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.
Similar content being viewed by others
References
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.
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.
R.K. Jyothi, Rare-earth Metal Recovery for Green Technologies: Methods and Applications, Springer Nature, 2020.
A.R. Jha, Rare earth materials: properties and applications, CRC Press, 2014.
V.R. Sastri, J. Perumareddi, V.R. Rao, G. Rayudu, and J.-C. Bünzli, Modern aspects of rare earths and their complexes, Elsevier, 2003.
N. Alonso-Vante, Chalcogenide Materials for Energy Conversion: Pathways to Oxygen and Hydrogen Reactions, Springer, 2018.
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.
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.
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.
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.
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.
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.
H.L. Lukas, S.G. Fries, and B. Sundman, Computational thermodynamics: the Calphad method. Cambridge University Press, Cambridge, 2007.
L. Kaufman, H. Bernstein, Computer Calculation of Phase Diagrams with Special Reference to Refractory Metals, Academic Press, 1970.
N. Saunders, and A.P. Miodownik, CALPHAD (calculation of phase diagrams): a comprehensive guide, Elsevier, 1998.
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.
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.
M. Abdusalyamova, and O. Rachmatov, The investigation of phase diagrams of erbium pnictides, Zeitschrift für Naturforschung A, 2002, 57(1–2), p 98–100.
T.B. Massalski, and O. Okamoto, ASM International, Binary alloy phase diagrams, 2nd ed., Materials Park, Ohio : ASM International, 1990.
W.G. Moffatt, The handbook of binary phase diagrams, General Electric, Schenectady, N.Y., 1981.
K. Yoshihara, J. Taylor, L. Calvert, and J. Despault, Rare-earth bismuthides, Journal of the Less Common Metals, 1975, 41(2), p 329–337.
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.
K. Gschneidner, and F. Calderwood, The bismuth-rare earth systems, Bulletin of Alloy Phase Diagrams, 1989, 10(4), p 419–427.
K. Gschneidner, and F. Calderwood, The Bi−Er (Bismuth-Erbium) system, Bulletin of Alloy Phase Diagrams, 1989, 10(4), p 433–434.
H. Okamoto, and Bi-Er (bismuth-erbium), Journal of Phase Equilibria, 1997, 18(6), p 671.
V. Abulkhaev, Phase diagram of the system Er-Bi, Inorg. Mater., 1993, 28(10–11), p 1717–1720.
A. Iandelli, Rare Earth Research (E. v. Kleber), McMillan, New York, 1961, Atti accad. nazl. Lincei, 1961, 30, p 201.
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.
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.
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.
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.
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.
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
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.
V. Sidorko, Thermodynamic properties of erbium monobismuthide, Powder Metall. Met. Ceram., 2011, 50(5–6), p 350–355.
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.
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.
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.
E. Abrikosov, L. Poretskaya, and E. Skudnova, Rare Earth Metals, Alloys and Compounds, ed., Moscow: Nauka, 1973
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.
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.
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.
K. Stoewe, Crystal Structure, Conductivity, and Magnetic Susceptibility of Er2Te3, Z. Anorg. Allg. Chem., 1998, 624, p 872–876.
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
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.
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.
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.
V. Vassiliev, and V. Lysenko, A new approach for the study of thermodynamic properties of lanthanide compounds, Electrochim. Acta, 2016, 222, p 1770–1777.
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.
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.
K.C. Mills, Thermodynamic data for inorganic sulphides, selenides and tellurides, Butterworths, 1974.
W. Kohn, and L.J. Sham, Self-Consistent Equations Including Exchange and Correlation Effects, Phys. Rev., 1965, 140(4A), p A1133–A1138.
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.
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.
G. Kresse, and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B, 1999, 59(3), p 1758–1775.
P.E. Blöchl, Projector augmented-wave method, Phys. Rev. B, 1994, 50(24), p 17953–17979.
J.P. Perdew, K. Burke, and M. Ernzerhof, Generalized Gradient Approximation Made Simple, Phys. Rev. Lett., 1996, 77(18), p 3865–3868.
Z. Liu, First-principles calculations and CALPHAD modeling of thermodynamics, J. Phase Equilib. Diffus., 2009, 30(5), p 517–534.
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.
A.T. Dinsdale, SGTE data for pure elements, Calphad, 1991, 15(4), p 317–425.
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.
F. Sommer, Association model for the description of thermodynamic functions of liquid alloys, Z. Met., 1982, 73(2), p 77–86.
G. Kresse, M. Marsman, and J. Furthmüller, VASP the guide, University of Vienna, 2012.
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.
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.
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.
B. Sundman, B. Jansson, and J.O. Andersson, The thermo-calc databank system, Calphad, 1985, 9(2), p 153–190.
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
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
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11669-022-00947-8