Microstructure Evolution Basic Review of Thermodynami cs ByeongJoo
Microstructure Evolution Basic Review of Thermodynami cs Byeong-Joo Lee POSTECH - MSE calphad@postech. ac. kr Byeong-Joo Lee www. postech. ac. kr/~calphad
Objective Ø Understanding and Utilizing Thermodynamic Laws ü ü State function Thermodynamic Laws Statistical thermodynamics Gibbs energy Ø Extension of Thermodynamics ü ü ü Multi-Phase System Multi-Component System Partial Molar Quantities Ø Utilization of Thermodynamics ü ü Phase Diagrams Defect Thermodynamics Byeong-Joo Lee www. postech. ac. kr/~calphad
1 -2. Extension of Thermodynamics ü Multi-Phase System ü Multi-Component System ü Partial Molar Quantities Byeong-Joo Lee www. postech. ac. kr/~calphad
Phase Diagram for H 2 O Byeong-Joo Lee www. postech. ac. kr/~calphad
Phase Diagram for Fe Byeong-Joo Lee www. postech. ac. kr/~calphad
Phase Diagram for Fe Byeong-Joo Lee www. postech. ac. kr/~calphad
Equilibrium • Thermal, Mechanical and Chemical Equilibrium • Concept of Chemical Potential In a one component system, • Temperature and Pressure dependence of Gibbs free energy Byeong-Joo Lee www. postech. ac. kr/~calphad
Temperature Dependence of Gibbs Energy Byeong-Joo Lee www. postech. ac. kr/~calphad
Temperature Dependence of Gibbs Energy for H 2 O Byeong-Joo Lee www. postech. ac. kr/~calphad
Temperature & Pressure Dependence of Gibbs Energy Clausius-Clapeyron equation For equilibrium between the vapor phase and a condensed phase constant Byeong-Joo Lee www. postech. ac. kr/~calphad
Phase Diagram - for H 2 O for S/L equilibrium Byeong-Joo Lee www. postech. ac. kr/~calphad
Equilibrium vapor pressures vs. Temperature Byeong-Joo Lee www. postech. ac. kr/~calphad
Equilibrium vapor pressures vs. Temperature Byeong-Joo Lee www. postech. ac. kr/~calphad
Example - Phase Transformation of Graphite to • Diamond Calculate graphite→diamond transformation pressure at 298 K, given H 298, gra – H 298, dia = -1900 J S 298, gra = 5. 74 J/K S 298, dia = 2. 37 J/K density of graphite at 298 K = 2. 22 g/cm 3 density of diamond at 298 K = 3. 515 g/cm 3 Byeong-Joo Lee www. postech. ac. kr/~calphad
1 -2. Extension of Thermodynamics ü Multi-Phase System ü Multi-Component System ü Partial Molar Quantities Solution Thermodynamics Byeong-Joo Lee www. postech. ac. kr/~calphad
Thermodynamic Properties of Gases - mixture of ideal gases 1 mole of ideal gas @ constant T: Mixture of Ideal Gases Definition of Mole fraction: xi Definition of partial pressure: pi Partial molar quantities: Byeong-Joo Lee www. postech. ac. kr/~calphad
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 Byeong-Joo Lee www. postech. ac. kr/~calphad
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 Byeong-Joo Lee www. postech. ac. kr/~calphad
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 o. C Byeong-Joo Lee www. postech. ac. kr/~calphad
Solution Thermodynamics - Mixture of Condensed Phases Vapor A: o. PA Vapor B: o. PB + Condensed Phase A Vapor A+ B: PA + PB → Condensed Phase B Condensed Phase A + B for gas Byeong-Joo Lee www. postech. ac. kr/~calphad
Solution Thermodynamics - ideal vs. non-ideal solution Ideal Solution Nonideal Solution Byeong-Joo Lee www. postech. ac. kr/~calphad
Solution Thermodynamics - Thermodynamic Activity of a Component in Solution → for ideal solution Draw a composition-activity curve for an ideal and nonideal solution Henrian vs. Raoultian Byeong-Joo Lee www. postech. ac. kr/~calphad
Solution Thermodynamics - Partial Molar Property ▷ Partial Molar Quantity ▷ Molar Properties of Mixture Gibbs-Duhem Equation Byeong-Joo Lee www. postech. ac. kr/~calphad
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? Byeong-Joo Lee www. postech. ac. kr/~calphad
