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

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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

Phase Diagram for Fe

Phase Diagram for Fe

- Thermal, Mechanical and Chemical Equilibrium
- Concept of Chemical Potential
- In a one component system,

- Temperature and Pressure dependence of Gibbs free energy

Temperature Dependence of Gibbs Energy

Temperature Dependence of Gibbs Energy - for H2O

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

Equilibrium vapor pressures vs. Temperature

- 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

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

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

- PhaseDiagrams
- Defect Thermodynamics
- - Size Effect

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)