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Thermodynamic Assessment of the Glass-Forming Cu–Ti–Hf System

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In the framework of the CALPHAD method, the thermodynamic assessment of the Cu–Ti–Hf system has been performed for the first time. This assessment considers the existence of homogeneity regions for Cu3Ti2, Cu4Ti3, CuTi, Cu5Hf, Cu51Hf14, and Cu10Hf7 compounds and the formation of a continuous solid solution of Cu(Ti, Hf)2 (γ-phase) in the ternary system. The thermodynamic assessments of the boundary binary systems and data on phase transformations and mixing enthalpy of melts in the ternary system became the basis for calculations. The Compound Energy Formalism was used to model the thermodynamic properties of intermetallic compounds with a homogeneity region. The associated solution model was used to describe the complex temperature dependence of the thermodynamic properties of melts from the temperature at which equilibrium melts exist to the glass-formation temperature. Upon the calculations, isothermal sections, vertical sections, projections of the liquidus and solidus surfaces, and reaction scheme of the phase diagram were presented. The liquid phase participates in eleven four-phase invariant reactions occurring in the temperature range 1138–1541 K. The diagrams of metastable phase transformations involving supercooled Cu–Ti–Hf melts and boundary solid solutions based on pure components were calculated. It is shown that supercooled melts in wide concentration ranges are thermodynamically stable in relation to boundary solid solutions based on pure components. The concentration region of glass formation for Cu–Ti–Hf melts by liquid quenching, predicted by the relative position of the \({T}_{0}^{L/\phi }\) and \({x}_{0}^{L/\phi }\) lines, is xCu ≈ 0.16–0.80.

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References

  1. M. Sakata, N. Cowlam, and H.A. Davies, “Chemical short-range order in liquid and amorphous 66:34 copper–titanium alloys,” J. Phys. F: Met. Phys., 11, No. 7, L157–L162 (1981).

    Article  CAS  Google Scholar 

  2. Ch.-H. Hwang, Y.-Jo Ryeom, and K. Cho, “Electrical resistivity and crystallization of amorphous Cu–Ti alloys,” J. Less-Common Met., 86, 187–194 (1982).

  3. K.H.J. Buschow, “Effect of short-range ordering on the thermal stability of amorphous titanium–copper alloys,” Scr. Metall., 17, No. 9, 1135–1139 (1983).

    Article  CAS  Google Scholar 

  4. J. Reeve, G.P. Gregan, and H.A. Davies, “Glass forming ability studies in the copper–titanium system,” in: Proc. 5th Int. Conf., Meeting Date 1984, North-Holland, Amsterdam (1985), Vol. 1, pp. 203–206.

  5. C.G. Woychik, D.H. Lowndes, and T.B. Massalski, “Solidification structures in melt-spun and pulsed laser-quenched copper-titanium alloys,” Acta Metall., 33, No. 10, 1861–1871 (1985).

    Article  CAS  Google Scholar 

  6. K. Aoki and T. Masumoto, Proc. Inst. Meet. Advanced Materials Research Society, Pittsburgh, PA (1989), Vol. 3, pp. 393–398.

  7. C. Colinet, A. Pasturel, and K. Buschow, “Enthalpies of formation of Ti–Cu intermetallic and amorphous phases,” J. Alloys Compd., 247, No. 1, 15–19 (1997).

    Article  CAS  Google Scholar 

  8. K.H.J. Buschow and N.M. Beekmans, “Thermal stability of amorphous alloys,” Solid State Commun., 35, No. 3, 233–236 (1980).

    Article  CAS  Google Scholar 

  9. T. Zhang, A. Inoue, and T. Masumoto, “Amorphous (Ti, Zr, Hf) Ni Cu ternary alloys with a wide supercooled liquid region,” Mater. Sci. Eng. A, 181, 1423–1426 (1994).

    Article  CAS  Google Scholar 

  10. A. Inoue, “High-strength Cu-based bulk glassy alloys in Cu–Zr–Ti and Cu–Hf–Ti ternary systems,” Acta Mater., 49, 2645–2652 (2001).

