Skip to main content
SpringerLink
Log in

Phase Equilibria in Binary and Ternary Systems with Chemical and Magnetic Ordering

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

Abstract

Univariant and invariant phase equilibria for systems that display second-order transformations such as chemical and magnetic ordering are arranged consistently aiming to construct complete Scheil’s reaction schemes. For this purpose it is assumed that univariant phase boundaries representing second-order (or higher-order) transformations are nothing else than phase fields collapsed into infinitely thin thickness. This implies that second-order transformations can be formally treated like first-order transformations. Adequate notations and representation guidelines are proposed for the Scheil’s scheme. Examples are given for binary Al-Fe and ternary Al-Fe-Ta systems using recently obtained thermodynamic descriptions.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21

Similar content being viewed by others

Notes

  1. In accordance with Inden[4] there is no need to distinguish second-order from higher-order transformations in phase diagram calculations and representation due to their qualitatively similar contribution to the Gibbs energy. It is often sufficient to classify the transformations into first-order and continuous.

  2. The D03 phase is the binary limitrophe of L21 phase.[17,24]

  3. The A2 ↔ D03 transformation was obtained by artificially adjusting the enthalpic term in the GB2ALFe and GD03FEAL functions[8] for +1000 and −1000 J mol−1, respectively. This and further adjustments are given in the legends of Fig. 2(b) through (d).

  4. The continuous transitions are characterized by singularities in the thermodynamic functions that in phase diagrams occur at critical points or along critical lines or surfaces.[5]

  5. According to this description, a miscibility gap occurs between Heusler L21 (Fe2TaAl) phase and its D03 (Fe3Al) limitrophe. The Thermo-Calc software starts to label it as L21#2 and L21#1, respectively, according to distinct composition sets. To improve the readability of the reaction scheme and of relevant figures, we replaced L21#1, which has tiny solubility of Ta, with D03 and L21#2 with L21.

References

  1. E. Scheil, Darstellung von Dreistoffsystemen, Arch. Eisenhüttenwes., 1936, 9, p 571-573, in German

    Google Scholar 

  2. E. Gebhard and G. Petzow, Über den Aufbau des Vierstoffsystems Silber-Kupfer-Kadmium-Zinn, Z. Metallkd., 1960, 51, p 368-375, in German

    Google Scholar 

  3. H.L. Lukas, E.-T. Henig, and G. Petzow, 50 Years Reaction Scheme after Erich Scheil, Z. Metallkd., 1986, 77(6), p 360-367

    Google Scholar 

  4. G. Inden, The Effect of Continuous Transformations on Phase Diagrams, Bull. Alloy Phase Diagr., 1982, 2(4), p 412-422

    Article  Google Scholar 

  5. S.M. Allen and J.W. Cahn, Phase Diagrams Features Associated with Multicritical Points in Alloy Systems, Bull. Alloy Phase Diagr., 1982, 3(3), p 287-295

    Article  Google Scholar 

  6. B. Sundman, B. Jansson, and J.-O. Andersson, The Thermo-Calc Databank System, Calphad, 1985, 9, p 153-190

    Article  Google Scholar 

  7. Thermo-Calc Software, Thermo-Calc Classic ver. S, http://www.thermocalc.com/ThermoCalcClassic.htm

  8. B. Sundman, I. Ohnuma, N. Dupin, U.R. Kattner, and S.G. Fries, An Assessment of the Entire Al-Fe System Including D03 Ordering, Acta Mater., 2009, 57, p 2896-2908

    Article  Google Scholar 

  9. V.T. Witusiewicz, A.A. Bondar, U. Hecht, V.M. Voblikov, N.I. Tsyganenko, O.S. Fomichov, M.V. Karpets, V.M. Petyukh, T. Ya. Velikanova, and S. Rex, Experimental Study and Thermodynamic Modelling of the Ternary Al-Fe-Ta System, Intermetallics, 2011, in press

