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Thermodynamics Basic Review of Byeong-Joo Lee Microstructure Evolution
POSTECH - MSE
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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
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Multi-Phase System Multi-Component System Partial Molar Quantities
1-2. Extension of Thermodynamics Multi-Phase System Multi-Component System Partial Molar Quantities
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Phase Diagram for H2O
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Phase Diagram for Fe
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Phase Diagram for Fe
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Equilibrium Thermal, Mechanical and Chemical Equilibrium
Concept of Chemical Potential In a one component system, Temperature and Pressure dependence of Gibbs free energy
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Temperature Dependence of Gibbs Energy
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Temperature Dependence of Gibbs Energy - for H2O
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Temperature & Pressure Dependence of Gibbs Energy
Clausius-Clapeyron equation For equilibrium between the vapor phase and a condensed phase constant constant
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Phase Diagram - for H2O for S/L equilibrium
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Equilibrium vapor pressures vs. Temperature
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Equilibrium vapor pressures vs. Temperature
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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
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Multi-Component System Partial Molar Quantities
1-2. Extension of Thermodynamics Multi-Phase System Multi-Component System Partial Molar Quantities Solution Thermodynamics
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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:
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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
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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
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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
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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
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Solution Thermodynamics - ideal vs. non-ideal solution
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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
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Solution Thermodynamics - Partial Molar Property
▷ Partial Molar Quantity ▷ Molar Properties of Mixture Gibbs-Duhem Equation
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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?
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Solution Thermodynamics - Partial Molar Quantities
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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)
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Solution Thermodynamics - Non-Ideal Solution
▷ Activity Coefficient ▷ Behavior of Dilute Solutions
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Solution Thermodynamics - Quasi-Chemical Model, Guggenheim, 1935.
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Solution Thermodynamics - Regular Solution Model
Sn-In Sn-Bi
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Solution Thermodynamics - Sub-Regular Solution Model
Sn-Zn Fe-Ni
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Solution Thermodynamics - Regular Solution Model
Composition and temperature dependence of Ω Extension into ternary and multi-component system Inherent Inconsistency Advanced Model → Sublattice Model
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Solution Thermodynamics - Advanced Gibbs Energy Model
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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
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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.
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Phase Diagrams Defect Thermodynamics
1-3. Utilization of Thermodynamics Phase Diagrams Defect Thermodynamics
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Property of a Regular Solution
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Property of a Regular Solution
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Standard States
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Standard States
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Standard States Which standard states shall we use?
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Phase Diagrams - Relation with Gibbs Energy of Solution Phases
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Phase Diagrams - Binary Systems
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Phase Equilibrium 1. Conditions for equilibrium 2. Gibbs Phase Rule 3. How to interpret Binary and Ternary Phase Diagrams ▷ Lever-Rule
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Gibbs energy of ternary alloys
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Defect Thermodynamics - Size Effect
1-3. Utilization of Thermodynamics Phase Diagrams Defect Thermodynamics - Size Effect
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Introduction - Melting Point Depression of Nano Particles
Au In M. Zhang et al. Phy. Rev. B 62 (2000) Sn S.L. Lai et al., Phys. Rev. Lett. 77 (1996) 99.
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Introduction - VLS Growth of Nanowires
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Interface Energy - Curvature effect
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Curvature Effect – Capillary Pressure
System condition T = constant Vα = Vβ = V = constant @ equilibrium
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Curvature Effect – on Vapor Pressure and Solubility
Solubility of pure B phase in a dilute solution
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Curvature Effect – Capillary Pressure Effect on Melting Point - 1
M. Zhang et al. Phy. Rev. B 62 (2000)
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Curvature Effect – Capillary Pressure Effect on Melting Point - 2
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Curvature Effect – Capillary Pressure Effect on Melting Point - 2
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Size dependence of SiGe nanowire composition – an example
I. Sa et. al., CALPHAD (2008)
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