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Electronic Structure, Optical Response, Thermal and Mechanical Behavior of B6X (X = S, Se) under Pressure: A Comprehensive Ab-initio Exploration

T0 review · 3 major / 6 minor · reviewed 2026-07-11 · grok-4.5

Pith's one-line read Under pressure up to 20 GPa, orthorhombic B6S and B6Se stay hard, brittle, dynamically stable semiconductors with low thermal conductivity suited to thermal-barrier coatings.

desk verdict Solid pressure-scan DFT survey of two known hard phases; TBC claim is oversold on semi-empirical kph, but the elastic/phonon/optical data are usable. read the letter →

arxiv 2607.04116 v1 pith:M6K2QYZB submitted 2026-07-05 cond-mat.mtrl-sci

classification cond-mat.mtrl-sci
keywords Boron-richchalcogenidesDFTElectronicstructureOptoelectronicpropertiesThermomechanicalEffectofpressureThermalbarriercoatingsB6SB6Se
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 uses density-functional theory to map how hydrostatic pressure from 0 to 20 GPa changes the structure, bonding, elasticity, phonons, electronic bands, optics and thermal transport of the boron-rich chalcogenides B6S and B6Se. Both compounds remain mechanically and dynamically stable hard brittle phases; their elastic constants, moduli and hardness stay high while lattice thermal conductivity stays low. They are wide indirect-gap semiconductors whose gaps shrink modestly under compression, and their optical spectra show strong ultraviolet absorption that shifts with pressure. The authors conclude that the combination of hardness, thermal stability and low heat transport makes the materials promising for harsh-environment mechanical use and especially for thermal-barrier coatings, with pressure offering a clean tuning knob.

What carries the argument

Plane-wave DFT (CASTEP, GGA-PBE) calculations of pressure-dependent elastic stiffness tensors Cij, phonon dispersions, electronic band structures/DOS, dielectric functions and semi-empirical thermal-conductivity models (Slack, Clarke) that together quantify stability and thermomechanical response.

What would settle it

Measure the room-temperature lattice thermal conductivity and Vickers hardness of phase-pure B6S or B6Se under controlled hydrostatic pressure up to 20 GPa and compare with the predicted low kph (~1–1.5 W m−1 K−1) and high hardness (~28–35 GPa).

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Extended reading notes

Core claim

Orthorhombic B6S and B6Se remain structurally, mechanically and dynamically stable hard brittle semiconductors across 0–20 GPa (5–20 GPa for B6Se). Their elastic moduli, hardness and melting temperatures stay high, phonon spectra show no soft modes, band gaps remain indirect and decrease with pressure, and low lattice thermal conductivity together with low thermal-expansion coefficients mark them as strong thermal-barrier-coating candidates.

Load-bearing premise

The chosen GGA-PBE functional, pseudopotentials and semi-empirical hardness/thermal-conductivity formulas are assumed accurate enough to rank the materials as excellent thermal-barrier candidates.

Editorial extensions

If this is right

  • Both compounds can serve as pressure-tunable hard phases in high-temperature, high-stress mechanical environments.
  • Low phonon thermal conductivity and high Debye/melting temperatures qualify them as thermal-barrier coating materials whose performance can be adjusted by external pressure.
  • Indirect band gaps that shrink under compression open a route to pressure-tuned ultraviolet optoelectronic or photovoltaic response.
  • Elastic and optical anisotropy implies direction-dependent mechanical failure and light–matter interaction that device design must respect.

Reading between the lines

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

  • If the predicted low thermal conductivity survives experiment, B6X coatings could compete with established zirconia-based TBCs in aerospace or power-generation turbines.
  • Pressure-induced gap reduction may allow reversible switching of optical absorption edges without chemical doping, useful for adaptive UV filters.
  • The mixed covalent–ionic bonding and B12-icosahedral framework suggest that related B-rich chalcogenides or pnictides could form a broader family of hard, low-k thermal barriers.
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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 / 6 minor

Summary. The manuscript reports a comprehensive DFT (CASTEP, GGA-PBE) study of orthorhombic B6S and B6Se under hydrostatic pressures of 0–20 GPa (5–20 GPa for B6Se). It computes structural parameters, single-crystal elastic constants and VRH polycrystalline moduli, elastic anisotropy (ELATE), Debye and melting temperatures, Slack/Clarke thermal conductivities, Mulliken/Hirshfeld populations and charge-density maps, optical spectra for three polarizations, electronic band structures and DOS, and DFPT phonon dispersions. The central claims are that both compounds remain mechanically and dynamically stable hard brittle indirect-gap semiconductors up to 20 GPa, exhibit pressure-tunable UV optical response, and possess low lattice thermal conductivity that makes them excellent thermal-barrier-coating candidates.

Significance. Boron-rich chalcogenides with B12 icosahedra are of genuine interest for high-temperature, high-pressure, and hard-phase applications; the experimental synthesis of orthorhombic B6X is recent. A pressure-dependent survey that simultaneously covers elastic stability, phonons, optics, bonding, and thermophysical estimates fills a documented gap relative to earlier ambient or limited studies. The calculations follow standard, reproducible CASTEP workflows (Born criteria under pressure, VRH averages, Kramers–Kronig optics, DFPT phonons) and the elastic constants agree with prior work. If the TBC and optoelectronic claims are appropriately caveated, the data set is a useful reference for experimental groups working on these phases.

