Calculate solubility vs. temperatures for new designed phases or solid solutions

[sydxajie]

Dear Colleagues,
Recently I'm learning the kinetic modeling, but have a very basic issue but puzzled me a lot. That is the calculation of the thermochemical parameters for added phases.
In the llnl.dat database, a lot of end-member minerals were designed. How about a mixture mineral which we can see it as an ideal solid solution, The question is how to get the log_k, -analytic, and -delta_H parameters. Here is the case:
1.  NaAlSi3O8 from llnl.dat

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NaAlSi3O8 +4.0000 H+  =  + 1.0000 Al+++ + 1.0000 Na+ + 2.0000 H2O + 3.0000 SiO2
        log_k           2.7645
-delta_H -51.8523 kJ/mol # Enthalpy of formation: -939.68 kcal/mol
        -analytic -1.1694e+001 1.4429e-002 1.3784e+004 -7.2866e+000 -1.6136e+006
#       -Range:  0-3002.  CaAl2Si2O8

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CaAl2Si2O8 +8.0000 H+  =  + 1.0000 Ca++ + 2.0000 Al+++ + 2.0000 SiO2 + 4.0000 H2O
        log_k           26.5780
-delta_H -303.039 kJ/mol # Enthalpy of formation: -1007.55 kcal/mol
        -analytic 3.9717e-001 -1.8751e-002 1.4897e+004 -6.3078e+000 -2.3885e+005
#       -Range:  0-300
If a mixture of solid solution and its reactions are:

Ca0.4Na0.6Al1.4Si2.6O8 (equals to 0.6NaAlSi3O8 and 0.4CaAl2Si2O8, presume it as ideal solid solution)

Ca0.4Na0.6Al1.4Si2.6O8 + 5.6H+ + 2.4H2O = 0.4Ca+2 + 0.6Na+ + 1.4Al+3 + 2.6H4SiO4

So, how can I get the  log_k, -analytic and/or -delta_H parameters from the two end-members?

What I know is after getting the data for Log_k vs Temp, we can use Matlab to get the -analytic parameters.

[dlparkhurst]

As a first approximation, if you are adding fractions of albite and anorthite, the log K and delta H are the fractional sums of the end-member values, or the fractional sum of the parameters of the end-member analytical-expression parameters. Note that you are considering the new phase as a fixed-composition phase that dissolves and precipitates in the fixed stoichiometry.

SOLID_SOLUTION is another possibility, which allows for a variable composition solid. If you define an ideal SOLID_SOLUTION, then, at equilibrium, the mass-action equations for albite and anorthite will be satisfied, with the addition of a mole fraction factor in the denominator:

K(alb) = SR(alb)/x(alb),

where K is equilibrium constant, SR is saturation ratio, and x is mole fraction. The solid solution will be a variable composition solid that adjusts to equilibrium with the solution. A solid solution is always more stable than either of the end members.

There are other options for a non-ideal binary solid solution. The parameters for a non-ideal solid solution can be defined in multiple ways, but the result is that an activity coefficient is defined such that the following equation is satisfied:

K(alb) = SR(alb) / [x(alb)*g(alb)],

where g is the activity coefficient; and also for anorthite. Again, as in the ideal case, this will be a variable composition solid solution.

Kinetic modeling of a solid solution is another issue. One approach is to define a SOLID_SOLUTION, with zero moles of each component. Then, you kinetically introduce the fixed composition solid solution. Ultimately, a variable composition solid solution will begin to precipitate. Maybe this approach is appropriate or not, you will have to decide your conceptual model.