Estimation of Enthalpy of Formation of TiCu by Density Functional Method

Abstract—The enthalpies of formation of γ- and δ-modifications of the TiCu phase were estimated using the density-functional method. The enthalpies of formation are –22 and –12.8 kJ/mol for the γ- and δ-TiCu, respectively. The comparison of X-ray data and quantum-chemical calculations demonstrates that the discrepancy in the experimental values of enthalpy of formation of the TiCu crystals correlates with different content of the γ and δ modifications in the TiCu alloy.

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  1. 1

    U. Gelius, A. B. Kolpachev, O. V. Kolpacheva, Ya. Nikiforov, and A. A. Chularis, “Electronic energy structure of TiCu and Ti2Cu,” Russ. J. Struct. Chem. 42, No. 4, 578–582 (2001).

    CAS  Article  Google Scholar 

  2. 2

    V. G. Shmorgun, O. V. Slautin, D. A. Evstropov, A. O. Taube, and Yu. I. Bondarenko, “Structure and mechanical properties of metal-intermetallic composites of Ti–Cu system,” Izv. Vuzov. Poroshkovaya Metallurgiya i Funktsional’nye Pokrytiya, No. 4, 36–40 (2014).

    Google Scholar 

  3. 3

    G. P. Luchinskii, Chemistry of Titanium (Khimiya, Moscow, 1971), p. 472.

    Google Scholar 

  4. 4

    M. Konieczny, “Mechanical properties and deformation behaviour of laminated titanium-intermetallic composites synthesised using Ti and Cu foils,” Kovove Mater. 48, No. 1, 47–53 (2010).

  5. 5

    I. Shon, N. Kim, S-L. Du, S-W. Cho, and W. Kimet, “Rapid consolidation of nanostructured TiCu compound by high frequency induction heating and its mechanical properties,” Mater. Trans. 51, No. 11, 2129–2131 (2010).

    CAS  Article  Google Scholar 

  6. 6

    M. Karlsson, “An X-ray study of the phases in the copper-titanium system,” J. Inst. Met. 79, 391 (1951).

    CAS  Google Scholar 

  7. 7

    A. S. Rogachev, S. G. Vadchenko, A. S. Shchukin, S. D. Kovalev, and A. S. Aronin, “Self-propagating crystallization wavesin the TiCu amorphous alloy,” JETP Lett. 104, No. 10, 726–729 (2016).

    CAS  Article  Google Scholar 

  8. 8

    Landolt-Börnstein, Numerical Data and Functional Relationships in Science and Technology. New Series. Group III: Condensed Matter. Volume 43. Crystal Structures of Inorganic Compounds. Subvolume A. Structure Types. Part 11. Space groups (135) P4 2 /mbc – (123) P4/mmm, Ed. by P. Villars and K. Cenzual (Springer, Berlin, 2012), Vol. 126, p. 362.

  9. 9

    M. Arita, R. Kinaka, and M. Someno, “Application of the metal-hydrogen equilibration for determining thermodynamic properties in the Ti-Cu system,” Metall. Trans. A 10, No. 5, 529–534 (1979).

    Article  Google Scholar 

  10. 10

    O. J. Kleppa and Sh. Watanabe, “Thermochemistry of alloys of transition metals: Part III. Copper–Silver, ‒Titanium, Zirconium, and –Hafnium at 1373 K,” Metal. Trans. B 13, No. 3, 391–401 (1982).

    Article  Google Scholar 

  11. 11

    N. Saunders, “Phase diagram calculation for eight glass forming alloys system,” Calphad 9, No. 4, 297–309 (1985).

    CAS  Article  Google Scholar 

  12. 12

    C. Colinet, F. Pasturel, and R. H. J. Buschow, “Enthalpy of formation of Ti-Cu intermetallic and amorphous phases,” J. Alloys Compd. 247, No. 2, 15–19 (1997). 02590-X

  13. 13

    M. A. Turchanin, P. G. Agraval, and A. R. Abdulov, “Thermodynamics of liquid alloys and metastable phase transformations in the copper-titanium system,” Powder Metall. Met. Ceram. 47, No. 5–6, 259–263 (2008).

