TY - JOUR

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

AU - Cheng, Weiji

AU - Ganguly, Jibamitra

N1 - Funding Information:
Acknowledgments-This researchw as supportedb y US National ScienceF oundatione rantsE AR 8903995an dEAR 9 I 17927T. hanks are due to Drs. Jar& D. Myers and BernardJ. Wood for careful formalr eviewso f them anuscriptW. e havea lsob enefitedco nsiderably from critical commentsb y Drs. GeorgeH elffich, Mats Hillert, AI-exandraN avrotsky,a nd Guilio Ottonello.W e aree speciallyg rateful to Dr. Hillert for manyd iscussionst,h roughc orrespondenceo.n the

PY - 1994/9

Y1 - 1994/9

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

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

M3 - Article

AN - SCOPUS:0028557533

SN - 0016-7037

VL - 58

SP - 3763

EP - 3767

JO - Geochimica et Cosmochimica Acta

JF - Geochimica et Cosmochimica Acta

IS - 18

ER -