  10. P. Ehrenfest, Phasenumwandlungen im üblichen und erweiterten Sinn, klassifiziert nach den entsprechenden Singularitäten des thermodynamischen Potentiales, Proc. K. Ned. Akad. Wet., 1933, 36, p 153-157, in German

    MATH  Google Scholar 

  11. J.W. Stout, Second-Order Transitions in Two-Component Systems. Application to Solutions of He3 in He4, Phys. Rev., 1948, 74(5), p 605-609

    Article  ADS  MATH  Google Scholar 

  12. L.D. Landau and E.M. Lifshitz, Statistical Physics, Chap. XIV, Addison-Wisley, Reading, MA, 1958

  13. C.P. Bean and D.S. Rodbell, Magnetic Disorder as a First-Order Phase Transition, Phys. Rev., 1962, 126(1), p 104-115

    Article  ADS  Google Scholar 

  14. S.M. Allen and J.W. Cahn, Coherent and Incoherent Equilibria in Iron-Rich Iron-Aluminum Alloys, Acta Metall., 1975, 23(9), p 1017-1026

    Article  Google Scholar 

  15. M. Athènes, P. Bellon, G. Martin, and F. Haider, A Monte-Carlo Study of B2 Ordering and Precipitation via Vacancy Mechanism in B.C.C. Lattices, Acta Mater., 1996, 44(12), p 4739-4748

    Article  Google Scholar 

  16. I. Ohnuma, O. Ikeda, R. Kainuma, B. Sundman, and K. Ishida, Phase Separation Induced by Interaction Between Chemical and Magnetic Ordering in BCC Phase in Fe-Al Binary System, CALPHAD XXVII, May, 1998 (Beijing, PR China), 1988, p 17-22

  17. I. Ohnuma, C.G. Schön, R. Kainuma, G. Inden, and K. Ishida, Ordering and Phase Separation in the b.c.c. Phase of the Fe-Al-Ti System, Acta Mater., 1998, 46(6), p 2083-2094

    Article  Google Scholar 

  18. S. Matsumura, Linear Instability Criteria for Ordering and Phase Separation in Tricritical Systems, Z. Metallkd., 1998, 89(12), p 814-822

    Google Scholar 

  19. C.P. Wang, X.J. Liu, I. Ohnuma, R. Kainuma, and K. Ishida, Ordering and Phase Separation of the BCC Phase in the Fe-Cu-Al System, Z. Metallkd., 1998, 89(12), p 828-835

    Google Scholar 

  20. T. Nishizawa, M. Hasebe, and M. Ko, Thermodynamic Analysis of Solubility and Miscibility Gap in Ferromagnetic α Iron Alloys, Acta Metall., 1979, 27, p 817-828

    Article  Google Scholar 

  21. T. Nishizawa, S.M. Hao, M. Hasebe, and K. Ishida, Thermodynamic Analysis of Miscibility Gap due to Ordering in Ternary Systems, Acta Metall., 1983, 31(9), p 1403-1416

    Article  Google Scholar 

  22. M. Hillert, Historic Note on the Two-Peak Miscibility Gap, J. Phase Equilib., 1994, 15(1), p 35-36

    Article  Google Scholar 

  23. J.C. Zhao, Ed., Methods for Phase Diagram Determination, Elsevier, Amsterdam, 2007, p 505

    Google Scholar 

  24. W.B. Pearson, The Crystal Chemistry and Physics of Metals and Alloys, Wiley-Interscience, New York, 1972, p 806

    Google Scholar 

  25. D.E. Laughlin, K. Srinivasan, M. Tanase, and L. Wang, Crystallographic Aspects of L10 Magnetic Materials, Scripta Mater., 2005, 53, p 383-388

    Article  Google Scholar 

  26. S.G. Fries, H.L. Lukas, I. Ansara, and B. Sundman, The Bragg-Williams-Gorsky (BWG) Ordering Treatment in the Compound Energy Formalism (CEF), Ber. Bunsen. Phys. Chem., 1998, 102(9), p 1102-1110