major comments (3)
  1. Abstract, §3.3 (Eqs. 18–22, Table 8) and §4: the load-bearing claim that both compounds are “excellent thermal barrier coating materials” rests on Slack kph values of ~1.0–1.5 W m⁻¹ K⁻¹ and Clarke/Cahill kmin. These models are semi-empirical (A(γ) from Julian; γ from Poisson’s ratio via Eq. 19) and only order-of-magnitude for complex covalent crystals with B12 units. The manuscript itself notes the semi-empirical character yet still draws a strong application conclusion without comparison to established TBC benchmarks (e.g., YSZ) or any uncertainty estimate. The claim should be softened to “potentially promising” and the limitations of Slack/Clarke for these systems stated explicitly.
  2. §3.2 (text after Table 4 / Fig. 6) versus Table 4: the text states “B6S is substantially harder than B6Se at all pressures,” but Table 4 lists HV(B6S) ≈ 26–30 GPa and HV(B6Se) ≈ 33–35 GPa. The same section also asserts that higher kph implies stronger covalency and that B6Se has higher kph (Table 8), while Table 7 shows higher θD for B6S. These internal inconsistencies undermine the hardness ranking and the covalency–thermal-conductivity narrative that supports the TBC argument. The hardness formula used, the numerical values, and the comparative statements must be reconciled.
  3. §3.7 and Abstract: electronic band structures and DOS are obtained with GGA-PBE only. The manuscript correctly notes that GGA underestimates gaps, yet still presents the pressure-dependent gaps (Fig. 22) and “wide bandgap semiconducting” character as quantitative results suitable for “high-performance photovoltaic and optoelectronic applications.” At least a hybrid-functional or scissor-corrected estimate (or a clear statement that absolute gaps are not quantitative) is needed before the optoelectronic application claim can stand.
minor comments (6)
  1. Table 5 header is corrupted (“Table Error! No text of specified style in document.”); the compound label for the second block is written “B6S” instead of “B6Se”.
  2. §3.1: “Figure 1” is used both for the crystal-structure schematic and for the normalized lattice-parameter plots; renumber consistently.
  3. Abstract and §1: “B6S remains stable throughout 0–20 GPa, B6Se stabilizes under 5–20 GPa” is stated, but optical and electronic figures for B6Se sometimes begin at 0 GPa in the text; align the pressure windows.
  4. Eq. (6) for optical conductivity uses non-standard notation (Wcν, E⃗0); a brief definition or a standard reference would help.
  5. Several self-citations and related B6X papers are listed; a short explicit comparison of the present pressure-dependent elastic constants and gaps with Hossain et al. and León-Flores et al. would clarify novelty.
  6. Phonon section (§3.8): “Relatively small PHDOS for low frequency branches are responsible for low thermal conductivity” is qualitative; a short link to the Slack formula would tighten the argument.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: standard DFT pipeline (elastic constants o VRH moduli o Anderson/Slack/Clarke thermal models) with only non-load-bearing self-comparisons to prior ambient studies.

full rationale

All primary quantities (Cij via stress-strain, band structures/DOS, dielectric function and derived optics, phonon dispersions via DFPT, Mulliken/Hirshfeld charges, charge-density maps) are obtained directly from CASTEP GGA-PBE total-energy calculations under hydrostatic pressure; no free parameters are fitted to any target observable and then re-used as a “prediction.” Polycrystalline B/G/Y, Poisson ratio, Cauchy pressure, machinability, Kleinman parameter, anisotropy indices (ELATE), Debye temperature (Anderson formula from vl/vt), melting temperature (empirical linear combination of C11/C33), Grüneisen parameter (from ν), lattice thermal conductivity (Slack model), and kmin (Clarke/Cahill) are algebraic post-processing of the same ab-initio elastic tensor; the TBC candidacy is an interpretive claim based on the resulting low kph values, not a circular re-statement of an input. Self-citations ([28],[29],[93] etc.) serve only for lattice-parameter or ambient elastic-constant comparison and do not supply uniqueness theorems, ansätze, or load-bearing premises that close a logical loop. The derivation chain is therefore self-contained against external benchmarks and exhibits none of the six enumerated circularity patterns.

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

The work rests on standard DFT machinery and well-known semi-empirical estimators; no new physical entities or free parameters are invented. The main domain assumptions are the adequacy of GGA-PBE and the transferability of Slack/Clarke formulas to these boron-rich phases.

assumptions (4)
  • domain assumption GGA-PBE exchange-correlation functional plus Vanderbilt ultrasoft pseudopotentials adequately describe structure, elasticity and electronic structure of B6X
    Stated in §2; used for all subsequent results.
  • domain assumption Voigt–Reuss–Hill averaging yields reliable polycrystalline moduli from single-crystal Cij
    Standard materials-science practice invoked in §3.2.
  • domain assumption Slack’s formula and Clarke’s minimum-conductivity model give realistic lattice thermal conductivities
    Used without additional validation in §3.3.
  • standard math Born mechanical-stability criteria under hydrostatic pressure remain valid for orthorhombic crystals
    Eq. (8) and surrounding text.

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Cite this review

Pith. "Pith review of Electronic Structure, Optical Response, Thermal and Mechanical Behavior of B6X (X = S, Se) under Pressure: A Comprehensive Ab-initio Exploration." pith.science (2026). https://pith.science/paper/M6K2QYZB

@misc{pith2026260704116,
  author       = {Pith},
  title        = {Pith review of: Electronic Structure, Optical Response, Thermal and Mechanical Behavior of B6X (X = S, Se) under Pressure: A Comprehensive Ab-initio Exploration},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/M6K2QYZB}},
  note         = {Machine review of arXiv:2607.04116}
}
read the original abstract

This study presents a comprehensive investigation of the pressure dependent structural, electronic, optical, mechanical, and bonding properties of orthorhombic boron rich chalcogenides B6S and B6Se. Calculations were performed using density functional theory across a wide range of hydrostatic pressures. The computed elastic constants, bulk, Young, shear moduli, and Poisson ratio, revealed mechanical robustness and strong resistance to deformation, even under significant compression. Electronic band structure and density of states analyses indicate that the materials exhibit indirect bandgap semiconducting behavior. Optical results reveal clear pressure induced spectral shifts, particularly in the visible and ultraviolet regions, suggesting modified light matter interaction under compression. Phonon dispersion curves verified the dynamical stability of both materials within the investigated pressure range. Hardness estimations, combined with elastic parameters, and melting temperatures, further indicate that B6S and B6Se possess significant mechanical strength suitable for applications under harsh environments. The thermal properties suggest that both these compounds possess features suitable to be used as excellent thermal barrier coating materials.

