Microstructure Evolution. Basic Review of Thermodynamics. Byeong-Joo Lee POSTECH - MSE [email protected] Objective. Understanding and Utilizing Thermodynamic Laws State function Thermodynamic Laws Statistical thermodynamics Gibbs energy Extension of Thermodynamics
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Microstructure Evolution
Byeong-Joo Lee
POSTECH - MSE
Objective
1-2.Extensionof Thermodynamics
Phase Diagram for Fe
Phase Diagram for Fe
Temperature Dependence of Gibbs Energy
Temperature Dependence of Gibbs Energy - for H2O
Temperature & Pressure Dependence of Gibbs Energy
constant
constant
Phase Diagram - for H2O
Equilibrium vapor pressures vs. Temperature
1-2.Extensionof Thermodynamics
SolutionThermodynamics
Thermodynamic Properties of Gases - mixture of ideal gases
1 mole of ideal gas @ constant T:
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
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
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
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
Solution Thermodynamics - ideal vs. non-ideal solution
Ideal Solution
Nonideal Solution
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
Solution Thermodynamics - Partial Molar Property
▷ Partial Molar Quantity
▷ Molar Properties of Mixture
Gibbs-Duhem Equation
Solution Thermodynamics - Partial Molar Quantity of Mixing
definition of solution and mechanical mixing
where
is a pure state value per mole
whyuse partial molar quantity?
Solution Thermodynamics - Partial Molar Quantities
Solution Thermodynamics - Partial Molar Quantities
example)
example)
Solution Thermodynamics - Non-Ideal Solution
▷ Activity Coefficient
▷ Behavior of Dilute Solutions
Solution Thermodynamics - Quasi-Chemical Model, Guggenheim, 1935.
Solution Thermodynamics - Regular Solution Model
Sn-In Sn-Bi
Solution Thermodynamics - Sub-Regular Solution Model
Sn-Zn Fe-Ni
Solution Thermodynamics - Regular Solution Model
Summary - Gibbs Energy, ChemicalPotential 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
Example
1-3.Utilizationof Thermodynamics
Propertyof a Regular Solution
Propertyof a Regular Solution
Standard States
Standard States
Standard States
Which standard states
shall we use?
Phase Diagrams- Relation with Gibbs Energy of Solution Phases
Phase Diagrams- Binary Systems
Phase Equilibrium
1. Conditions for equilibrium
2. Gibbs Phase Rule
3. How to interpret Binary and Ternary Phase Diagrams
▷ Lever-Rule
1-3.Utilization of Thermodynamics
Au
In
M. Zhang et al. Phy. Rev. B 62 (2000) 10548.
Sn
S.L. Lai et al., Phys. Rev. Lett. 77 (1996) 99.
Interface Energy - Curvature effect
Curvature Effect – Capillary Pressure
System condition
T = constant
Vα = Vβ = V = constant
@ equilibrium
Curvature Effect – on Vapor Pressure and Solubility
Vapor Pressure
Solubility of pure B phase in a dilute solution
Curvature Effect – Capillary Pressure Effect on Melting Point - 1
M. Zhang et al. Phy. Rev. B 62 (2000) 10548.
Curvature Effect – Capillary Pressure Effect on Melting Point - 2
Curvature Effect – Capillary Pressure Effect on Melting Point - 2
I. Sa et. al., CALPHAD (2008)