Microstructure Evolution
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Microstructure Evolution. Basic Review of Thermodynamics. Byeong-Joo Lee POSTECH - MSE [email protected] Objective. Understanding and Utilizing Thermodynamic Laws State function Thermodynamic Laws Statistical thermodynamics Gibbs energy Extension of Thermodynamics

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Byeong joo lee postech mse calphad postech ac kr

Microstructure Evolution

  • BasicReviewof

    • Thermodynamics

Byeong-Joo Lee

POSTECH - MSE

[email protected]


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


Byeong joo lee postech mse calphad postech ac kr

1-2.Extensionof Thermodynamics

  • Multi-Phase System

  • Multi-Component System

  • Partial Molar Quantities


Phase diagram for h 2 o

Phase Diagram for H2O


Byeong joo lee postech mse calphad postech ac kr

Phase Diagram for Fe


Byeong joo lee postech mse calphad postech ac kr

Phase Diagram for Fe


Equilibrium

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 postech mse calphad postech ac kr

Temperature Dependence of Gibbs Energy


Byeong joo lee postech mse calphad postech ac kr

Temperature Dependence of Gibbs Energy - for H2O


Byeong joo lee postech mse calphad postech ac kr

Temperature & Pressure Dependence of Gibbs Energy

  • Clausius-Clapeyron equation

  • For equilibrium between the vapor phase and a condensed phase

constant

constant


Byeong joo lee postech mse calphad postech ac kr

Phase Diagram - for H2O

  • for S/L equilibrium


Equilibrium vapor pressures vs temperature

Equilibrium vapor pressures vs. Temperature


Byeong joo lee postech mse calphad postech ac kr

Equilibrium vapor pressures vs. Temperature


Example phase transformation of graphite to diamond

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


Byeong joo lee postech mse calphad postech ac kr

1-2.Extensionof Thermodynamics

  • Multi-Phase System

  • Multi-Component System

  • Partial Molar Quantities

SolutionThermodynamics


Byeong joo lee postech mse calphad postech ac kr

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 postech mse calphad postech ac kr

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 postech mse calphad postech ac kr

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 postech mse calphad postech ac kr

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


Byeong joo lee postech mse calphad postech ac kr

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


Byeong joo lee postech mse calphad postech ac kr

Solution Thermodynamics - ideal vs. non-ideal solution

Ideal Solution

Nonideal Solution


Byeong joo lee postech mse calphad postech ac kr

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


Byeong joo lee postech mse calphad postech ac kr

Solution Thermodynamics - Partial Molar Property

▷ Partial Molar Quantity

▷ Molar Properties of Mixture

Gibbs-Duhem Equation


Byeong joo lee postech mse calphad postech ac kr

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?


Byeong joo lee postech mse calphad postech ac kr

Solution Thermodynamics - Partial Molar Quantities


Byeong joo lee postech mse calphad postech ac kr

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)


Byeong joo lee postech mse calphad postech ac kr

Solution Thermodynamics - Non-Ideal Solution

▷ Activity Coefficient

▷ Behavior of Dilute Solutions


Byeong joo lee postech mse calphad postech ac kr

Solution Thermodynamics - Quasi-Chemical Model, Guggenheim, 1935.


Byeong joo lee postech mse calphad postech ac kr

Solution Thermodynamics - Regular Solution Model

Sn-In Sn-Bi


Byeong joo lee postech mse calphad postech ac kr

Solution Thermodynamics - Sub-Regular Solution Model

Sn-Zn Fe-Ni


Byeong joo lee postech mse calphad postech ac kr

Solution Thermodynamics - Regular Solution Model

  • Composition and temperature dependence of Ω

  • Extension into ternary and multi-component system

  • Inherent Inconsistency

  • Advanced Model → Sublattice Model


Solution thermodynamics advanced gibbs energy model

Solution Thermodynamics - AdvancedGibbs Energy Model


Byeong joo lee postech mse calphad postech ac kr

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


Byeong joo lee postech mse calphad postech ac kr

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.


Byeong joo lee postech mse calphad postech ac kr

1-3.Utilizationof Thermodynamics

  • PhaseDiagrams

  • Defect Thermodynamics


Byeong joo lee postech mse calphad postech ac kr

Propertyof a Regular Solution


Byeong joo lee postech mse calphad postech ac kr

Propertyof a Regular Solution


Byeong joo lee postech mse calphad postech ac kr

Standard States


Byeong joo lee postech mse calphad postech ac kr

Standard States


Byeong joo lee postech mse calphad postech ac kr

Standard States

Which standard states

shall we use?


Byeong joo lee postech mse calphad postech ac kr

Phase Diagrams- Relation with Gibbs Energy of Solution Phases


Byeong joo lee postech mse calphad postech ac kr

Phase Diagrams- Binary Systems


Byeong joo lee postech mse calphad postech ac kr

Phase Equilibrium

1. Conditions for equilibrium

2. Gibbs Phase Rule

3. How to interpret Binary and Ternary Phase Diagrams

▷ Lever-Rule


Gibbs energy of ternary alloys

Gibbs energy of ternary alloys


Byeong joo lee postech mse calphad postech ac kr

1-3.Utilization of Thermodynamics

  • PhaseDiagrams

  • Defect Thermodynamics

  • - Size Effect


Introduction melting point depression of nano particles

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.


Introduction vls growth of nanowires

Introduction - VLS Growth of Nanowires


Byeong joo lee postech mse calphad postech ac kr

Interface Energy - Curvature effect


Byeong joo lee postech mse calphad postech ac kr

Curvature Effect – Capillary Pressure

System condition

T = constant

Vα = Vβ = V = constant

@ equilibrium


Byeong joo lee postech mse calphad postech ac kr

Curvature Effect – on Vapor Pressure and Solubility

Vapor Pressure

Solubility of pure B phase in a dilute solution


Byeong joo lee postech mse calphad postech ac kr

Curvature Effect – Capillary Pressure Effect on Melting Point - 1

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


Byeong joo lee postech mse calphad postech ac kr

Curvature Effect – Capillary Pressure Effect on Melting Point - 2


Byeong joo lee postech mse calphad postech ac kr

Curvature Effect – Capillary Pressure Effect on Melting Point - 2


Size dependence of sige nanowire composition an example

Size dependence of SiGe nanowire composition – an example

I. Sa et. al., CALPHAD (2008)


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