 doi

  63. [72]

    Pugh, XCII

    S.F. Pugh, XCII. Relations between the elastic moduli and the plastic properties of polycrystalline pure metals, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 45 (1954) 823–843. https://doi.org/10.1080/14786440808520496

    1954 doi

  64. [73]

    Nye, Physical Properties of Crystals: Their Representation by Tensors and Matrices

    J.F. Nye, Physical Properties of Crystals: Their Representation by Tensors and Matrices. Clarendon Press, 1985

    1985

  65. [74]

    Timoshenko, J.N

    S.P. Timoshenko, J.N. Goodier, Theory of Elasticity. McGraw-Hill

  66. [75]

    Teter, Computational Alchemy: The Search for New Superhard Materials, MRS Bulletin, 23 (1998) 22–27

    D.M. Teter, Computational Alchemy: The Search for New Superhard Materials, MRS Bulletin, 23 (1998) 22–27. https://doi.org/10.1557/S0883769400031420

    1998 doi

  67. [76]

    Greaves, A

    G. Greaves, A. Greer, R. Lakes, T. Rouxel, Poisson’s ratio and modern materials, Nature materials, 10 (2011) 986. https://doi.org/10.1038/nmat3177

    2011 doi

  68. [77]

    incompressible

    P. Mott, J. Dorgan, C. Roland, The bulk modulus and Poisson’s ratio of “incompressible” materials, Journal of Sound and Vibration, 312 (2008) 572 –575. https://doi.org/10.1016/j.jsv.2008.01.026

    2008 doi

  69. [78]

    H. Fu, D. Li, F. Peng, T. Gao, X. Cheng, Ab initio calculations of elastic constants and thermodynamic properties of NiAl under high pressures, Computational Materials Science - COMPUT MATER SCI, 44 (2008) 774–778. https://doi.org/10.1016/j.commatsci.2008.05.026

    2008 doi

  70. [79]

    Kelly, W.R

    A. Kelly, W.R. Tyson, A.H. Cottrell, Ductile and brittle crystals, Philosophical Magazine, 15 (1967) 567–586. https://doi.org/10.1080/14786436708220903

    1967 doi

  71. [80]

    Šimůnek, How to estimate hardness of crystals on a pocket calculator, Physical Review B, 75 (2007) 172108

    A. Šimůnek, How to estimate hardness of crystals on a pocket calculator, Physical Review B, 75 (2007) 172108. https://doi.org/10.1103/PhysRevB.75.172108

    2007 doi

  72. [81]

    Hossain, M.A

    M.M. Hossain, M.A. Ali, M.M. Uddin, A.K.M.A. Islam, S.H. Naqib, Origin of high hardness and optoelectronic and thermo -physical properties of boron -rich compounds B 6X (X = S, Se): A comprehensive study via DFT approach , J. Appl. Phys., 129 (2021) 175109. https://doi.org/10....

    2021 doi

  73. [82]

    F. Gao, J. He, E. Wu, S. Liu, D. Yu, D. Li, S. Zhang, Y. Tian, Hardness of Covalent Crystals, Physical Review Letters, 91 (2003) 015502. https://doi.org/10.1103/PhysRevLett.91.015502

    2003 doi

  74. [83]

    X.-Q. Chen, H. Niu, D. Li, Y. Li, Modeling hardness of polycrystalline materials and bulk metallic glasses, Intermetallics, 19 (2011) 1275 –1281. https://doi.org/10.1016/j.intermet.2011.03.026. 32 | P a g e

    2011 doi

  75. [84]

    Ravindran, L

    P. Ravindran, L. Fast, P.A. Korzhavyi, B. Johansson, J. Wills, O. Eriksson, Density functional theory for calculation of elastic properties of orthorhombic crystals: Application to TiSi 2, Journal of Applied Physics, 84 (1998) 4891–4904. https://doi.org/10.1063/1.368733

    1998 doi

  76. [85]

    C.M. Kube, M. de Jong, Elastic constants of polycrystals with generally anisotropic crystals, Journal of Applied Physics, 120 (2016) 165105. https://doi.org/10.1063/1.4965867

    2016 doi

  77. [86]

    Hadi, Md

    M.A. Hadi, Md. Roknuzzaman, F. Parvin, S.H. Naqib, A.K.M.A. Islam, Md. Aftabuzzaman, New MAX Phase Superconductor Ti 2GeC: A First -principles Study , Journal of Scientific Research, 6 (2013) 11 - 27. https://doi.org/10.3329/jsr.v6i1.16604

    2013 doi

  78. [87]

    Ranganathan, M

    S.I. Ranganathan, M. Ostoja -Starzewski, Universal Elastic Anisotropy Index, Physical Review Letters, 101 (2008) 055504. https://doi.org/10.1103/PhysRevLett.101.055504