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Works this paper leans on

95 extracted references · 58 canonical work pages

  1. [1]

    Waste recycling in thermoelectric materials,

    A. Bahrami, G. Schierning, and K. Nielsch, "Waste recycling in thermoelectric materials," Advanced Energy Materials, 10(19), 1904159 (2020). https://doi.org/10.1002/aenm.201904159

  2. [2]

    New and old concepts in thermoelectric materials,

    J. R. Sootsman, D. Y . Chung, and M. G. Kanatzidis, "New and old concepts in thermoelectric materials," Angewandte Chemie International Edition, 48(46), 8616–8639 (2009). https://doi.org/10.1002/anie.200900598

  3. [3]

    Review of various application of thermoelectric module,

    C. Jangonda, K. Patil, A. Kinikar, R. Bhokare, and M. D. Gavali, "Review of various application of thermoelectric module," International Journal of Innovative Research in Science, Engineering and Technology, 5(3), 3393–3400 (2016)

  4. [4]

    Improving the solar still productivity using thermoelectric materials: A review,

    M. Elgendi, A. E. Kabeel, and F. A. Essa, "Improving the solar still productivity using thermoelectric materials: A review," Alexandria Engineering Journal, 65, 963–980 (2023). https://doi.org/10.1016/j.aej.2022.10.011

  5. [5]

    Recent progress of thermoelectric applications for cooling/heating, power generation, heat flux sensor and potential prospect of their integrated applications,

    L. Huang, Y . Zheng, L. Xing, and B. Hou, "Recent progress of thermoelectric applications for cooling/heating, power generation, heat flux sensor and potential prospect of their integrated applications," Thermal Science and Engineering Progress, 45, 102064 (2023). https://doi.org/10.1016/j.tsep.2023.102064

  6. [6]

    LTCC- based Y-type thermoelectric generator with an improved heat flow guide for automotive 44 | P a g e waste heat recovery,

    N. Jaziri, N. Gutzeit, H. Bartsch, A. Boughamoura, J. Müller, and F. Tounsi, "LTCC- based Y-type thermoelectric generator with an improved heat flow guide for automotive 44 | P a g e waste heat recovery," Sustainable Energy & Fuels, 6(10), 2330–2341 (2022). https://doi.org/10.1039/D2SE00048B

  7. [7]

    An innovative tubular thermoelectric generator (TTEG) for enhanced waste heat recovery in industrial and automotive applications,

    K.-W. Du and C.-I. Wu, "An innovative tubular thermoelectric generator (TTEG) for enhanced waste heat recovery in industrial and automotive applications," Applied Sciences, 14(2), 685 (2024). https://doi.org/10.3390/app14020685

  8. [8]

    Wearable thermoelectric generator to harvest body heat for powering a miniaturized accelerometer,

    Y . Wang, Y . Shi, D. Mei, and Z. Chen, "Wearable thermoelectric generator to harvest body heat for powering a miniaturized accelerometer," Applied Energy, 215, 690–699 (2018). https://doi.org/10.1016/j.apenergy.2018.02.062

Show all 95 references
  1. [9]

    Review of thermoelectric materials and its properties with applications,

    N. Swarnkar, "Review of thermoelectric materials and its properties with applications," Journal of Emerging Technologies and Innovative Research, 6(5), 131–136 (2019)

  2. [10]

    A review of performance analysis & potential applications of thermoelectric refrigeration system,

    D. Suryawanshi, V . Pokale, N. Pokharkar, A. Walgude, and P. Patunkar, "A review of performance analysis & potential applications of thermoelectric refrigeration system," International Journal of Research and Scientific Innovation, 3(3), 29–34 (2016)

  3. [11]

    D. M. Rowe, CRC Handbook of Thermoelectrics, CRC Press, Boca Raton (1995)

  4. [12]

    Advances in thermoelectric materials research: Looking back and moving forward,

    J. He and T. M. Tritt, "Advances in thermoelectric materials research: Looking back and moving forward," Science, 357(6358), eaak9997 (2017). https://doi.org/10.1126/science.aak9997

  5. [13]

    Rational design of advanced thermoelectric materials,

    J. Yang, H. L. Yip, and A. K. Y . Jen, "Rational design of advanced thermoelectric materials," Advanced Energy Materials, 3(5), 549–565 (2013). https://doi.org/10.1002/aenm.201200514

  6. [14]

    Closo clusters with unusual electron numbers: Molecular orbital considerations and localized bonding schemes,

    M. E. O’Neill and K. Wade, "Closo clusters with unusual electron numbers: Molecular orbital considerations and localized bonding schemes," Inorganic Chemistry, 21(2), 461– 464 (1982). https://doi.org/10.1021/ic00131a093

  7. [15]

    Closo clusters with unusual electron numbers: Localized bond schemes for n-atom clusters with n, (n + 1) or (n + 2) skeletal electron pairs,

    M. E. O’Neill and K. Wade, "Closo clusters with unusual electron numbers: Localized bond schemes for n-atom clusters with n, (n + 1) or (n + 2) skeletal electron pairs," Polyhedron, 3(2), 199–212 (1984). https://doi.org/10.1016/S0277-5387(00)88051-1

