Journal of Phase Equilibria and Diffusion

, Volume 38, Issue 3, pp 319–331 | Cite as

High Entropy Alloys, Miscibility Gaps and the Rose Geometry

  • J. E. MorralEmail author
  • S.-L. Chen


Recent review articles on high entropy alloys (HEAs) provide little information about miscibility gaps in multicomponent systems, especially about how to respond with alloying should they be found. Also, there is a lack of information about how miscibility gaps might appear on calculated or measured multicomponent phase diagrams. In this work concepts concerning miscibility gaps that form in binary and ternary systems are reviewed. Then the work is extended to alloys with more components including HEAs. The previous work predicts that there are significant differences between binary systems and those with three or more components. For example, miscibility gaps do not form in binary systems that have a negative heat of mixing, but they do form in ternary systems. Also, ternary systems with a positive heat of mixing can have their stability temperature lowered by adding ternary components that add positive heats of mixing. The morphology and topology of multicomponent/multiphase miscibility gaps differ from typical phase diagrams, as well. For example, one type of miscibility gap is said to have the rose geometry, because of its floral design. Normally only 2-phase miscibility gaps can form in binary and ternary systems. However using the Graph Method it is suggested that 3-phase miscibility gaps might form in HEA systems, even while trying to avoid them. A conclusion of this investigation is that with additional computational and experimental work it may be possible to expand the boundaries of where HEAs can be found.


high entropy alloys miscibility gaps phase diagram thermodynamic modeling thermodynamic stability 