    Article  CAS  Google Scholar 

  11. A. Inoue and W. Zhang, “Formation, thermal stability and mechanical properties of Cu–Zr and Cu–Hf binary glassy alloy rods,” Mater. Trans., 45, No. 2, 584–587 (2004).

    Article  CAS  Google Scholar 

  12. R. Ristic, “Properties and atomic structure of amorphous early transition metals,” J. Alloys Compd., 504, S194–S197 (2010).

    Article  Google Scholar 

  13. I.A. Figerua, H. Davies, and I. Todd, “Formation of Cu–Hf–Ti bulk metallic glasses,” J. Alloys Compd., 434, 164–166 (2007).

    Article  Google Scholar 

  14. J. Basu and S. Ranganathan, “Glass forming ability and stability: Ternary Cu bearing Ti, Zr, Hf alloys,” Intermetallics, 17, No. 3, 128–135 (2009).

    Article  CAS  Google Scholar 

  15. H. Choi-Yim and R. Conner, “Amorphous alloys in the Cu–Hf–Ti system,” J. Alloys Compd., 459, No. 1, 160–162 (2008).

    Article  CAS  Google Scholar 

  16. M.A. Turchanin, P.G. Agraval, and A.R. Abdulov, “Thermodynamic assessment of the Cu–Ti–Zr system. I. Cu−Ti system,” Powder Metall. Met. Ceram., 47, No. 5–6, 344–360 (2008).

    Article  CAS  Google Scholar 

  17. M.A. Turchanin and P.G. Agraval, “Thermodynamic assessment of the copper−hafnium system,” Powder Metall. Met. Ceram., 47, No. 3–4, 223–233 (2008).

    Article  CAS  Google Scholar 

  18. H. Bittermann and P. Rogl, “Critical assessment and thermodynamic calculation of the ternary system boron–hafnium–titanium (B–Hf–Ti),” J. Phase Equilib., 18, No. 1, 24–47 (1997).

    Article  CAS  Google Scholar 

  19. J.L. Liu, “Experimental investigation on phase equilibria of Cu–Ti–Hf system and performance of Cu (Ti, Hf) 2 phase,” J. Mater. Sci., 53, No. 10, 7809–7821 (2018).

    Article  CAS  Google Scholar 

  20. V. Ronto, “Investigation of solidification behavior in Cu-based Cu–Hf–Ti alloy system,” IOP Conf. Ser.: Mater. Sci. Eng., 27, 012022 (2012).

  21. V. Ronto, “Microstructure and phase analysis by TEM in Cu–Hf–Ti alloys,” Mater. Sci. Forum, 729, 266–271 (2013).

    Article  CAS  Google Scholar 

  22. A.A. Vodopyanova, M.A. Turchanin, L.A. Dreval, and P.G. Agraval, “Partial and integral mixing enthalpies for liquid alloys in the Cu–Ti–Hf system,” Herald DSEA, No. 2 (41), 19–23 (2017).

    Google Scholar 

  23. A.T. Dinsdale, “SGTE data for pure elements,” CALPHAD, 15, No. 4, 317–425 (1991).

    Article  CAS  Google Scholar 

  24. F. Sommer, “Homogeneous equilibria in liquid alloys and glass formation,” Ber. Bunsen Ges. Phys. Chem., 87, No. 9, 749–756 (1983).

    Article  CAS  Google Scholar 

  25. M.A. Turchanin, I.V. Belokonenko, and P.G. Agraval, “On the application of the theory of ideal associated solution (TAS) for description of the temperature–concentration dependence of thermodynamic properties of binary melts,” Rasplavy, No. 1, 58–69 (2001).

    Google Scholar 

  26. A.A. Turchanin, M.A. Turchanin, and P.G. Agraval, “Thermodynamics of undercooled liquid and amorphous binary metallic alloys,” J. Metastable Nanocryst. Mater., 10, 481–486 (2001).

