Skip to main content

Advertisement

Log in

Elastic properties, fracture toughness, ideal tensile strength and thermal conductivities of the stable hexagonal WB2, W2B5, WB3 and WB4

  • Published:
Applied Physics A Aims and scope Submit manuscript

Abstract

In the present study, we calculated the effects of boron content on the elastic properties, fracture toughness, ideal tensile strength ([0001] and [11\(\overline{2}\)1] directions) and thermal conductivities of the stable hexagonal tungsten borides (hP12-WB2, hP16-W2B5, hP16-WB3 and hP10-WB4) by the first-principles calculations. The results showed that the hardness of the four tungsten borides is ranked in the order hP16-WB3 > hP10-WB4 > hP16-W2B5 > hP12-WB2, and hP16-WB3 is the hardest with the hardness of 36.9 Gpa and can be considered as a potentially superhard material. The fracture toughness of these tungsten borides decreases as the boron content increases. Moreover, the [0001]-direction ideal tensile strength and the thermal conductivities increase with the increase in boron content. The [0001]-direction ideal tensile strength is in the sequence of hP10-WB4 > hP16-WB3 > hP16-W2B5 > hP12-WB2. Finally, the thermal conductivities of these borides are anisotropic and in the order of hP10-WB4 > hP16-WB3 > hP16-W2B5 > hP12-WB2.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. A. Waśkowska, L. Gerward, J.S. Olsen, K.R. Babu, G. Vaitheeswaran, V. Kanchana, A. Svane, V.B. Filipov, G. Levchenko, A. Lyaschenko, Thermoelastic properties of ScB2, TiB2, YB4 and HoB4: experimental and theoretical studies. Acta Mater. 59, 4886–4894 (2011)

    Article  ADS  Google Scholar 

  2. J.B. Levine, S.H. Tolbert, R.B. Kaner, Advancements in the search for superhard ultra-incompressible metal borides. Adv. Funct. Mater. 19, 3519–3533 (2009)

    Article  Google Scholar 

  3. J. Yang, H. Sun, C. Chen, Is osmium diboride an ultra-hard material? J. Am. Chem. Soc. 130, 7200–7201 (2008)

    Article  Google Scholar 

  4. V.L. Solozhenko, E. Gregoryanz, Synthesis of superhard materials. Mater. Today 8, 44–51 (2005)

    Article  Google Scholar 

  5. T. Taniguchi, M. Akaishi, S. Yamaoka, Mechanical properties of polycrystalline translucent cubic boron nitride as characterized by the Vickers indentation method. J. Am. Ceram. Soc. 79, 547–549 (2010)

    Article  Google Scholar 

  6. D. He, Y. Zhao, L. Daemen, J. Qian, T.D. Shen, T.W. Zerda, Boron suboxide: as hard as cubic boron nitride. Appl. Phys. Lett. 81, 643–645 (2002)

    Article  ADS  Google Scholar 

  7. V.L. Solozhenko, D. Andrault, G. Fiquet, M. Mezouar, D.C. Rubie, Synthesis of superhard cubic BC2n. Appl. Phys. Lett. 78, 1385–1387 (2001)

    Article  ADS  Google Scholar 

  8. M.S. Koval' Chenko, L.G. Bodrova, Densification kinetics of higher molybdenum and tungsten borides in hot pressing. Metall. 14, 469–473 (1975)

  9. R. Mohammadi, A.T. Lech, M. Xie, B.E. Weaver, M.T. Yeung, S.H. Tolbert, R.B. Kaner, Tungsten tetraboride, an inexpensive superhard material. Natl. Acad. Sci. USA 108, 10958 (2011)

    Article  ADS  Google Scholar 

  10. M. Xie, R. Mohammadi, Z. Mao, M.M. Armentrout, A. Kavner, R.B. Kaner, S.H. Tolbert, Exploring the high-pressure behavior of superhard tungsten tetraboride. Phys. Rev. B 8, 5064118 (2012)

    Google Scholar 

  11. Q. Gu, G. Krauss, W. Steurer, Cheliform abstract transition metal borides: superhard versus ultra-incompressible. Adv. Mater. 20, 3620 (2008)

    Article  Google Scholar 

  12. H.Y. Chung, M.B. Weinberger, J.B. Levine, A. Kavner, J.M. Yang, S.H. Tolbert, R.B. Kaner, Synthesis of ultra-incompressible superhard rhenium diboride at ambient pressure. Science 316, 436–439 (2007)