    2008 doi

  79. [88]

    Ledbetter, Elastic properties of zinc: A compilation and a review, Journal of Physical and Chemical Reference Data, 6 (1977) 1181–1203

    H.M. Ledbetter, Elastic properties of zinc: A compilation and a review, Journal of Physical and Chemical Reference Data, 6 (1977) 1181–1203. https://doi.org/10.1063/1.555564

    1977 doi

  80. [89]

    Marder, Condensed Matter Physics

    M.P. Marder, Condensed Matter Physics. John Wiley & Sons, 2010

    2010

  81. [90]

    Harrison, Electronic Structure and the Properties of Solids: The Physics of the Chemical Bond

    W.A. Harrison, Electronic Structure and the Properties of Solids: The Physics of the Chemical Bond. New York: Dover Publications, 1989

    1989

  82. [91]

    Ashcroft, N

    N. Ashcroft, N. Mermin, Solid State Physics. New York: Cengage Learning, 1976

    1976

  83. [92]

    Vergniory, L

    M.G. Vergniory, L. Elcoro, C. Felser, N. Regnault, B.A. Bernevig, Z. Wang, A complete catalogue of high -quality topological materials, Nature, 566 (2019) 480 –485. https://doi.org/10.1038/s41586-019-0954-4

    2019 doi

  84. [93]

    Bradlyn, L

    B. Bradlyn, L. Elcoro, J. Cano, M.G. Vergniory, Z. Wang, C. Felser, M.I. Aroyo, B.A. Bernevig, Topological quantum chemistry, Nature, 547 (2017) 298 –305. https://doi.org/10.1038/nature23268

    2017 doi

  85. [94]

    Setyawan, S

    W. Setyawan, S. Curtarolo, High -throughput electronic band structure calculations: challenges and tools, Computational Materials Science, 49 (2010) 299 –312. https://doi.org/10.1016/J.Commatsci.2010.05.010

    2010 doi

  86. [95]

    Burkov, Topological Semimetals, Nature Materials, 15 (2016) 1145 –1148

    A.A. Burkov, Topological Semimetals, Nature Materials, 15 (2016) 1145 –1148. https://doi.org/10.1038/nmat4788

    2016 doi

  87. [96]

    B. Yan, C. Felser, Topological Materials: Weyl Semimetals, Annual Review of Condensed Matter Physics, 8 (2017) 337–354. https://doi.org/10.1146/annurev-conmatphys-031016-025458

    2017 doi

  88. [97]

    Armitage, E.J

    N.P. Armitage, E.J. Mele, A. Vishwanath, Weyl and Dirac semimetals in three -dimensional solids, Reviews of Modern Physics, 90 (2018) 015001. https://doi.org/10.1103/RevModPhys.90.015001

    2018 doi

  89. [98]

    Manchon, H.C

    A. Manchon, H.C. Koo, J. Nitta, S.M. Frolov, R.A. Duine, New Perspectives for Rashba Spin- Orbit Coupling, Nature Materials, 14 (2015) 871–882. https://doi.org/10.1038/nmat4360

    2015 doi

  90. [99]

    Dresselhaus, Spin-Orbit Coupling Effects in Zinc Blende Structures, Physical Review, 100 (1955) 580–586

    G. Dresselhaus, Spin-Orbit Coupling Effects in Zinc Blende Structures, Physical Review, 100 (1955) 580–586. https://doi.org/10.1103/PhysRev.100.580

    1955 doi

  91. [100]

    Bzdušek, Q

    T. Bzdušek, Q. Wu, A. Rüegg, M. Sigrist, A.A. Soluyanov, Nodal-chain metals, Nature, 538 (2016) 75–78. https://doi.org/10.1038/nature19099. 33 | P a g e

    2016 doi

  92. [101]

    Kim, B.J

    Y. Kim, B.J. Wieder, C.L. Kane, A.M. Rappe, Dirac Line Nodes in Inversion -Symmetric Crystals, Physical Review Letters, 115 (2015) 036806. https://doi.org/10.1103/PhysRevLett.115.036806

    2015 doi

  93. [102]

    C. Fang, H. Weng, X. Dai, Z. Fang, Topological nodal line semimetals, Chinese Physics B, 25 (2016) 117106. https://doi.org/10.1088/1674-1056/25/11/117106

    2016 doi

  94. [103]

    Hasan, S

    M.Z. Hasan, S. -Y. Xu, G. Bian, Topological insulators, topological superconductors and Weyl fermion semimetals: discoveries, perspectives and outlooks, Physica Scripta, 2015 (2015) 014001. https://doi.org/10.1088/0031-8949/2015/T164/014001

