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Thermodynamic Study of Er-Bi and Er-Te Systems by Combination of First-Principles Calculations and the CALPHAD Method

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Abstract

The CALPHAD method combined with first-principles calculations was used to estimate the thermodynamic properties of the intermediate phases in the Er-Bi and Er-Te systems and thermodynamic descriptions of the phase diagrams of these systems. The enthalpies of formation of the ErBi2, ErBi, Er5Bi3, ErTe3, Er2Te3, and ErTe compounds at 0 K were calculated by first-principles method to supply the thermochemical data for this optimization. The associated solution model was used to describe the Gibbs energy of the liquid phase of both systems, while the intermetallic phases were modeled as stoichiometric compounds. A set of self-consistent thermodynamic parameters of the Er-Bi and Er-Te systems is obtained.

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References

  1. B. Zhou, Z. Li, Y. Zhao, C. Zhang, and Y. Wei, Rare Earth Elements supply vs. clean energy technologies: new problems to be solve, Gospodarka Surowcami Mineralnymi, 2016, 32, p 29−44.

  2. B.S. Van Gosen, P.L. Verplanck, K.R. Long, J. and Gambogi, R.R. Seal II, The rare-earth elements: vital to modern technologies and lifestyles, Report No. 2327-6932, U.S. Geological Survey, 2014.

  3. R.K. Jyothi, Rare-earth Metal Recovery for Green Technologies: Methods and Applications, Springer Nature, 2020.

  4. A.R. Jha, Rare earth materials: properties and applications, CRC Press, 2014.

  5. V.R. Sastri, J. Perumareddi, V.R. Rao, G. Rayudu, and J.-C. Bünzli, Modern aspects of rare earths and their complexes, Elsevier, 2003.

  6. N. Alonso-Vante, Chalcogenide Materials for Energy Conversion: Pathways to Oxygen and Hydrogen Reactions, Springer, 2018.

  7. Y. Tang, B. Hu, J. Wang, Q. Gao, Y. Du, X. Yuan, and D. Živković, Thermodynamic modeling of the La-B and La-Bi systems supported by first-principles calculations, J. Phase Equilib. Diffus., 2013, 34(4), p 297–306.

    Article  Google Scholar 

  8. M. Shevchenko, M. Ivanov, V. Berezutski, and V. Sudavtsova, Thermodynamic properties of alloys of the binary Bi-Yb system, Russ. J. Phys. Chem. A, 2016, 90(4), p 723–734.

    Article  Google Scholar 

  9. Y. Djaballah, A.S. Amer, Ş Uğur, G. Uğur, A. Hidoussi, and A. Belgacem-Bouzida, Thermodynamic description of the Bi–Cs and Bi–Tm system supported by first-principles calculations, Calphad, 2015, 48, p 72–78.

    Article  Google Scholar 

  10. C. Wang, H. Zhang, A. Tang, F. Pan, and X. Liu, Thermodynamic assessments of the Bi–Nd and Bi–Tm systems, J. Alloy. Compd., 2010, 502(1), p 43–48.

    Article  Google Scholar 

  11. J. Wang, C. Li, C. Guo, Z. Du, and B. Wu, Thermodynamic assessment of the Gd–Bi and the Ho–Bi systems, Calphad, 2013, 41, p 1–5.

    Article  Google Scholar 

  12. S. Wang, Z. Hu, F. Gao, C. Wang, and X. Liu, Thermodynamic assessments of the Bi-Tb and Bi-Y systems, J. Phase Equilib. Diffus., 2011, 32(5), p 441–446.

    Article  Google Scholar 

  13. H.L. Lukas, S.G. Fries, and B. Sundman, Computational thermodynamics: the Calphad method. Cambridge University Press, Cambridge, 2007.

    Book  MATH  Google Scholar 

  14. L. Kaufman, H. Bernstein, Computer Calculation of Phase Diagrams with Special Reference to Refractory Metals, Academic Press, 1970.