  8. [16]

    Optical phonon modes in rhombohedral boron monosulfide under high pressure,

    K. A. Cherednichenko, P. S. Sokolov, A. Kalinko, Y . Le Godec, A. Polian, J.-P. Itié, and V . L. Solozhenko, "Optical phonon modes in rhombohedral boron monosulfide under high pressure," Journal of Applied Physics, 117(18), 185904 (2015). https://doi.org/10.1063/1.4921099

  9. [17]

    Boron: Elementary challenge for experimenters and theoreticians,

    B. Albert and H. Hillebrecht, "Boron: Elementary challenge for experimenters and theoreticians," Angewandte Chemie International Edition, 48(46), 8640–8668 (2009). https://doi.org/10.1002/anie.200903246

  10. [18]

    Equation of state of boron subarsenide B12As2 to 47 GPa,

    K. A. Cherednichenko, Y . Le Godec, and V . L. Solozhenko, "Equation of state of boron subarsenide B12As2 to 47 GPa," High Pressure Research, 38(3), 224–231 (2018). https://doi.org/10.1080/08957959.2018.1476507

  11. [19]

    Discovery of new boron-rich chalcogenides: Orthorhombic B6X (X=S, Se),

    K. A. Cherednichenko, V . A. Mukhanov, Z. Wang, A. R. Oganov, A. Kalinko, I. Dovgaliuk, and V . L. Solozhenko, "Discovery of new boron-rich chalcogenides: Orthorhombic B6X (X=S, Se)," Scientific Reports, 10, 9277 (2020). https://doi.org/10.1038/s41598-020-66316-y 45 | P a g e

  12. [20]

    High-pressure synthesis and crystal structure of B2S3,

    T. Sasaki, H. Takizawa, K. Uheda, T. Yamashita, and T. Endo, "High-pressure synthesis and crystal structure of B2S3," Journal of Solid State Chemistry, 166(1), 164–170 (2002). https://doi.org/10.1006/jssc.2002.9575

  13. [21]

    Predicted structural evolution and detailed insight into configuration correlation, mechanical properties of silicon–boron binary compounds,

    B. Zhang, L. Wu, and Z. Li, "Predicted structural evolution and detailed insight into configuration correlation, mechanical properties of silicon–boron binary compounds," RSC Advances, 7(26), 16109–16118 (2017). https://doi.org/10.1039/C7RA00592J

  14. [22]

    An α-rhombohedral boron-related compound with sulfur: Synthesis, structure and thermoelectric properties,

    O. Sologub, Y . Matsushita, and T. Mori, "An α-rhombohedral boron-related compound with sulfur: Synthesis, structure and thermoelectric properties," Scripta Materialia, 68(5), 289–292 (2013). https://doi.org/10.1016/j.scriptamat.2012.10.044

  15. [23]

    Superhard and superconducting B6C,

    K. Xia, M. Ma, C. Liu, H. Gao, Q. Chen, J. He, J. Sun, H.-T. Wang, Y . Tian, and D. Xing, "Superhard and superconducting B6C," Materials Today Physics, 3, 76–84 (2017). https://doi.org/10.1016/j.mtphys.2017.12.003

  16. [24]

    A novel metallic silicon hexaboride, Cmca-B6Si,

    Z. Yuan, M. Xiong, and D. Yu, "A novel metallic silicon hexaboride, Cmca-B6Si," Physics Letters A, 384(3), 126075 (2020). https://doi.org/10.1016/j.physleta.2019.126075

  17. [27]

    Finite strain isotherm and velocities for single‐crystal and polycrystalline NaCl at high pressures and 300°K,

    F. Birch, "Finite strain isotherm and velocities for single‐crystal and polycrystalline NaCl at high pressures and 300°K," Journal of Geophysical Research, 83(B3), 1257–1268 (1978). https://doi.org/10.1029/JB083iB03p01257

  18. [28]

    Discovery of new boron-rich chalcogenides: Orthorhombic B6X (X=S, Se); Fracture Toughness of Diamond Single Crystals,

    K. A. Cherednichenko, V. A. Mukhanov, Z. Wang, A. R. Oganov, A. Kalinko, I. Dovgaliuk, V. L. Solozhenko, N. V. Novikov, and S. Dub, "Discovery of new boron-rich chalcogenides: Orthorhombic B6X (X=S, Se); Fracture Toughness of Diamond Single Crystals," Journal of Hard Materials...

  19. [29]

    M. M. Hossain, M. A. Ali, M. M. Uddin, S. H. Naqib, and A. K. M. A. Islam, "Newly Synthesized Three-Dimensional Boron-Rich Chalcogenides B12X (X = S and Se): Theoretical Characterization of the Physical Properties for Optoelectronic and Mechanical Applications," Physica Status...

  20. [30]

    Generalized Gradient Approximation Made Simple,

    J. P. Perdew, K. Burke, and M. Ernzerhof, "Generalized Gradient Approximation Made Simple," Physical Review Letters, 77(18), 3865–3868 (1996). https://doi.org/10.1103/PhysRevLett.77.3865

  21. [31]

    Meneve, K

    J. Meneve, K. Vercammen, E. Dekempeneer, and J. Smeets, Thin tribological coatings: Magic or design, Surface and Coatings Technology, 94–95, 476–482 (1997). https://doi.org/10.1016/S0257-8972(97)00504-7 46 | P a g e

  22. [32]

    Liu and M

    Z. Liu and M. G. Scanlon, Modelling Indentation of Bread Crumb by Finite Element Analysis, Biosystems Engineering, 85(4), 477–484 (2003). https://doi.org/10.1016/S1537- 5110(03)00069-4

