Skip to main content
SpringerLink
Log in

Temperature-dependent mechanical properties of TaC and HfC

  • Ceramics
  • Published:
Journal of Materials Science Aims and scope Submit manuscript

Abstract

TaC and HfC are recognized as potential ultra-high temperature ceramics for application in refractories and coating materials. However, the test of mechanical property under high temperature is difficult. In this paper, the mechanical properties of TaC and HfC at high temperature are systematically investigated by density functional theory. The results revealed that their elastic constants, elastic moduli and elastic anisotropy all display a monotonic decreasing trend with increasing temperature, and the anisotropy of TaC is stronger than that of HfC at a given temperature. TaC and HfC both have eight possible dislocations. As the applied shear stress increases, the activation energies and critical resolved shear stress (CRSS) of all dislocations are decreased. As the temperature increases, the CRSS is decreased. Moreover, the yield strength and hardness of TaC and HfC both decreased with the increase of temperature. The hardness decrease from 0 to 400 K is mainly due to the proportion change of the two major dislocations (\(1/2\left\langle {1\bar{1}0} \right\rangle\) 0° perfect dislocations and \(1/6\left\langle {1\bar{2}1} \right\rangle\) 30° partial dislocations). Then the hardness sharply decreases at 400 K, which is attributed to the activation of \(1/6\left\langle {11\bar{2}} \right\rangle\) 90° partial dislocations. The hardness decrease from 500 K is attributed to the CRSS change of \(1/6\left\langle {11\bar{2}} \right\rangle\) 90° partial dislocations and \(1/6\left\langle {1\bar{2}1} \right\rangle \) 30° partial dislocations. In addition, the influence of strain rate and dislocation density are revealed, which shows that their hardness are both increased with increasing strain rate, while decreased with increasing dislocation density.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10

Similar content being viewed by others

References

  1. Jhi SH, Louie SG, Cohen ML, Ihm J (2001) Vacancy Hardening and Softening in Transition Metal Carbides and Nitrides. Phys Rev Lett 86(15):3348

    Article  CAS  Google Scholar 

  2. Csanádi T, Castle E, Reece M, Dusza J (2019) Strength enhancement and slip behaviour of high-entropy carbide grains during micro-compression. Sci Rep 9:10200

    Article  Google Scholar 

  3. Toth Louis E (1971) Transition Metal Carbides and Nitrides. Academic Press, New York and London

  4. Hong QJ, Walle AVD (2015) Prediction of the material with highest known melting point from Ab initio molecular dynamics calculations. Phys Rev B 92(2):020104

    Article  Google Scholar 

  5. Cedillos-Barraza O, Grasso S, Nasiri NA, Jayaseelan D, Reece MJ, Lee WE (2016) Sintering behaviour, solid solution formation and characterisation of Tac, Hfc and Tac-Hfc fabricated by spark plasma sintering. J Eur Ceram Soc 36(7):1539

    Article  CAS  Google Scholar 

  6. Xg A, Liang WB, Ng A, Ll B, Gz A, Cs A, Ys B, Jg B (2021) Microstructure and mechanical properties of multi-phase reinforced Hf-Mo-Nb-Ti-Zr refractory high-entropy alloys. Inter J Refract Metals Hard Mater 102:105723

    Google Scholar 

  7. Yang C, Bian H, Aoyagi K, Hayasaka Y, Yamanaka K, Chiba A (2021) Synergetic strengthening in hfmonbtati refractory high-entropy alloy via disordered nanoscale phase and semicoherent refractory particle. Mater Des 212:110248

    Article  CAS  Google Scholar 

  8. Ferro D, Barinov SM, Rau JV, Latini A, Scandurra R, Brunetti B (2006) Vickers and knoop hardness of electron beam deposited Zrc and Hfc thin films on titanium. Surf Coat Technol 200(16):4701

    Article  CAS  Google Scholar 

  9. Zhang Z, Liang H, Chen H, Wang J, Peng F, Cheng Lu (2019) Exploring physical properties of tantalum carbide at high pressure and temperature. Inorg Chem 59(3):1848–1852