    2015 doi

  95. [104]

    Amaricci, J.C

    A. Amaricci, J.C. Budich, M. Capone, B. Trauzettel, G. Sangiovanni, Strong correlation effects on topological quantum phase transitions in three dimensions, Physical Review B, 93 (2016) 235112. https://doi.org/10.1103/PhysRevB.93.235112

    2016 doi

  96. [105]

    Reshak, V.V

    A.H. Reshak, V.V. Atuchin, S. Auluck, I.V. Kityk, First and second harmonic generation of the optical susceptibilities for the non -centro-symmetric orthorhombic AgCd 2GaS4, Journal of Physics: Condensed Matter, 20 (2008) 325234. https://doi.org/10.1088/0953-8984/20/32/325234

    2008 doi

  97. [106]

    H. Wang, Y. Chen, Y. Kaneta, S. Iwata, First-principles study on effective doping to improve the optical properties in spinel nitrides, Journal of Alloys and Compounds, 491 (2010) 550 –559. https://doi.org/10.1016/j.jallcom.2009.10.267

    2010 doi

  98. [107]

    S. Li, R. Ahuja, M.W. Barsoum, P. Jena, B. Johansson, Optical properties of Ti 3SiC2and Ti4AlN3, Applied Physics Letters, 92 (2008) 221907. https://doi.org/10.1063/1.2938862

    2008 doi

  99. [108]

    Drude model, Wikipedia. Apr. 28, 2026. Accessed: May 14, 2026. [Online]. Available: https://en.wikipedia.org/w/index.php?title=Drude_model&oldid=1351572680

    2026

  100. [109]

    G. Fan, K. Sun, Q. Hou, Z. Wang, Y. Liu, R. Fan, Epsilon-negative media from the viewpoint of materials science, EPJ Applied Metamaterials, 8 (2021) 11. https://doi.org/10.1051/epjam/2021005

    2021 doi

  101. [110]

    Vos, P.L

    M. Vos, P.L. Grande, Simple model dielectric functions for insulators, Journal of Physics and Chemistry of Solids, 104 (2017) 192–197. https://doi.org/10.1016/j.jpcs.2016.12.015

    2017 doi

  102. [111]

    Kittel, Introduction to Solid State Physics, Global Edition

    C. Kittel, Introduction to Solid State Physics, Global Edition. John Wiley & Sons, 2018

    2018

  103. [112]

    Boukortt, S

    A. Boukortt, S. Berrah, R. Hayn, A. Zaoui, First -principle calculation of the optical properties of zinc -blende Zn 1-xCdxSySe1-y, Physica B: Condensed Matter, 405 (2010) 763 –769. https://doi.org/10.1016/j.physb.2009.09.102

    2010 doi

  104. [113]

    Naderizadeh, S.M

    S. Naderizadeh, S.M. Elahi, M.R. Abolhassani, F. Kanjouri, N. Rahimi, J. Jalilian, Electronic and optical properties of Full -Heusler alloy Fe 3−xMnxSi, The European Physical Journal B, 85 (2012) 144. https://doi.org/10.1140/epjb/e2012-20919-3

    2012 doi

  105. [114]

    Romaniello, Optical properties of bcc transition metals in the range 0 -40 eV, Physical Review B, 73 (2006)

    P. Romaniello, Optical properties of bcc transition metals in the range 0 -40 eV, Physical Review B, 73 (2006). https://doi.org/10.1103/PhysRevB.73.075115

    2006 doi

  106. [115]

    Sun, H.-T

    J. Sun, H.-T. Wang, J. He, Y. Tian, Ab initio investigations of optical properties of the high- pressure phases of ZnO, Physical Review B, 71 (2005) 125132. https://doi.org/10.1103/PhysRevB.71.125132. 34 | P a g e

    2005 doi

  107. [116]

    Blanco, A.M

    M.A. Blanco, A.M. Pendás, E. Francisco, J.M. Recio, R. Franco, Thermodynamical properties of solids from microscopic theory: applications to MgF2and Al2O3, Journal of Molecular Structure: THEOCHEM, 368 (1996) 245–255. https://doi.org/10.1016/S0166-1280(96)90571-0

    1996 doi

  108. [117]

    Müller, H

    K.A. Müller, H. Burkard, SrTiO 3 : An intrinsic quantum paraelectric below 4 K, Physical Review B, 19 (1979) 3593–3602. https://doi.org/10.1103/PhysRevB.19.3593

    1979 doi

  109. [118]

    Helal, T

    M.A. Helal, T. Mori, S. Kojima, Softening of infrared -active mode of perovskite BaZrO 3 proved by terahertz time -domain spectroscopy, Applied Physics Letters, 106 (2015) 182904. https://doi.org/10.1063/1.4919913