  23. [33]

    Elastic stability criteria of seven crystal systems and their application under pressure,

    J. Wang, et al., "Elastic stability criteria of seven crystal systems and their application under pressure," Journal of Applied Physics, 133(13), 135901 (2023). https://doi.org/10.1063/5.0139232

  24. [34]

    Structural, elastic, electronic, bonding, and optical properties of topological CaSn3 semimetal,

    M. I. Naher and S. H. Naqib, "Structural, elastic, electronic, bonding, and optical properties of topological CaSn3 semimetal," Journal of Alloys and Compounds, 829, 154509 (2020). https://doi.org/10.1016/j.jallcom.2020.154509

  25. [35]

    First-principles calculations of the structural, electronic, mechanical and thermodynamic properties of MAX phase Mon+1GeCn (n= 1 – 3) compounds,

    H. Mebtouche, O. Baraka, A. Yakoubi, R. Khenata, S. A. Tahir, R. Ahmed, S. H. Naqib, A. Bouhemadou, S. B. Omran, and X. Wang, "First-principles calculations of the structural, electronic, mechanical and thermodynamic properties of MAX phase Mon+1GeCn (n= 1 – 3) compounds," Mat...

  26. [36]

    Recently synthesized (Ti1-xMox)2AlC (0 ≤ x ≤ 0.20) solid solutions: Deciphering the structural, electronic, mechanical and thermodynamic properties via ab initio simulations,

    M. A. Ali and S. H. Naqib, "Recently synthesized (Ti1-xMox)2AlC (0 ≤ x ≤ 0.20) solid solutions: Deciphering the structural, electronic, mechanical and thermodynamic properties via ab initio simulations," RSC Advances, 10(52), 31535–31551 (2020). https://doi.org/10.1039/D0RA05570K

  27. [37]

    First principles study of M2InC (M = Zr, Hf and Ta) MAX phases: The effect of M atomic species,

    F. Sultana, M. M. Uddin, M. A. Ali, M. M. Hossain, S. H. Naqib, and A. Islam, "First principles study of M2InC (M = Zr, Hf and Ta) MAX phases: The effect of M atomic species," Results in Physics, 11, 869–877 (2018). https://doi.org/10.1016/j.rinp.2018.10.038

  28. [38]

    Structural, elastic, electronic, and optical properties of layered TiNX (X = F, Cl, Br, I) compounds: A density functional theory study,

    M. M. Hossain and S. H. Naqib, "Structural, elastic, electronic, and optical properties of layered TiNX (X = F, Cl, Br, I) compounds: A density functional theory study," Molecular Physics, 118(1), e1609706 (2020). https://doi.org/10.1080/00268976.2019.1609706

  29. [39]

    Mechanical and electronic properties of Ti2AlN and Ti4AlN3: A first-principles study,

    W. Feng and S. Cui, "Mechanical and electronic properties of Ti2AlN and Ti4AlN3: A first-principles study," Canadian Journal of Physics, 92(12), 1652–1658 (2014). https://doi.org/10.1139/cjp-2013-0579

  30. [40]

    Theoretical predictions of structure and related properties of intermetallics,

    D. G. Pettifor, "Theoretical predictions of structure and related properties of intermetallics," Materials Science and Technology, 8(4), 345–349 (1992). https://doi.org/10.1179/mst.1992.8.4.345

  31. [41]

    Critical Poisson’s ratio between toughness and brittleness,

    J. Cao and F. Li, "Critical Poisson’s ratio between toughness and brittleness," Philosophical Magazine Letters, 96(11), 425–431 (2016). https://doi.org/10.1080/09500839.2016.1241926

  32. [42]

    Poisson’s ratio and modern materials,

    G. N. Greaves, A. L. Greer, R. S. Lakes, and T. Rouxel, "Poisson’s ratio and modern materials," Nature Materials, 10(11), 823–837 (2011). https://doi.org/10.1038/nmat3134

  33. [43]

    Cubic Hf3N4 and Zr3N4: A class of hard materials,

    M. Mattesini, R. Ahuja, and B. Johansson, "Cubic Hf3N4 and Zr3N4: A class of hard materials," Physical Review B, 68(18), 184108 (2003). https://doi.org/10.1103/PhysRevB.68.184108 47 | P a g e

  34. [44]

    Density functional theory for calculation of elastic properties of orthorhombic crystals: Application to TiSi2,

    P. Ravindran, L. Fast, P. A. Korzhavyi, B. Johansson, J. Wills, and O. Eriksson, "Density functional theory for calculation of elastic properties of orthorhombic crystals: Application to TiSi2," Journal of Applied Physics, 84(9), 4891–4904 (1998). https://doi.org/10.1063/1.368733

  35. [46]

    A comparative ab-initio investigation of the physical properties of cubic Laves phase compounds XBi2 (X = K, Rb),

    J. Hassan, M. A. Masum, and S. H. Naqib, "A comparative ab-initio investigation of the physical properties of cubic Laves phase compounds XBi2 (X = K, Rb)," Computational Condensed Matter, 39, e00905 (2024). https://doi.org/10.1016/j.cocom.2024.e00905

  36. [47]

    Fundamentals and applications of instrumented indentation in multidisciplinary research,

    Y.-T. Cheng, T. F. Page, G. M. Pharr, M. V. Swain, and K. J. Wahl, "Fundamentals and applications of instrumented indentation in multidisciplinary research," Journal of Materials Research, 19(1), 1–2 (2004). https://doi.org/10.1557/jmr.2004.19.1.1

  37. [48]

    Scaling, dimensional analysis, and indentation measurements,

    Y.-T. Cheng and C.-M. Cheng, "Scaling, dimensional analysis, and indentation measurements," Materials Science and Engineering: R: Reports, 44(4–5), 91–149 (2004). https://doi.org/10.1016/j.mser.2004.05.001