    Article  Google Scholar 

  10. Gautam GS, Kumar KH (2014) Elastic, thermochemical and thermophysical properties of rock salt-type transition metal carbides and nitrides: a first principles study. J Alloy Compd 587:380

    Article  Google Scholar 

  11. Yu X, Weinberger C, Thompson G (2014) Ab initio investigations of the phase stability in tantalum carbides. Acta Mater 80:341

    Article  CAS  Google Scholar 

  12. Wen B, Shao T, Melnik R, Kawazoe Y, Tian Y (2013) Temperature and pressure dependent geometry optimization and elastic constant calculations for arbitrary symmetry crystals: applications to Mgsio3 Perovskites. J Appl Phys 113(10):103501

    Article  Google Scholar 

  13. Feng X, Xiao J, Wen B, Zhao J, Xu B, Wang Y, Tian Y (2021) Temperature-dependent hardness of Zinc-Blende structured covalent materials. Sci. China-Mater 64(9):2280

    Article  CAS  Google Scholar 

  14. Hafner J (2008) Ab-initio simulations of materials using vasp: density-functional theory and beyond. J Comput Chem 29:2044

    Article  CAS  Google Scholar 

  15. Kresse G, Furthmüller J (1996) Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys Rev B 54:11169

    Article  CAS  Google Scholar 

  16. Perdew JP, Burke K, Ernzerhof M (1996) Generalized gradient approximation made simple. Phys Rev Lett 77(18):3865

    Article  CAS  Google Scholar 

  17. Blöchl PE (1994) Projector augmented-wave method. Phys Rev B 50:17953

    Article  Google Scholar 

  18. Mann S, Rani P, Kumar R, Jindal VK (2015) DFT study of phonon dispersion in pure graphene. AIP Publishing.

  19. Shao T, Wen B, Melnik R, Shan Y, Kawazoe Y, Tian Y (2012) Temperature Dependent Elastic Constants for Crystals with Arbitrary Symmetry: Combined First Principles and Continuum Elasticity Theory. J Appl Phys 111(8):137

    Article  Google Scholar 

  20. Haines J, Leger JM, Bocquillon G (2001) Synthesis and design of superhard materials. Annu Rev Mater Res, Palo Alto, pp 1–23

  21. Hill R (1952) The elastic behaviour of a crystalline aggregate. Proceed Phys Soci 65(5):349

    Article  Google Scholar 

  22. Monkhorst HJ, Pack JD (1976) Special points for brillouin-zone integrations. Phys. Rev. B 13(12):5188–5192

    Article  Google Scholar 

  23. Barnett MR, Student ZK, Ma X (2006) A semianalytical sachs model for the flow stress of a magnesium alloy. Metall and Mater Trans A 37(7):2283

    Article  Google Scholar 

  24. Zong C, Mao WM, Zhu GH (2014) Analysis of yield strength anisotropy of pipeline steel based on crystallographic model. Mater ence Technol 30(12):1419

    Article  CAS  Google Scholar 

  25. Cahoon JR, Broughton WH, Kutzak AR (1971) The determination of yield strength from hardness measurements. Metall Transact 2(7):1979–1983

    Article  CAS  Google Scholar 

  26. Bowman A (1961) The variation of lattice parameter with carbon content of tantalum carbide. J Phys Chem 65:1596

    Article  CAS  Google Scholar 

  27. Villars P, Calvert LD, Pearson WB (1985) Pearson's Handbook of Crystallographic Data for Intermetallic Phases. Acta Cryst 40(a1):C444

    Article  Google Scholar 

  28. Togo A, Tanaka I (2015) First Principles Phonon Calculations in Materials Science. Scripta Mater 108:1

    Article  CAS  Google Scholar 

  29. Chong X, Hu M, Wu P, Shan Q, Jiang YH, Li ZL, Feng J (2019) Tailoring the Anisotropic Mechanical Properties of Hexagonal M7x3 (M=Fe, Cr, W, Mo; X=C, B) by Multialloying. Acta Mater 169:193

    Article  CAS  Google Scholar 

  30. Brown HL, Armstrong PE, Kempter CP (1966) Elastic Properties of Polycrystalline Sc, Re, Ru and Pt21 Ir. J Less-Common Metals 11(2):135