    2015 doi

  110. [119]

    Anderson, A simplified method for calculating the debye temperature from elastic constants, Journal of Physics and Chemistry of Solids, 24 (1963) 909 - 917

    Orson L. Anderson, A simplified method for calculating the debye temperature from elastic constants, Journal of Physics and Chemistry of Solids, 24 (1963) 909 - 917. DOI: 10.1016/0022- 3697(63)90067-2

    1963 doi

  111. [120]

    Naher, M

    M.I. Naher, M. Mahamudujjaman, A. Tasnim, R.S. Islam, S.H. Naqib, Ab -initio insights into the elastic, bonding, phonon, optoelectronic and thermophysical properties of SnTaS 2, Solid State Sciences, 131 (2022) 106947. https://doi.org/10.1016/j.solidstatesciences.2022.106947

    2022 doi

  112. [121]

    Baroni, P

    S. Baroni, P. Giannozzi, E. Isaev, Thermal properties of materials from ab -initio quasi - harmonic phonons, Reviews in Mineralogy and Geochemistry, 71 (2010) 39 –57. https://doi.org/10.2138/rmg.2010.71.3

    2010 doi

  113. [122]

    Hossain, M.A

    A. Hossain, M.A. Ali, M.M. Uddin, S.H. Naqib, M.M. Hossain, Theoretical studies on phase stability, electronic, optical, mechanical and thermal properties of chalcopyrite semiconductors HgXN2 (X=Si, Ge and Sn): A comprehensive DFT analysis, Materials Science in Semiconductor P...

    2024 doi

  114. [123]

    B. Li, L. Bao, A. Yang, Y. Duan, M. Peng, X. Wang, Y. Cao, M. Li, First -principles prediction of thermodynamic properties and mechanical properties of Ti2AX (A=Al, Ga; X=C, N) M2AX phase at different pressures and temperatures, Vacuum, 204 (2022) 111380. https://doi.org/10.10...

    2022 doi

  115. [124]

    M. Born, K. Huang, Dynamical Theory Of Crystal Lattices. Oxford University PressNew York, NY, 1996. https://doi.org/10.1093/oso/9780192670083.001.0001

    1996 doi

  116. [125]

    Wallace, H

    D.C. Wallace, H. Callen, Thermodynamics of Crystals, American Journal of Physics, 40 (1972) 1718–1719. https://doi.org/10.1119/1.1987046

    1972 doi

  117. [126]

    X. Hao, J. Liu, H. Luo, Y. Han, W. Hu, J. Liu, J. Li, X. He, Crystal Structure Optimization and Gibbs Free Energy Comparison of Five Sulfathiazole Polymorphs by the Embedded Fragment QM Method at the DFT Level, Crystals, 9 (2019) 256. https://doi.org/10.3390/cryst9050256

    2019 doi

  118. [127]

    McMillan, Transition Temperature of Strong -Coupled Superconductors, Physical Review, 167 (1968) 331–344

    W.L. McMillan, Transition Temperature of Strong -Coupled Superconductors, Physical Review, 167 (1968) 331–344. https://doi.org/10.1103/PhysRev.167.331

    1968 doi

  119. [128]

    Allen, R.C

    P.B. Allen, R.C. Dynes, Transition temperature of strong -coupled superconductors reanalyzed, Physical Review B, 12 (1975) 905–922. https://doi.org/10.1103/PhysRevB.12.905

    1975 doi

  120. [129]

    Parvin, S.H

    F. Parvin, S.H. Naqib, Pressure dependence of structural, elastic, electronic, thermodynamic, and optical properties of van der Waals-type NaSn2P2 pnictide superconductor: Insights from DFT study, Results in Physics, 21 (2021) 103848. https://doi.org/10.1016/j.rinp.2021.103848...

    2021 doi

  121. [130]

    Mridha, S.H

    M.M. Mridha, S.H. Naqib, Pressure dependent elastic, electronic, superconducting, and optical properties of ternary barium phosphides (BaM 2P2; M = Ni, Rh): DFT based insights , Physica Scripta, 95 (2020) 105809. DOI 10.1088/1402-4896/abb968

    2020 doi

  122. [131]

    Islam, S.H

    R.S. Islam, S.H. Naqib, A.K.M.A. Islam, Modeling of the Complex Doping Dependence of dTc/dP of YBa 2Cu3O6+x, Journal of Superconductivity, 13 (2000) 485 - 490. https://doi.org/10.1023/A:1007775630383

    2000 doi

Pith tools

Reviewed July 11, 2026 · model on record in the stance chip above.