Skip to main content
Log in

Thermodynamic Properties of Alloys in the Binary Ca–Ge System

  • Published:
Journal of Phase Equilibria and Diffusion Aims and scope Submit manuscript

Abstract

Mixing enthalpies of the liquid alloys in the binary Ca–Ge system were measured by isoperibolic solution calorimetry within the concentration ranges 0 < x Ge < 0.08 at 1270–1300 K, and 0.54 < x Ge < 1 at 1370–1520 K. The experimental data show great exothermic effects of alloy formation; the partial mixing enthalpies at infinite dilution of the components are \( \Delta \overline{H}_{\text{Ca}}^{\infty } \) = −138 to −140 kJ mol−1 and \( \Delta \overline{H}_{\text{Ge}}^{\infty } \) = −200 kJ mol−1 (at 1300 K). The Gibbs energies and entropies of mixing, activities of the components, and molar fractions of associates in the melts were calculated over a wide temperature range, using models of ideal and regular associated solutions, according to the data in literature for the thermodynamic properties of solid alloys and the phase diagram of the Ca–Ge system.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. M. Notin, J. Mejbar, A. Bouhajib, J. Charles, and J. Hertz, The thermodynamic properties of calcium intermetallic compounds, J. Alloys Compd., 1995, 220, p 62-75. doi:10.1016/0925-8388(94)06001-0

    Article  Google Scholar 

  2. J. Mejbar, These de Doctorat, l’Universite de Nancy I (24 September 1993).

  3. Z. Yang, D. Shi, B. Wen, R. Melnik, S. Yao, and T. Li, First-principle studies of Ca–X (X = Si, Ge, Sn, Pb) intermetallic compounds, J. Solid State Chem., 2010, 183, p 136-143. doi:10.1016/j.jssc.2009.11.007

    Article  ADS  Google Scholar 

  4. Y. Djaballah, A. Pasturel, and A. Belgacem-Bouzida, Thermodynamic assessment of the calcium–germanium system, J. Alloys Compd., 2010, 497, p 74-79. doi:10.1016/j.jallcom.2010.02.189

    Article  Google Scholar 

  5. B. Predel, Ca–Ge (Calcium–Germanium), Landolt-Börnstein-Group IV Physical Chemistry, Springer-Verlag, Berlin Heidelberg, 2012, 12B, p 160-161. doi:10.1007/978-3-540-44756-6_111

    Article  Google Scholar 

  6. I.V. Nikolaenko, G.I. Batalin, E.A. Beloborodova, and M.A. Turchanin, Enthalpy of mixing of calcium with germanium, Metally, 1987, 2, p 39-40 (in Russian)

    Google Scholar 

  7. V.V. Litovskii, Enthalpies of formation of the binary alloys of earth-alkaline metals with silicon, germanium and tin, Synopsis of diss. Cand. Phys.-Math. Sci., Sverdlovsk (1986) (in Russian)

  8. Yu.O. Yesin, V.V. Litovskii, and M.S. Petrushevskii, Partial and integral enthalpies of formation of the liquid alloys of calcium with silicon, germanium and tin, in V Union Conference on the thermodynamics of metallic alloys, Moscow (19–21 March 1985) 13 (in Russian).

  9. K.A. Bolshakov, E.B. Sokolov, P.I. Fedorov, and A.V. Chirkin, Investigation of the melting diagram of the germanium–calcium system by the method of thermal analysis, Inorg. Mater., 1965, 1(10), p 1646 (in Russ. original, p 1822–1825).

  10. T.B. Massalski, Binary Alloy Phase Diagrams, ASM International, Materials Park, 1990

    Google Scholar 

  11. A. Palenzona, P. Manfrinetti, and M.L. Fornasini, The phase diagram of the Ca–Ge system, J. Alloys Compd., 2002, 345, p 144-147. doi:10.1016/S0925-8388(02)00326-2

    Article  Google Scholar 

  12. H. Okamoto, Ca-Ge (Calcium-Germanium), J. Phase Equilib. Diff., 2013, 34(2), p 172-173. doi:10.1007/s11669-012-0179-9

    Article  Google Scholar 

  13. P.H. Tobash and S. Bobev, Synthesis, structure and electronic structure of a new polymorph of CaGe2, J. Solid State Chem., 2007, 180, p 1575-1581. doi:10.1016/j.jssc.2007.03.003

    Article  ADS  Google Scholar 

  14. H. Bouderba, Y. Djaballah, A. Belgacem-Bouzida, and R. Beddiaf, Temperature and pressure effects on phase stabilities in the Ca–Ge system from first-principles calculations and Debye-Gruneisen model, Intermetallics, 2012, 28, p 108-119. doi:10.1016/j.intermet.2012.04.013

    Article  Google Scholar 

  15. M. Ivanov, V. Berezutski, and N. Usenko, Mixing enthalpies in liquid alloys of manganese with the lanthanides, Int. J. Mater. Res., 2011, 102(3), p 277-281. doi:10.3139/146.110474

    Article  Google Scholar 

  16. A.T. Dinsdale, SGTE data for pure elements, CALPHAD, 1991, 15, p 319-427. doi:10.1016/0364-5916(91)90030-N

    Article  Google Scholar 

  17. I. Barin, Thermochemical data of pure substances, VCH, Weinheim; New York; Basel; Cambridge; Tokyo, 1995

    Book  Google Scholar 

  18. D.R. Lide (ed), CRC Handbook of Chemistry and Physics, 84th Edition. CRC Press. Boca Raton, Florida (2003); Section 6, Fluid Properties; Vapor Pressure.

