Building theoretical model for phase seperation

[susdu]

I have three elements, A, B, C, that under certain conditions (rapid heating and cooling)
form one ABC phase solid. Sometimes when I add a fourth element, D, I get two phase (AB,CD) solid.
Obviously this phenomena is thermodynamically favourable. My guess (still undergraduate)
is that there is a solubility limit in the solid phase of these elements in a way that beyond a
certain amount of D, the chemical potential of the ABCD phase is higher than that of two-phase
solid.

I want to offer a model that will explain this phenomena. Problems are:
1. This is a process that occurs in high temperatures and pressure (4000K and 40,000psi in 1 millisecond) so it can't be easily reproduced in the lab.
2. I didn't find any phase diagrams of A-B-C-D and their combinations.
3. Prior research on the subject is almost non existent.

I really don't know where to start. This is not homework, it's a research project I'm interested in.
I'll appreciate any help/direction.

 

[Bobbywhy]

The conditions of your experiment are indeed difficult to reproduce in any laboratory! Some shock tubes for blast wave simulation have been operated at such temperatures and pressures, but are rare and expensive. An overview can be found here:
http://en.wikipedia.org/wiki/Shock_tube

Here a powerful and high pressure system is described:
http://arxiv.org/ftp/arxiv/papers/1105/1105.4670.pdf

Here is one computational method that possibly could be applicable:
“The Bhatnagar–Gross–Krook (BGK) model of the Boltzmann Equation”
http://www.math.ust.hk/~makxu/PAPER/aiaa-shock.pdf

One more computational method:
High temperature shock wave interaction in heavy gases - Computations
Bei Wang, Maryland, Univ., College Park; Harland Glaz, Maryland, Univ., College Park
http://arc.aiaa.org/doi/abs/10.2514/6.1999-3577

May I suggest you use the units “Pascals” for pressure, and not psi? These units are used throughout the literature.
40 000 pound/square inch = 275 790 291.2 pascal, or 275.8 Mpa