    Article  ADS  Google Scholar 

  13. S. Otani, M.M. Korsukova, T. Aizawa, High-temperature hardness of ReB2 single crystals. J. Alloy. Compd. 477, L28–L29 (2009)

    Article  Google Scholar 

  14. R.W. Cumberland, M.B. Weinberger, J.J. Gilman, S.M. Clark, S.H. Tolbert, R.B. Kaner, Osmium diboride, an ultra-incompressible, hard material. J. Am. Chem. Soc. 127, 7264–7265 (2005)

    Article  Google Scholar 

  15. L. Silvestroni, S. Guicciardi, C. Melandri, D. Sciti, TaB2-based ceramics: microstructure, mechanical properties and oxidation resistance. J. Eur. Ceram. Soc. 32, 97–105 (2012)

    Article  Google Scholar 

  16. H.Y. Chung, M.B. Weinberger, J.M. Yang, S.H. Tolbert, R.B. Kaner, Correlation between hardness and elastic moduli of the uptrain compressible transition metal diborides RuB2, OsB2, and ReB2. Appl. Phys. Lett. 92, 261904 (2008)

  17. R.B. Kaner, J.J. Gilman, S.H. Tolbert, Designing superhard materials. Mater. Sci. 308, 1268 (2005)

    Google Scholar 

  18. R.F. Zhang, D. Legut, R. Niewa, A.S. Argon, S.V eprek, Shear-induced structural transformation and plasticity in ultrain compressible ReB2 limit its hardness. Phy. Rev. B 82, 1041041–1041047 (2010)

  19. P. Li, L.S. Ma, M.J. Peng, B.P. Shu, Y.H. Duan, Elastic anisotropies and thermal conductivities of WB2 diborides in different crystal structures: a first-principles calculation. J. Alloy. Compd. 747, 905–915 (2018)

    Article  Google Scholar 

  20. X.Y. Cheng, X.Q. Chen, D.Z. Li, Y.Y. Li, Computational materials discovery: the case of the W-B system. Acta Crystallogr. C 70, 85–103 (2014)

    Article  Google Scholar 

  21. W.Z. Bao, D. Liu, Y.H. Duan, A first-principles prediction of anisotropic elasticity and thermal properties of potential superhard WB3. Ceram. Int. 272, 311–350 (2018)

    Google Scholar 

  22. X. Zhang, X. Bai, E. Zhao, Z. Wu, L. Fu, Q. Hou, First-principles calculation of structural, thermodynamic and mechanical properties of 5d transitional metal tribromides TMB3 (TM= Hf-Au). Comput. Condens. Matter 3, 53–60 (2015)

    Article  Google Scholar 

  23. Y. Wang, Q. Xia, Y. Yu, First principles calculation on electronic structure, chemical bonding, elastic and optical properties of novel tungsten tribromides. J. Cent. South Univ. 21, 500–505 (2014)

    Article  Google Scholar 

  24. Y. Liang, Y. Gou, X. Yuan, Z. Zhong, W. Zhang, Unexpectedly hard and highly stable WB3 with a noncompact structure. Chem. Phys. Lett. 580, 48–52 (2013)

    Article  ADS  Google Scholar 

  25. M. Maździarz, T. Mościcki, Structural, mechanical and optical properties of potentially superhard WBx polymorphs from first principles calculations. Mater. Chem. Phys. 179, 92–102 (2016)

    Article  Google Scholar 

  26. Y. Liang, Z. Zhong, W. Zhang, A thermodynamic criterion for designing superhard transition-metal borides with ultimate boron content. Comput. Mater. Sci. 68, 222–228 (2013)

    Article  Google Scholar 

  27. G. Zhang, T. Bai, Y. Zhao, Y. Hu, A new superhard phase and physical properties of ZrB3 from first-principles calculations. Materials 9, 703 (2016)

    Article  ADS  Google Scholar 

  28. S.Q. Feng, X.D. Li, L. Su, H.N. Li, H. Yang, Pressure effect on the hardness of diamond and W2B5: first-principle calculations. Mod. Phys. Lett. B 31, 1750137 (2017)

    Article  ADS  Google Scholar 

  29. Z. Wu, Y. Long, H.T. Lin, F. Zhang, Effect of tantalum on phase transition and thermal stability of metastable tungsten tetra-boride. Ceram. Int. 46, 17217–17223 (2020)

    Article  Google Scholar 

  30. G. Gu, W. Krauss, Steurer, Transition metal borides: superhard versus ultr-ncompressible. Adv. Mater. 20, 3620–3626 (2008)

