Skip to main content
Log in

Thermodynamic Modeling of B-Ta and B-C-Ta Systems

  • Published:
Journal of Phase Equilibria and Diffusion Aims and scope Submit manuscript

Abstract

A thermodynamic assessment of the B-Ta system is performed using the CALPHAD method incorporating the latest experimental data and results from first-principles calculations of the formation enthalpies of TaB2, Ta3B4, TaB, Ta3B2, and Ta2B. The sublattice model of (Ta, B)0.333(Ta, B)0.667 is used to describe the homogeneity range of TaB2, while the other four intermetallic compounds are treated as stoichiometric compounds. As a results, noticeable improvement were made over previous thermodynamic description of the B-Ta system. The thermodynamic parameters obtained in this study can effectively reproduce the most recently published experimental data. The thermodynamic assessment of the ternary phase diagram of B-C-Ta system could be carried out by combining the thermodynamic parameters of the C-Ta and B-C systems from the literature with the re-assessed B-Ta system. Reliable experimental data are satisfactorily accounted for the present thermodynamic description.

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

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Similar content being viewed by others

References

  1. M.M. Opeka, I.G. Talmy, and J.A. Zaykoski, Oxidation-Based Materials Selection for 2000°C + Hypersonic Aerosurfaces: Theoretical Considerations and Historical Experience, J. Mater. Sci., 2004, 39(19), p 5887-5904

    Article  ADS  Google Scholar 

  2. J.F. Justin and A. Jankowiak, Ultra High Temperature Ceramics: Densification, Properties and Thermal Stability, AerospaceLab, 2011, 3, p 1-11

    Google Scholar 

  3. X. Zhang, G.E. Hilmas, and W.G. Fahrenholtz, Densification and Mechanical Properties of TaC-Based Ceramics, Mater. Sci. Eng. A, 2009, 501(1-2), p 37-43

    Article  Google Scholar 

  4. L. Liu, F. Ye, X. He et al., Densification Process of TaC/TaB2 Composite in Spark Plasma Sintering, Mater. Chem. Phys., 2011, 126(3), p 459-462

    Article  Google Scholar 

  5. E. Khaleghi, Y.S. Lin, M.A. Meyers et al., Spark Plasma Sintering of Tantalum Carbide, Scr. Mater., 2010, 63(6), p 577-580

    Article  Google Scholar 

  6. I.G. Talmy, J.A. Zaykoski, and M.M. Opeka, Synthesis, Processing and Properties of TaC-TaB2-C Ceramics, J. Eur. Ceram. Soc., 2010, 30(11), p 2253-2263

    Article  Google Scholar 

  7. L. Zhong, L. Liu, C. Worsch et al., Transient Liquid Phase Sintering of Tantalum Carbide Ceramics by Using Silicon as the Sintering Aid and Its Effects on Microstructure and Mechanical Properties, Mater. Chem. Phys., 2015, 149, p 505-511

    Article  Google Scholar 

  8. B. Mehdikhani, G.H. Borhani, S.R. Bakhshi et al., Investigation of TaC-TaB2 Ceramic Composites, B Mater. Sci., 2016, 39(1), p 79-84

    Article  Google Scholar 

  9. K. Frisk and A.F. Guillermet, Gibbs Energy Coupling of the Phase Diagram and Thermochemistry in the Tantalum-Carbon System, J. Alloys Compd., 1996, 238(1-2), p 167-179

    Article  Google Scholar 

  10. H. Wiesenberger, W. Lengauer, and P. Ettmayer, Reaction Diffusion and Phase Equilibria in the V-C, Nb-C, Ta-C and Ta-N Systems, Acta Mater., 1998, 46(2), p 451-666

    Article  Google Scholar 

  11. P. Rogl, The System Boron-Carbon-Tantalum in Phase Diagrams of Ternary Metal-Boron-Carbon Systems, MSI, G. Effenberg, Ed., ASM International, Materials Park, 1998, p 257-268

    Google Scholar 

  12. A. Saengdeejing, J.E. Saal, V.R. Manga, and Z.K. Liu, Defects in Boron Carbide: First-Principles Calculations and CALPHAD Modeling, Acta Mater., 2012, 60(20), p 7207-7215

    Article  Google Scholar 

  13. L. Kaufman, Coupled Thermochemical and Phase Diagram Data for Tantalum Based Binary Alloys, Calphad, 1991, 15(3), p 243-259

