Thermodynamic description for concentrated metallic solutions using interaction parameters

Abstract

The integral molar excess Gibbs energy of a multicomponent system is expressed in terms of interaction parameters, from which the analytical formulae of the activity coefficients of the solutes and solvent, as Eqs.[23] and [24], were deduced. This approach, named the approach, is able to describe quantitatively the thermodynamic properties of multicomponent systems. It features thermodynamic consistency, high accuracy, and a rather small influence of the higher-interaction parameters on the thermodynamic properties of metallic solutions. A simple modification to the first-order interaction parameters extends the approach, to be applicable to systems with strong interactions between components at both low and concentrated levels.

The effects of sulfur, silicon, water, and oxygen fugacity on carbon solubility and partitioning in Fe-rich alloy and silicate melt systems at 3 GPa and 1600 °C: Implications for core–mantle differentiation and degassing of magma oceans and reduced planetary mantles

“…(Holzheid et al, 1997;O'Neill and Eggins, 2002). Activity coefficients of Fe in Fe-rich melt, γ Fe , were calculated using the ε-approach, which takes into account the non-ideal interaction between all the components in the Fe-rich alloy melt (Ma, 2001;Chi et al, 2014;Wood et al, 2013). The online "Metal Activity Calculator" (http://www.earth.ox.ac.uk/~expet/metalact/) provided by the University of Oxford (Wood et al, 2013) √ : measured; X: not measured.…”

The effects of composition and temperature on chalcophile and lithophile element partitioning into magmatic sulphides

“…Taking the epsilon model (Ma, 2001) and simplifying for the case of highly dilute trace element M yields, for MS n/2 dissolved in an FeS-FeO-NiS-CuS 0.5 matrix:…”

A Derivation of a Quadratic Activity Coefficient vs Composition Relationship in a Quaternary System, A-B-C-D

“…Similarly, the proposed relations e ij = (e ii + e jj )/2, e ijk = (e iii + e jjj + e kkk )/3, and so on are often invalid. Even more recently, the e approach of Ma [10] is introduced, which is much like the formalism of Hajra et al [4] and which uses the MacLaurin infinite series of concentration terms and the first-order interaction coefficients to express the behavior of multicomponent concentrated metallic solutions. The two formalisms coincide in the case of a binary system and, as would be expected, have the same limitations, too.…”

“…[16] of the expressions of ln c A , ln c B , ln c C , and lnc D from Eqs. [8], [10], [12], and [15] after rearrangement gives the following:…”

“…Final form of ln c C Following the same procedure as for ln c B and recalling that c 0 ¼ ln c 0 C ; the following modified form of Eq. [10] is obtained:…”