Office: 33-313 Telephone: 880-7221Email: espark@snu.ac.krOffice hours: by appointment

2020 Spring

Advanced Solidification

Eun Soo Park

04.13.2020

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Text: “Principles of Solidification”, BRUCE CHALMERS, John & Sons, Inc (1964)

References: 1) “Solidification Processing,” MERTON C. FLEMINGS,

McGraw-Hill Book Company, INC (1974)

2) “Fundamentals of Solidification,” W. KURZ,

TRANS TECH PUBLICATION (1984)

3) “Solidification and Casting,” G.J. DAVIES,

JOHN WILEY & SONS (1973)

Additional reading materials will be provided.

• Web lecture assistance: http://etl.snu.ac.kr- All materials will be posted at the webpage.- text message will be sent for the important and urgent notice.

• Hand out copied materials or scanned materials in website

Introduction

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Contents for today’s class I

Course GoalsThis course provides a critical review of the state ofknowledge and understanding of the process ofsolidification, defined for this purpose as the discontinuouschange of state from liquid to crystalline solid. In particular,this course is intended to provide an understanding of thephysical processes that relate to solidification and to showhow these processes combine to produce the phenomenaobserved in practical situations. An essential aim of manysolidification processes is to obtain optimum properties inthe resultant material. This course can provide a workingknowledge of how the solidification principles can beutilized to produce structures with improved mechanical orphysical properties, which then can be used to solveproblems involving materials and process design. By theend of the semester, you will be able to understand keyconcepts, experimental techniques, and open questions inthe solidification phenomena of various materials.

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Contents in Phase Transformation

(Ch1) Thermodynamics and Phase Diagrams

(Ch2) Diffusion: Kinetics

(Ch3) Crystal Interface and Microstructure

(Ch4) Solidification: Liquid → Solid

(Ch5) Diffusional Transformations in Solid: Solid → Solid

(Ch6) Diffusionless Transformations: Solid → Solid

Backgroundto understandphase transformation

RepresentativePhase transformation

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Scheduleweek 1 Brief introduction : the relevant thermodynamic laws, properties,

and relationships

week 2 Solidification as an Atomic Process I

week 3 Solidification as an Atomic Process II

week 4 Nucleation I

week 5 Nucleation II

week 6 Microscopic Heat Flow Consideration I

week 7 Microscopic Heat Flow Consideration II

week 8 Reduction of Solute during solidification I

week 9 Reduction of Solute during solidification II

week 10 Polyphase Solidification I

week 11 Polyphase Solidification II

week 12 Macroscopic Heat Flow and Fluid Flow I

week 13 Macroscopic Heat Flow and Fluid Flow II

week 14 The Structure of Cast Metals I

week 15 The Structure of Cast Metals II 5

Components of Your Grade:1) Exams (midterm: 35% + final: 40%)There will be two exams, each of which will take 2-3 hours. I will not use classtime for the exams and instead will reserve separate time slots. The exams willbe conceptual and difficult.

2) Reports and Presentation (15%)Assignments handed in after the start of class lose credit depending on thetiming. If you wish, you may work together on homework assignments. But, youmust hand in your own work, in your own words.

3) Attendance (10%)

Remarks: The weight of each grade component may change up to 5%depending on the student’s achievement.

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Wednesday, Friday , Wednesday, nothing thereafter.

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Liquid Undercooled Liquid Solid

<Thermodynamic>

Solidification: Liquid Solid

• Interfacial energy ΔTN

Melting: Liquid Solid

• Interfacial energy

SVLVSL γγγ <+

No superheating required!

No ΔTN

Tm

vapor

Melting and Crystallization are Thermodynamic Transitions

Incentive Homework 1: Please find an example of superheating (PPT 3 pages)

Chapter 1 Introduction of Solidification

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Contents for today’s class II

Melting and Crystallization are Thermodynamic Transitions

Chapter 1 Introduction of Solidification

4 Fold Anisotropic Surface Energy/2 Fold Kinetics, Many Seeds

Solidification: Liquid Solid

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Thermodynamic Transitions: Δ G = 0

1) GL versus GS

2) Interfacial free energy

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(1) Homogeneous Nucleation

LVLS GVVG )(1 += SLSL

LVL

SVS AGVGVG γ++=2

LV

SV GG ,

SLSLS

VL

VS AGGVGGG γ+−−=−=∆ )(12

SLVr rGrG γππ 23 434

+∆−=∆

: free energies per unit volume

for spherical nuclei (isotropic) of radius : r

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1) Homogeneous Nucleation

Fig. 4.2 The free energy change associated with homogeneous nucleation of a sphere of radius r.

r < r* : unstable (lower free E by reduce size)r > r* : stable (lower free E by increase size)r* : critical nucleus size

Why r* is not defined by ∆Gr = 0?

r* dG=0

Unstable equilibrium

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mTTLG ∆

=∆

L : ΔH = HL – HS

(Latent heat)T = Tm - ΔT

GL = HL – TSL

GS = HS – TSS

ΔG = ΔH -T ΔS ΔG =0= ΔH-TmΔS

ΔS=ΔH/Tm=L/Tm

ΔG =L-T(L/Tm)≈(LΔT)/Tm

(eq. 1.17)

2) Driving force for solidification

= Equilibrium between Solid and Liquid

1.8 Themodynamic Criteria for Equilibrium (at Tm)

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*

2rT

TLG SL

m

γ=

∆=∆

Liquid Solidsolidification

SLVr rGrG γππ 23 434

+∆−=∆

2) Driving force for solidification

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Liquid Undercooled Liquid Solid

<Thermodynamic>

Solidification: Liquid Solid

• Interfacial energy ΔTN

Tm

Melting and Crystallization are Thermodynamic Transitions

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Although nucleation during solidification usually requires some undercooling, melting invariably occurs at the equilibrium melting temperature even at relatively high rates of heating.

