Pith. sign in

REVIEW 2 major objections 2 minor 52 references

Synthesizability and Mechanical Properties of High-Entropy Borides: First-Principles and Machine Learning Studies

T0 review · 2 major / 2 minor · reviewed 2026-06-30 · grok-4.3

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

Pith's one-line read The entropy forming ability (EFA) descriptor ranks the single-phase synthesizability of all 126 five-metal high-entropy borides in the AlB2 structure, agreeing with experiments and identifying Cr-containing compounds as often unstable.

desk verdict The exhaustive screen of all 126 five-metal HEB combinations is the concrete new piece, but EFA synthesizability rankings rest on agreement with experiment for only an unspecified subset of cases. read the letter →

arxiv 2606.30540 v1 pith:P4HURWIK submitted 2026-06-29 cond-mat.mtrl-sci

Luke Moore , Ethan Fox , Bria Storr , Jayden R. Palomino , Shane A. Catledge , Yogesh K. Vohra , Cheng-Chien Chen This is my paper · ORCID
classification cond-mat.mtrl-sci
keywords high-entropyboridesentropyformingabilitydensityfunctionaltheorymachinelearningmechanicalpropertiessynthesizabilitytransitionmetal
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

The paper conducts density functional theory calculations on 126 possible five-metal combinations from nine transition metals in the hexagonal AlB2 boride structure. It applies the entropy forming ability descriptor to predict which compositions can form single-phase high-entropy borides and compares these predictions to experimental data for selected cases. Mechanical properties are evaluated using special quasi-random structures, showing that several compounds, mainly those with chromium, are mechanically unstable and correspondingly less synthesizable. Machine learning models are built to further analyze the computed properties and synthesizability trends. This work maps out promising compositions for mechanically strong single-phase high-entropy borides.

What carries the argument

The entropy forming ability (EFA) descriptor applied to DFT-relaxed structures to rank single-phase synthesizability, with special quasi-random structures used to compute mechanical properties.

What would settle it

An experiment synthesizing a Cr-containing high-entropy boride predicted to be unstable by EFA and SQS that nevertheless forms a stable single phase.

Watch

Extended reading notes

Core claim

EFA predictions show good agreement with the experimental data for selected HEBs, and several mechanically unstable compounds, primarily those containing Cr, are predicted to be less synthesizable.

Load-bearing premise

That the entropy forming ability descriptor reliably ranks single-phase synthesizability across the 126 compositions when using DFT-relaxed structures and special quasi-random structures for stability.

Editorial extensions

If this is right

  • EFA can screen large numbers of compositions for likely single-phase formation.
  • Mechanically unstable HEBs are less likely to be synthesizable as single phases.
  • Chromium-containing five-metal borides tend to be both unstable and hard to synthesize.
  • Machine learning models trained on DFT data can accelerate identification of superior HEBs.

Reading between the lines

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

  • This screening method might apply to high-entropy materials beyond borides, such as carbides or nitrides.
  • Focus on non-Cr compositions could yield better candidates for high-temperature or wear-resistant applications.
  • Validating the ML models on new compositions would test the predictive power of the approach.
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, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 2 minor

Summary. The manuscript reports DFT calculations on all 126 five-metal combinations from nine group 4-6 transition metals in the hexagonal AlB2 structure. It applies the entropy forming ability (EFA) descriptor to rank single-phase synthesizability, computes mechanical properties via special quasi-random structures (SQS), identifies Cr-containing compositions as mechanically unstable and less synthesizable, and trains ML models on the resulting data to provide a design roadmap. The abstract states that EFA predictions show good agreement with experiment for selected HEBs.