  38. [49]

    Theoretical investigation on the transition-metal borides with Ta3B4-type structure: A class of hard and refractory materials,

    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," Computational Materials Science, 50(5), 1559–1665 (2011). https://doi.org/10.1016/j.commatsci.2010.12.012

  39. [50]

    First-principles study of structural, electronic and elastic properties of Nb4AlC3,

    A. Bouhemadou, "First-principles study of structural, electronic and elastic properties of Nb4AlC3," Brazilian Journal of Physics, 40(1), 52–57 (2010). https://doi.org/10.1590/S0103-97332010000100010

  40. [51]

    Modeling hardness of polycrystalline materials and bulk metallic glasses,

    X.-Q. Chen, H. Niu, D. Li, and Y. Li, "Modeling hardness of polycrystalline materials and bulk metallic glasses," Intermetallics, 19(9), 1275–1281 (2011). https://doi.org/10.1016/j.intermet.2011.03.026

  41. [52]

    On the Fracture Toughness of Advanced Materials,

    M. E. Launey and R. O. Ritchie, "On the Fracture Toughness of Advanced Materials," Advanced Materials, 21(20), 2103–2110 (2009). https://doi.org/10.1002/adma.200803322

  42. [53]

    Microscopic theory of hardness and design of novel superhard crystals,

    Y. Tian, B. Xu, and Z. Zhao, "Microscopic theory of hardness and design of novel superhard crystals," International Journal of Refractory Metals and Hard Materials, 33, 93–106 (2012). https://doi.org/10.1016/j.ijrmhm.2012.02.017

  43. [54]

    Computational alchemy: The search for new superhard materials,

    D. M. Teter, "Computational alchemy: The search for new superhard materials," MRS Bulletin, 23(1), 22–27 (1998). https://doi.org/10.1557/S088376940003117X

  44. [55]

    A model of hardness and fracture toughness of solids,

    E. Mazhnik and A. R. Oganov, "A model of hardness and fracture toughness of solids," Journal of Applied Physics, 126(12), 125109 (2019). https://doi.org/10.1063/1.5113622

  45. [56]

    W. A. Harrison, Electronic Structure and the Properties of Solids: The Physics of the Chemical Bond, Courier Corporation, New York (2012). (Book)

  46. [57]

    Deformation Potentials in Silicon. I. Uniaxial Strain,

    L. Kleinman, "Deformation Potentials in Silicon. I. Uniaxial Strain," Physical Review, 128(6), 2614–2621 (1962). https://doi.org/10.1103/PhysRev.128.2614 48 | P a g e

  47. [58]

    Elasticity of hexagonal BeO,

    V. Milman and M. C. Warren, "Elasticity of hexagonal BeO," Journal of Physics: Condensed Matter, 13(2), 241–245 (2001). https://doi.org/10.1088/0953-8984/13/2/302

  48. [59]

    Stability and elastic properties of Y–C binary compounds investigated by first principles calculations,

    X. Gao, Y. Jiang, R. Zhou, and J. Feng, "Stability and elastic properties of Y–C binary compounds investigated by first principles calculations," Journal of Alloys and Compounds, 587, 819–826 (2014). https://doi.org/10.1016/j.jallcom.2013.10.254

  49. [60]

    Elastic constants of polycrystals with generally anisotropic crystals,

    C. M. Kube and M. De Jong, "Elastic constants of polycrystals with generally anisotropic crystals," Journal of Applied Physics, 120(16), 164905 (2016). https://doi.org/10.1063/1.4966118

  50. [61]

    Universal Elastic Anisotropy Index,

    S. I. Ranganathan and M. Ostoja-Starzewski, "Universal Elastic Anisotropy Index," Physical Review Letters, 101(5), 055504 (2008). https://doi.org/10.1103/PhysRevLett.101.055504

  51. [62]

    Vahldiek, Anisotropy in Single-Crystal Refractory Compounds, Springer Science & Business Media, New York (2013)

    F. Vahldiek, Anisotropy in Single-Crystal Refractory Compounds, Springer Science & Business Media, New York (2013). (Book)

  52. [63]

    The elastic anisotropy of crystals,

    D. H. Chung and W. R. Buessem, "The elastic anisotropy of crystals," Journal of Applied Physics, 38(5), 2010–2035 (1967). https://doi.org/10.1063/1.1709819

  53. [64]

    ELATE: An open-source online application for analysis and visualization of elastic tensors,

    R. Gaillac, P. Pullumbi, and F.-X. Coudert, "ELATE: An open-source online application for analysis and visualization of elastic tensors," Journal of Physics: Condensed Matter, 28(27), 275201 (2016). https://doi.org/10.1088/0953-8984/28/27/275201

  54. [66]

    Theoretical investigation of the electronic and optical properties of ZrX2 (X = S, Se and Te),

    A. H. Reshak and S. Auluck, "Theoretical investigation of the electronic and optical properties of ZrX2 (X = S, Se and Te)," Physica B: Condensed Matter, 353(3–4), 230– 237 (2004). https://doi.org/10.1016/j.physb.2004.09.098

  55. [67]

    J. R. Christman, Fundamentals of Solid State Physics, John Wiley & Sons, New York (1988). (Book)

  56. [68]

    A simplified method for calculating the Debye temperature from elastic constants,

    O. L. Anderson, "A simplified method for calculating the Debye temperature from elastic constants," Journal of Physics and Chemistry of Solids, 24(7), 909–917 (1963). https://doi.org/10.1016/0022-3697(63)90067-2

  57. [69]