    Article  Google Scholar 

  14. H. Bolmgren, T. Lundström, L.E. Tergenius, S. Okada, and I. Higashi, The Crystal Structure of Ta5B6, J. Less Common Metals, 1990, 161, p 341-345

    Article  Google Scholar 

  15. C.L. Yeh and H.J. Wang, A Comparative Study on Combustion Synthesis of Ta-B Compounds, Intermetallics, 2011, 37(5), p 1569-1573

    Google Scholar 

  16. S. Okada, K. Kudou, I. Higashi, and T. Lundström, Single Crystals of TaB, Ta5B6, Ta3B4, and TaB2, as Obtained from High-temperature Metal Solutions, and Their Properties, J. Cryst. Growth, 1993, 128(1-4), p 1120-1124

    Article  ADS  Google Scholar 

  17. E. Rudy, Ternary Phase Equilibria in Transition Metal-Boron-Carbon-Silicon Systems. Part V. Compendium of Phase Diagram Data, Wright-Patterson Air Force Base, Ohio: 1969, p 209-211

    Google Scholar 

  18. V.M. Chad, É.C.T. Ramos, G.C. Coelho, C.A. Nunes, P.A. Suzuki, F. Ferreira, and P. Rogl, Evaluation of the Invariant Reactions in the Ta-Rich Region of the Ta-B System, J Phase Equilibria Diffus., 2006, 27(5), p 452-455

    Article  Google Scholar 

  19. H. Nowotny, F. Benesovsky, and R. Kieffer, An Essay on the Structure of the Systems of Niob-Bor and Tantal-Bor, Z. Metallkd., 1959, 50(7), p 417-423

    Google Scholar 

  20. J.M. Leitnaker, M.G. Bowman, and P.W. Gilles, High-Temperature Phase Studies in the Tantalum-Boron System between Ta and TaB, J. Electrochem. Soc., 1961, 108(6), p 568-572

    Article  Google Scholar 

  21. K.I. Portnoi, V.M. Romashov, and S.E. Sah’bekov, Binary Constitution Diagrams of Systems Composed of Various Elements and Boron—A Review, Poroshk. Metall., 1971, 11, p 89-91, in Russian; TR: Sov. Powder Metall. Met. Ceram., 1971, 10(11), P 925-927

    Google Scholar 

  22. H. Okamoto, Comment on B-Ta, J Phase Equilibria Diffus., 1993, 14(3), p 393-394

    Article  Google Scholar 

  23. J.M. Leitnaker, M.G. Bowman, and P.W. Gilles, Thermodynamic Properties of the Tantalum and Tungsten Borides, J. Electrochem. Soc. Absorbed Electrochem. Technol., 1962, 109(5), p 441-443

    Article  Google Scholar 

  24. E.P. Kirpichev, Y.I. Rubtsov, T.V. Sorokina, and V.K. Prokudina, Standard Enthalpy of Formation of Transition Metal Borides, J. Phys. Chem., 1979, 53, p 1128-1130

    Google Scholar 

  25. G.K. Johnson, E. Greenberg, J.L. Margrave et al., Fluorine Bomb Calorimetry. Enthalpies of Formation of the Diborides of Niobium and Tantalum, J. Chem. Eng. Data, 1967, 12(4), p 597-600

    Article  Google Scholar 

  26. S.V. Meschel and O.J. Kleppa, Standard Enthalpies of Formation of NbB2, MoB, and ReB2 by High-temperature Direct Synthesis Calorimetry, Metall. Mater. Trans. A, 1993, 24(4), p 947-950

    Article  ADS  Google Scholar 

  27. C. Qi, Y. Jiang, and R. Zhou, First Principles Study the Stability and Mechanical Properties of M3B2 (M = V, Nb and Ta) Compounds, Rare Metal Mater. Eng., 2014, 43(12), p 2898-2902

    Article  Google Scholar 

  28. C.J. Qi, J. Feng, R.F. Zhou, Y.H. Jiang, and R. Zhou, First Principles Study on the Stability and Mechanical Properties of MB (M = V, Nb and Ta) Compounds, Chin. Phys. Lett., 2013, 30(11), p 2898-2902

