In this screencast I am going to describe a solid liquid phase diagram.
This is for 2 components, titanium and uranium, and indicate which phases are present and
the relative amounts of those phases at different conditions of temperature and mole fraction
of uranium.
I am going to demonstrate this using an interactive simulation from the wolfram demonstration
project.
I have given the link here.
This is developed by some one else but you can go to that site and use it without requiring
a copy of an proprietary software.
You just have to download a free program which runs these simulations.
This simulation is developed by some one else so it looks slightly different on the website.
We just modified it a bit to make it a little easier to see in this screencast.
What I want to show you is the varies regions.
I am plotting temperature as a function of mole fraction of uranium.
It is pure uranium on the right hand side and pure titanium on the left hand side.
This line corresponds to a stoichiometric compound.
The region above is all liquid.
The region here consists of titanium plus liquid in equilibrium.
Likewise the region here consists of the stoichiometric compound plus liquid in equilibrium as does
this region.
This small region consists of uranium plus liquid in equilibrium.
These regions are all two phases.
When I say titanium I mean solid titanium compound and likewise solid uranium.
In this region below we have two solids.
One is the stoichiometric compound and the other is uranium.
Here we have two solids, titanium plus the stoichiometric compound.
If we look at a point here in that two phase region what that represents is so much liquid
and so much of the stoichiometric compound.
Over here are the relative amounts.
You can see we have more liquid because this point is not at the center but closer to the
liquid line and the lever rule, described in other screencasts, will allow you to calculate
how much in each phase.
This representation here is the relative amounts of each phase just from the lever rule and
then this is the composition.
The mole fraction is 0.48 for the liquid and the mole fraction for the compound to two
significant figures is 0.67 uranium because it is a 2 to 1 stoichiometric compound.
Now let's look at the interactive simulation briefly to give you an idea of what phases
are present under varies conditions.
What the simulation allows you to do is to move the location of this point.
I am just selecting it and moving it with the mouse.
The region here is all liquid with a mole fraction of 36 percent uranium.
If I were to cool this liquid down I would reach a point where now I have liquid plus
a small amount of this stoichiometric compound.
If we continue to cool it you can see the mole fraction of the liquid is 0.31 and the
mole fraction of the solid is 0.67.
From the lever rule we have much more liquid.
If I were to change the composition I can get to the region of two solids, pure uranium
and the stoichiometric compound.
If I move to a certain region which is hard to represent in this simulation but we can
have 3 phases present.
We can have the two solids and as the temperature rises we have liquid.
Again by continuing to raise the temperature we eventually have all liquid.
This simulation gives you an idea of what phases are present at different conditions
and the lever rule allows us to tell how much of each phase.