**Isomorphous Binary Phase Diagrams**

03/15/17

*“Can we make a phase diagram that takes into account gradual phase transitions?”*

Classical phase diagram charts treat separate phases (solid, liquid, gas, etc.) as being completely discrete from one another. However, in the real world, phases do not immediately transition from one to another but instead undergo a gradual change in which both phases will be present. So how could we take this information and use it to reinvent phase diagrams? Well, let’s take a look. First, let’s draw out the regions where the material will be completely one phase and completely another. The empty boundary in between these regions will be where more than one phase will be present. Now how can we determine the phase composition of the material at any point within this boundary? This can be accomplished as follows. First, draw the point in which the temperature and phase composition meet. Then, draw a horizontal line from this point so that it touches both phases on opposite ends. Take the mass composition reading from these points. Then, split up these lines into two discrete regions, a for the line traveling to the phase on the left and b for the one traveling to the phase on the right. The length of A and B can be found by taking the absolute difference of the composition of the intersection and the composition given as an input. Then divide these lengths by the total length C, and that will give you the respective mass composition of each phase respectively!