Calculation of Phase Diagram with regular solution model in coherent phase transformation


This project looks like the same one above, but due to the totally different background, it is actually an overhaul of the project above. I put much effort on this program. Unfortunately, maybe it is too hard, I have gained little result. However, those output we could get from this program is pretty interesting and challenging for me.

Description

In the coherent phase transformaion, there could be some misfit between different phases. As a result, if there is misfit between matrix and new phase, elastic energy has to be introduced during the phase transformation. This elastic energy consume driving force of phase transformation, consequently, phase transformation needs more over heating or under cooling to provide driving force. If this kind of information be displayed on the phase diagram, it will be that during the cooling process,the equal lines of phases will move down, and during the heating process, the lines of euqal phases will move up.

The total free energy of system that two phases coexist could be expressed in the equation below:
F=(1-x)F1+xF2+Ex(1-x)--------------------------1
Here F1 is the free energy of phase 1 and F2 is the free energy of phase 2. x is the portion of phase 2 in whole system.

And one more condition is that
C = (1-x)C1 + xC2------------------------------2
Here C1 is the concentration of phase 1 and C2 is the concentration of phase 2. C is the concentration of the whole system. x is the portion of phase 2 in the whole system.

And if we put equation 1 and equation 2 together in this way.
Phi = F + kC
And then get partial derivative of Phi to C1, C2 and x, we could get that
d(Phi)/dC1 = d( Phi)/dC2 = ( F2( C2 ) - F1( C1) + E( 1 - 2x ) )/( C2 - C1 )

Then the work will be how could we solve this equatioin group.

Current work

A Java applet has been coded to calculate the phase diagram under coherent condition.

How to use it

This applet come with some initial values. Just click the button with "calculate"