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“Phase Transformation in Materials”

Eun Soo Park

Office: 33-313

Telephone: 880-7221 Email: espark@snu.ac.kr

Office hours: by an appointment

2018 Fall

09.27.2018

1

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2

• Effect of Temperature on Solid Solubility

• Equilibrium Vacancy Concentration

• Influence of Interfaces on Equilibrium

• Gibbs-Duhem Equation: Be able to calculate the change in chemical potential that result from a change in alloy composition.

r G 2Vm

Gibbs-Thomson effect

2 2

ln ln

1 1

ln ln

A B

A B

A B

d G d d

X X RT RT

dX d X d X

- Gibbs Phase Rule F = C − P + 1 (constant pressure) Gibbs' Phase Rule allows us to construct phase diagram to represent and interpret phase equilibria in heterogeneous geologic systems.

Contents for previous class:

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3 n

V

m

G G per unit volume of

V

0

V e

G X where X X X

   

Total Free Energy Decrease per Mole of Nuclei

Driving Force for Precipitate Nucleation

G0=-VGV +Aγ + VGs

A XA B XB

G

1

A XA B XB

G

2

1

2 G

G

Gn

For dilute solutions,

T X

GV

: 변태를 위한 전체 구동력/핵생성을 위한 구동력은 아님

: Decrease of total free E of system by removing a small amount of material with the nucleus composition (XBβ) (P point)

: Increase of total free E of system by forming β phase with composition XBβ (Q point)

: driving force for β precipitation

undercooling below Te (length PQ)

GV Chapter 5.1

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What are ternary phase diagram?

Diagrams that represent the equilibrium

between the various phases that are formed between three components, as a function of temperature.

Normally, pressure is not a viable variable in ternary phase diagram construction, and is therefore held constant at 1 atm.

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5

Gibbs Phase Rule for 3-component Systems

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Gibbs Triangle

An Equilateral triangle on which the pure components are represented by each corner.

Concentration can be expressed as either “wt. %” or “at.% = molar %”.

XA+XB+XC = 1

Used to determine

the overall composition

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7

Overall Composition

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Overall Composition

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9

Ternary Isomorphous System

Isomorphous System: A system (ternary in this case) that has only one solid phase. All components are totally soluble in the other components. The ternary system is therefore made up of three binaries that exhibit total solid solubility.

The Liquidus surface: A plot of the temperatures above which a homogeneous liquid forms for any given overall composition.

The Solidus Surface: A plot of the temperatures below which a (homogeneous) solid phase forms for any given overall composition.

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Ternary Isomorphous System

TA

TB TC

TA

TC

TC TB

TB

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11

Ternary Isomorphous System

TB

TC

TA

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Ternary Isomorphous System

TB

TC

TA

TB

TC

TA

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13

Ternary Isomorphous System

TB

TC

TA

TB TC

TA

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Ternary Isomorphous System

Isothermal section → F = C - P

TB

TC

TA

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15

Ternary Isomorphous System

Isothermal section

TB

TC

TA

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Ternary Isomorphous System

Isothermal section → F = C - P

Fig. 1.41 (a) Free energy surface of a liquid and three solid phases of a ternary system.

(b) A tangential plane construction to the free energy surfaces defined equilibrium between s and l in the ternary system

(c) Isothermal section through a ternary phase diagram

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17

Ternary Isomorphous System

Locate overall composition using Gibbs triangle

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19

Ternary Eutectic System

(No Solid Solubility) TA

TB

TC TA

TA

TB

TC TA

TB

TC

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Ternary Eutectic System

Liquidus projection (No Solid Solubility)

TA

TB

TC

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21

Ternary Eutectic System

(No Solid Solubility)

TA

TB

TC

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Ternary Eutectic System

(No Solid Solubility)

TA

TB

TC

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23

Ternary Eutectic System

(No Solid Solubility)

TA

TB

TC

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Ternary Eutectic System

(No Solid Solubility)

TA

TB

TC

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25

Ternary Eutectic System

(No Solid Solubility)

TA

TB

TC

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Ternary Eutectic System

(No Solid Solubility)

TA

TB

TC

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27

Ternary Eutectic System

(No Solid Solubility) T= ternary eutectic temp.

A C

B L+A+C

L+A+B L+B+C

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Ternary Eutectic System

(with Solid Solubility)

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29

Ternary Eutectic System

(with Solid Solubility)

TA

TB TC

TC

TB TA

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Ternary Eutectic System

(with Solid Solubility)

TA

TB TC

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31

Ternary Eutectic System

(with Solid Solubility)

TA TB

TC

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Ternary Eutectic System

(with Solid Solubility)

TA TB

TC

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33

Ternary Eutectic System

(with Solid Solubility)

TA TB

TC

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Ternary Eutectic System

(with Solid Solubility)

TA

TB TC

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35

Ternary Eutectic System

(with Solid Solubility)

TA TB

TC

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Ternary Eutectic System

(with Solid Solubility) T= ternary eutectic temp.