Significance. A validated high-throughput EFA ranking across the full combinatorial space, coupled with SQS-derived mechanical trends and ML analysis, would constitute a useful systematic resource for high-entropy boride design. The scale of the enumeration and the explicit linkage of mechanical instability to synthesizability are potentially valuable if the experimental anchor for EFA is shown to be representative rather than limited to already-known cases.

major comments (2)
  1. [Abstract] Abstract: The statement that EFA predictions 'show good agreement with the experimental data for selected HEBs' provides no information on the size or identity of the comparison set, nor any quantitative metric (correlation, accuracy, or confusion matrix). Because the central claim is that EFA produces a reliable ordering for all 126 compositions, the absence of this information leaves the extrapolation without an independent anchor and raises the possibility that the reported agreement reflects post-hoc selection of already-stable cases.
  2. [Results] Results (mechanical stability section): The claim that Cr-containing compounds are both mechanically unstable and less synthesizable is presented as a joint finding, yet no explicit cross-check (e.g., correlation between EFA values and the mechanical instability metric, or a statistical test separating the two effects) is described. Without this, it is unclear whether the synthesizability ranking is independently supported or simply inherits the mechanical filter.
minor comments (2)
  1. [Methods] The abstract and methods should clarify whether the DFT-relaxed structures used for EFA are the same as the SQS cells used for elastic constants, or whether separate relaxations were performed.
  2. [Figures/Tables] Figure captions and table legends should report the exact number of experimental HEBs used for EFA validation and the numerical measure of agreement.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. We address each major comment below and indicate where revisions will be made to strengthen the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The statement that EFA predictions 'show good agreement with the experimental data for selected HEBs' provides no information on the size or identity of the comparison set, nor any quantitative metric (correlation, accuracy, or confusion matrix). Because the central claim is that EFA produces a reliable ordering for all 126 compositions, the absence of this information leaves the extrapolation without an independent anchor and raises the possibility that the reported agreement reflects post-hoc selection of already-stable cases.

    Authors: We agree that the abstract statement is insufficiently specific. The full manuscript contains the underlying comparison (a set of previously reported HEBs with known single-phase or multi-phase outcomes), but this detail is not reflected in the abstract. In the revised version we will expand the abstract to state the size of the comparison set, list the specific compositions, and report a quantitative metric (Pearson correlation between EFA and the experimental stability classification). revision: yes

  2. Referee: [Results] Results (mechanical stability section): The claim that Cr-containing compounds are both mechanically unstable and less synthesizable is presented as a joint finding, yet no explicit cross-check (e.g., correlation between EFA values and the mechanical instability metric, or a statistical test separating the two effects) is described. Without this, it is unclear whether the synthesizability ranking is independently supported or simply inherits the mechanical filter.

    Authors: EFA and the mechanical-stability analysis (Born criteria on SQS elastic tensors) are computed from independent DFT workflows. Nevertheless, the referee correctly notes that no explicit correlation or statistical separation is shown. In the revised manuscript we will add a figure and accompanying text that plots EFA versus the mechanical-instability indicator for the full set, with a separate panel or table restricted to Cr-containing compositions, together with a simple rank-correlation coefficient. This will make clear that the two observations are not redundant. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; derivation anchored by external experimental validation

full rationale

The paper computes EFA from DFT on AlB2 structures for 126 compositions and reports agreement with external experimental data for selected HEBs. Mechanical stability uses SQS on the same structures, and ML analyzes the computed results. No quoted step shows a prediction reducing to a fitted input by construction, a self-definitional loop, or a load-bearing self-citation chain that replaces independent verification. External benchmarks and standard use of prior descriptors keep the chain self-contained.

Assumptions & free parameters 0 free parameters · 2 assumptions · 0 invented entities

Abstract-only review prevents exhaustive extraction; the work rests on standard DFT approximations and the pre-existing EFA descriptor rather than new postulates.

assumptions (2)
  • domain assumption Standard DFT exchange-correlation functionals and pseudopotentials are adequate for ranking EFA and elastic constants in these borides
    Implicit in all DFT-based materials screening; invoked by the choice of method in the abstract.
  • domain assumption The EFA descriptor, calibrated on prior experimental HEBs, transfers to the full 126-composition space without additional fitting
    Central to the synthesizability claim; location is the sentence on EFA predictions in the abstract.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Synthesizability and Mechanical Properties of High-Entropy Borides: First-Principles and Machine Learning Studies." pith.science (2026). https://pith.science/paper/P4HURWIK

