### Abstract

If an initially homogeneous system at high temperature is
rapidly cooled, a temporary para-equilibrium state may
result in which rapidly diffusing elements have reached
equilibrium but more slowly diffusing elements have
remained essentially immobile. The best known example
occurs when homogeneous austenite is quenched. A
para-equilibrium phase assemblage may be calculated
thermodynamically by Gibbs free energy minimization under
the constraint that the ratios of the slowly diffusing
elements are the same in all phases. Several examples of
calculated para-equilibrium phase diagram sections are
presented and the application of the Phase Rule is
discussed. Although the rules governing the geometry of
these diagrams may appear at first to be somewhat
different from those for full equilibrium phase diagrams,
it is shown that in fact they obey exactly the same rules
with the following provision. Since the molar ratios of
non-diffusing elements are the same in all phases at
para-equilibrium, these ratios act, as far as the
geometry of the diagram is concerned, like "potential"
variables (such as T, pressure or chemical potentials)
rather than like "normal" composition variables which
need not be the same in all phases. A general algorithm
to calculate para-equilibrium phase diagrams is
presented. In the limit, if a para-equilibrium
calculation is performed under the constraint that no
elements diffuse, then the resultant phase diagram shows
the single phase with the minimum Gibbs free energy at
any point on the diagram; such calculations are of
interest in physical vapor deposition when deposition is
so rapid that phase separation does not occur

Original language | English |
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Pages (from-to) | 16-22 |

Number of pages | 7 |

Journal | The Journal of Chemical Thermodynamics |

Volume | 72 |

DOIs | |

Publication status | Published - 2014 |

MoE publication type | A1 Journal article-refereed |

### Keywords

- Para-equilibrium
- phase diagrams
- phase rule
- physical vapor deposition
- thermodynamics

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## Cite this

Pelton, A. D., Koukkari, P., Pajarre, R., & Eriksson, G. (2014). Para-equilibrium phase diagrams.

*The Journal of Chemical Thermodynamics*,*72*, 16-22. https://doi.org/10.1016/j.jct.2013.12.023