Activities in the liquid system NaF-MgF 2 -AIF 3
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I.
INTRODUCTION
K1=
aM------L"(aA1F3) 2/3 aMgF2
[3]
g 2 = aN----~a"(aAIF3) 1/3 aNaF
[4]
g
preliminary version of this work was presented in 1972 at a conference in Czechoslovakia. m In this fuller version, the experimental results are presented in detail, the theoretical treatment is improved, the auxiliary data are updated, and comparison is made with some vapor-pressure measurements which have only recently appeared. The NaF-MgF2-A1F3 system is of practical interest to the aluminum industry, since MgF2 is one of the relatively few materials which can be added to the electrolyte of aluminum electrolysis cells. It is inevitable, however, that the metal produced is contaminated with Mg. The aim of this work is to provide measurements of the equilibrium involved and to elucidate the thermodynamics of the appropriate area of the ternary NaF-MgF2A1F3 system. II.
THEORY
The theory given here is similar to that developed for the LiF-NaF-A1F3 system, tEl b u t some changes in the equations are necessary, since Mg is a divalent element and Li is monovalent. From the experimental point of view, the quantities which can be measured are the amounts of Mg and Na in A1 in equilibrium with a salt melt of a known composition. The equilibria are 2 2 MgF2 + - A 1 = -A1F3 + Mg(A1) 3 3
[1]
and
(The activity of A1 is always so close to 1 that it is omitted.) Replacement of activities (a) in the salt phase with molar fractions (N) and activity coefficients (y) leads to two functions (~) defined by (NAIF3) 2/3 I~Mg = aMg
NMgF2
(NA1F3) 1/3 0Na =
aya' NNaF
[51
TNaF
K2 I'~
~1/3 \ /'AIF3 ]
[6]
The expressions between the pairs of equal signs can be evaluated from the experimental data, while those on the right contain quantities which are to be found. Since there are three unknown activity coefficients, a third equation is necessary, and it is the Gibbs-Duhem equation: NNa F d In 'YNaF + NMgF2 d In YMgF2
+ NAtF3d In YAW3= 0
[7]
To get Eqs. [5] and [6] into a form compatible With Eq. [7], it is necessary to take logarithms and differentiate, leading to 2 d In I]/Mg = d In YMgF2- -
[2]
for which the equilibrium constants are, respectively,
E.W. DEWING, Principal Scientist, is with the Alcan International Laboratory, P.O. Box 8400, Kingston, ON K7L 5L9, Canada. E.Th. van der KOUWE is with the South African Atomic Energy Board, Pretoria, South Africa. The experimental work was carried out when both authors were at what was then the Arvida, Quebec, Laboratory of The Aluminum Company of Canada Ltd. Manuscript submitted November 29, 1988. METALLURGICAL TRANSACTIONS B
K1 (,~AIF3)2/3
and
and 1 1 NaF + - A1 = - A1F3 + Na(A1) 3 3
"YMgF2
--
3
d In "YA1F3
[8]
and 1 d In I~Na = d In YNaF-- -- d In YAW3 3
[9]
The easiest way to solve these equations is to multiply Eq. [8] by N M g F 2 and Eq. [9] by NNaF, and then to add both to Eq. [7]. This leads to 3 d In 'YAIF3 = --
2NAIF3 -t- NMgF2 nt- 1
9 [NMgF2d In ~bMg+ NNRFd In ~bNa] [10] VOLUME 20B, OCTOBER 1989--671
One can derive expressions for the other two activity
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