A degenerate electron gas model for solutions of aluminum in cryolite melts
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I.
INTRODUCTION
IT has
long been known that aluminum has a small solubility in cryolite melts, and that reoxidation of such dissolved metal is responsible for loss of Faradaic efficiency during commercial electrolytic production, but there remains doubt about the chemical species present in the solution. The most recent, and apparently the most accurate, measurements are those of (Ddeg~rd et al. m and they analyzed them in terms o f Na being the major solute species in NaF-rich melts, the AIF2 ion (containing monovalent A1) being predominant under the normal commercial conditions of molar NaF/A1F3 ratio = 2.25 to 2.7, and AI2F3-, A13F4, and AlaF5 being of significance in melts very rich in A1F3. It is the purpose of this article to consider the hypothesis that solutions of aluminum in cryolite melts can be regarded as a degenerate Fermi electron gas, rather than as containing identifiable and discrete chemical species. This is equivalent to saying that there is a conduction band of allowed energy levels which the electrons introduced with the dissolved metal can occupy, and that the Fermi level is, in general, well above the bottom of that band. Although the treatment is modeled on that given by Rickert t2] for excess silver in a-Ag2S, a major extension and some additional assumptions are necessary. Rickert dealt with the solubility of Ag in a constant solvent (Ag2S) as a function of the activity of the solute, which was controlled electrochemically. In the present case, the solute (AI) is always at unit activity, while the solvent is changing. The interest is to account for the observed change of solubility as the NaF/A1F3 ratio is varied. Calculations of electron energy as a function of electron density yield energies referred to the level of the bottom of the band, and some assumption must be made as to how that level varies with changing solvent composition. The assumption made is that it does not vary. The matter is discussed later. It is also assumed that the
ERNEST W. D E W I N G , formerly a Principal Scientist with Alcan International Laboratory, Kingston, ON K7L 5L9, Canada, is retired. Manuscript submitted July 10, 1990. METALLURGICAL TRANSACTIONS B
effective electron mass, m*, is constant, independent of the composition of the solvent and of the Fermi level, but it is not assumed that m* is equal to the mass of an isolated electron in vacuum, m ~ At first, that assumption was made, and it blocked progress with this work for several years, but Rickert [2J found that electrons in c~-Ag2S at 300 ~ have an effective mass m* = 0.23 m ~ a value in good agreement with optical measurements, t3J and it seems that values o f m * / m ~ < 1 are very common. With the assumptions above, it seems, at first sight, that the solubility of AI in cryolite melts ought to be independent of NaF/A1F3 ratio. The Fermi level of liquid A1 is fixed; the level of the bottom of the conduction band is assumed constant: should this not lead automatically to a fixed density of electrons in the molten salt when in equilibrium with
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