### Abstract

We have shown that two of the most commonly used multicomponent formulations of excess Gibbs free energy of mixing, those by Wohl (1946, 1953) and Redlich and Kister (1948), are formally equivalent if the binaries are constrained to have subregular properties, and also that other subregular multicomponent formulations developed in the mineralogical and geochemical literature are equivalent to, or higher order extensions of, these formulations. We have also presented a compact derivation of a multicomponent subregular solution leading to the same expression as derived by Helffrich and Wood (1989). It is shown that Wohl's multicomponent formulation involves combination of binary excess free energies, which are calculated at compositions obtained by normal projection of the multicomponent composition onto the bounding binary joins, and is, thus, equivalent to the formulation developed by Muggianu et al. (1975). Finally, following the lead of Hillert (1980), we have explored the limiting behavior of regular and subregular ternary solutions when a pair of components become energetically equivalent, and have, thus, derived an expression for calculating the ternary interaction parameter in a ternary solution from a knowledge of the properties of the bounding binaries, when one of these binaries is nearly ideal.

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

Pages (from-to) | 3763-3767 |

Number of pages | 5 |

Journal | Geochimica et Cosmochimica Acta |

Volume | 58 |

Issue number | 18 |

DOIs | |

State | Published - 1994 |

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### ASJC Scopus subject areas

- Geochemistry and Petrology

### Cite this

**Some aspects of multicomponent excess free energy models with subregular binaries.** / Cheng, Weiji; Ganguly, Jibamitra.

Research output: Contribution to journal › Article

*Geochimica et Cosmochimica Acta*, vol. 58, no. 18, pp. 3763-3767. https://doi.org/10.1016/0016-7037(94)90361-1

}

TY - JOUR

T1 - Some aspects of multicomponent excess free energy models with subregular binaries

AU - Cheng, Weiji

AU - Ganguly, Jibamitra

PY - 1994

Y1 - 1994

N2 - We have shown that two of the most commonly used multicomponent formulations of excess Gibbs free energy of mixing, those by Wohl (1946, 1953) and Redlich and Kister (1948), are formally equivalent if the binaries are constrained to have subregular properties, and also that other subregular multicomponent formulations developed in the mineralogical and geochemical literature are equivalent to, or higher order extensions of, these formulations. We have also presented a compact derivation of a multicomponent subregular solution leading to the same expression as derived by Helffrich and Wood (1989). It is shown that Wohl's multicomponent formulation involves combination of binary excess free energies, which are calculated at compositions obtained by normal projection of the multicomponent composition onto the bounding binary joins, and is, thus, equivalent to the formulation developed by Muggianu et al. (1975). Finally, following the lead of Hillert (1980), we have explored the limiting behavior of regular and subregular ternary solutions when a pair of components become energetically equivalent, and have, thus, derived an expression for calculating the ternary interaction parameter in a ternary solution from a knowledge of the properties of the bounding binaries, when one of these binaries is nearly ideal.

AB - We have shown that two of the most commonly used multicomponent formulations of excess Gibbs free energy of mixing, those by Wohl (1946, 1953) and Redlich and Kister (1948), are formally equivalent if the binaries are constrained to have subregular properties, and also that other subregular multicomponent formulations developed in the mineralogical and geochemical literature are equivalent to, or higher order extensions of, these formulations. We have also presented a compact derivation of a multicomponent subregular solution leading to the same expression as derived by Helffrich and Wood (1989). It is shown that Wohl's multicomponent formulation involves combination of binary excess free energies, which are calculated at compositions obtained by normal projection of the multicomponent composition onto the bounding binary joins, and is, thus, equivalent to the formulation developed by Muggianu et al. (1975). Finally, following the lead of Hillert (1980), we have explored the limiting behavior of regular and subregular ternary solutions when a pair of components become energetically equivalent, and have, thus, derived an expression for calculating the ternary interaction parameter in a ternary solution from a knowledge of the properties of the bounding binaries, when one of these binaries is nearly ideal.

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UR - http://www.scopus.com/inward/citedby.url?scp=0028557533&partnerID=8YFLogxK

U2 - 10.1016/0016-7037(94)90361-1

DO - 10.1016/0016-7037(94)90361-1

M3 - Article

AN - SCOPUS:0028557533

VL - 58

SP - 3763

EP - 3767

JO - Geochmica et Cosmochimica Acta

JF - Geochmica et Cosmochimica Acta

SN - 0016-7037

IS - 18

ER -