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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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Presentation Transcript
slide1

Microstructure Evolution

  • BasicReviewof
    • Thermodynamics

Byeong-Joo Lee

POSTECH - MSE

[email protected]

slide2

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
slide3

1-2.Extensionof Thermodynamics

  • Multi-Phase System
  • Multi-Component System
  • Partial Molar Quantities
equilibrium
Equilibrium
  • Thermal, Mechanical and Chemical Equilibrium
  • Concept of Chemical Potential
    • In a one component system,
  • Temperature and Pressure dependence of Gibbs free energy
slide10

Temperature & Pressure Dependence of Gibbs Energy

  • Clausius-Clapeyron equation
  • For equilibrium between the vapor phase and a condensed phase

constant

constant

slide11

Phase Diagram - for H2O

  • for S/L equilibrium
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
slide15

1-2.Extensionof Thermodynamics

  • Multi-Phase System
  • Multi-Component System
  • Partial Molar Quantities

SolutionThermodynamics

slide16

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:
slide17

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

slide18

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

slide19

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

slide20

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

slide22

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

slide23

Solution Thermodynamics - Partial Molar Property

▷ Partial Molar Quantity

▷ Molar Properties of Mixture

Gibbs-Duhem Equation

slide24

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?

slide26

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)

slide27

Solution Thermodynamics - Non-Ideal Solution

▷ Activity Coefficient

▷ Behavior of Dilute Solutions

slide31

Solution Thermodynamics - Regular Solution Model

  • Composition and temperature dependence of Ω
  • Extension into ternary and multi-component system
  • Inherent Inconsistency
  • Advanced Model → Sublattice Model
slide33

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

slide34

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.
slide35

1-3.Utilizationof Thermodynamics

  • PhaseDiagrams
  • Defect Thermodynamics
slide40

Standard States

Which standard states

shall we use?

slide46

Phase Equilibrium

1. Conditions for equilibrium

2. Gibbs Phase Rule

3. How to interpret Binary and Ternary Phase Diagrams

▷ Lever-Rule

slide48

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.

slide52

Curvature Effect – Capillary Pressure

System condition

T = constant

Vα = Vβ = V = constant

@ equilibrium

slide53

Curvature Effect – on Vapor Pressure and Solubility

Vapor Pressure

Solubility of pure B phase in a dilute solution

slide54

Curvature Effect – Capillary Pressure Effect on Melting Point - 1

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

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