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CHAPTER 2 MATERIALS AND METHODS
The activity coefficients of the non-ideal binary solid solution are calculated as:
lnγi = X 2 2 [0 –1 (3 X1 – X2)]
lnγ2 = X 2 1[0 –1 (3 X2 – X1)]
The software MBSSAS [59] was used to derive the Guggenheim parameters a0 and a1
based on experimentally-observed compositional boundaries of the miscibility gap in
the investigated binary solid solution series. A detailed description of MBSSAS is
given elsewhere [59].
Lippmann developed an algorithm to describe the phase diagram of a binary solid
solution and its relation to the composition of the aqueous phase. A total solubility
product (ΣΠ) was introduced. If the system is in equilibrium, the total solubility product
of a binary solid solution (B1-xCxA) is the sum of the partial solubility products of each
end member. The total solubility product of a binary solid solution (B1-xCxA) can be
calculated from the sum of the partial solubility product of each end members (see the
equations below).
ΣΠSolidus = KBA.XBA.γBA + KCA.XCA.γCA
KBA.XBA.γBA = [B + ][A - ]
KCA.XCA.γCA = [C + ][A - ]
where KBA and KCA are the solubility products of the end members BA and CA; XBA and
XCA are mole fractions of BA and CA in the solid; γBA and γCA are the activity
coefficients as expressed first by the Guggenheim expansion series and then modified by
Redlich and Kister [60]. The above equations are used to derive the solidus curve of the
Lippmann phase diagram as a function of the solid phase. The solutus curve in the
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