Solution Thermodynamics - Partial Molar Quantities Byeong-Joo Lee www. postech. ac. kr/~calphad
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 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) Byeong-Joo Lee www. postech. ac. kr/~calphad
Solution Thermodynamics - Non-Ideal Solution ▷ Activity Coefficient ▷ Behavior of Dilute Solutions Byeong-Joo Lee www. postech. ac. kr/~calphad
Solution Thermodynamics - Quasi-Chemical Model, Guggenheim, 1935. Byeong-Joo Lee www. postech. ac. kr/~calphad
Solution Thermodynamics - Regular Solution Model Sn-In Sn-Bi Byeong-Joo Lee www. postech. ac. kr/~calphad
Solution Thermodynamics - Sub-Regular Solution Model Sn-Zn Fe-Ni Byeong-Joo Lee www. postech. ac. kr/~calphad
Solution Thermodynamics - Regular Solution Model • Composition and temperature dependence of Ω • Extension into ternary and multi-component system • Inherent Inconsistency • Advanced Model → Sublattice Model Byeong-Joo Lee www. postech. ac. kr/~calphad
Solution Thermodynamics - Advanced Gibbs Energy Model Byeong-Joo Lee www. postech. ac. kr/~calphad
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 Byeong-Joo Lee www. postech. ac. kr/~calphad
Example 1. 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. Byeong-Joo Lee www. postech. ac. kr/~calphad
1 -3. Utilization of Thermodynamics ü Phase Diagrams ü Defect Thermodynamics Byeong-Joo Lee www. postech. ac. kr/~calphad
Property of a Regular Solution Byeong-Joo Lee www. postech. ac. kr/~calphad
Property of a Regular Solution Byeong-Joo Lee www. postech. ac. kr/~calphad
Standard States Byeong-Joo Lee www. postech. ac. kr/~calphad
Standard States Byeong-Joo Lee www. postech. ac. kr/~calphad
Standard States Which standard states shall we use? Byeong-Joo Lee www. postech. ac. kr/~calphad
Byeong-Joo Lee www. postech. ac. kr/~calphad
Byeong-Joo Lee www. postech. ac. kr/~calphad
Byeong-Joo Lee www. postech. ac. kr/~calphad
Phase Diagrams - Relation with Gibbs Energy of Solution Phases Byeong-Joo Lee www. postech. ac. kr/~calphad
Phase Diagrams - Binary Systems Byeong-Joo Lee www. postech. ac. kr/~calphad
Phase Equilibrium 1. Conditions for equilibrium 2. Gibbs Phase Rule 3. How to interpret Binary and Ternary Phase Diagrams ▷ Lever-Rule Byeong-Joo Lee www. postech. ac. kr/~calphad
Gibbs energy of ternary alloys Byeong-Joo Lee www. postech. ac. kr/~calphad
1 -3. Utilization of Thermodynamics ü Phase Diagrams ü Defect Thermodynamics - Size Effect Byeong-Joo Lee www. postech. ac. kr/~calphad
Introduction - Melting Point Depression of Nano Particles Au In M. Zhang et al. Phy. Rev. B 62 (2000) 10548. Sn S. L. Lai et al. , Phys. Rev. Lett. 77 (1996) 99. Byeong-Joo Lee www. postech. ac. kr/~calphad
Introduction - VLS Growth of Nanowires Byeong-Joo Lee www. postech. ac. kr/~calphad
Interface Energy - Curvature effect Byeong-Joo Lee www. postech. ac. kr/~calphad
Curvature Effect – Capillary Pressure System condition T = constant Vα = Vβ = V = constant @ equilibrium Byeong-Joo Lee www. postech. ac. kr/~calphad
Curvature Effect – on Vapor Pressure and Solubility Vapor Pressure Solubility of pure B phase in a dilute solution Byeong-Joo Lee www. postech. ac. kr/~calphad
Curvature Effect – Capillary Pressure Effect on Melting Point - 1 M. Zhang et al. Phy. Rev. B 62 (2000) 10548. Byeong-Joo Lee www. postech. ac. kr/~calphad
Curvature Effect – Capillary Pressure Effect on Melting Point - 2 Byeong-Joo Lee www. postech. ac. kr/~calphad
Curvature Effect – Capillary Pressure Effect on Melting Point - 2 Byeong-Joo Lee www. postech. ac. kr/~calphad
Size dependence of Si. Ge nanowire composition – an example I. Sa et. al. , CALPHAD (2008) Byeong-Joo Lee www. postech. ac. kr/~calphad
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