@misc{pith2026260630540,
  author       = {Pith},
  title        = {Pith review of: Synthesizability and Mechanical Properties of High-Entropy Borides: First-Principles and Machine Learning Studies},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/P4HURWIK}},
  note         = {Machine review of arXiv:2606.30540}
}
abstract

We perform density functional theory (DFT) calculations to investigate five-metal high-entropy borides (HEBs) in the hexagonal AlB$_2$ structure, considering all 126 possible elemental combinations among the nine group 4-6 transition metals (Ti, V, Cr, Zr, Nb, Mo, Hf, Ta, and W). The entropy forming ability (EFA) descriptor is employed to evaluate their single-phase synthesizability, and the resulting EFA predictions show good agreement with the experimental data for selected HEBs. Mechanical properties are computed using special quasi-random structures. Several mechanically unstable compounds -- primarily those containing Cr -- are also predicted to be less synthesizable. Machine learning (ML) models are developed to analyze the results. This combined ab initio and ML study provides a systematic roadmap for identifying mechanically superior single-phase HEBs.

Figures

Figures reproduced from arXiv: 2606.30540 by the authors.

Figure 1
Figure 1. FIG. 1. Symmetry-distinct 15-atom unit cells for five-metal high-entropy borides in the hexagonal AlB [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) Histograms of the total energies of POCC structures for three representative high-entropy borides with high [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Entropy-forming ability (EFA) versus the mean [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4. (a) 60-atom special quasi-random structure (SQS) of hexagonal five-metal high-entropy boride (HEB), visualized by [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Joint scatter plot and marginal histograms of the [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. (a) DFT-calculated bulk modulus ( [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

52 extracted references

  1. [1]

    Zhang, D.-W

    G.-J. Zhang, D.-W. Ni, J. Zou, H.-T. Liu, W.-W. Wu, J.- X. Liu, T. S. Suzuki, and Y. Sakka, Inherent anisotropy in transition metal diborides and microstructure/property tailoring in ultra-high temperature ceramics–a review, Journal of the European Ceramic Society38, 371 (2018)

    2018

  2. [2]

    B. R. Golla, A. Mukhopadhyay, B. Basu, and S. K. Thimmappa, Review on ultra-high temperature boride ceramics, Progress in Materials Science111, 100651 (2020)

    2020

  3. [3]

    B. C. Wyatt, S. K. Nemani, G. E. Hilmas, E. J. Opila, and B. Anasori, Ultra-high temperature ceramics for ex- treme environments, Nature reviews materials9, 773 (2024)

    2024

  4. [4]

    J. Gild, Y. Zhang, T. Harrington, S. Jiang, T. Hu, M. C. Quinn, W. M. Mellor, N. Zhou, K. Vecchio, and J. Luo, High-entropy metal diborides: a new class of high- entropy materials and a new type of ultrahigh tempera- ture ceramics, Scientific reports6, 37946 (2016)

    2016

  5. [5]

    C. Oses, C. Toher, and S. Curtarolo, High-entropy ce- ramics, Nature Reviews Materials5, 295 (2020)

    2020

  6. [6]

    A. J. Wright, Q. Wang, C. Huang, A. Nieto, R. Chen, and J. Luo, From high-entropy ceramics to compositionally- complex ceramics: A case study of fluorite oxides, Jour- nal of the European Ceramic Society40, 2120 (2020)

    2020

  7. [7]

    L. Feng, W. G. Fahrenholtz, and D. W. Brenner, High- entropy ultra-high-temperature borides and carbides: a new class of materials for extreme environments, Annual review of materials research51, 165 (2021)

    2021

  8. [8]

    T. C. Dube and J. Zhang, Underpinning the relationship between synthesis and properties of high entropy ceram- ics: A comprehensive review on borides, carbides and ox- ides, Journal of the European Ceramic Society44, 1335 (2024)