    Article  CAS  Google Scholar 

  31. Lu XG, Selleby M, Bo S (2007) Calculations of thermophysical properties of cubic carbides and nitrides using the debye-grüneisen model. Acta Mater 55(4):1215

    Article  CAS  Google Scholar 

  32. Jong M, Wei C, Angsten T, Jain A, Notestine R, Gamst A, Sluiter M, Ande CK, Zwaag S, Plata JJ (2015) Charting the complete elastic properties of inorganic crystalline compounds. Scientific Data 2:150009

    Article  Google Scholar 

  33. Weber W (1973) Lattice dynamics of transition-metal carbides. Phys Rev B 8(11):5082

    Article  CAS  Google Scholar 

  34. Hui L, Zhang L, Zeng Q, Kang G, Li K, Ren H, Liu S, Cheng L (2011) Structural, elastic and electronic properties of transition metal carbides Tmc (Tm=Ti, Zr, Hf and Ta) from first-principles calculations. Solid State Commun 151(8):602

    Article  Google Scholar 

  35. Marmier A, Lethbridge Z, Walton R, Smith C, Parker S, Evans K (2010) Elam: a computer program for the analysis and representation of anisotropic Elastic properties. Comput Phys Commun 181(12):2102

    Article  CAS  Google Scholar 

  36. Setyawan W, Curtarolo S (2010) High-throughput electronic band structure calculations: challenges and tools. Computat Mater ence 49(2):299

    Article  Google Scholar 

  37. Ranganathan SI, Ostoja-Starzewski M (2008) Universal Elastic Anisotropy Index. Phys Rev Lett 101(5):055504

    Article  Google Scholar 

  38. Rowcliffe D, Hollox G (1971) Plastic flow and fracture of tantalum carbide and hafnium carbide at low temperatures. J Mater Sci 6:1261

    Article  CAS  Google Scholar 

  39. Kim C, Gottstein G, Grummon D (1994) Plastic flow and dislocation structures in tantalum carbide: deformation at low and intermediate homologous temperatures. Acta Metall Mater 42:2291

    Article  CAS  Google Scholar 

  40. De Leon N, Yu X, Yu H, Weinberger C, Thompson G (2015) Bonding effects on the slip differences in the B1 monocarbides. Phys Rev Lett 114:165502

    Article  Google Scholar 

  41. Sciti D, Guicciardi S, Nygren M (2008) Densification and mechanical behavior of Hfc and Hfb2 fabricated by spark plasma sintering. J Am Ceram Soc 91(5):1433

    Article  CAS  Google Scholar 

  42. Song K, Xu Y, Zhao N, Zhong L, Shang Z, Shen L, Wang J (2016) Evaluation of fracture toughness of tantalum carbide ceramic layer: a vickers indentation method. J Mater Eng Perform 25(7):3057

    Article  CAS  Google Scholar 

  43. Ferro D, Rau JV, Albertini VR, Generosi A, Barinov SM (2008) Pulsed laser deposited Hard Tic, Zrc, Hfc and Tac films on titanium: hardness and an Energy-dispersive x-ray diffraction study. Surf Coat Technol 202(8):1455

    Article  CAS  Google Scholar 

  44. Zhang C, Gupta A, Seal S, Boesl B, Agarwal A (2017) Solid solution synthesis of tantalum carbide-hafnium carbide by spark plasma sintering. J Am. Ceram Soc 100(5):1853–1862

    Article  CAS  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 51925105, 51771165), National Key R&D Program of China (Grant No. YS2018YFA070119) and National Postdoctoral Program for Innovative Talents (Grant No. BX20200285).

Author information

Authors and Affiliations

  1. State Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao, 066004, China

    Hailiang Liu, Ke Tong, Xing Feng, Sha Liu & Bin Wen

Authors
  1. Hailiang Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ke Tong
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xing Feng
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Sha Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Bin Wen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bin Wen.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Handling Editor: David Cann.

Publisher's Note

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, H., Tong, K., Feng, X. et al. Temperature-dependent mechanical properties of TaC and HfC. J Mater Sci 58, 157–169 (2023). https://doi.org/10.1007/s10853-022-08026-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10853-022-08026-6

Search

Navigation