Journal of Phase Equilibria

, Volume 12, Issue 2, pp 148–168 | Cite as

Thermodynamically Improbable Phase Diagrams

  • Hiroaki Okamoto
  • T.B Massalski


Phase diagrams showing very unlikely boundaries, while not explicitly violating thermodynamic principles or phase rules, are discussed. Phase rule violations in proposed phase diagrams often become apparent when phase boundaries are extrapolated into metastable regions. In addition to phase rule violations, this article considers difficulties regarding an abrupt change of slope of a phase boundary, asymmetric or unusually pointed liquidus boundaries, location of miscibility gaps, and gas/liquid equilibria. Another frequent source of phase diagram errors concerns the initial slopes of liquidus and solidus boundaries in the very dilute regions near the pure elements. Useful and consistent prediction can be made from the application of the van’t Hoff equation for the dilute regions.


Phase Diagram Alloy Phase Diagram Atomic Percent Initial Slope Allotropic Transformation 
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Copyright information

© ASM International 1991

Authors and Affiliations

  • Hiroaki Okamoto
    • T.B Massalski
      • 1
    1. 1.Carnegie Mellon University Pittsburgh

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