The modified quasi-chemical model: Part II. Multicomponent solutions

Abstract

Further improvements to the modified quasi-chemical model in the pair approximation for shortrange ordering (SRO) in liquids are extended to multicomponent solutions. The energy of pair formation may be expanded in terms of the pair fractions or in terms of the component fractions, and coordination numbers are permitted to vary with composition. The model permits complete freedom of choice to treat any ternary subsystem with a symmetric or an asymmetric model. An improved general functional form for "ternary terms" in the excess Gibbs energy expression is proposed. These terms are related to the effect of a third component upon the binary pair interaction energies. It is shown how binary subsystems that have been optimized with the quasi-chemical model can be combined in the same multicomponent Gibbs energy equation with binary subsystems that have been optimized with a random-mixing Bragg-Williams model and a polynomial expression for the excess Gibbs energy. This is of much practical importance in the development of large databases for multicomponent solutions. The model also applies to SRO in solid solutions as a special case, when the number of lattice sites and coordination numbers are constant.

Quasi-Chemical Viscosity Model for Fully Liquid Slag in the Al2O3-CaO-MgO-SiO2 System—Part I: Revision of the Model

“…The concentrations of SUs in the present study are determined using the quasi-chemical thermodynamic model of the liquid slag [22,24,25] that takes into account short-range ordering of second-nearest-neighbor cations in the ionic melt. For a binary MeO-SiO 2 slag, the quasichemical thermodynamic model considers the formation of two nearest-neighbor pairs (Si-Me) from (Me-Me) and (Si-Si) pairs, referred to as ''second nearest neighbour bonds'' (SNNB).…”

“…For a binary MeO-SiO 2 slag, the quasichemical thermodynamic model considers the formation of two nearest-neighbor pairs (Si-Me) from (Me-Me) and (Si-Si) pairs, referred to as ''second nearest neighbour bonds'' (SNNB). [22,24,25] The concentrations of the various viscous flow SUs are equal to the concentrations of the corresponding second-nearest-neighbor bonds of the quasi-chemical thermodynamic model (see Figure 1). The quasi-chemical thermodynamic model as part of the FactSage computer package [26] has been successfully applied to describe experimental phase equilibria, thermodynamic and other types of data in many slag systems from binary to multi-component systems, and the SNNB concentrations calculated with the quasi-chemical thermodynamic model were taken as a reasonable approximation of the slag internal structure.…”

“…The trends given in Figure 3 were also used as a guide to determine corresponding molar energies of the pure oxide liquids in addition to the experimental data in the corresponding unary, binary, and ternary systems. [22,24,25] and the FactSage computer package [26] -the so-called ordering tendency (preference to form Si-Me over Me-Me and Si-Si SNNB) decreases from the Na 2 O-, K 2 O-, and CaO-to MgO-, ''FeO''-, and Al 2 O 3 -silicate system. An important point is that at high SiO 2 concentrations, the Si-Me and Si-Si are predominant SUs and therefore determine the viscosity in the melts.…”

Experimental Study and Thermodynamic Re-optimization of the FeO-Fe2O3-SiO2 System

“…The liquid FeO-FeO 1.5 -SiO 2 slag was modelled using the modified quasichemical model, [56][57][58][59] which takes into account the short-range ordering (SRO) of second-nearestneighbor (SNN) cations. In the case of binary FeO-SiO 2 system, the SNN SRO can be expressed by the following pair exchange reaction: applied to describe the interactions between FeO-FeO 1.5 and FeO 1.5 -SiO 2 components in the melt.…”

“…The q ijk ABðCÞ parameters describe the effects of the third component C upon binary interactions between components A and B. [57] The optimized model parameters for the slag are given in Table 3.…”