    Schreiber, O

    E. Schreiber, O. L. Anderson, and N. Soga, Elastic Constants and Their Measurement, McGraw-Hill, New York (1975). (Book)

  58. [70]

    Elastic constants versus melting temperature in metals,

    M. E. Fine, L. D. Brown, and H. L. Marcus, "Elastic constants versus melting temperature in metals," Scripta Metallurgica, 18(9), 951–956 (1984). https://doi.org/10.1016/0036-9748(84)90267-0

  59. [71]

    First and second harmonic generation of the optical susceptibilities for the non-centro-symmetric orthorhombic AgCd2GaS4,

    A. H. Reshak, V. V. Atuchin, S. Auluck, and I. V. Kityk, "First and second harmonic generation of the optical susceptibilities for the non-centro-symmetric orthorhombic AgCd2GaS4," Journal of Physics: Condensed Matter, 20(32), 325234 (2008). https://doi.org/10.1088/0953-8984/2...

  60. [72]

    Optical properties of Ti3SiC2 and Ti4AlN3,

    S. Li, R. Ahuja, M. W. Barsoum, P. Jena, and B. Johansson, "Optical properties of Ti3SiC2 and Ti4AlN3," Applied Physics Letters, 92(22), 221907 (2008). https://doi.org/10.1063/1.2938862

  61. [73]

    The Thermal Conductivity of Nonmetallic Crystals,

    G. A. Slack, "The Thermal Conductivity of Nonmetallic Crystals," Solid State Physics, 34, 1–71 (1979). https://doi.org/10.1016/S0081-1947(08)60359-8

  62. [74]

    Theory of Heat Conduction in Rare-Gas Crystals,

    C. L. Julian, "Theory of Heat Conduction in Rare-Gas Crystals," Physical Review, 137(1A), A128–A137 (1965). https://doi.org/10.1103/PhysRev.137.A128

  63. [75]

    Materials selection guidelines for low thermal conductivity thermal barrier coatings,

    D. R. Clarke, "Materials selection guidelines for low thermal conductivity thermal barrier coatings," Surface and Coatings Technology, 163, 67–74 (2003). https://doi.org/10.1016/S0257-8972(02)00593-5

  64. [76]

    Lower limit to the thermal conductivity of disordered crystals,

    D. G. Cahill, S. K. Watson, and R. O. Pohl, "Lower limit to the thermal conductivity of disordered crystals," Physical Review B, 46(10), 6131–6140 (1992). https://doi.org/10.1103/PhysRevB.46.6131

  65. [77]

    A comprehensive DFT based insights into the physical properties of tetragonal superconducting Mo5PB2,

    M. I. Naher, M. A. Afzal, and S. H. Naqib, "A comprehensive DFT based insights into the physical properties of tetragonal superconducting Mo5PB2," Results in Physics, 28, 104612 (2021). https://doi.org/10.1016/j.rinp.2021.104612

  66. [78]

    The wear of metals by hard abrasives,

    R. C. D. Richardson, "The wear of metals by hard abrasives," Wear, 10(4), 291–309 (1967). https://doi.org/10.1016/0043-1648(67)90013-1

  67. [79]

    Theoretical model of intrinsic hardness,

    F. Gao, "Theoretical model of intrinsic hardness," Physical Review B, 73(13), 132104 (2006). https://doi.org/10.1103/PhysRevB.73.132104

  68. [80]

    Comprehensive Understanding of Thermal Barrier Coatings (TBCs): Applications, Materials, Coating Design and Failure Mechanisms

    Bogdan, M.; Peter, I. A “Comprehensive Understanding of Thermal Barrier Coatings (TBCs): Applications, Materials, Coating Design and Failure Mechanisms”, Metals 2024, 14(5), 575. https://doi.org/10.3390/met14050575

  69. [81]

    Pressure-induced incompressibility of ReC and effect of metallic bonding on its hardness

    H. Gou, L. Hou, J. Zhang, and F. Gao, “Pressure-induced incompressibility of ReC and effect of metallic bonding on its hardness”, Applied Physics Letters, 92(24), 241901 (2008). https://doi.org/10.1063/1.2944267

  70. [82]

    Electronic Population Analysis on LCAO-MO Molecular Wave Functions. I,

    R. S. Mulliken, "Electronic Population Analysis on LCAO-MO Molecular Wave Functions. I," The Journal of Chemical Physics, 23(10), 1833–1840 (1955). https://doi.org/10.1063/1.1740588

  71. [83]

    Bonded-atom fragments for describing molecular charge densities,

    F. L. Hirshfeld, "Bonded-atom fragments for describing molecular charge densities," Theoretica Chimica Acta, 44(2), 129–138 (1977). https://doi.org/10.1007/BF00549096

  72. [84]

    An ab initio study on structural, elastic, electronic, bonding, thermal, and optical properties of topological Weyl semimetal TaX (X = P, As),

    M. I. Naher and S. H. Naqib, "An ab initio study on structural, elastic, electronic, bonding, thermal, and optical properties of topological Weyl semimetal TaX (X = P, As)," Scientific Reports, 11, 5592 (2021). https://doi.org/10.1038/s41598-021-85085-w

  73. [85]

    Electronic structure, chemical bonding, and optical properties of paraelectric BaTiO3,

    S. Saha, T. P. Sinha, and A. Mookerjee, "Electronic structure, chemical bonding, and optical properties of paraelectric BaTiO3," Physical Review B, 62(13), 8828–8834 (2000). https://doi.org/10.1103/PhysRevB.62.8828

  74. [86]

    First-principles simulation: Ideas, illustrations and the CASTEP code,

    M. D. Segall, P. J. D. Lindan, M. J. Probert, C. J. Pickard, P. J. Hasnip, S. J. Clark, and M. C. Payne, "First-principles simulation: Ideas, illustrations and the CASTEP code," 50 | P a g e Journal of Physics: Condensed Matter, 14(11), 2717–2744 (2002). https://doi.org/10.108...