    Google Scholar 

  27. D.N. Saulov, I.G. Vladimirov, and A.Y. Klimenko, “Modified associate formalism without entropy paradox: Part I: Model description,” J. Alloys Compd., 473, No. 1–2, 167–175 (2009).

    Article  CAS  Google Scholar 

  28. P.G. Agraval, L.A. Dreval, and M.A. Turchanin, “Interaction of components in Cu–Fe glass-forming melts with titanium, zirconium, and hafnium. II. Temperature–concentration dependence of thermodynamic mixing functions,” Powder Metall. Met. Ceram., 56, No. 5–6, 323–332 (2017).

    Article  CAS  Google Scholar 

  29. M.A. Turchanin, I.V. Belokonenko, and P.G. Agraval, “Heats of formation of liquid alloys of nickel with IVA-metals,” Rasplavy, No. 3, 53–60 (2001).

    Google Scholar 

  30. M.A. Turchanin and P.G. Agraval, “Enthalpies of mixing of titanium, zirconium, and hafnium liquid alloys with cobalt,” Rasplavy, No. 2, 8–16 (2002).

    Google Scholar 

  31. M.A. Turchanin, P.G. Agraval, A.N. Fesenko, and A.R. Abdulov, “Thermodynamics of liquid alloys and metastable phase transformations in the copper–titanium system,” Powder Metall. Met. Ceram., 44, No. 5–6, 259–270 (2005).

    Article  CAS  Google Scholar 

  32. M.A. Turchanin, “Phase equilibria and thermodynamics of binary copper systems with 3d-metals. VII. Concentration–temperature dependences of the thermodynamic functions of mixing for liquid alloys of copper and transition metals,” Powder Metall. Met. Ceram., 46, No. 11–12, 565–581 (2007).

    Article  CAS  Google Scholar 

  33. M.A. Turchanin, P.G. Agraval, and A.R. Abdulov, “Thermodynamic assessment of the Cu–Ti–Zr system. II. Cu–Zr and Ti–Zr systems,” Powder Metall. Met. Ceram., 47, No. 7–8, 428–446 (2008).

    Article  CAS  Google Scholar 

  34. M.A. Turchanin, “Temperature–composition dependence of thermodynamic mixing functions of liquid alloys of copper with rare-earth metals,” Powder Metall. Met. Ceram., 50, No. 7–8, 512–527 (2011).

    Article  CAS  Google Scholar 

  35. P.G. Agraval, L.A. Dreval, and M.A. Turchanin, “Thermodynamic properties of iron melts with titanium, zirconium, and hafnium,” Powder Metall. Met. Ceram., 55, No. 11–12, 707–716 (2017).

    Article  CAS  Google Scholar 

  36. M.A. Turchanin, T.Ya. Velikanova, P.G. Agraval, A.R. Abdulov, and L.A. Dreval’, “Thermodynamic assessment of the Cu–Ti–Zr system. III. Cu–Ti–Zr system,” Powder Metall. Met. Ceram., 47, No. 9–10, 586–606 (2008).

  37. M. Turchanin, P. Agraval, L. Dreval, and A. Vodopyanova, “Calorimetric investigation of the mixing enthalpy of liquid Hf–Ni–Ti alloys and thermodynamic properties and chemical ordering in quaternary liquid Cu–Hf–Ni–Ti alloys,” J. Phase Equilib. Diffus., 41, No. 4, 469–490 (2020).

    Article  CAS  Google Scholar 

  38. M. Turchanin, P. Agraval, L. Dreval, and A. Vodopyanova, “Thermodynamics and chemical ordering of liquid Cu–Hf–Ni–Ti–Zr alloys,” J. Phase Equilib. Diffus., 42, No. 5, 623–646 (2021).

    Article  CAS  Google Scholar 

  39. M.A. Turchanin, L.O. Dreval, P.G. Agraval, V.A. Korsun, A.O. Vodopyanova, “Interaction of components in glass-forming melts of iron and nickel with titanium, zirconium, and hafnium. II. Temperature–concentration dependence of thermodynamic mixing functions of liquid alloys,” Powder Metall. Met. Ceram., 60, No. 11–12, 727–737 (2022).

