Microstructure Evolution
This presentation is the property of its rightful owner.
Sponsored Links
1 / 57

Byeong-Joo Lee POSTECH - MSE [email protected] PowerPoint PPT Presentation


  • 154 Views
  • Uploaded on
  • Presentation posted in: General

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

Download Presentation

Byeong-Joo Lee POSTECH - MSE [email protected]

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Microstructure Evolution

  • BasicReviewof

    • 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

    • 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 H2O


Phase Diagram for Fe


Phase Diagram for Fe


Equilibrium

  • 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


Equilibrium vapor pressures vs. Temperature


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


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


Solution Thermodynamics - AdvancedGibbs Energy 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


Gibbs energy of ternary alloys


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.


Introduction - VLS Growth of Nanowires


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


Size dependence of SiGe nanowire composition – an example

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


  • Login