Correct Expressions of Enthalpy of Mixing and Excess Entropy from MIVM and Their Simplified Forms
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tion numbers and molar volumes of some components in liquid state, such as P, C, Ta, TiO2, V2O5, Cu2S, FeS, NaCl, MgCl2, CaSiO3, and so on. This would hinder application of the MIVM to many practical systems. For this reason, the author tried to simplify the MIVM reasonably. In its simplification process, however, the incorrect expressions thermodynamically were found in its molar enthalpy of mixing and excess entropy.[11–14] So it is necessary to correct them in public. For a C-component system, the molar excess Gibbs energy GEm of the MIVM[5] can be expressed as 0C 1 P x B ln B ji C C C Bj¼1 j ji GEm X Vmi 1X B C ¼ xi ln C Zi xi B C C; @ A P P 2 RT i¼1 i¼1 xj Vmj Bji xj Bji j¼1
j¼1
½1 where R(J/mol K) is the gas constant, T(K) is the absolute temperature, C is the component number, xi, Vmi(cm3/mol), and Zi are the molar fraction, molar volume, and coordination number of component i, respectively, and Bji and Bij are the pair potential parameters of the ij binary system which are defined as Bji ¼ exp½NA ðeji eii Þ=RT
Bij ¼ exp½NA ðeij ejj Þ=RT;
½2 DOI: 10.1007/s11663-015-0460-5 Ó The Minerals, Metals & Materials Society and ASM International 2015
At present, thermodynamic models still are important methods to solve problems relating to thermodynamic properties of liquid alloys and silicate melts, such as chemical interaction in Cu-Zr melts,[1] interfacial energies in the fcc Au-Ni, liquid Ga-Pb, and liquid Al-Bi,[2] mixing functions in binary silicate and aluminate melts,[3] element partitioning between plagioclase and melt,[4] and so forth. Especially, the molecular interaction volume model (MIVM)[5] has been successfully applied to some practical systems.[6–10] But in the model calculation it is often difficult to find out the
DONG-PING TAO, Professor, is with the Faculty of Metallurgical and Energy Engineering, Kunming University of Science and Technology, Kunming 650093, Yunnan, P.R. China. Contact e-mail: [email protected] Manuscript submitted January 11, 2015. METALLURGICAL AND MATERIALS TRANSACTIONS B
where eii (J) is the ii pair potential energy and NA (1/mol) is the Avogadro constant. It can be seen that the temperature dependence of the MIVM is determined by Eq. [2], that is, if both hji ¼ NA ðeji eii Þ=R and hij ¼ NA ðeij ejj Þ=R are constant, the binary parameters Bji and Bij gradually approach unity as temperature increases. It indicates that the non-ideality of solutions will diminish at high temperatures. This case of the MIVM is consistent with the tendency described by the rule of Lupis and Elliott (LE rule) which was reformulated and rationalized by Kaptay[15] (LE rule: ‘‘Real solid, liquid and gaseous solutions (and pure gases) gradually approach the state of an ideal solution (perfect gas) as temperature increases at any fixed pressure and composition.’’). At limited temperatures, if real solutions want to approach the state of an ideal solution, then the necessary conditions from the MIVM are as follows: all of Bji are equal to a same constant and all of Vmi are equal to a
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