    Article  Google Scholar 

  31. A. Brewer, P.D. Worhunsky, J.R. Gray, Y.Y. Tang, W.H. Kober, Meditation experience is associated with differences in default mode network activity and connectivity. Proc. Natl. Acad. Sci. USA 108, 20254–20259 (2011)

    Article  ADS  Google Scholar 

  32. M.D. Segall, P.J.D. Lindan, M.J. Probert, C.J. Pickard, S.J. Clark, M.C. Payne, First-principles simulation: ideas, illustrations and the CASTEP code. J. Phys. Condens. Matter. 44, 142717 (2002)

  33. J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple. Phys. Rev. Lett. 65, 7738 (1996)

    Google Scholar 

  34. L. Quan, D. Zhou, W. Zheng, Y. Ma, C. Chen, Global structural optimization of tungsten borides. Phys. Rev. Lett. 13, 136403 (2013)

  35. R.F. Zhang, D. Legut, Z.J. Lin, Y.S. Zhao, H.K. Mao, S. Veprek, Stability and strength of transition-metal tetraborides and triborides. Phys. Rev. Lett. 108, 255502 (2012)

  36. V. Vadim, G. Alexander, J. Hemlemy, WB2 to WB3 phase change during reactive spark plasma sintering and pulsed laser ablation/deposition processes. Ceram. Int. 41, 8273–8828 (2015)

    Article  Google Scholar 

  37. M. Wang, Y. Li, T. Cui, Y. Ma, G. Zou, Origin of hardness in WB4 and its implications for ReB4, TaB4, MoB4, TcB4, and OsB4. Appl. Phys. Lett. 24, 456–486 (2008)

    Google Scholar 

  38. A.J. Wang, S.L. Shang, Y. Du, Y. Kong, L.J. Zhang, L. Chen, D.D. Zhao, Z.K. Liu, Structural and elastic properties of cubic and hexagonal TiN and AlN from first-principles calculations. Comp. Mater. Sci. 9, 48705 (2010)

    Google Scholar 

  39. E.J. Zhao, J.A. Meng, Y.M. Ma, Z.J. Wu, Phase stability and mechanical properties of tungsten borides from first principles calculations. Comp. Mater. Sci. 12, 13158–13165 (2010)

    Google Scholar 

  40. X. Hao, Y. Xu, Z. Wu, D. Zhou, X. Liu, X. Cao, J. Meng, Low-compressibility and hard materials ReB2 and WB2: prediction from first-principles study. Phys. Rev. B 74, 224112 (2006)

  41. H. Gou, Z. Li, L.M. Wang, Peculiar structure and tensile strength of WB4: nonstoichiometric origin. Aip Adv. 2, 21–26 (2012)

    Article  Google Scholar 

  42. J. Dong, H. Li, Z. Guo, X. Hao, D. Chen, Extraordinary local structure deformation of superhard tungsten tetraboride under compression. J. Alloy. Compd. 817, 152989 (2019)

  43. H. Ozisik, E. Deligoz, K. Colakoglu, G. Surucu, Structural and mechanical stability of rare-earth diborides. Chin. Phys. B 40, 46202 (2013)

    Article  Google Scholar 

  44. W. Voigt, Handbook of Crystal Physics (Taubner, Leipzig, 1928)

    Google Scholar 

  45. A. Reuss, Z. Angew, Calculation of the flow limits of mixed crystals on the basis of the plasticity of monocrystals. Math. Mech. 9, 49–58 (1929)

    Google Scholar 

  46. R. Hill, The elastic behaviour of a crystalline aggregate. Proc. Phys. Soc. A 65, 349 (1952)

    Article  ADS  Google Scholar 

  47. X.Y. Cheng, W. Zhang, X. Q. Chen, H. Niu, P. Liu, K. Du, G. Liu, D. Li, H.M. Cheng, H. Ye, Y. Li, Interstitial-boron solution strengthened WB3+x. Appl. Phys. Lett. 103, 171903 (2013)

  48. Y.J. Tian, B. Xu, Z.S. Zhao, Microscopic theory of hardness and design of novel superhard crystals. Int. J. Refract. Met. 33, 93–106 (2012)

    Article  Google Scholar 

  49. D. Qu, C. Li, L. Bao, Z. Kong, Y. Duan, Structural, electronic, and elastic properties of orthorhombic, hexagonal, and cubic Cu3Sn intermetallic nitrides in Sn–Cu lead-free solder. J. Phys. Chem. Solids 138, 109253 (2020)

