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Pressure-dependent phase diagrams and elastic properties of TixCo1−x: first-principle and Monte-Carlo calculations

  • Regular Article - Statistical and Nonlinear Physics
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Abstract

We investigated (using Monte-Carlo and first-principle calculations) the effect of pressure on the phase diagrams and elastic properties of TixCo1−x (a superalloy candidate). USPEX (Universal Structure Predictor: Evolutionary Xtallography) generated the parent structures required by the Monte-Carlo calculation of the phase diagrams at different pressures (0–100 GPa). The calculated space groups and formation energies qualitatively conform with the experiment within the Co-rich region at 0 GPa. We observed pressure-induced structural transition from the cubic to the tetragonal phase around 80 GPa, comparable with the reported 66 GPa transition pressure. Widening of the phases’ miscibility gaps with the pressure was regarded as an indication for the increase of the melting points. Interestingly, the dependence of the calculated chemical potential on pressure and temperature was consistent with the thermodynamic activity for the binary solid mixture. Finally, enhancement of the elastic properties of the parent structures was observed with increasing pressure.

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All data generated during this study are included in this published article.

References

  1. F. Stein, M. Merali, P. Watermeyer, The Co–Ti system revisited: about the cubic-to-hexagonal Laves phase transformation and other controversial features of the phase diagram. Calphad 67, 101681 (2019)

    Article  Google Scholar 

  2. Y. Zhang, H. Fu, X. Zhou, Y. Zhang, H. Dong, J. Xie, Microstructure evolution of multicomponent γ′-strengthened co-based superalloy at 750° C and 1000° C with different Al and Ti contents. Metall. Mater. Trans. A 51(4), 1755–1770 (2020)

    Article  Google Scholar 

  3. J. Ruan et al., Novel Co-Ti-V-base superalloys reinforced by L12-ordered γ′ phase. Intermetallics 92, 126–132 (2018)

    Article  Google Scholar 

  4. J. Sato, T. Omori, K. Oikawa, I. Ohnuma, R. Kainuma, K. Ishida, Cobalt-base high-temperature alloys. Science 312(5770), 90–91 (2006)

    Article  ADS  Google Scholar 

  5. S. Banerjee, P. Mukhopadhyay, Phase transformations: examples from titanium and zirconium alloys (Elsevier, Amsterdam, 2010)

    Google Scholar 

  6. A. Davydov et al., Determination of the CoTi congruent melting point and thermodynamic reassessment of the Co-Ti system. Metall. Mater. Trans. A 32(9), 2175–2186 (2001)

    Article  Google Scholar 

  7. D.K. Ganji, G. Rajyalakshmi, Influence of alloying compositions on the properties of nickel-based superalloys: a review, in Recent Advances in Mechanical Engineering. (Springer, New York, 2020), pp. 537–555

    Chapter  Google Scholar 

  8. G. Sabol, R. Stickler, Microstructure of nickel-based superalloys. Phys. Status Solidi B 35(1), 11–52 (1969)

    Article  ADS  Google Scholar 

  9. Z. Wen, Y. Zhao, J. Li, H. Hou, Phase stability and thermo-physical properties of nickel-aluminum binary chemically disordered systems via first-principles study. Met. Mater. Int. 27, 1–9 (2019)

    ADS  Google Scholar 

  10. Y. Shin, W.-S. Jung, Y.-S. Lee, First-principles study on the thermal expansion of Ni-X binary alloys based on the quasi-harmonic Debye model. Met. Mater. Int. 22(6), 1065–1072 (2016)

    Article  ADS  Google Scholar 

  11. H.L. Lukas, S.G. Fries, B. Sundman et al., Computational Thermodynamics: The Calphad Method, vol. 131 (Cambridge University Press, Cambridge, 2007)

    Book  Google Scholar 

  12. R.G. Parr, Density functional theory of atoms and molecules, in Horizons of Quantum Chemistry. (Springer, New York, 1980), pp. 5–15

    Chapter  Google Scholar 

  13. M. Debbarma et al., Density functional calculations of elastic and thermal properties of zinc-blende mercury–cadmium-chalcogenide ternary alloys. Met. Mater. Int. 43, 1–16 (2020)

    Google Scholar 

  14. J. Han et al., Phase separation in ternary Co–Gd–Ti liquids. J. Phys. Condens. Matter 25(24), 245104 (2013)

    Article  ADS  Google Scholar 

  15. R. Haleoot, B. Hamad, Thermodynamic and thermoelectric properties of CoFeYGe (Y= Ti, Cr) quaternary Heusler alloys: first principle calculations. J. Phys. Condens. Matter 32(7), 075402 (2019)

