Byeong-Joo Lee POSTECH - MSE calphad@postech.ac.kr

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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

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

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

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 - 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 - 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 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.

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

M. Zhang et al. Phy. Rev. B 62 (2000) 10548.