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Microstructure Evolution. Basic Review of Thermodynamics. Byeong-Joo Lee POSTECH - MSE calphad@postech.ac.kr. Objective. Understanding and Utilizing Thermodynamic Laws State function Thermodynamic Laws Statistical thermodynamics Gibbs energy Extension of Thermodynamics
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Microstructure Evolution • BasicReviewof • Thermodynamics Byeong-Joo Lee POSTECH - MSE calphad@postech.ac.kr
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
1-2.Extensionof Thermodynamics • Multi-Phase System • Multi-Component System • Partial Molar Quantities
Equilibrium • Thermal, Mechanical and Chemical Equilibrium • Concept of Chemical Potential • In a one component system, • Temperature and Pressure dependence of Gibbs free energy
Temperature & Pressure Dependence of Gibbs Energy • Clausius-Clapeyron equation • For equilibrium between the vapor phase and a condensed phase constant constant
Phase Diagram - for H2O • for S/L equilibrium
Example - Phase Transformation of Graphite to Diamond • Calculate graphite→diamond transformation pressure at 298 K, given • H298,gra – H298,dia = -1900 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 = 3.515 g/cm3
1-2.Extensionof Thermodynamics • Multi-Phase System • Multi-Component System • Partial Molar Quantities SolutionThermodynamics
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:
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 • 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)
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 • Composition and temperature dependence of Ω • Extension into ternary and multi-component system • Inherent Inconsistency • Advanced Model → Sublattice 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 • What is the difference between Gibbs energy of formation • andGibbs 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 aHenrian behavior • in dilute region and a Raoultian behavior in rich region, • if the molar Gibbs energy is expressed as follows.
1-3.Utilizationof Thermodynamics • PhaseDiagrams • Defect Thermodynamics
Standard States Which standard states shall we use?
Phase Diagrams- Relation with Gibbs Energy of Solution Phases
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 • PhaseDiagrams • Defect Thermodynamics • - Size Effect
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.