    2024

Show all 52 references
  1. [9]

    Qureshi, M

    T. Qureshi, M. M. Khan, and H. S. Pali, high-entropy borides?challenges and opportunities, Journal of Materi- als Science59, 15921 (2024)

    2024

  2. [10]

    Yeh, S.-K

    J.-W. Yeh, S.-K. Chen, S.-J. Lin, J.-Y. Gan, T.-S. Chin, T.-T. Shun, C.-H. Tsau, and S.-Y. Chang, Nanostruc- tured high-entropy alloys with multiple principal ele- ments: novel alloy design concepts and outcomes, Ad- vanced engineering materials6, 299 (2004). 10

    2004

  3. [11]

    Cantor, I

    B. Cantor, I. T. Chang, P. Knight, and A. Vincent, Microstructural development in equiatomic multicompo- nent alloys, Materials Science and Engineering: A375, 213 (2004)

    2004

  4. [12]

    Hsu, C.-W

    W.-L. Hsu, C.-W. Tsai, A.-C. Yeh, and J.-W. Yeh, Clar- ifying the four core effects of high-entropy materials, Na- ture Reviews Chemistry8, 471 (2024)

    2024

  5. [13]

    L. Feng, F. Monteverde, W. G. Fahrenholtz, and G. E. Hilmas, Superhard high-entropy alb2-type diboride ce- ramics, Scripta Materialia199, 113855 (2021)

    2021

  6. [14]

    Iwan, C.-M

    S. Iwan, C.-M. Lin, C. Perreault, K. Chakrabarty, C.-C. Chen, Y. Vohra, R. Hrubiak, G. Shen, and N. Velisavlje- vic, High-entropy borides under extreme environment of pressures and temperatures, Materials15, 3239 (2022)

    2022

  7. [15]

    Storr, L

    B. Storr, L. Moore, K. Chakrabarty, Z. Mohammed, V. Rangari, C.-C. Chen, and S. A. Catledge, Properties of high entropy borides synthesized via microwave-induced plasma, APL Materials10(2022)

    2022

  8. [16]

    Storr, C

    B. Storr, C. Amezaga, L. Moore, S. Iwan, Y. K. Vohra, C.-C. Chen, and S. A. Catledge, High entropy borides synthesized by the thermal reduction of metal oxides in a microwave plasma, Materials16, 4475 (2023)

    2023

  9. [17]

    Y. Yang, J. Bi, K. Sun, L. Qiao, G. Liang, H. Wang, J. Yuan, and Y. Chen, The effect of chemical element on hardness in high-entropy transition metal diboride ceramics, Journal of the European Ceramic Society43, 5774 (2023)

    2023

  10. [18]

    Sarker, T

    P. Sarker, T. Harrington, C. Toher, C. Oses, M. Samiee, J.-P. Maria, D. W. Brenner, K. S. Vecchio, and S. Cur- tarolo, High-entropy high-hardness metal carbides dis- covered by entropy descriptors, Nature communications 9, 4980 (2018)

    2018

  11. [19]

    Divilov, H

    S. Divilov, H. Eckert, D. Hicks, C. Oses, C. Toher, R. Friedrich, M. Esters, M. J. Mehl, A. C. Zettel, Y. Led- erer,et al., Disordered enthalpy–entropy descriptor for high-entropy ceramics discovery, Nature625, 66 (2024)

    2024

  12. [20]

    D. Dey, L. Liang, and L. Yu, Mixed enthalpy–entropy descriptor for the rational design of synthesizable high- entropy materials over vast chemical spaces, Journal of the American Chemical Society146, 5142 (2024)

    2024

  13. [21]

    Kretschmer and P

    A. Kretschmer and P. H. Mayrhofer, Explaining the entropy forming ability for carbides with the effective atomic size mismatch, Scientific Reports14, 7210 (2024)

    2024

  14. [22]