    Article  ADS  Google Scholar 

  16. A. van de Walle, G. Ceder, Automating first-principles phase diagram calculations. J. Phase Equilibria 23(4), 348 (2002)

    Article  Google Scholar 

  17. J.M. Sanchez, The cluster expansion method, in Theory and Applications of the Cluster Variation and Path Probability Methods. ed. by J.L. Morán-López, J.M. Sanchez (Springer US, Boston, 1996), pp. 175–185. https://doi.org/10.1007/978-1-4613-0419-7_11

    Chapter  Google Scholar 

  18. J. Čížek, On the use of the cluster expansion and the technique of diagrams in calculations of correlation effects in atoms and molecules. Adv. Chem. Phys. (1969). https://doi.org/10.1002/9780470143599.ch2

    Article  Google Scholar 

  19. W. Zhou, R. Sahara, K. Tsuchiya, First-principles study of the phase stability and elastic properties of Ti-X alloys (X= Mo, Nb, Al, Sn, Zr, Fe Co, and O). J. Alloys Compd. 727, 579–595 (2017)

    Article  Google Scholar 

  20. M.-A. Xue, X. Yuan, C. Zhong, P. Wan, First principles calculations on elastic, thermodynamic and electronic properties of Co2Zr and Co2Ti at high temperature and pressure. Appl. Sci. 10(6), 2097 (2020)

    Article  Google Scholar 

  21. A. Van De Walle, M. Asta, and G. Ceder, The Alloy Theoretic Automated Toolkit: A User Guide. ArXiv Prepr. Cond-Mat0212159, 2002.

  22. C.W. Glass, A.R. Oganov, N. Hansen, USPEX—evolutionary crystal structure prediction. Comput. Phys. Commun. 175(11–12), 713–720 (2006)

    Article  ADS  Google Scholar 

  23. P. Giannozzi et al., QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. J. Phys. Condens. Matter 21(39), 395502 (2009)

    Article  Google Scholar 

  24. Z. Raza, I. Errea, A.R. Oganov, A.M. Saitta, Novel superconducting skutterudite-type phosphorus nitride at high pressure from first-principles calculations. Sci. Rep. 4(1), 1–7 (2014)

    Google Scholar 

  25. Z. Wu, R.E. Cohen, More accurate generalized gradient approximation for solids. Phys. Rev. B 73(23), 235116 (2006)

    Article  ADS  Google Scholar 

  26. H.J. Monkhorst, J.D. Pack, Special points for Brillouin-zone integrations. Phys. Rev. B 13(12), 5188 (1976)

    Article  ADS  MathSciNet  Google Scholar 

  27. A.R. Denton, N.W. Ashcroft, Vegard’s law. Phys. Rev. A 43(6), 3161 (1991)

    Article  ADS  Google Scholar 

  28. J.-O. Andersson, T. Helander, L. Höglund, P. Shi, B. Sundman, Thermo-Calc & DICTRA, computational tools for materials science. Calphad 26(2), 273–312 (2002)

    Article  Google Scholar 

  29. A.K. Kushwaha, C.G. Ma, M.G. Brik, S. Bin Omran, R. Khenata, Zone-center phonons and elastic properties of ternary chalcopyrite ABSe 2 (A = Cu and Ag; B = al, Ga and In). Mater. Chem. Phys. 227(January), 324–331 (2019). https://doi.org/10.1016/j.matchemphys.2019.02.024

    Article  Google Scholar 

  30. Charpin, T., A package for CalCulating elastic tensors of cubic phases using WIEN.

  31. P. Blaha, K. Schwarz, G.K.H.M.D.K.J. Luitz, R.L.F. Tran, L.D. Marks, WIEN2k, vol. 1 (University of Technology, Vienna, 2019)

    Google Scholar 

  32. R. Golesorkhtabar, P. Pavone, J. Spitaler, P. Puschnig, C. Draxl, ElaStic: a tool for calculating second-order elastic constants from first principles. Comput. Phys. Commun. 184(8), 1861–1873 (2013). https://doi.org/10.1016/j.cpc.2013.03.010

    Article  ADS  Google Scholar 

  33. H.T. Stokes, D.M. Hatch, FINDSYM: program for identifying the space-group symmetry of a crystal. J. Appl. Crystallogr. 38(1), 237–238 (2005)

    Article  Google Scholar 

  34. H. T. Stokes, D. M. Hatch, B. J. Campbell, ISOTROPY Software Suite. https://iso.byu.edu/iso/isotropy.php. Accessed 3 Sep 2021.

  35. D. Hicks et al., The AFLOW library of crystallographic prototypes: part 2. Comput. Mater. Sci. 161, S1–S1011 (2019)

    Article  Google Scholar 

  36. S. Trolier-McKinstry and R. E. Newnham, Materials engineering: bonding, structure, and structure-property relationships. Cambridge University Press, 2018.

