1. Summer School for Integrated Computational Materials Education 2018 Thermodynamics Module Q&A

2. Thermodynamic Properties
CALPHAD Methodology
Fundamental
Theory
Empirical
Rules
Experimental
Data
Models
Experimental Determination
Ab Initio Calculation
Parameter
Optimization
Database
Thermodynamic Properties
Equilibrium States
Phase Diagrams

3. Thermodynamic Modeling
Gibbs energy per mole for a solution phase is normally divided in:
excess term
reference surface
physical contribution
configurational contribution
Ideal solution model
Regular solution model
Real solution

4. Different Models (Binary)
Ideal solution
Regular solution
Real solution
Summer School for Integrated Computational Materials Education Ann Arbor, MI June 4-15, 2018

5. Q1. Which model to use?
For teaching, simple models are sufficient and instructive
Ideal solution term has a single well
Preferred interactions between the same species penalizes mixing
Single phase to two phase transition
For scientific & engineering predications, accurate models & parameters are required
Summer School for Integrated Computational Materials Education Ann Arbor, MI June 4-15, 2018

6. Q2. How is extrapolation done
There are many parameters that comes with the models
As the number of components increases, so does the number of parameters
Fits to experimental data sets the parameters, but the range is limited
Interpolation if within the range; extrapolation if outside
Summer School for Integrated Computational Materials Education Ann Arbor, MI June 4-15, 2018

7. Q3. How can the concentration be different if the chemical potential is the same? Q4. Phase diagrams/minimum free energy

8. Phase Stability: Common Tangent Const.
+ 
Thermodynamics in Materials Engineering R.E. Napolitano

9. Chemical Equilibrium
When chemical potential of each species is constant throughout, the system is in chemical equilibrium
In single phase material, the chemical potential is constant when the concentration of all species are constant.
When multiple phases are present, the equilibrium concentration must be constant in each phase, but they can be different from one phase to another so that the chemical potential of each species are constant.
Thornton

10. Phase Stability: Common Tangent Const.
+ 
Thornton
MSE 454 F15
Used with permission
Thermodynamics in Materials Engineering R.E. Napolitano

11. Phase Stability: Const. of Phase Diagram
GA vs T
GB vs T G   T  XB
Thornton
MSE 454 F15
Used with permission
Thermodynamics in Materials Engineering R.E. Napolitano

12. Phase Stability: Const. of Phase Diagram
GA vs T
GB vs T G   T  XB
Thornton
MSE 454 F15
Used with permission
Thermodynamics in Materials Engineering R.E. Napolitano

13. Phase Stability: Const. of Phase Diagram
GA vs T
GB vs T G   T XB
Thornton
MSE 454 F15
Used with permission
Thermodynamics in Materials Engineering R.E. Napolitano

14. Phase Stability: Const. of Phase Diagram
GA vs T
GB vs T G   T XB
Thornton
MSE 454 F15
Used with permission
Thermodynamics in Materials Engineering R.E. Napolitano

15. Phase Stability: Const. of Phase Diagram
GA vs T
GB vs T G   T XB
Thornton
MSE 454 F15
Used with permission
Thermodynamics in Materials Engineering R.E. Napolitano

16. Phase Stability: Const. of Phase Diagram
GA vs T
GB vs T G   T XB
Thornton
MSE 454 F15
Used with permission
Thermodynamics in Materials Engineering R.E. Napolitano

17. Phase Stability: Const. of Phase Diagram
GA vs T
GB vs T G  T  XB
Thornton
MSE 454 F15
Used with permission
Thermodynamics in Materials Engineering R.E. Napolitano

18. Phase Stability: Const. of Phase Diagram
GA vs T
GB vs T G   T  XB
Thornton
MSE 454 F15
Used with permission
Thermodynamics in Materials Engineering R.E. Napolitano

19. Phase Stability: Const. of Phase Diagram
GA vs T
GB vs T G  T  XB
Thornton
MSE 454 F15
Used with permission
Thermodynamics in Materials Engineering R.E. Napolitano

20. Phase Stability: Const. of Phase Diagram
GA vs T
GB vs T G  T  XB
Thornton
MSE 454 F15
Used with permission
Thermodynamics in Materials Engineering R.E. Napolitano

21. Phase Stability: Const. of Phase Diagram
GA vs T
GB vs T G   T   XB
Thornton
MSE 454 F15
Used with permission
Thermodynamics in Materials Engineering R.E. Napolitano

22. Double-Well Free Energy Case
Ag-Cu system: Free energy & phase diagram
Thornton
MSE454 F16

23. Q5. Isopleth Q6. Multicomponent system

24. Isotherm & Isopleth Ternary phase diagram is actually 3D
To plot on paper quantitatively, you need to cut in some direction
Isotherm (T=constant)
Isopleth (one composition = constant)
Figure by Elmer Prenzlow
Summer School for Integrated Computational Materials Education Ann Arbor, MI June 4-15, 2018

25. Systems with more than 3 components
In order to visualize, additional concentration must be fixed
If there is a component that has low solubility, they precipitate out (so fix it at the solubility limit)
Multiple sections are needed to fully represent the phase diagram
Isothermal sections are also made along constant concentration (isopleth)
Summer School for Integrated Computational Materials Education Ann Arbor, MI June 4-15, 2018

26. Drawing common tangent electronically
My students typically use power point to do this.
Summer School for Integrated Computational Materials Education Ann Arbor, MI June 4-15, 2018