Technical Physics

, Volume 63, Issue 3, pp 369–373 | Cite as

Titanium Melting Curve: Data Consistency Assessment, Problems and Achievements

  • E. Yu. Kulyamina
  • V. Yu. Zitserman
  • L. R. Fokin
Solid State


Experimental data for the thermodynamic properties of titanium on the melting curve in the pressure range from atmospheric value to 90 GPa are analyzed and brought into correspondence. The problems that have been considered are (i) the lack of data for the solid β-phase density near the normal melting point and (ii) the formation probability of a triple point on the melting curve for the coexisting β-, ω-, and liquid phases of titanium. To estimate the change of the volume upon melting 3d elements from Mendeleev’s periodic system, a correlation between the change of the volume, ΔV m , and the change of the entropy, ΔS m , on the melting curve at atmospheric pressure is suggested and effectively used.


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  1. 1.
    A. V. Bushman and V. E. Fortov, Sov. Phys. Usp. 26, 465 (1983)ADSCrossRefGoogle Scholar
  2. 2.
    D. K. Belashchenko, Phys.-Usp. 56, 1176 (2013)ADSCrossRefGoogle Scholar
  3. 3.
    E. Yu. Kulyamina, V. Yu. Zitserman, and L. R. Fokin, Tech. Phys. 62, 68 (2017).CrossRefGoogle Scholar
  4. 4.
    V. Ya. Chekhovskoi, L. R. Fokin, V. E. Peletskii, V. A. Petukhov, and B. A. Shur, Handbook of Titanium- Based Materials: Thermophysical Properties, Data and Studies (Begell House, New York, 2007).Google Scholar
  5. 5.
    E. Yu. Tonkov, Phase Diagrams of Elements under High Pressure (Fizmatlit, Moscow, 1979).Google Scholar
  6. 6.
    D. A. Yang, Phase Diagrams of Elements (Univ. of California Press, 1991).Google Scholar
  7. 7.
    E. Yu. Tonkov and E. G. Ponytovsky, Phase Transformation of Elements under High Pressure (CRC Press, Boca Raton, 2007).Google Scholar
  8. 8.
    D. Errandonea, B. Schwager, R. Ditz, et al., Phys. Rev. 63, 132104 (2001).CrossRefGoogle Scholar
  9. 9.
    G. Shen, V. Prakapenka, M. Rivers, and S. Sutton, Phys. Rev. Lett. 92, 185701 (2004).ADSCrossRefGoogle Scholar
  10. 10.
    L. F. Vereshagin and N. S. Fateeva, High Temp.-High Pressures 9, 619 (1977).Google Scholar
  11. 11.
    L. R. Fokin, Monit. Nauka Tekhnol., No. 4, 103 (2011).Google Scholar
  12. 12.
    R. Hrubiak, Y. Meng, and G. Shen, Nat. Commun. 8, 14562 (2017).ADSCrossRefGoogle Scholar
  13. 13.
    D. Errandonea, J. Phys. Chem. Solids 67, 2018 (2006).ADSCrossRefGoogle Scholar
  14. 14.
    V. Stutzmann, A. Dewaele, J. Bouchet, et al., Phys. Rev. B 92, 224110 (2015).ADSCrossRefGoogle Scholar
  15. 15.
    R. F. Trunin, G. V. Simakov, and A. V. Medvedev, High Temp. 37, 851 (1999).Google Scholar
  16. 16.
    D. Errandonea, Phys. Rev. 87, 054108 (2013).ADSCrossRefGoogle Scholar
  17. 17.
    G. I. Kerley, Report No. 2003-3785 (Sandia National Laboratories, Albuquerque, 2003).Google Scholar
  18. 18.
    S. Pecker, S. Eliezer, D. Fisher, and Z. Hines, J. Appl. Phys. 98, 043516 (2005).ADSCrossRefGoogle Scholar
  19. 19.
    Y.-M. Kim, B.-J. Lee, and M. I. Baskes, Phys. Rev. 74, 014101 (2006).CrossRefGoogle Scholar
  20. 20.
    Z.-Y. Zeng, L.-C. Cai, X.-R. Chen, and F.-Q. Jing, J. Appl. Phys. 109, 043503 (2011).ADSCrossRefGoogle Scholar
  21. 21.
    A. T. Dinsdale, CALPHAD: Comput. Coupling Phase Diagrams Thermochem. 15, 317 (1991).CrossRefGoogle Scholar
  22. 22.
    S. V. Stankus, Preprint No. 247-91 (Inst. of Thermophysics, Novosibirsk, 1991).Google Scholar
  23. 23.
    G. R. Gathers, Int. J. Thermophys. 4, 271 (1983).ADSCrossRefGoogle Scholar
  24. 24.
    T. Sato, Y. Shiraishi, and Y. Sakuma, Trans. Iron Steel Inst. Jpn. 9, 118 (1969).Google Scholar
  25. 25.
    Physical Chemistry of Inorganic Materials, Vol. 2: Surface Tension and Thermodynamics of Metallic Melts, Ed. by V. N. Eremenko (Naukova Dumka, Kiev, 1988), pp. 59–103.Google Scholar
  26. 26.
    T. Ishikawa and P.-F. Paradis, Adv. Mater. Res. 11, 173 (2009).CrossRefGoogle Scholar
  27. 27.
    D. N. Williams, Trans. Metall. Soc. AIME 221, 411 (1961).Google Scholar
  28. 28.
    N. Schmitz-Pranghe and P. Dunner, Z. Metallkd. 58, 377 (1968).Google Scholar
  29. 29.
    N. P. Lyakishev and M. I. Gasik, Chromium Metallurgy (ELIZ, Moscow, 1999).Google Scholar
  30. 30.
    R. N. Abdullaev, Yu. M. Kozlovski, R. A. Khairulin, and S. V. Stankus, Int. J. Thermophys. 36, 603 (2015).ADSCrossRefGoogle Scholar
  31. 31.
    F. P. Bundy, Report No. 63-RL-3184C (GE Research Lab., 1963).Google Scholar
  32. 32.
    R. Hrubiak, PhD Thesis (Florida Int. Univ., Miami, 2012).Google Scholar
  33. 33.
    A. Dawaele, V. Stutzmann, J. Fouchet, et al., Phys. Rev. B 91, 134108 (2015).ADSCrossRefGoogle Scholar
  34. 34.
    L. R. Fokin and A. N. Kalashnikov, J. Eng. Phys. Thermophys. 89, 249 (2016).CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • E. Yu. Kulyamina
    • 1
  • V. Yu. Zitserman
    • 1
  • L. R. Fokin
    • 1
  1. 1.Joint Institute for High TemperaturesRussian Academy of SciencesMoscowRussia

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