    Google Scholar 

  27. A.G. Khachaturyan, Theory of Structural Transformations in Solids, John Wiley and Sons Inc., New York, NY, 1983, p 574

    Google Scholar 

  28. W.A. Soffa and D.E. Laughlin, Decomposition and Ordering Processes Involving Thermodynamically First-Order Order → Disorder Transformations, Acta Metall., 1989, 37(11), p 3019-3028

    Article  Google Scholar 

  29. J. Soltys, Order-Disorder Phase Transitions in the Ternary Alloys Cu3-xMnxAl, Phys. Stat. Sol. A, 1981, 63, p 401-406

    Article  ADS  Google Scholar 

  30. M. Jurado, T. Castán, L. Mañosa, A. Planes, J. Bassas, X. Alocbé, and M. Morin, Study of the Order-Disorder Phase Transitions in Cu-Al-Be Shape Memory Alloys, Philos. Mag. A, 1997, 75(5), p 1237-1250

    Article  ADS  Google Scholar 

  31. H.E. Cook, Continuous Transformations, Mater. Sci. Eng., 1976, 25(1-2), p 127-134

    Google Scholar 

  32. M.T. Ochoa-Lara, H. Flores-Zúňiga, D. Rios-Jara, and G. Lara-Rodríguez, In Situ X-Ray Study of Order-Disorder Phase Transformations in Cu-Al-Be Melt Spun Ribbons, J. Mater. Sci., 2006, 41, p 4755-4758

    Article  ADS  Google Scholar 

  33. F. Lanzini, R. Romero, and M.L. Castro, Influence of Be addition on order-disorder transformations in β Cu-Al, Intermetallics, 2008, 16, p 1090-1094

    Article  Google Scholar 

  34. S. Sarkar and S. Bansalm, Atomic Disorder-Order Phase Transformation in Nanocrystalline Fe-Al, J. Alloys Compd., 2002, 334, p 135-142

    Article  Google Scholar 

  35. S.M. Hao, T. Takayama, K. Ishida, and T. Nishizawa, Miscibility Gap in Fe-Ni-Al and Fe-Ni-Al-Co Systems, Metall. Trans. A, 1984, 15A, p 1819-1828

    ADS  Google Scholar 

  36. M. Palm and J. Lacaze, Assessment of the Al-Fe-Ti system, Intermetallics, 2006, 14, p 1291-1303

    Article  Google Scholar 

  37. Y. Shen and D.E. Laughin, Magnetic Effects on the Symmetry of CBED Patterns of Ferromagnetic PrCo5, Philos. Mag. Lett., 1990, 62(3), p 187-193

    Article  ADS  Google Scholar 

  38. D.E. Laughlin, M.A. Willard, and M.E. McHenry, Magnetic Ordering: Some Structural Aspects, Phase Transformations and Evolution in Materials, P. Turchi and A. Gonis, Ed., The Minerals, Metals and Materials Society, 2000, p 121-137

  39. V. Talanquer, C. Varea, and A. Robledo, Global Phase Diagram for Binary Alloys with One Magnetic Component, Phys. Rev. B, 1989, 39(10), p 7030-7038

    Article  ADS  Google Scholar 

  40. J.L. Meijering, Miscibility Gaps in Ferromagnetic Alloy Systems, Philips Res. Rep., 1963, 13, p 318-330

    Google Scholar 

  41. M. Yamashita and H. Nakano, Phase Separation Accompanied by Magnetic Ordering in Binary Mixtures of Paramagnetic Atoms, Progr. Theor. Phys., 1979, 61(3), p 764-775

    Article  ADS  Google Scholar 

  42. G. Inden, The Role of Magnetism in the Calculation of Phase Diagrams, Physica, 1981, 103B, p 82-100

    Google Scholar 

  43. Y.A. Chang, Magnetic-Induced Tricritical Point in Alloys and the Low-Temperature Fe-Ni and Fe-Ni-Cr Phase Diagrams, Bull. Alloy Phase Equilib., 1989, 10(5), p 513-521