    Google Scholar 

  14. 14

    J. Rodriguez-Carvaja, “Recent Developments of the Program FULLPROF,” in Commission on Powder Diffraction (IUCr) (IUCr Newsletter, 2001), Vol. 26, pp. 12–19.

  15. 15

    C. F. Macrae, I. J. Bruno, J. A. Chisholm, P. R. Edgington, P. McCabe, E. Pidcock, L. Rodriguez-Monge, R. Taylor, J. Van de Streek, and P. A. Wood, “Mercury CSD 2.0 – new features for the visualization and investigation of crystal structures,” J. Appl. Crystallogr. 41, 466–470 (2008).

    CAS  Article  Google Scholar 

  16. 16

    G. Kresse and J. Furthmuller, “Efficient iterative schemes for ab initio total-energy calculations using,” Phys. Rev. 54, No. 16, 11169–1187 (1996).

    CAS  Article  Google Scholar 

  17. 17

    G. Kresse and J. Furthmuller, “Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set Comput,” Mater. Sci. 6, No. 1, 15–50.

  18. 18

    S. Grimme, J. Antjny, S. Ehrlich, and S. A. Krieg, “A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu,” J. Chem. Phys. 132, No. 15, 154104–154107 (2010).

    CAS  Article  Google Scholar 

  19. 19

    S. Grimme, S. Ehrlich, and L. Goerigk, “Effect of the damping function in dispersion corrected density functional theory,” J. Comput. Chem. 32, No. 7, 1456–1465 (2011).

    CAS  Article  Google Scholar 

  20. 20

    Zh-S. Nong, J-Ch. Zhu, H-L. Yu, and Zh-H. Lai, “First principles calculation of intermetallic compounds in FeTiCoNiVCrMncuAl system high entropy alloy,” Trans. Nonferrous Met. Soc. China 22, No. 6, 1437–1444 (2012).

    CAS  Article  Google Scholar 

  21. 21

    C. Colinet, “Ab-initio calculation of enthalpies of formation of intermetallic compounds and enthalpies of mixing of solid solutions,” Intermetallics 11, 1095–1102 (2003).

    CAS  Article  Google Scholar 

  22. 22

    T. Uesugi, S. Miyamae, and K. Higashi, “Enthalpies of solution in Ti–X (X = Mo, Nb, V and W) alloys from first principlies calculations,” Mater. Trans. 54, No. 4, 484–492 (2013).

    CAS  Article  Google Scholar 

  23. 23

    W. Casior and F. Debski, “Enthalpy of formation of intermetallic phases from Fe-Ni-Ti system. Comparative studies,” Arch. Metall. Mater. 57, No. 4, 1095–1104 (2012).

    CAS  Article  Google Scholar 

  24. 24

    Q. Guo and O. I. Kleppa, “Standard enthalpies of formation of some alloys formed between group IV elements and group VIII elements, determined by high-temperature direct synthesis calorimetry II. Alloys of (Ti, Zr, Hf) with (Co, Ni),” J. Alloys Compd. 269, Nos. 1–2, 181–186 (1998).

    CAS  Article  Google Scholar 

  25. 25

    Q. Guo and O. I. Kleppa, “Standard enthalpies of formation of some alloys formed between group IV elements and group VIII elements, determined by high-temperature direct synthesis calorimetry II. Alloys of (Ti, Zr, Hf) with (Rh, Pd, Pt),” J. Alloys Compd. 266, Nos. 1–2, 224–229 (1998).

    CAS  Article  Google Scholar 

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The work is performed within the state assignment ISMAN (theme 44 No. 0091-2018-0001). S.A. Guda acknowledges the financial support of The Southern Federal University (VnGr-07/2017-08).

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Correspondence to S. V. Konovalihin.

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Translated by O. Golovnya

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Konovalihin, S.V., Chuev, I.I., Guda, S.A. et al. Estimation of Enthalpy of Formation of TiCu by Density Functional Method. Phys. Metals Metallogr. 121, 1188–1192 (2020).

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  • intermetallic TiCu
  • enthalpy of formation
  • density-functional method