  19. M.I. Ivanov, V.V. Berezutski, M.O. Shevchenko, V.G. Kudin, and V.S. Sudavtsova, Interaction in the alloys of the systems containing europium, Dopovidi (Reports) NAS of Ukraine, 2013, 8, p 90-99 (in Ukrainian)

    Google Scholar 

  20. V.G. Kudin, M.A. Shevchenko, I.V. Mateiko, and V.S. Sudavtsova, Thermodynamic properties of melts of the Al-La system, Russ. J. Phys. Chem., 2013, 87(3), p 364-370 (in Russian)

    Google Scholar 

  21. V.S. Sudavtsova, M.I. Ivanov, V.V. Berezutski, V.G. Kudin, and M.A. Shevchenko, Enthalpy of mixing of the Al–Yb melts, Russ. J. Phys. Chem., 2012, 86(8), p 1311-1315 (in Russian)

    Google Scholar 

  22. M.A. Shevchenko, V.G. Kudin, N.G. Kobylinskaya, and V.S. Sudavtsova, Thermodynamic properties and phase diagram of the Ce–Si system, Ukr. Chem. J., 2012, 78(6), p 96-102 (in Russian)

    Google Scholar 

  23. V.V. Berezutskii, M.A. Shevchenko, M.I. Ivanov, and V.S. Sudavtsova, Thermodynamic properties of liquid alloys Ni–Eu and Ni–Yb, Russ. J. Phys. Chem. A, 2014, 88(9), p 1463-1471. doi:10.1134/S0036024414090064

    Article  Google Scholar 

  24. G. Kaptay, On the abilities and limitations of the linear, exponential and combined models to describe the temperature dependence of the excess Gibbs energy of solutions, CALPHAD, 2014, 44, p 81-94. doi:10.1016/j.calphad.2013.08.007

    Article  Google Scholar 

  25. G. Kaptay, On the tendency of solutions to tend towards ideal solutions at high temperatures, Metall. Mater. Trans. A, 2012, 43, p 531-543. doi:10.1007/s11661-011-0902-x

    Article  Google Scholar 

  26. M. Ohno, A. Kozlov, R. Arroyave, Z.K. Liu, and R. Schmid-Fetzer, Thermodynamic modeling of the Ca-Sn system based on finite temperature quantities from first-principles and experiment, Acta Mater., 2006, 54, p 4939-4951. doi:10.1016/j.actamat.2006.06.017

    Article  Google Scholar 

  27. K. Li, S. Liu, C. Sha, and Y. Du, A thermodynamic reassessment of the Si-Sr system, CALPHAD, 2011, 35, p 594-600. doi:10.1016/j.calphad.2011.09.007

    Article  Google Scholar 

  28. M. Idbenali, C. Servant, N. Selhaoui, and L. Bouirden, A thermodynamic reassessment of the Ca–Pb system, CALPHAD, 2008, 32, p 64-73. doi:10.1016/j.calphad.2007.10.004

    Article  Google Scholar 

  29. C.B. Alcock, M.W. Chase, and V. Itkin, Thermodynamic properties of the Group IIA Elements, J. Phys. Chem. Ref. Data, 1993, 22(1), p 1-85. doi:10.1063/1.555935

    Article  ADS  Google Scholar 

  30. A.A.A.P. da Silva, G.C. Coelho, C.A. Nunes, P.A. Suzuki, J.M. Fiorani, N. David, and M. Vilasi, Experimental determination of the Ta–Ge phase diagram, J. Alloys Compd., 2013, 576, p 38-42. doi:10.1016/j.jallcom.2013.04.070

    Article  Google Scholar 

  31. F.R. de Boer, R. Boom, W.C.M. Mattens, A.R. Miedema, and A.K. Niessen, Cohesion in Metals Transition Metal Alloys, North Holland, Amsterdam, 1988

    Google Scholar 

  32. T. Geng, C. Li, Z. Du, C. Guo, X. Zhao, and H. Xu, Thermodynamic assessment of the Nb–Ge system, J. Alloys Compd., 2011, 509, p 3080-3088. doi:10.1016/j.jallcom.2010.12.005

