1. Thermodynamics Basic Review of Byeong-Joo Lee Microstructure Evolution
POSTECH - MSE

2. Understanding and Utilizing Thermodynamic Laws
Objective
Understanding and Utilizing Thermodynamic Laws
State function
Thermodynamic Laws
Statistical thermodynamics
Gibbs energy
Extension of Thermodynamics
Multi-Phase System
Multi-Component System
Partial Molar Quantities
Utilization of Thermodynamics
Phase Diagrams
Defect Thermodynamics

3. Multi-Phase System Multi-Component System Partial Molar Quantities
1-2. Extension of Thermodynamics
Multi-Phase System
Multi-Component System
Partial Molar Quantities

4. Phase Diagram for H2O

5. Phase Diagram for Fe

6. Phase Diagram for Fe

7. Equilibrium Thermal, Mechanical and Chemical Equilibrium
Concept of Chemical Potential
In a one component system,
Temperature and Pressure dependence of Gibbs free energy

8. Temperature Dependence of Gibbs Energy

9. Temperature Dependence of Gibbs Energy - for H2O

10. Temperature & Pressure Dependence of Gibbs Energy
Clausius-Clapeyron equation
For equilibrium between the vapor phase and a condensed phase
constant
constant

11. Phase Diagram - for H2O
for S/L equilibrium

12. Equilibrium vapor pressures vs. Temperature

13. Equilibrium vapor pressures vs. Temperature

14. Example - Phase Transformation of Graphite to Diamond
Calculate graphite→diamond transformation pressure at 298 K, given
H298,gra – H298,dia = J
S298,gra = 5.74 J/K
S298,dia = 2.37 J/K
density of graphite at 298 K = 2.22 g/cm3
density of diamond at 298 K = g/cm3

15. Multi-Component System Partial Molar Quantities
1-2. Extension of Thermodynamics
Multi-Phase System
Multi-Component System
Partial Molar Quantities
Solution Thermodynamics

16. Thermodynamic Properties of Gases - mixture of ideal gases
1 mole of ideal constant T:
Mixture of Ideal Gases
Definition of Mole fraction: xi
Definition of partial pressure: pi
Partial molar quantities:

17. Thermodynamic Properties of Gases - mixture of ideal gases
Heat of Mixing of Ideal Gases
Gibbs Free Energy of Mixing of Ideal Gases
Entropy of Mixing of Ideal Gases

18. Thermodynamic Properties of Gases - Treatment of nonideal gases
Introduction of fugacity, f as
For Equation of state
※ actual pressure of the gas is the geometric mean of the fugacity and the ideal P
※ The percentage error involved in assuming the fugacity to be equal to the
pressure is the same as the percentage departure from the ideal gas law

19. Thermodynamic Properties of Gases - Treatment of nonideal gases
Alternatively,
Example) Difference between the Gibbs energy at P=150 atm and P=1 atm
for 1 mole of nitrogen at 0 oC

20. Solution Thermodynamics - Mixture of Condensed Phases
Vapor A: oPA
Condensed Phase A
Vapor B: oPB
Condensed Phase B
Vapor A+ B: PA + PB
Condensed Phase A + B + →
for gas

21. Solution Thermodynamics - ideal vs. non-ideal solution

22. Solution Thermodynamics - Thermodynamic Activity
Thermodynamic Activity of a Component in Solution →
for ideal solution
Draw a composition-activity curve for an ideal and non-ideal solution
Henrian vs. Raoultian

23. Solution Thermodynamics - Partial Molar Property
▷ Partial Molar Quantity
▷ Molar Properties of Mixture
Gibbs-Duhem Equation

24. Solution Thermodynamics - Partial Molar Quantity of Mixing
definition of solution and mechanical mixing
where
is a pure state value per mole
why use partial molar quantity?

25. Solution Thermodynamics - Partial Molar Quantities

26. Solution Thermodynamics - Partial Molar Quantities
Evaluation of Partial Molar Properties in 1-2 Binary System
Partial Molar Properties from Total Properties
example)
Partial molar & Molar Gibbs energy
Gibbs energy of mixing vs. Gibbs energy of formation
Graphical Determination of Partial Molar Properties: Tangential Intercepts
Evaluation of a PMP of one component from measured values of a PMP
of the other
example)

27. Solution Thermodynamics - Non-Ideal Solution
▷ Activity Coefficient
▷ Behavior of Dilute Solutions

28. Solution Thermodynamics - Quasi-Chemical Model, Guggenheim, 1935.

29. Solution Thermodynamics - Regular Solution Model
Sn-In Sn-Bi

30. Solution Thermodynamics - Sub-Regular Solution Model
Sn-Zn Fe-Ni

31. Solution Thermodynamics - Regular Solution Model
Composition and temperature dependence of Ω
Extension into ternary and multi-component system
Inherent Inconsistency
Advanced Model → Sublattice Model

32. Solution Thermodynamics - Advanced Gibbs Energy Model

33. Summary - Gibbs Energy, Chemical Potential and Activity
▷ Gibbs energy of mixing vs. Gibbs energy of formation
▷ activity wrt. liquid A or B
▷ activity wrt. “ref” A or B
▷ activity wrt. [ ] i
▷ activity wrt. [ ] i

34. Example What is the difference between Gibbs energy of formation
and Gibbs energy of mixing?
2. What do Henrian behavior and Raoultian behavior mean for
a solution? Consider an A-B binary solution phase.
Show that each component shows a Henrian behavior
in dilute region and a Raoultian behavior in rich region,
if the molar Gibbs energy is expressed as follows.

35. Phase Diagrams Defect Thermodynamics
1-3. Utilization of Thermodynamics
Phase Diagrams
Defect Thermodynamics

36. Property of a Regular Solution

37. Property of a Regular Solution

38. Standard States

39. Standard States

40. Standard States
Which standard states
shall we use?

44. Phase Diagrams - Relation with Gibbs Energy of Solution Phases

45. Phase Diagrams - Binary Systems

46. Phase Equilibrium
1. Conditions for equilibrium
2. Gibbs Phase Rule
3. How to interpret Binary and Ternary Phase Diagrams
▷ Lever-Rule

47. Gibbs energy of ternary alloys

48. Defect Thermodynamics - Size Effect
1-3. Utilization of Thermodynamics
Phase Diagrams
Defect Thermodynamics
- Size Effect

49. Introduction - Melting Point Depression of Nano ParticlesAu In
M. Zhang et al. Phy. Rev. B 62 (2000) Sn
S.L. Lai et al., Phys. Rev. Lett. 77 (1996) 99.

50. Introduction - VLS Growth of Nanowires

51. Interface Energy - Curvature effect

52. Curvature Effect – Capillary Pressure
System condition
T = constant
Vα = Vβ = V = constant
@ equilibrium

53. Curvature Effect – on Vapor Pressure and Solubility
Solubility of pure B phase in a dilute solution

54. Curvature Effect – Capillary Pressure Effect on Melting Point - 1
M. Zhang et al. Phy. Rev. B 62 (2000)

55. Curvature Effect – Capillary Pressure Effect on Melting Point - 2

56. Curvature Effect – Capillary Pressure Effect on Melting Point - 2

57. Size dependence of SiGe nanowire composition – an example
I. Sa et. al., CALPHAD (2008)