    X. Gu, Y. Shan, W. Lu, H. Pan, S. Huang, X. Xi- ang, H. Fu, K. Zhang, and S. Zhao, A robust criterion for designing superhard high-entropy transition metal di- borides, Acta Materialia296, 121310 (2025)

    2025

  15. [23]

    Zunger, S.-H

    A. Zunger, S.-H. Wei, L. G. Ferreira, and J. E. Bernard, Special quasirandom structures, Physical review letters 65, 353 (1990)

    1990

  16. [24]

    Van De Walle, M

    A. Van De Walle, M. Asta, and G. Ceder, The alloy the- oretic automated toolkit: A user guide, Calphad26, 539 (2002)

    2002

  17. [25]

    Wang, G.-Y

    Y.-P. Wang, G.-Y. Gan, W. Wang, Y. Yang, and B.-Y. Tang, Ab initio prediction of mechanical and electronic properties of ultrahigh temperature high-entropy ceram- ics (hf0. 2zr0. 2ta0. 2m0. 2ti0. 2) b2 (m= nb, mo, cr), physica status solidi (b)255, 1800011 (2018)

    2018

  18. [26]

    Y. Yang, W. Wang, G.-Y. Gan, X.-F. Shi, and B.-Y. Tang, Structural, mechanical and electronic properties of (tanbhftizr) c high entropy carbide under pressure: Ab initio investigation, Physica B: Condensed Matter550, 163 (2018)

    2018

  19. [27]

    Xiong, B.-W

    K. Xiong, B.-W. Wang, Z.-P. Sun, W. Li, C.-C. Jin, S.-M. Zhang, S.-Y. Xu, L. Guo, and Y. Mao, Frist- principles prediction of elastic, electronic, and ther- modynamic properties of high entropy carbide ceramic (tizrnbta) c, Rare Metals41, 1002 (2022)

    2022

  20. [28]

    Z. Xiao, L. Zhang, and Z. Guo, Ab initio investigation of phase stability, thermo-physical and mechanical proper- ties of (mo0. 2cr0. 2ta0. 2nb0. 2x0. 2) si2 (x= w, v) high- entropy refractory metal silicides, Computational Mate- rials Science203, 111116 (2022)

    2022

  21. [29]

    J. Mo, C. Zhu, S. Qiu, C. Huang, W. Yang, L. Xue, and H. Liu, Chromium-driven severe lattice distortion in high-entropy diboride ceramics, Journal of Materials Research and Technology (2026)

    2026

  22. [30]

    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 A65, 349 (1952)

    1952

  23. [31]

    Ravindran, L

    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 tisi 2, Journal of Applied Physics84, 4891 (1998)

    1998

  24. [32]

    Kresse and J

    G. Kresse and J. Hafner, Ab initio molecular dynamics for liquid metals, Physical review B47, 558 (1993)

    1993

  25. [33]

    Kresse and J

    G. Kresse and J. Furthm¨ uller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Physical review B54, 11169 (1996)

    1996

  26. [34]

    J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Physical review let- ters77, 3865 (1996)

    1996

  27. [35]

    Curtarolo, W

    S. Curtarolo, W. Setyawan, G. L. Hart, M. Jahnatek, R. V. Chepulskii, R. H. Taylor, S. Wang, J. Xue, K. Yang, O. Levy,et al., Aflow: An automatic framework for high- throughput materials discovery, Computational Materi- als Science58, 218 (2012)

    2012

  28. [36]

    K. Yang, C. Oses, and S. Curtarolo, Modeling off- stoichiometry materials with a high-throughput ab-initio approach, Chemistry of Materials28, 6484 (2016)

    2016

  29. [37]

    C. Oses, M. Esters, D. Hicks, S. Divilov, H. Eckert, R. Friedrich, M. J. Mehl, A. Smolyanyuk, X. Campi- longo, A. Van De Walle,et al., aflow++: A c++ frame- work for autonomous materials design, Computational Materials Science217, 111889 (2023)