    Article  Google Scholar 

  44. R.J. Harrison, Magnetic Transitions in Minerals, Rev. Mineral. Geochem., 2000, 39(1), p 175-202

    Article  Google Scholar 

  45. P. Robinson, R. Harrison, S.A. McEnrof, and R.B. Hargraves, Nature and Origin of Lamellar Magnetism in the Hematite-Ilmenite Series, Am. Mineral., 2004, 89, p 725-747

    Google Scholar 

  46. J. Mira, F. Rivadulla, J. Rivas, A. Fondado, T. Guidi, R. Caciuffo, F. Carsughi, P.G. Radaelli, and J.B. Goodenough, Structural Transformation Induced by Magnetic Field and “Colosal-Like” Magnetoresistance Response above 313 K in MnAs, Phys. Rev. Lett., 2003, 90(9), p 097203-(1-4)

    Google Scholar 

  47. F.C. Nascimento, A.O. dos Santos, A. de Campos, S. Gama, and L.P. Cardoso, Structural and Magnetic Study of the MnAs Magnetocaloric Compound, Mater. Res., 2006, 9(1), p 111-114

    Article  Google Scholar 

  48. P.E. Markin and N.V. Mushnikov, Magnetic Properties and Structural Transition in (MnCo)1-xGe, Solid State Phen., 2009, 152-153, p 489-492

    Article  Google Scholar 

  49. N.T. Trung, V. Biharie, L. Zhang, L. Caron, K.H.J. Buschow, and E. Brük, From Single- to Double-First-Order Magnetic Phase Transition in Magnetocaloric Mn1-xCrxCoGe Compounds, Appl. Phys. Lett., 2010, 96, p 162507-(1-3)

    Google Scholar 

  50. T. Jo and K. Hirai, Lattice Distortion and Multiple Spin Density Wave State in γMn Alloys, J. Phys. Soc. Jpn., 1986, 55(6), p 2017-2023

    Article  ADS  Google Scholar 

  51. J. Bratberg and B. Sundman, A Thermodynamic Assessment of the Co-V System, J. Phase Equilib., 2003, 24(6), p 495-503

    Article  Google Scholar 

  52. T.B. Massalski, P.R. Subramanian, H. Okomoto, and L. Kasprzak, Ed., Binary Alloy Phase Diagrams, 2nd ed. in 3 Vols, ASM, Metals Park, OH, 1990

  53. L. Eleno, K. Friskm, and A. Schneider, Assessment of the Fe-Ni-Ta system, Intermetallics, 2006, 14, p 1276-1290

    Article  Google Scholar 

  54. N.G. Parsonage and L.A.K. Stavelay, Disorder in Crystals. International Series of Monographs on Chemistry, Clarendon Press, Oxford, 1978, p 926

    Google Scholar 

  55. M. Fallot, Les Alliages du Fer avec les Métaux de la Famille du Platine, Ann. Phys., 1938, 10, p 291-332, in France

    Google Scholar 

Download references

Acknowledgments

The authors gratefully acknowledge Dr. S. Rex for fruitful discussions. This work was supported by the German Federal Ministry of Research (Contract FKZ 50WM0843).

Author information

Authors and Affiliations

  1. ACCESS e.V., Intzestr. 5, 52072, Aachen, Germany

    V. T. Witusiewicz & U. Hecht

  2. Frantsevich Institute for Problems of Materials Science, Krzhyzhanovsky Str. 3, Kyiv, 03680, Ukraine

    A. A. Bondar & T. Y. Velikanova

Authors
  1. V. T. Witusiewicz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. A. Bondar
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. U. Hecht
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. T. Y. Velikanova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. T. Witusiewicz.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Witusiewicz, V.T., Bondar, A.A., Hecht, U. et al. Phase Equilibria in Binary and Ternary Systems with Chemical and Magnetic Ordering. J. Phase Equilib. Diffus. 32, 329–349 (2011). https://doi.org/10.1007/s11669-011-9910-1

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11669-011-9910-1

Keywords

Search

Navigation