C

L+β+γ

L+α+γ L+α+β

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37

Ternary Eutectic System

(with Solid Solubility)

정해솔 학생 제공 자료 참조: 실제 isothermal section의 온도에 따른 변화 http://www.youtube.com/watch?v=yzhVomAdetM

TA TB

TC

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Ternary Eutectic System

3) Solidification Sequence: liquidus surface

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39

Ternary Eutectic System

* The horizontal lines are not tie lines.

(no compositional information)

* Information for equilibrium phases at different tempeatures

* Vertical section

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Vertical section Location of vertical section 10.1. THE EUTECTIC EQUILIBRIUM

(l = )

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Vertical section Location of vertical section

10.1. THE EUTECTIC EQUILIBRIUM (l = )

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Vertical section Location of vertical section

10.1. THE EUTECTIC EQUILIBRIUM (l = )

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< Quaternary phase Diagrams >

Four components: A, B, C, D

A difficulty of four-dimensional geometry

→ further restriction on the system Most common figure:

“ equilateral tetrahedron “ Assuming isobaric conditions, Four variables: XA, XB, XC and T

4 pure components 6 binary systems 4 ternary systems A quarternary system

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a+b+c+d=100

%A=Pt=c,

%B=Pr=a,

%C=Pu=d,

%D=Ps=b

* Draw four small equilateral tetrahedron

→ formed with edge lengths of a, b, c, d

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Construction of pseudo‐binary phase diagram for multi‐component alloy system

1MAR2017 / TMS 2017

0 10 20 30 40 50 60 70 80 90 100

600 700 800 900 1000 1100 1200 1300 1400 1500 1600

Temperature ()

Cu composition (at. %)

α β

0 10 20 30 40 50 60 70 80 90 100

600 700 800 900 1000 1100 1200 1300 1400 1500 1600

Temperature ()

Cu composition (at. %)

α β

0 10 20 30 40 50 60 70 80 90 100

600 700 800 900 1000 1100 1200 1300 1400 1500 1600

Temperature ()

Cu composition (at. %)

α β

Phase diagram was expected to optimize composition and microstructure of phase separating HEA

Thermodynamic calculation

X‐ray diffraction

TGA/DSC FE‐EPMA

• Expecting approximation of phase diagram

• Determination of phases

• Finding out temperatures of phase transformations

• Confirming invariant reaction points

• Investigation of equilibrium composition at each

temperature

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Pseudo‐binary phase diagram of PS‐HEA

Pseudo-binary system between FeCoCrNi and Cu shows monotectic reaction having liquid separation region.

Calculation courtesy of J.H.Kim et al.

Experiment Calculation

L

L 1 + L 2 FCC 1 + L 2

FCC 1 + FCC 2 FCC 2

Dendrite → Droplet → Dendrite

0 10 20 30 40 50 60 70 80 90 100

400 600 800 1000 1200 1400 1600

Temperature ()

Cu content (at%) Cu

FeCoCrNi

Posted on L‐88 (HEA V: Poster session)

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MoVNbTiZr: Construction of pseudo‐ternary phase diagram MoVNbTiZr: Construction of pseudo‐ternary phase diagram

Nb,Ti

Mo,V Zr

bcc IC+bc c

bcc Mo, V, Nb, Ti : Complete S.S.

V-Zr, Mo-Zr Ti-Zr, Nb-Zr

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TiNbMoVZr: Construction of pseudo‐ternary phase diagram TiNbMoVZr: Construction of pseudo‐ternary phase diagram

1500K 1300K

1100K

Calculated pseudo‐ternary isothermal sections of the MoNbTiVZr system

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MoVNbTiZr: Construction of pseudo‐ternary phase diagram MoVNbTiZr: Construction of pseudo‐ternary phase diagram

X‐ray diffraction analysis of the as‐cast samples

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Construction of pseudo‐ternary phase diagram Construction of pseudo‐ternary phase diagram

BCC1+BCC2+IC BCC1+IC / BCC2+IC BCC1+BCC2

Single BCC

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1.0 0.0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

20

25 26

23 24

22

21

19 11

10

12 13

14 15

16 17

18 9 7

8 5

6 4

2 3

MoV Zr

NbTi

NbTi Mo

V

Zr

1

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51

Homework1 :

Please explain how to calculate muti-component phase diagram

reflecting excess Gibbs energy based on session 1.9. (within 3 pages PPT)

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* Incentive Homework 1

Please submit ternary phase diagram model which can clearly express 3D structure of ternary system by October 12 in Bldg. 33-313.

You can submit the model individually or with a small group under 2 persons.

* Homework 2 : Exercises 1 (pages 61-63) Good Luck!!

참조

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