  50. M. Ashby, Materials selection in mechanical design. J. Phys. IV 03 (1993)

  51. T. Liao, J.Y. Wang, Y.C. Zhou, Deformation modes and ideal strengths of ternary layered Ti2AlC and Ti2AlN from first-principles calculations. Phys. Rev. B 21, 73–78 (2006)

    Google Scholar 

  52. H. Talebi, M. Silani, T. Rabczuk, Concurrent multiscale modeling of three dimensional crack and dislocation propagation. Adv. Eng. Softw. 80, 82–92 (2015)

    Article  Google Scholar 

  53. H. Talebi, M. Silani, S.P.A. Bordas, P. Kerfriden, T. Rabczuk, A computational library for multiscale modeling of material failure. Comput. Mech. 53, 1047–1071 (2014)

    Article  MathSciNet  Google Scholar 

  54. H. Niu, S. Niu, A.R. Oganov, Simple and accurate model of fracture toughness of solids. J. Appl. Phys. 6, 125 (2019)

    Google Scholar 

  55. B. Huang, Y.H. Duan, W.C. Hu, Y. Sun, S. Chen, Structural, anisotropic elastic and thermal properties of MB (M = Ti, Zr and Hf) monoborides. Ceram. Int. 41, 6831–6843 (2015)

    Article  Google Scholar 

  56. L. Ma, Y. Duan, R. Li, Structural, elastic and electronic properties of C14-type Al2M (M = Mg, Ca, Sr and Ba) laves phases. Physica B 507, 147–155 (2017)

    Article  Google Scholar 

  57. S.I. Ranganathan, M. Ostoja-Starzewski, Universal elastic anisotropy index. Phys. Rev. Lett. 1010, 55504 (2008)

    Article  Google Scholar 

  58. D.H. Chung, W.R. Buessem, F.W. Vahldiek, S.A. Mersol, Anisotropy in Single Crystal Refractory Compound (Plenum, New York, 1968)

  59. J.F. Nye, Physical Properties of Crystals (Oxford University Press, Oxford, 1985)

    Google Scholar 

  60. R.F.S. Hearmon, A.A. Maradudin, An introduction to applied anisotropic elasticity. Phys. Today 14, 48 (1961)

    Article  Google Scholar 

  61. Y.F. Li, B. Xiao, G.L. Wang, L. Sun, Q.L. Zheng, Z.W. Liu, Revealing the novel fracture mechanism of the interfaces of TiB2/Fe composite from a first principles investigation. Acta Mater. 156, 13596454–18305081 (2018)

    Article  Google Scholar 

  62. O.H. Nielsen, R.M. Martin, Quantum-mechanical theory of stress and force. Phys. Rev. B 32, 3780–3791 (1985)

    Article  ADS  Google Scholar 

  63. O.H. Nielsen, R.M. Martin, Erratum: quantum mechanical theory of stress and force. Phys. Rev. B 35, 9308–9308 (1987)

    Article  ADS  Google Scholar 

  64. A.C. Yang, L.K. Bao, M.J. Peng, Y.H. Duan, Explorations of elastic anisotropies and thermal properties of the hexagonal TMSi2 (TM = Cr, Mo, W) silicides from first-principles calculations. Mater. Today Commun. 23, 102474 (2021)

  65. D.R. Clarke, Materials selection guidelines for low thermal conductivity thermal barrier coatings. Surf. Coat. Technol. 163, 67–74 (2003)

    Article  Google Scholar 

  66. D.R. Clarke, C.G. Levi, Materials design for the next generation thermal barrier coatings. Annu. Rev. Mater. Res. 33, 383–417 (2003)

    Article  ADS  Google Scholar 

  67. D.G. Cahill, S.K. Watson, R.O. Pohl, Lower limit to the thermal conductivity of disordered crystals. Phys. Rev. B 46, 6131 (1992)

    Article  ADS  Google Scholar 

  68. J. Callaway, Model for lattice thermal conductivity at low temperatures. Phys. Rev. 113, 1046–1051 (1959)

    Article  ADS  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant No. 51761023 and the Yunnan Ten Thousand Talents Plan Young & Elite Talents Project under Grant No. YNWR-QNBJ-2018-044.

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Yonghua Duan or Huarong Qi.

Ethics declarations

Conflict of interest

We declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, A., Duan, Y., Peng, M. et al. Elastic properties, fracture toughness, ideal tensile strength and thermal conductivities of the stable hexagonal WB2, W2B5, WB3 and WB4. Appl. Phys. A 128, 152 (2022). https://doi.org/10.1007/s00339-022-05299-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00339-022-05299-1

Keywords

Navigation