  37. K.K. Sharma, L. Sharma, A Textbook of Physical Chemistry (Vikas Publishing House, Ahmedabad, 2016)

    Google Scholar 

  38. A. D. McNaught, A. Wilkinson, IUPAC. Compendium of Chemical Terminology, 2nd ed. Blackwell Scientific Publications, Oxford (1997). Online version (2019-) created by S. J. Chalk. [Online]. https://goldbook.iupac.org/terms/view/A00116

  39. R. Murugeswari, R. Rajeswarapalanichamy, A.M.F. Benial, Pressure-induced phase transition in titanium alloys. Int. J. Mod. Phys. B 32(12), 1850141 (2018)

    Article  ADS  Google Scholar 

  40. S. Amari, R. Mebsout, S. Méçabih, B. Abbar, B. Bouhafs, First-principle study of magnetic, elastic and thermal properties of full Heusler Co2MnSi. Intermetallics 44, 26–30 (2014). https://doi.org/10.1016/j.intermet.2013.08.009

    Article  Google Scholar 

  41. A. Azzouz-Rached, M.A. Hadi, H. Rached, T. Hadji, D. Rached, A. Bouhemadou, Pressure effects on the structural, elastic, magnetic and thermodynamic properties of Mn2AlC and Mn2SiC MAX phases. J. Alloys Compd. (2021). https://doi.org/10.1016/j.jallcom.2021.160998

    Article  Google Scholar 

  42. M. Fine, L. Brown, H. Marcus, Elastic constants versus melting temperature in metals. Scr. Metall. 18, 951–956 (1984)

    Article  Google Scholar 

  43. Z.L.Y. Li, X. Juan, Q. Liu, F. Liu, H. Ma, G. Kong, First-principles calculations of the structural, elastic and thermodynamic properties of tetragonal copper-titanium intermetallic compounds. J. Alloys Compd. 687, 984–989 (2016)

    Article  Google Scholar 

  44. R. Hill, The elastic behaviour of a crystalline aggregate. Proc. Phys. Soc. 65(5), 349–354 (1952)

    Article  ADS  Google Scholar 

  45. H. Liu et al., The pressure-effects on phase transitions, band structures, electronic and elastic properties of ternary compounds ZnXP 2 (X = Si, Ge, Sn) by first principle calculations. Mater. Res. Express 5, 126303 (2018). https://doi.org/10.1088/2053-1591/aae11e

    Article  ADS  Google Scholar 

  46. R. Jain, V.K. Jain, A.R. Chandra, V. Jain, N. Lakshmi, Study of the electronic structure, magnetic and elastic properties and half-metallic stability on variation of lattice constants for CoFeCrZ (Z = P, As, Sb) Heusler alloys. J. Supercond. Nov. Magn. 31(8), 2399–2409 (2018). https://doi.org/10.1007/s10948-017-4460-3

    Article  Google Scholar 

  47. S. Tariq, A. Batool, M.A. Faridi, M. Imran Jamil, A.A. Mubarak, N. Akbar, Influence of pressure on electro-mechanical properties of SrNbO3: a DFT study. High Temp. High Press. 48(5–6), 399–411 (2019). https://doi.org/10.32908/hthp.v48.763

    Article  Google Scholar 

  48. A.A. Mubarak, The first-principle study of the electronic, optical and thermoelectric properties of XTiO 3 (X = Ca, Sr and Ba) compounds. Int. J. Mod. Phys. B 30(20), 1–24 (2016). https://doi.org/10.1142/S0217979216501411

    Article  Google Scholar 

  49. Z. Li, M. Yang, J.S. Park, S.H. Wei, J.J. Berry, K. Zhu, Stabilizing perovskite structures by tuning tolerance factor: formation of formamidinium and cesium lead iodide solid-state alloys. Chem. Mater. 28(1), 284–292 (2016). https://doi.org/10.1021/ACS.CHEMMATER.5B04107

    Article  Google Scholar 

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Contributions

BA: conceptualization, methodology, software, formal analysis, investigation, writing—original draft. AMI: conceptualization, methodology. MAHK: conceptualization, methodology, software, formal analysis, investigation, resources, writing—original draft, writing—review and editing, supervision.

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Correspondence to Mohammed A. H. Khalafalla.

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Alsobhi, B.O., Ibraheem, A.M. & Khalafalla, M.A.H. Pressure-dependent phase diagrams and elastic properties of TixCo1−x: first-principle and Monte-Carlo calculations. Eur. Phys. J. B 95, 51 (2022). https://doi.org/10.1140/epjb/s10051-022-00310-3

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