MSE 508
Solid State Thermodynamics
Dept. of Materials Science & Engineering
Bill Knowlton
Project 2
Computational Generation of Equilibrium Binary Compositional Phase Diagrams
(Due Thursday April 7th)
Project:
The project contains several parts due at various times.
Part 1: Go to the equilibrium binary phase diagrams of the binary systems on the Facility for the
Analysis of Chemical Thermodynamics (FACT) website:
http://www.crct.polymtl.ca/fact/
Choose an Equilibrium Binary Phase Diagram system that you would like to generate with your
program that must have the following aspects:
 Eutectic or peritectic phase diagram
 Visible solidus and liquidus on both sides of the diagram
o Examples: Ag-Cu, Ag-Cd, Bi-Pb (extra credit if your program can draw this one),
Bi-Sn, Pb-Sn, Ag-Pt, Au-Cr, Er-Tb, Pb-Hg, Pb-Cd, Rh-Ru, Pt-Ru, In-Pb
 Journal or conference publication with data required
Due: In class, March 24th; First one to turn one in, then it is off limits to others.
Part 2: Unless you have already done this in a previous/current problem set, you will first
mathematically derive the equations to:
1. Plot the Gmix’s for ,  and L over a range of temperatures.
2. To generate an equilibrium phase diagram for ,  and L. Specifically, the equations you
derive should be able to be used to calculate composition points of phase equilibrium
from free energy versus composition curves over a range of temperatures. One approach
to this part is to start with the equilibrium conditions for the system.
The equations should be in general form. Then, apply the equations to the regular solution
model. Please provide a description of your approach to the derivations.
Due: March 31st
Part 3: You will write a program using a mathematical numerical program of your choice (not
Excel). The program will incorporate your equations to calculate composition points of phase
equilibrium from free energy versus composition curves over a range of temperatures. The
program will plot both the free energy versus composition curves of various phases and the
composition points of phase equilibrium for any number of 2-phase regions and combine them
on one temperature versus composition plot. The plot should label all the single and 2-phase
regions. The program should be able to do so using a variety of solution models including the
ideal, regular and sub or non regular solution (e.g., Redlich-Kister Model, AppendixD, DeHoff)
models. Yes, your program should prompt the user as to which model it should use.
Due: Thursday after spring break (April 8th)
Program Capability:
Input:
xs
xs
xs
 Gmix
and/or H mix
and/or S mix
which provides an input for the solution model of choice
by the user.
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MSE 508
Solid State Thermodynamics
Dept. of Materials Science & Engineering
Bill Knowlton

H kop1  p2 and/or Skop1  p2 and/or Gkop1  p2 for all phases and components. The Tmelt for all
pure components should be included or checked relative to the assumption
H kop1  p2  Tmelt ,k S kop1  p2

Solution model’s accompanying input data such as fitting parameters
Output: (simultaneously – i.e., in the same program)
?
 Plot of free energy curves ( Gmix
?;? ) versus X2 over a range of temperatures, T
?
o Extra Credit: If the tangent lines are included with the Gmix
?;? versus X2

Plot an equilibrium phase diagram, T versus X2, using equilibria data from free energy curves
versus X2.
Note: I should be able to run the program and obtain both the free energy curves and the phase
diagram.
Specific Problem to Solve:
Specifically, have your program generate the data and plot the equilibrium binary phase
diagrams of the binary systems some of which can be found on the Facility for the Analysis of
Chemical Thermodynamics (FACT) website:
http://www.crct.polymtl.ca/fact/
In order to determine the melting points and H kop1  p2 or Skop1  p2 to determine the equation for
Gkop1  p2 , you will need to obtain references for the data. Furthermore, the references will most
likely use a form of the Redlich-Kister approach (see Appendix D, DeHoff), so you will need to
obtain the Redlich-Kister fitting parameters as well.
Note: You may work together to examine various approaches to solve the problem and develop
algorithms. However, each person must generate their own program. Copy each other’s program
is not allowed.
Related Information
 Each person does their own project
 Email me your:
o Phase diagram
o Program
o Copies of your references (e.g., journal articles, reference articles, etc.)
 You will present your program to me personally either during office hours or at a makeup class time
 Put your program on the W:\everyone drive BEFORE visiting me if your program is
Mathematica
 Alternatively, have your laptop with you with the program on it
 Provide a hard copy of the program to me
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MSE 508
Solid State Thermodynamics



Dept. of Materials Science & Engineering
Bill Knowlton
Cite all references used. Limit your use of online material in your reference list unless it
is a refereed paper or it is referenced and you run it by me. However, you can use the
online material to familiarize yourself with the subject
Provide actual phase diagram examples of the phase diagrams you generated
Your program should be thoroughly documented with comments throughout and be
straightforward to understand your methodology and easy to follow and read. The
program should be in a word processing style.
Grading
 See grade sheet
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