  75. [87]

    First-principles insights into the mechanical, optoelectronic, thermophysical, and lattice dynamical properties of binary topological semimetal BaGa2,

    M. I. Naher and S. H. Naqib, "First-principles insights into the mechanical, optoelectronic, thermophysical, and lattice dynamical properties of binary topological semimetal BaGa2," Results in Physics, 37, 105507 (2022). https://doi.org/10.1016/j.rinp.2022.105507

  76. [88]

    Material Classes, Structure, and Properties,

    M. F. Ashby, P. J. Ferreira, and D. L. Schodek, "Material Classes, Structure, and Properties," Nanomaterials, Nanotechnologies and Design, Elsevier, 121–165 (2009). https://doi.org/10.1016/B978-0-7506-8149-0.00006-4

  77. [89]

    Structural, elastic, electronic, thermodynamic, and optical properties of layered BaPd2As2 pnictide superconductor: A first principles investigation,

    F. Parvin and S. H. Naqib, "Structural, elastic, electronic, thermodynamic, and optical properties of layered BaPd2As2 pnictide superconductor: A first principles investigation," Journal of Alloys and Compounds, 780, 452–463 (2019). https://doi.org/10.1016/j.jallcom.2018.12.021

  78. [91]

    Pressure dependent elastic, electronic, superconducting, and optical properties of ternary barium phosphides (BaM2P2; M = Ni, Rh): DFT based insights,

    M. M. Mridha and S. H. Naqib, "Pressure dependent elastic, electronic, superconducting, and optical properties of ternary barium phosphides (BaM2P2; M = Ni, Rh): DFT based insights," Physica Scripta, 95(10), 105809 (2020). https://doi.org/10.1088/1402- 4896/abb54e

  79. [92]

    Structures, Mechanical Properties, Equations of State, and Electronic Properties of β-HMX under Hydrostatic Pressures: A DFT-D2 study,

    Q. Peng, Rahul, G. Wang, G. Liu, and S. De, "Structures, Mechanical Properties, Equations of State, and Electronic Properties of β-HMX under Hydrostatic Pressures: A DFT-D2 study," Physical Chemistry Chemical Physics, 16(37), 19972–19983 (2014). https://doi.org/10.1039/C4CP02074D

  80. [93]

    Origin of high hardness and optoelectronic and thermo-physical properties of boron-rich compounds B6X (X = S, Se): A comprehensive study via DFT approach,

    M. M. Hossain, M. A. Ali, M. M. Uddin, A. K. M. A. Islam, and S. H. Naqib, "Origin of high hardness and optoelectronic and thermo-physical properties of boron-rich compounds B6X (X = S, Se): A comprehensive study via DFT approach," Journal of Applied Physics, 129(17), 175902 (...

  81. [94]

    Structural, mechanical and optoelectronic properties of B6X (X = Se, S) chalcogenides under hydrostatic pressure,

    J. León-Flores, J. E. Antonio, H. Muñoz-González, J. L. Rosas-Huerta, and R. Escamilla, "Structural, mechanical and optoelectronic properties of B6X (X = Se, S) chalcogenides under hydrostatic pressure," Physica Scripta, 98(9), 095902 (2023). https://doi.org/10.1088/1402-4896/ace82f

  82. [95]

    A comprehensive study of the thermophysical and optoelectronic properties of Nb2P5 via ab-initio technique,

    M. Naher and S. Naqib, "A comprehensive study of the thermophysical and optoelectronic properties of Nb2P5 via ab-initio technique," Results in Physics, 28, 104623 (2021). https://doi.org/10.1016/j.rinp.2021.104623

  83. [96]

    A comprehensive ab-initio insights into the pressure dependent mechanical, phonon, bonding, electronic, optical, and thermal properties of CsV3Sb5 Kagome compound,

    M. Naher, M. Ali, M. Hossain, M. Uddin, and S. Naqib, "A comprehensive ab-initio insights into the pressure dependent mechanical, phonon, bonding, electronic, optical, and thermal properties of CsV3Sb5 Kagome compound," Results in Physics, 51, 106742 (2023). https://doi.org/10...

  84. [97]

    Transition temperature of strong-coupled superconductors,

    W. L. McMillan, "Transition temperature of strong-coupled superconductors," Physical Review, 167(2), 331–344 (1968). https://doi.org/10.1103/PhysRev.167.331

  85. [98]

    The maximum Tc of conventional superconductors at ambient pressure,

    K. Gao, T. F. T. Cerqueira, A. Sanna, Y. Fang, Đ. Dangić, I. Errea, H. Wang, S. Botti, and M. A. L. Marques, "The maximum Tc of conventional superconductors at ambient pressure," Nature Communications, 16(1), 8253 (2025). https://doi.org/10.1038/s41467- 025-54602-x

  86. [99]

    Ab initio Force Constant Approach to Phonon Dispersion Relations of Diamond and Graphite,

    G. Kresse, J. Furthmüller, and J. Hafner, "Ab initio Force Constant Approach to Phonon Dispersion Relations of Diamond and Graphite," Europhysics Letters, 32(9), 729–734 (1995). https://doi.org/10.1209/0295-5075/32/9/005

  87. [100]

    First-Principles Determination of the Soft Mode in Cubic ZrO2,

    K. Parlinski, Z. Q. Li, and Y. Kawazoe, "First-Principles Determination of the Soft Mode in Cubic ZrO2," Physical Review Letters, 78(21), 4063–4066 (1997). https://doi.org/10.1103/PhysRevLett.78.4063

Pith tools

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