Thermodynamics of constrained and unconstrained equilibrium systems and their phase rules

Z. K. Liu, J. Ågren

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7 Scopus citations


The two types of phase equilibria, the normal unconstrained one and the constrained one, and their thermodynamics are discussed. The concepts of potential and phase rule, which have recently been discussed in the literature, are reconsidered, and their formal definitions are analyzed in some detail. It is realized that in the unconstrained equilibrium system, the properly defined chemical potentials of all components must be constant across the phase interface in both the hydrostatically and nonhydrostatically stressed systems. It is demonstrated that in a constrained equilibrium system, e.g. with a coherent equilibrium or paraequilibrium, the discussion of the phase rule is rather meaningless even though it is possible to find a relationship between the number of independent potentials and phases. On the other hand, a constrained equilibrium system may be treated as a normal equilibrium by describing its equilibrium features with a different definition of the system.

Original languageEnglish (US)
Pages (from-to)30-35
Number of pages6
JournalJournal of Phase Equilibria
Issue number1
StatePublished - Feb 1 1995

All Science Journal Classification (ASJC) codes

  • General Materials Science
  • Physical and Theoretical Chemistry
  • Metals and Alloys


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