### Abstract

Original language | English |
---|---|

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 |

### Fingerprint

### Keywords

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

### Cite this

*The Journal of Chemical Thermodynamics*,

*72*, 16-22. https://doi.org/10.1016/j.jct.2013.12.023

}

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

**Para-equilibrium phase diagrams.** / Pelton, Arthur D. (Corresponding Author); Koukkari, Pertti; Pajarre, Risto; Eriksson, Gunnar.

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - Para-equilibrium phase diagrams

AU - Pelton, Arthur D.

AU - Koukkari, Pertti

AU - Pajarre, Risto

AU - Eriksson, Gunnar

PY - 2014

Y1 - 2014

N2 - 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

AB - 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

KW - Para-equilibrium

KW - phase diagrams

KW - phase rule

KW - physical vapor deposition

KW - thermodynamics

U2 - 10.1016/j.jct.2013.12.023

DO - 10.1016/j.jct.2013.12.023

M3 - Article

VL - 72

SP - 16

EP - 22

JO - The Journal of Chemical Thermodynamics

JF - The Journal of Chemical Thermodynamics

SN - 0021-9614

ER -