  1. 1.
    D.B. Miracle and O.N. Senkov, A Critical Review of High Entropy Alloys and Related Concepts, Acta Mater., 2017, 122, p 448–511CrossRefGoogle Scholar
  2. 2.
    Y. Zhang, T.T. Zuo, Z. Tang, M.C. Gao, K.A. Dahmen, P.K. Liaw, and Z.P. Lu, Microstructure and Properties of High Entropy Alloys, Prog. Mater. Sci., 2014, 61, p 1–93CrossRefGoogle Scholar
  3. 3.
    A. Takeuchi, K. Amiya, T. Wada, K. Yubuta, W. Zhang, and A. Makino, Entropies in Alloy Design for High-Entropy and Bulk Glassy Alloys, Entropy, 2013, 15, p 3810–3821ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    J.L. Meijering, Segregation in Regular Ternary Solutions, Part I, Philips Res. Rep., 1950, 5, p 333–356Google Scholar
  5. 5.
    J.L. Meijering, Segregation in Regular Ternary Solutions, Part II, Philips Res. Rep., 1951, 6, p 183–210Google Scholar
  6. 6.
    J.E. Morral and H. Gupta, Two Dimensional Sections of Miscibility Gaps: The Rose Geometry, J. Chem. Phys., 1993, 1993(90), p 421–427Google Scholar
  7. 7.
    S.L. Chen, J.-Y. Zhang, X.-G. Lu, K.C. Chou, W.A. Oates, R. Schmid-Fetzer, and Y.A. Chang, Calculation of Rose Geometry, Acta Mater., 2007, 55, p 243–250CrossRefGoogle Scholar
  8. 8.
    F.N. Rhines, Phase Diagrams in Metallurgy, McGraw-Hill, New York, 1956, p 155Google Scholar
  9. 9.
    ASM Alloy Phase Diagram Database.
  10. 10.
    D. de Fontaine, Configurational Thermodynamics of Solid Solutions, Solid State Phys., 1979, 34, p 74–371Google Scholar
  11. 11.
    R. Koningsveld, W.H. Stockmayer, and E. Nies, Polymer Phase Diagrams, Oxford Univ. Press, New York, 2001, p 86–91Google Scholar
  12. 12.
    X.J. Liu, Y. Liu, Y.H. Guo, D. Wang, S.Y. Yang, Y. Lu, and C.P. Wang, Experimental Investigation and Thermodynamic Calculation of Phase Equilibria in the Cu-Nb-Zr Ternary System, J. Phase Equilib. Diffus., 2016, 37, p 513–523CrossRefGoogle Scholar
  13. 13.
    I. Prigogine, Sur les phénomènes critique de dissolution dans les systems ternaires (On Critical Phenomena of Dissolution in Ternary Systems), Bull. Soc. Chim. Belg., 1943, 52, p 115–123Google Scholar
  14. 14.
    R. Kikuchi, D. de Fontaine, M. Murakami, and T. Nakamura, Ternary Phase Diagram Calculations, Acta Metall., 1977, 25, p 207CrossRefGoogle Scholar
  15. 15.
    J.E. Morral, On Characterizing Stability Limits for Ternary Systems, Acta Metall., 1972, 20, p 1061–1067CrossRefGoogle Scholar
  16. 16.
    J.E. Morral, Stability Limits for Ternary Regular Systems, Acta Metall., 1972, 20, p 1069–1076CrossRefGoogle Scholar
  17. 17.
    J. Timmermans, Die kritische Lösungstemperatur von ternären Gemengen (The Critical Dissolution Temperature of Ternary Mixtures), Z. Phys. Chem., 1907, 58, p 129–213CrossRefGoogle Scholar
  18. 18.
    G.V. Raynor, Au-Cu-Ni phase diagram, Ternary Gold Alloys, Inst. Met, London, 1990, p 226–234Google Scholar
  19. 19.
    J.W. Gibbs, The Scientific Papers, vol. I: Thermodynamics (Longmans, Green & Co, 1906) and (Dover reprint, 1961, N.Y.)Google Scholar
  20. 20.
    H.W. Bakhuis Roozeboom. Die heterogenen Gleichgewichte von Standpunkte der Phasenlehre (Heterogeneous equilibria from the standpoint of phase theory): Vol III by F.A.H. Schreinemakers, Die ternären Gleichgewichte (The ternary equilibria), Part 1, (Vieweg, Braunschweig, 1911)Google Scholar
  21. 21.
    L.S. Palatnik and A.I. Landau, Phase equilibria in multicomponent systems, Holt Rinehart and Winston, New York, 1964, p 258Google Scholar
  22. 22.
    J.E. Morral and R.H. Davies, Thermodynamics of Isolated Miscibility Gaps, J. Chim. Phys., 1997, 94, p 861–868Google Scholar
  23. 23.
    J.E. Morral and H. Gupta, Phase Boundary, ZPF, and Topological Lines on Phase Diagrams, Scr. Metall. Mater., 1991, 25, p 393–1396CrossRefGoogle Scholar
  24. 24.
    J.E. Morral, Two-Dimensional Phase Fraction Charts, Scr. Metall., 1984, 18, p 407–410CrossRefGoogle Scholar
  25. 25.
    H. Gupta, J.E. Morral, and H. Nowotny, Constructing Multicomponent Phase Diagrams by Overlapping ZPF Lines, Scr. Metall., 1986, 20, p 889–894CrossRefGoogle Scholar
  26. 26.
    E.M. Slyusarenko, EYu Kerimov, and M.V. Sofin, Analysis of the Phase Equilibria in Multicomponent Systems Using Graphs, Mendeleev Commun., 1999, 9, p 56–59CrossRefGoogle Scholar
  27. 27.
    E. Kerimov, S. Nikolaev, and E. Slyusarenko, Phase Equilibria in the Quaternary Ni-Re-Nb-Cr System at 1375 K Determined Using the Graph Method, J. Phase Equilib. Diffus., 2016, 37, p 135–148CrossRefGoogle Scholar
  28. 28.
    M.V. Sofin, EYu Kerimov, A.E. Chastukhin, N.A. Bazhanova, YuV Balykova, and E.M. Slyusarenko, Determination of Phase Equilibria in the Ni-V-Nb-Ta-Cr-Mo-W System at 1375 K Using the Graph Method, J. Alloys Compd., 2001, 321, p 102–131CrossRefGoogle Scholar
  29. 29.
    E.M. Slyusarenko, V.A. Borisov, M.V. Sofin, EYu Kerimov, and A.E. Chastukhin, Determination of Phase Equilibria in the System Ni-V-Cr-Mo-Re at 1425 K by Using the Graph Method, J. Alloys Compd., 1999, 284, p 171–189CrossRefGoogle Scholar

Copyright information

© ASM International 2017

Authors and Affiliations

  1. 1.Department of Materials Science and EngineeringThe Ohio State UniversityColumbusUSA
  2. 2.CompuTherm, LLCMiddletonUSA

Personalised recommendations