  15. N. Saunders, and A.P. Miodownik, CALPHAD (calculation of phase diagrams): a comprehensive guide, Elsevier, 1998.

  16. J. Wang, C. Li, C. Guo, Z. Du, and B. Wu, Thermodynamic assessment of the Bi–Er and the Bi–Dy systems, Thermochim. Acta, 2013, 566, p 44–49.

    Article  Google Scholar 

  17. Y. Wang, W. Zhou, S. Guo, and J. Zhang, Thermodynamic properties of fission products (Pr, Ce, Er) in liquid bismuth by thermodynamic assessment, J. Nucl. Mater., 2017, 495, p 181–191.

    Article  Google Scholar 

  18. M. Abdusalyamova, and O. Rachmatov, The investigation of phase diagrams of erbium pnictides, Zeitschrift für Naturforschung A, 2002, 57(1–2), p 98–100.

    Article  Google Scholar 

  19. T.B. Massalski, and O. Okamoto, ASM International, Binary alloy phase diagrams, 2nd ed., Materials Park, Ohio : ASM International, 1990.

  20. W.G. Moffatt, The handbook of binary phase diagrams, General Electric, Schenectady, N.Y., 1981.

  21. K. Yoshihara, J. Taylor, L. Calvert, and J. Despault, Rare-earth bismuthides, Journal of the Less Common Metals, 1975, 41(2), p 329–337.

    Article  Google Scholar 

  22. B. Kovenskaya, M. Abdusalamova, M. Abdusalyamova, and V. Abulkhaev, Thermal and physical properties of rare earth metal yttrium subgroup monobismuthides, Teplofiz. Vys. Temp., 1977, 15(5), p 1000–1004.

    Google Scholar 

  23. K. Gschneidner, and F. Calderwood, The bismuth-rare earth systems, Bulletin of Alloy Phase Diagrams, 1989, 10(4), p 419–427.

    Article  Google Scholar 

  24. K. Gschneidner, and F. Calderwood, The Bi−Er (Bismuth-Erbium) system, Bulletin of Alloy Phase Diagrams, 1989, 10(4), p 433–434.

    Article  Google Scholar 

  25. H. Okamoto, and Bi-Er (bismuth-erbium), Journal of Phase Equilibria, 1997, 18(6), p 671.

  26. V. Abulkhaev, Phase diagram of the system Er-Bi, Inorg. Mater., 1993, 28(10–11), p 1717–1720.

    Google Scholar 

  27. A. Iandelli, Rare Earth Research (E. v. Kleber), McMillan, New York, 1961, Atti accad. nazl. Lincei, 1961, 30, p 201.

  28. H. Okamoto, Supplemental literature review of binary phase diagrams: Bi-Ce, Bi-Er, C-Ce, C-La, C-Pr, Cd-I, Cr-Cu, Cu-Er, Er-Sb, F-Sm, F-Yb, and Fe-Gd, J. Phase Equilib. Diffus., 2013, 34(4), p 350–362.

    Article  Google Scholar 

  29. R. Robinson, A. Purwanto, M. Kohgi, P.C. Canfield, T. Kamiyama, T. Ishigaki, J. Lynn, R. Erwin, E. Peterson, and R. Movshovich, Crystallography and magnetism of the heavy-fermion compound YbBiPt, Phys. Rev. B, 1994, 50(13), p 9595–9598.

    Article  Google Scholar 

  30. M. Drzyzga, and J. Szade, Structure and magnetism of R5Bi3 (R= Tb, Dy, Ho, Er) and Tb4Bi3, J. Alloy. Compd., 2001, 321(1), p 27–34.

    Article  Google Scholar 

  31. M.G. Pravica, E. Romano, and Z. Quine, X-ray diffraction study of elemental erbium to 70 GPa, Physical Review B, 2005, 72(21), p 214122.

  32. L. Yamshchikov, V. Lebedev, I. Nichkov, S. Raspopin, and B. Karmanov, Thermodynamics properties of molten alloys of erbium with low-melting metals, Termodin. Svoistva Met. Rasplavov, Mater. Vses Soveshch. Termodin. Met. Splavov (Rasplavy), 1979, 2, p 181-185.