    Article  CAS  Google Scholar 

  40. L. Dreval, V. Korsun, P. Agraval, M. Turchanin, and A. Vodopyanova, “Thermodynamic mixing functions of the Fe–Ni–Zr liquid alloys,” Mater. Today: Proc., 62, No. P15, 7698–7702 (2022).

    Article  CAS  Google Scholar 

  41. L. Dreval, V. Korsun, P. Agraval, A. Vodopyanova, and M. Turchanin, “Interaction of the components in liquid glass-forming Fe–Hf–Ni alloys,” J. Chem. Thermodyn., 173, No. 10, 106851 (2022).

  42. M.A. Turchanin, P.G. Agraval, T.Ya. Velikanova, and A.A. Vodopyanova, “Predicting the composition ranges of amorphization for multicomponent melts in the framework of the CALPHAD method,” Powder Metall. Met. Ceram., 57, No. 1–2, 57–70 (2018).

    Article  CAS  Google Scholar 

  43. Y.M. Muggianu, M. Gambino, and J.P. Bros, “Enthalpies of formation of liquid alloys bismuth–gallium–tin at 723 K. Choice of an analytical representation of integral and partial excess functions of mixing,” J. Chim. Phys. Phys.-Chim. Biol., 72, 83–88 (1975).

    Article  CAS  Google Scholar 

  44. N. Saunders and A.P. Miodownik, CALPHAD (Calculation of Phase Diagrams): A Comprehensive Guide, Pergamon Press, Oxford (1998), p. 496.

    Google Scholar 

  45. M. Hillert, “The compound energy formalism,” J. Alloys Compd., 320, No. 2, 161–176 (2001).

    Article  CAS  Google Scholar 

  46. R.B. Schwarz, P. Nash, and D. Turnbull, “The use of thermodynamic models in the prediction of the glass-forming range of binary alloys,” J. Mat. Res., 2, No. 04, 456–460 (1987).

    Article  CAS  Google Scholar 

  47. R. Bormann, F. Gärtner, and K. Zöltzer, “Application of the CALPHAD method for the prediction of amorphous phase formation,” J. Less-Common Met., 145, 19–29 (1988).

    Article  CAS  Google Scholar 

  48. N. Saunders and A.P. Miodownik, “Free energy criteria for glass forming alloys,” Ber. Bunsen Ges. Phys. Chem., 87, No. 9, 830–834 (1983).

    Article  CAS  Google Scholar 

  49. P.G. Agraval, L.A. Dreval, and M.A. Turchanin, “Interaction of components in Cu–Fe glass-forming melts with titanium, zirconium, and hafnium. III. Modeling of metastable phase transformations with participation of liquid phase,” Powder Metall. Met. Ceram., 56, No. 7–8, 463–472 (2017).

    Article  CAS  Google Scholar 

  50. G. Duan, D. Xu, and W.L. Johnson, “High copper content bulk glass formation in bimetallic Cu–Hf system,” Metall. Mater. Trans. A, 36, No. 2, 455–458 (2005).

    Article  Google Scholar 

  51. K. Mondal and B. Murty, “On the parameters to assess the glass forming ability of liquids,” J. Non-Cryst. Solids, 351, No. 16–17, 1366–1371 (2005).

    Article  CAS  Google Scholar 

  52. C. Chattopadhyay, “Critical evaluation of glass forming ability criteria,” Mater. Sci. Technol., 32, No. 4, 380–400 (2016).

    Article  CAS  Google Scholar 

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Correspondence to M. A. Turchanin.

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Translated from Poroshkova Metallurgiya, Vol. 61, Nos. 11–12 (548), pp. 94–115, 2022.

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Turchanin, M.A., Agraval, P.G. & Vodopyanova, G.O. Thermodynamic Assessment of the Glass-Forming Cu–Ti–Hf System. Powder Metall Met Ceram 61, 708–726 (2023). https://doi.org/10.1007/s11106-023-00358-5

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