    2023

  30. [38]

    L. Ward, A. Agrawal, A. Choudhary, and C. Wolverton, A general-purpose machine learning framework for pre- dicting properties of inorganic materials, npj Computa- tional Materials2, 16028 (2016)

    2016

  31. [39]

    W.-C. Chen, J. N. Schmidt, D. Yan, Y. K. Vohra, and C.- C. Chen, Machine learning and evolutionary prediction of superhard bcn compounds, npj Computational Materials 7, 114 (2021)

    2021

  32. [40]

    S. P. Ong, W. D. Richards, A. Jain, G. Hautier, M. Kocher, S. Cholia, D. Gunter, V. L. Chevrier, K. A. Persson, and G. Ceder, Python materials genomics (py- matgen): A robust, open-source python library for mate- rials analysis, Computational Materials Science68, 314 (2013)

    2013

  33. [41]

    Chen and C

    T. Chen and C. Guestrin, Xgboost: A scalable tree boost- ing system, inProceedings of the 22nd acm sigkdd in- ternational conference on knowledge discovery and data mining(2016) pp. 785–794

    2016

  34. [42]

    D.-K. Choi, Data-driven materials modeling with xg- boost algorithm and statistical inference analysis for pre- diction of fatigue strength of steels, International Jour- 11 nal of Precision Engineering and Manufacturing20, 129 (2019)

    2019

  35. [43]

    A. D. Smith, S. B. Harris, R. P. Camata, D. Yan, and C.-C. Chen, Machine learning the relationship between debye temperature and superconducting transition tem- perature, Physical Review B108, 174514 (2023)

    2023

  36. [44]

    Bakhtiari, C

    S. Bakhtiari, C. Aldrich, V. M. Calo, and M. Iannuzzi, Xgboost model for the quantitative assessment of stress corrosion cracking, npj Materials Degradation8, 126 (2024)

    2024

  37. [45]

    Pang and A

    S. Pang and A. S. A. Mohamed, Physics-guided xgboost for small-data screening of high-entropy carbides, Mate- rials Today Communications , 115261 (2026)

    2026

  38. [46]

    Momma and F

    K. Momma and F. Izumi, Vesta 3 for three-dimensional visualization of crystal, volumetric and morphology data, Applied Crystallography44, 1272 (2011)

    2011

  39. [47]

    Kaufmann, D

    K. Kaufmann, D. Maryanovsky, W. M. Mellor, C. Zhu, A. S. Rosengarten, T. J. Harrington, C. Oses, C. To- her, S. Curtarolo, and K. S. Vecchio, Discovery of high- entropy ceramics via machine learning, Npj Computa- tional Materials6, 42 (2020)

    2020

  40. [48]

    Fawcett, Spin-density-wave antiferromagnetism in chromium, Reviews of Modern Physics60, 209 (1988)

    E. Fawcett, Spin-density-wave antiferromagnetism in chromium, Reviews of Modern Physics60, 209 (1988)

    1988

  41. [49]

    Chakrabarty, S

    K. Chakrabarty, S. Iwan, A. N. Shrestha, S. A. Catledge, and Y. K. Vohra, High hardness and oxidation-resistant cr-containing medium entropy zrtaw diboride, Journal of Alloys and Compounds , 189164 (2026)

    2026

  42. [50]

    Y. Tian, B. Xu, and Z. Zhao, Microscopic theory of hard- ness and design of novel superhard crystals, International Journal of Refractory Metals and Hard Materials33, 93 (2012)

    2012

  43. [51]

    D. M. Teter, Computational alchemy: the search for new superhard materials, MRS bulletin23, 22 (1998)

    1998

  44. [52]

    X.-Q. Chen, H. Niu, D. Li, and Y. Li, Modeling hardness of polycrystalline materials and bulk metallic glasses, In- termetallics19, 1275 (2011)

    2011

Pith tools

Reviewed June 30, 2026 · model on record in the stance chip above.