Thermodynamically Improbable Phase Diagrams


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.

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Okamoto, H., Massalski, T. Thermodynamically Improbable Phase Diagrams. JPE 12, 148–168 (1991).

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  • Phase Diagram
  • Alloy Phase Diagram
  • Atomic Percent
  • Initial Slope
  • Allotropic Transformation