Modeling short-range ordering (SRO) in solutions. Arthur D. Pelton and Youn-Bae Kang Centre de Recherche en Calcul Thermochimique, Départ ement de Génie Chimique, École Polytechnique P.O. Box 6079, Station "Downtown" Montréal, Québec H3C 3A7 Canada.
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Arthur D. Pelton and Youn-Bae Kang
Centre de Recherche en Calcul Thermochimique,
Département de Génie Chimique,
P.O. Box 6079, Station "Downtown"
Montréal, Québec H3C 3A7
(no short-range ordering)
A + B = AB ; wAS
AB “associates” and unassociated A and B are randomly distributed over the lattice sites.
Per mole of solution:
A and B distributed non-randomly on lattice sites
(A-A)pair + (B-B)pair = 2(A-B)pair ; wQM
ZXA = 2 nAA + nAB
ZXB = 2 nBB + nAB
Z = coordination number
nij= moles of pairs
Xij= pair fraction = nij /(nAA + nBB + nAB)
The pairs are distributed randomly over “pair sites”
Term for remaining lattice interactions
The quasichemical model with Z = 2 tends to give DH and DSconfig functions with minima which are too sharp. (The associate model also has this problem.)
Combining the quasichemical and Bragg-Williams models
DSconfig as for quasichemical model
This also results in DH and DSconfig functions with minima which are less sharp.
The drawback is that the entropy expression is now only approximate.
Let ZCa = 2 ZAl
ZAXA = 2 nAA + nAB
ZBXB = 2 nBB + nAB
Raoult’s Law is obeyed as XCa1.
Al-Sc binary liquids exhibit strong SRO
Mg-Sc and Al-Mg binary liquids are less ordered
positive deviations result along the AB-C join.
The Bragg-Williams modeloverestimatesthese deviations because it neglects SRO.
Taking SRO into account with the associate model makes thingsworse!
Now the positive deviations along the AB-C join are not predicted at all. Along this join the model predicts a random mixture of AB associates and C atoms.
Correct predictions are obtained but these depend upon the choice of the ratio (wBW /wQM) with Z = 2, or alternatively, upon the choice of Z if wBW= 0.
Short-range ordering with positive deviations from ideality (clustering)
Bragg-Williams model with wBW > 0 gives miscibility gaps which often are too rounded. (Experimental gaps have flatter tops.)
With Z = 2 and wQM > 0, positive deviations are predicted, but immiscibility never results.