A Density Model Based on the Modified Quasichemical Model and Applied to the NaF-AlF 3 -CaF 2 -Al 2 O 3 Electrolyte
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NTRODUCTION
A theoretical model for the density of multicomponent liquids based on the modified quasichemical model[1–4] has been presented in a previous article.[5] In the present article, this model is applied to the NaFAlF3-CaF2-Al2O3 base electrolyte used to produce aluminum by the Hall–He´roult process. All available density data for this system were collected and critically evaluated. Optimized temperature-dependent expansivities and molar volumes of the pure liquid fluorides and oxides, and optimized pressure-dependent model parameters, have been found. A thermodynamic database has previously been developed for the NaF-AlF3-CaF2-Al2O3 system.[6] A complete critical evaluation of all available phase diagram and thermodynamic data was performed for all condensed phases of this system and optimized model parameters were found. The NaF-AlF3-CaF2-Al2O3 liquid was modeled using the modified quasichemical model in the quadruplet approximation,[4] evaluating coupled first-nearest-neighbor (cation-anion) and second-nearest-neighbor (cation-cation and anion-anion) short-range order. In order to model the density of the NaF-AlF3-CaF2-Al2O3 liquid, pressure-dependent excess Gibbs energy parameters are now introduced. As discussed in Section VI, several empirical equations for the density of NaF-AlF3-CaF2-Al2O3 melts are available in the literature. However, most of them are not adequately accurate in some ranges of composition and temperature. The density model described in previCHRISTIAN ROBELIN, Research Associate, and PATRICE CHARTRAND, Assistant Professor, are with the Centre for Research in Computational Thermochemistry (CRCT), Department of Chemical Engineering, Ecole Polytechnique, Montre´al, PQ, Canada H3C 3A7. Contact e-mail: [email protected] Manuscript submitted May 1, 2007. Article published online October 30, 2007. METALLURGICAL AND MATERIALS TRANSACTIONS B
ous articles[5,7] and in the present article is suitable for multicomponent inorganic liquids such as liquid alloys (unpublished work), common-ion molten salt mixtures (NaCl-KCl-MgCl2-CaCl2 in Reference 5), and reciprocal molten salt mixtures (NaF-AlF3-CaF2-Al2O3 in the present article).
II.
THEORY
The NaF-AlF3-CaF2-Al2O3 molten salt is a reciprocal solution with more than one cation and more than one anion. The cations and anions considered in the liquid 2+ 3+ 6+ , and Fmodel are Na+, Al3+ V , AlIV , Al2 , and Ca and O2-, respectively. The Al3+ is the 5-coordinated V is the 4-coordinated Al3+; and Al6+ Al3+; Al3+ IV 2 represents the dimerized (F-bridged) Al3+. Pure (hypothetical) liquid aluminum fluoride was modeled as a 3+ 6+ mixture of Al3+ V , AlIV , Al2 , and F ions, in order to permit us to define three different compositions of maximum short-range ordering (near the Na2AlF5, NaAlF4, and NaAl2F7 compositions) in the NaF-AlF3 2binary system. The existence of AlF36 , AlF5 , and AlF4 ‘‘complex anions’’ in AF-AlF3 melts (where A = Li, Na, and K) was evidenced in the literature by Raman spectroscopy.[8–12] The liquid model assumes that the AlF36
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