### Abstract

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 language | English (US) |
---|---|

Pages (from-to) | 30-35 |

Number of pages | 6 |

Journal | Journal of Phase Equilibria |

Volume | 16 |

Issue number | 1 |

DOIs | |

State | Published - Feb 1 1995 |

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### All Science Journal Classification (ASJC) codes

- Materials Science(all)
- Physical and Theoretical Chemistry
- Metals and Alloys

### Cite this

*Journal of Phase Equilibria*,

*16*(1), 30-35. https://doi.org/10.1007/BF02646246

}

*Journal of Phase Equilibria*, vol. 16, no. 1, pp. 30-35. https://doi.org/10.1007/BF02646246

**Thermodynamics of constrained and unconstrained equilibrium systems and their phase rules.** / Liu, Z. K.; Ågren, J.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Thermodynamics of constrained and unconstrained equilibrium systems and their phase rules

AU - Liu, Z. K.

AU - Ågren, J.

PY - 1995/2/1

Y1 - 1995/2/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=51249167570&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=51249167570&partnerID=8YFLogxK

U2 - 10.1007/BF02646246

DO - 10.1007/BF02646246

M3 - Article

AN - SCOPUS:51249167570

VL - 16

SP - 30

EP - 35

JO - Journal of Phase Equilibria and Diffusion

JF - Journal of Phase Equilibria and Diffusion

SN - 1547-7037

IS - 1

ER -