    Google Scholar 

  29. X. Zhang, E. Zhao, and Z. Wu, Prediction of New High Pressure Phase of TaB3: First-Principles, J Alloys Compd., 2015, 632, p 37-43

    Article  Google Scholar 

  30. J.P. Perdew, K. Burke, and M. Ernzerhof, Generalized Gradient Approximation Made Simple, Phys. Rev. Lett., 1996, 77(18), p 3865-3868

    Article  ADS  Google Scholar 

  31. G. Kresse and J. Furthmueler, Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set, Phys. Rev. B, 1996, 54(16), p 11169-11186

    Article  ADS  Google Scholar 

  32. G. Kresse and D. Joubert, From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method, Phys. Rev. B, 1999, 59(3), p 1758-1775

    Article  ADS  Google Scholar 

  33. E.E. Havinga, H. Damsma, and P. Hokkeling, Compounds and Pseudo-binary Alloys with the CuAl2 (C16)-Type Structure I. Preparation and X-ray Results, J. Less Common Metals, 1972, 27, p 169-186

    Article  Google Scholar 

  34. R. Kiessling, The Borides of Tantalum, Acta Chem. Scand., 1949, 3, p 603-615

    Article  Google Scholar 

  35. S. Okada, K. Kudou, I. Higashi, and T. Lundström, Single Crystals of TaB, Ta5B6, Ta3B4 and TaB2, as Obtained from High-temperature Metal Solutions, and Their Properties, J. Cryst. Growth, 1993, 128, p 1120-1124

    Article  ADS  Google Scholar 

  36. O. Redlich and A. Kister, Thermodynamics of Nonelectrolyte Solutions x-y-t Relations in a Binary System, Ind. Eng. Chem., 1948, 40, p 345-348

    Article  Google Scholar 

  37. S.L. Shang, Y. Wang, R. Arroyave, and Z.K. Liu, Phase Stability in Alpha- and Beta-Rhombohedral Boron, Phys. Rev. B, 2007, 75(9), p 092-101

    Article  Google Scholar 

  38. M. Widom and M. Mihalkovicˇ, Symmetry-Broken Crystal Structure of Elemental Boron at Low Temperature, Phys. Rev. B, 2008, 77, p 064-113

    Article  Google Scholar 

  39. B. Sundman, B. Jansson, and J.O. Andwersson, Thermo-Calc Databank System, Calphad, 1985, 9(2), p 153-190

    Article  Google Scholar 

  40. L. Brewer and H. Haraldsen, The Thermodynamic Stability of Refractory Borides, J. Electrochem. Soc., 1955, 102, p 399-406

    Article  Google Scholar 

  41. E. Rudy, F. Benesovsky, and L.E. Toth, Investigation of Ternary System Between Va and VIa-Metals with Boron and Carbon, Z. Metallkd., 1963, 54(6), p 345-353 (in German)

    Google Scholar 

  42. Y.V. Levinskii, S.E. Salibekov, and M.K. Levinskaya, Interaction of Diborides of V, Nb, Ta with Carbon, Poroshk. Metall. (Kiev), 1965, 5(11), p 66-69 (in Russian)

    Google Scholar 

  43. S.S. Ordanyan, V.I. Unrod, V.S. Polishchuk, and N.M. Storonkina, Reactions in the System TaC-TaB2, Powder. Metall. Met. Ceram., 1976, 15(9), p 692-695 (translated from Poroshk. Metall., 1976, 9(165), p 40–43)

    Article  Google Scholar 

  44. S.S. Ordanyan, A.I. Dmitriev, K.T. Bizhev, and E.K. Stepanenko, The Interaction in B4C-MeVB2 Systems, Powder. Metall. Met. Ceram., 1987, 26(10), p 834-836, translated from Poroshk. Metall., 1987, 10(298), p 66–69

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported by national Natural Science Foundation of China (No. 51471141), Scientific Reasearch Fund of Hunan Provincial Science and Technology Department (No. 2016JC2005). The research was financially supported by the 2015 Opening subject of State Key Laboratory of Powder Metallurgy.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Fucheng Yin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

OuYang, X., Yin, F., Hu, J. et al. Thermodynamic Modeling of B-Ta and B-C-Ta Systems. J. Phase Equilib. Diffus. 38, 874–886 (2017). https://doi.org/10.1007/s11669-017-0603-2

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11669-017-0603-2

Keywords

Navigation