  33. S. Petrashkevich, V. Degtyar, L. Vnuchkova, and V. Serebrennikov, Interaction of erbium with bismuth and aluminum, 2nd All-Union Conf. Constitution and Properties of Metal and Sludge Melts, 1976, p 12

  34. G. Borzone, N. Parodi, and R. Ferro, Contribution to the thermochemistry of rare earth pnictides: The Sm-Bi system, Journal of Phase Equilibria, 1993, 14(4), p 485–493.

    Article  Google Scholar 

  35. V. Sidorko, Thermodynamic properties of erbium monobismuthide, Powder Metall. Met. Ceram., 2011, 50(5–6), p 350–355.

    Article  Google Scholar 

  36. C. Colinet, A. Pasturel, A. Percheron-Guegan, and J. Achard, Enthalpies of formation of liquid and solid binary alloys of lead, antimony and bismuth with rare earth elements, J Less Common Metals, 1984, 102(2), p 239–249.

    Article  Google Scholar 

  37. A. Takeuchi, and A. Inoue, Classification of bulk metallic glasses by atomic size difference, heat of mixing and period of constituent elements and its application to characterization of the main alloying element, Mater. Trans., 2005, 46(12), p 2817–2829.

    Article  Google Scholar 

  38. D. Haase, H. Steinfink, and E. Weiss, The Phase Equilibria and Crystal Chemistry of the Rare Earth Group VI Systems. II. Erbium-Tellurium, Inorganic chemistry, 1965, 4(4), p 541-543.

  39. E. Abrikosov, L. Poretskaya, and E. Skudnova, Rare Earth Metals, Alloys and Compounds, ed., Moscow: Nauka, 1973

  40. V.P. Vassiliev, V.I. Goriatcheva, and J.I. Gerasimov, Study of the Phase Equilibrium and Thermodynamic Properties of Er-Te Alloys, Solid State, Vestnik Moskovskogo Universiteta, Serie2, Chimie, 1980, 21, p 339–344.

    Google Scholar 

  41. I. Hinz, P. Kuhn, U. Vetter, E. Warkentin, H. Bergmann, and H. Hein, Rare Earth Elements and Tellurium, Gmelin Handbook of Inorganic Chemistry, H. Bergmann, H. Hein, I. Hinz, U. Vetter, Eds., Springer, Berlin, Heidelberg, 1986, p 247-251.

  42. G. Zhang, Z. Yongzhong, and L. Chunliu, Phase diagram of Er-Sn-Te system for diluted magnetic semiconductor developments, J. Rare Earths, 2013, 31(8), p 800–803.

    Article  Google Scholar 

  43. K. Stoewe, Crystal Structure, Conductivity, and Magnetic Susceptibility of Er2Te3, Z. Anorg. Allg. Chem., 1998, 624, p 872–876.

    Google Scholar 

  44. A. Khan, and C. Garcia, Crystal growth and phase studies in ternary rare earth (Ln) tellurides, Proceedings of the 12th rare earth research conference. Vol. II, 1976

  45. J.F. Cannon, and H.T. Hall, High-pressure, high-temperature syntheses of selected lanthanide-tellurium compounds, Inorg. Chem., 1970, 9(7), p 1639–1643.

    Article  Google Scholar 

  46. Y. Ohmasa, I. Yamamoto, M. Yao, and H. Endo, Structure and Electronic Properties of Te-Se Mixtures under High Pressure, J. Phys. Soc. Jpn., 1995, 64(12), p 4766–4789.

    Article  Google Scholar 

  47. L. Brixner, Structure and electrical properties of some new rare earth arsenides, antimonides and tellurides, J. Inorg. Nucl. Chem., 1960, 15(1–2), p 199–201.

    Article  Google Scholar 

  48. V. Vassiliev, and V. Lysenko, A new approach for the study of thermodynamic properties of lanthanide compounds, Electrochim. Acta, 2016, 222, p 1770–1777.

    Article  Google Scholar 

  49. V.P. Vassiliev, V.A. Lysenko, and M. Gaune-Escard, Relationship of thermodynamic data with Periodic Law, Pure Appl. Chem., 2019, 91(6), p 879–893.

