REVIEW 3 major objections 6 minor 95 references
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 →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
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).
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
- 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.
Signed reviews
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
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)
- 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.
- §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.
- §3.7 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)
- 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”.
- §3.1: “Figure 1” is used both for the crystal-structure schematic and for the normalized lattice-parameter plots; renumber consistently.
- 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.
- Eq. (6) for optical conductivity uses non-standard notation (Wcν, E⃗0); a brief definition or a standard reference would help.
- 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.
- 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
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
assumptions (4)
- domain assumption GGA-PBE exchange-correlation functional plus Vanderbilt ultrasoft pseudopotentials adequately describe structure, elasticity and electronic structure of B6X
- domain assumption Voigt–Reuss–Hill averaging yields reliable polycrystalline moduli from single-crystal Cij
- domain assumption Slack’s formula and Clarke’s minimum-conductivity model give realistic lattice thermal conductivities
- standard math Born mechanical-stability criteria under hydrostatic pressure remain valid for orthorhombic crystals
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.
Reference graph
Works this paper leans on
-
[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]
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]
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)
2016
-
[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]
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]
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]
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]
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
-
[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)
2019
-
[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)
2016
-
[11]
D. M. Rowe, CRC Handbook of Thermoelectrics, CRC Press, Boca Raton (1995)
1995
-
[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
2017 doi
-
[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
2013 doi
-
[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
1982 doi
-
[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
1984 doi
-
[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
2015 doi
-
[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
2009 doi
-
[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
2018 doi
-
[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
2020 doi
-
[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
2002 doi
-
[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
2017 doi
-
[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
2013 doi
-
[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
2017 doi
-
[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
2020 doi
-
[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
1978 doi
-
[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...
1992
-
[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...
2024 doi
-
[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
1996 doi
-
[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
1997 doi
-
[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
2003 doi
-
[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
2023 doi
-
[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
2020 doi
-
[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...
2020 doi
-
[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
2020 doi
-
[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
2018 doi
-
[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
2020 doi
-
[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
2014 doi
-
[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
1992 doi
-
[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
2016 doi
-
[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
2011 doi
-
[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
2003 doi
-
[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
1998 doi
-
[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
2024 doi
-
[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
2004 doi
-
[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
2004 doi
-
[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
2011 doi
-
[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
2010 doi
-
[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
2011 doi
-
[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
2009 doi
-
[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
2012 doi
-
[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
1998 doi
-
[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
2019 doi
-
[56]
W. A. Harrison, Electronic Structure and the Properties of Solids: The Physics of the Chemical Bond, Courier Corporation, New York (2012). (Book)
2012
-
[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
1962 doi
-
[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
2001 doi
-
[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
2014 doi
-
[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
2016 doi
-
[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
2008 doi
-
[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)
2013
-
[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
2010 doi
-
[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
2016 doi
-
[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
2004 doi
-
[67]
J. R. Christman, Fundamentals of Solid State Physics, John Wiley & Sons, New York (1988). (Book)
1988
-
[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
1963 doi
-
[69]
Schreiber, O
E. Schreiber, O. L. Anderson, and N. Soga, Elastic Constants and Their Measurement, McGraw-Hill, New York (1975). (Book)
1975
-
[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
1984 doi
-
[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...
2008 doi
-
[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
2008 doi
-
[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
1979 doi
-
[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
1965 doi
-
[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
2003 doi
-
[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
1992 doi
-
[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
2021 doi
-
[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
1967 doi
-
[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
2006 doi
-
[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
2024 doi
-
[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
2008 doi
-
[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
1955 doi
-
[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
1977 doi
-
[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
2021 doi
-
[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
2000 doi
-
[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...
2002 doi
-
[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
2022 doi
-
[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
2009 doi
-
[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
2019 doi
-
[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
2020 doi
-
[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
2014 doi
-
[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 (...
2021 doi
-
[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
2023 doi
-
[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
2021 doi
-
[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...
2023 doi
-
[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
1968 doi
-
[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
2025 doi
-
[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
1995 doi
-
[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
1997 doi
Reviewed July 11, 2026 · model on record in the stance chip above.
Discussion (0). Continue with ORCID to comment.