    Article  Google Scholar 

  33. E.A. Beloborodova, Thermodynamic properties of liquid alloys of germanium with d-transition metals, Powder Metall. Metal Ceram., 1996, 35(7–8), p 389-391

    Article  Google Scholar 

  34. I.H. Jung, D.H. Kang, W.J. Park, N.J. Kim, and S.H. Ahn, Thermodynamic modeling of the Mg–Si–Sn system, CALPHAD, 2007, 31, p 192-200. doi:10.1016/j.calphad.2006.12.003

    Article  Google Scholar 

  35. D. Nassyrov and I.H. Jung, Thermodynamic modeling of the Mg–Ge–Pb system, CALPHAD, 2009, 33, p 521-529. doi:10.1016/j.calphad.2009.01.005

    Article  Google Scholar 

  36. M. Heyrman and P. Chartrand, Thermodynamic evaluation and optimization of the Ca–Si system, J. Phase Equilib. Diff., 2006, 27(3), p 220-230. doi:10.1361/154770306X109755

    Article  Google Scholar 

  37. Y. Du, L. Li, J. Wang, J. Wang, and Z. Jin, A thermodynamic description of the Ge–Sr system acquired via a hybrid approach of CALPHAD and first-principles calculations, CALPHAD, 2009, 33, p 719-722. doi:10.1016/j.calphad.2009.09.004

    Article  Google Scholar 

  38. J. Zhao, Y. Du, L. Zhang, A. Wang, L. Zhou, D. Zhao, and J. Liang, Thermodynamic assessment of the Sn–Sr system supported by first-principles calculations, Thermochim. Acta, 2012, 529, p 74-79. doi:10.1016/j.tca.2011.11.026

    Article  Google Scholar 

  39. G. Bruzzone, E. Franceschi, and F. Merlo, On the Sr–Pb system, J. Less Common Met., 1981, 81, p 155-160

    Article  Google Scholar 

  40. H. Okamoto, Ba–Si (Barium–Silicon), J. Phase Equilib. Diff., 2008, 29(5), p 464. doi:10.1007/s11669-008-9361-5

    Article  Google Scholar 

  41. H. Okamoto, Ba–Ge (Barium–Germanium), J. Phase Equilib. Diff., 2009, 30(1), p 114. doi:10.1007/s11669-008-9428-3

    Article  Google Scholar 

  42. M. Idbenali, C. Servant, N. Selhaoui, and L. Bouirden, A thermodynamic modelling of the Ba–Pb system, CALPHAD, 2007, 31, p 479-489. doi:10.1016/j.calphad.2007.04.003

    Article  Google Scholar 

  43. V.V. Litovski, Enthalpies of formation of liquid binary alloys of alkaline-earth metals with silicon, germanium and tin, Thesis for Ph.D. in physics and mathematics, Sverdlovsk, 1986 (in Russian)

  44. R.C. King and O.J. Kleppa, A thermochemical study of some selected Laves phases, Acta Metall., 1964, 12(1), p 87-97

    Article  Google Scholar 

  45. J.R. Guadagno, M.J. Pool, and S.S. Shen, Thermodynamic investigation of liquid Ca–Sn, Sr–Sn, and Ba–Sn alloys, Metall. Trans., 1970, 1, p 1779-1780

    Article  Google Scholar 

  46. V.S. Sudavtsova and G.I. Batalin, Thermodynamic properties of binary melts of the systems Ca–Si(Sn), Izv. AN USSR, Inorg. Mater., 1988, 24(9), p 1578-1580 (in Russian)

    Google Scholar 

  47. A. Yassin and R. Castanet, Enthalpies of dissolution of elements in liquid tin: II. Transition, alkali and alkaline-earth metals, J. Alloys Compd., 2001, 314, p 160-166. doi:10.1016/S0925-8388(00)01228-7

    Article  Google Scholar 

  48. V.S. Sudavtsova, G.I. Batalin, and L.N. Zelenina, Thermodynamic properties of melts of the systems Si–(Mg, Sb), Ukr. Chim. Zhurn., 1988, 54(6), p 655-657 (in Russian)

    Google Scholar 

  49. F. Sommer, G. Borzone, N. Parodi, and R. Ferro, Enthalpy of formation of Ca–Pb and Ba–Pb alloys, Intermetallics, 2006, 14, p 287-296. doi:10.1016/j.intermet.2005.06.003

    Article  Google Scholar 

  50. F. Sommer, J.J. Lee, and B. Predel, Temperature dependence of the mixing enthalpies of liquid magnesium-lead and magnesium-tin alloys, Z. Metallkd., 1980, 71(12), p 818-821

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. O. Shevchenko.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shevchenko, M.O., Ivanov, M.I., Berezutski, V.V. et al. Thermodynamic Properties of Alloys in the Binary Ca–Ge System. J. Phase Equilib. Diffus. 36, 554–572 (2015). https://doi.org/10.1007/s11669-015-0408-0

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11669-015-0408-0

Keywords

Navigation