    Article  Google Scholar 

  50. S. Imamaliyeva, I. Mehdiyeva, D. Taghiyev, and M. Babanly, Thermodynamic investigations of the erbium tellurides by EMF method, Physics and chemistry of solid state, 2020, 21(2), p 312–318.

    Article  Google Scholar 

  51. K.C. Mills, Thermodynamic data for inorganic sulphides, selenides and tellurides, Butterworths, 1974.

  52. W. Kohn, and L.J. Sham, Self-Consistent Equations Including Exchange and Correlation Effects, Phys. Rev., 1965, 140(4A), p A1133–A1138.

    Article  MathSciNet  Google Scholar 

  53. G. Kresse, and J. Furthmüller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mater. Sci., 1996, 6(1), p 15–50.

    Article  Google Scholar 

  54. G. Kresse, and J. Furthmüller, 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  Google Scholar 

  55. G. Kresse, and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B, 1999, 59(3), p 1758–1775.

    Article  Google Scholar 

  56. P.E. Blöchl, Projector augmented-wave method, Phys. Rev. B, 1994, 50(24), p 17953–17979.

    Article  Google Scholar 

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

    Article  Google Scholar 

  58. Z. Liu, First-principles calculations and CALPHAD modeling of thermodynamics, J. Phase Equilib. Diffus., 2009, 30(5), p 517–534.

    Article  Google Scholar 

  59. C. Colinet, Ab-initio calculation of enthalpies of formation of intermetallic compounds and enthalpies of mixing of solid solutions, Intermetallics, 2003, 11(11–12), p 1095–1102.

    Article  Google Scholar 

  60. A.T. Dinsdale, SGTE data for pure elements, Calphad, 1991, 15(4), p 317–425.

    Article  Google Scholar 

  61. O. Redlich, and A.T. Kister, Thermodynamics of nonelectrolyte solutions x-y-t relations in a binary system, Ind. Eng. Chem., 1948, 40(2), p 341–345.

    Article  Google Scholar 

  62. F. Sommer, Association model for the description of thermodynamic functions of liquid alloys, Z. Met., 1982, 73(2), p 77–86.

    Google Scholar 

  63. G. Kresse, M. Marsman, and J. Furthmüller, VASP the guide, University of Vienna, 2012.

  64. S. Kirklin, J.E. Saal, B. Meredig, A. Thompson, J.W. Doak, M. Aykol, S. Rühl, and C. Wolverton, The Open Quantum Materials Database (OQMD): assessing the accuracy of DFT formation energies, npj Computational Materials, 2015, 1(1), p 1-15.

  65. A. Jain, S.P. Ong, G. Hautier, W. Chen, W.D. Richards, S. Dacek, S. Cholia, D. Gunter, D. Skinner, and G. Ceder, Commentary: The Materials Project: A materials genome approach to accelerating materials innovation, APL materials, 2013, 1(1), p 011002.

  66. C. Oses, E. Gossett, D. Hicks, F. Rose, M.J. Mehl, E. Perim, I. Takeuchi, S. Sanvito, M. Scheffler, and Y. Lederer, AFLOW-CHULL: cloud-oriented platform for autonomous phase stability analysis, J. Chem. Inf. Model., 2018, 58(12), p 2477–2490.

    Article  Google Scholar 

  67. B. Sundman, B. Jansson, and J.O. Andersson, The thermo-calc databank system, Calphad, 1985, 9(2), p 153–190.

    Article  Google Scholar 

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Acknowledgments

We acknowledge the financial assistance of the Directorate General for Research and Technological Development (DGRSDT)-Algeria (Grant No 02/UNIV-BATNA1/DGRSDT /2019), and Prof. Lorie Wood from the University of Colorado (USA) for the language help.

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Bennoui, S., Djaballah, Y., Vassiliev, V. et al. Thermodynamic Study of Er-Bi and Er-Te Systems by Combination of First-Principles Calculations and the CALPHAD Method. J. Phase Equilib. Diffus. 43, 126–138 (2022). https://doi.org/10.1007/s11669-022-00947-8

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