Why?

SVLVSL γγγ <+

In general, wetting angle = 0 No superheating required!

3) Nucleation of melting

(commonly)

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Liquid Undercooled Liquid Solid

<Thermodynamic>

Solidification: Liquid Solid

• Interfacial energy ΔTN

Melting: Liquid Solid

• Interfacial energy

SVLVSL γγγ <+

No superheating required!

No ΔTN

Tm

vapor

Melting and Crystallization are Thermodynamic Transitions

Incentive Homework 1: Example of Superheating (PPT 3 pages)

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(2) Change of interfacial free energy → Heterogeneous Nucleation

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• Nucleation in Pure Metals• Homogeneous Nucleation

• Heterogeneous Nucleation

• Nucleation of melting

* *hom( )hetG S Gθ∆ = ∆

SVLVSL γγγ <+ (commonly)

V

SL

Gr

∆=∗ γ2

22

23

2

3

)(1

316

)(316*

TLT

GG

V

mSL

V

SL

∆

=

∆=∆

πγγπ

r* & ΔG* ↓ as ΔT ↑

Solidification: Liquid Solid

32 3cos cos ( )4

A

A B

V SV V

θ θ θ− += =

+

220hom1~}

)(exp{

TTACfN o ∆∆

−≈

• Undercooling ΔT

• Interfacial energyγSL / S(θ) wetting angle

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Q. What is the meaning for the ΔT (undercooling)

during solidification?

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How to obtain large undercooling during cooling?

By dispersing a liquid into a large number of small droplets within a suitable medium, the catalytic effects of active nucleants may be restricted to a small fraction of the droplets so that many droplets will exhibit extensive undercooling.

John H. PEREPEZKO, MSE, 65 (1984) 125-135

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NANO STRUCTURED MATERIALS LAB.22

540 550 560 570 580 590 600 610 620 630

0.667 K/secTLC TL

0.667 K/s0.583 K/s0.5 K/s0.417 K/s0.333 K/s0.25 K/s0.167 K/s0.083 K/s

Mg65Cu20Ag5Y10 2mm plate

5 w

/g p

er d

iv.

Temperature ( K )

TS

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Trg 1/4 1/2 2/3

Rc = 1010 K/s

Rc = 106 K/sRc = 3x103 K/sRc = 3.5x101 K/s

TTT versus CCT

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Q. How to classify thermodynamic transition?

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The First-Order Transitions

G

T

S

T

∆S = L/T

T

CP

NPP T

STC,

∂∂

=

Latent heatEnergy barrier

Discontinuous entropy, heat capacity

Compressibility at constant T or S

Heat capacityat constant P or V

Coefficient ofThermal expansion

The Second Order Transition

G

TS

T

∆S=0

Second-order transition

T

CP

No Latent heat Continuous entropy

∞→

∂∂

=NP

P TSTC

,

Q. How to obtain kinetic transition?

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400

600

800

1000

Recalescence Recalescence

ΔT = 90℃ΔT = 84℃

Tem

per

ature

(℃

)

Time (sec)

Tm = 666℃

Over threshold temperature & time

Cyclic Cooling Curves of Zr41.2Ti13.8Cu12.5Ni10Be22.5 (VIT 1)

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Glass Formation is Controlled by Kinetics• Glass-forming liquids are those that

are able to “by-pass” the melting point, Tm

• Liquid may have a “high viscosity” that makes it difficult for atoms of the liquid to diffuse (rearrange) into the crystalline structure

• Liquid maybe cooled so fast that it does not have enough time to crystallize

• Two time scales are present– (1)“Internal” time scale controlled

by the viscosity (bonding) of the liquid for atom/molecule arrangement

– (2) “External” timescale controlled by the cooling rate of the liquid

TemperatureM

ola

r Vo

lum

e

liquid

glass

Glass transition(1) ≈ (2)

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Schematic of the glass transition showing the effects of temperature on the entropy, viscosity, specific heat, and free energy. Tx is the crystallization onset temperature.

continuous(V

, S,

H)

(αT

CP

κ T)

discontinuous

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Chapter 1 Introduction of Solidification

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Melting and Crystallization are Thermodynamic Transitions(1st order transition)

Glass transition is kinetic Transitions(pseudo 2nd order transition)

Melting Temp. (Tm) Δ G = 0 1) GL versus GS 2) Interfacial free energy

Glass transition (Tg) “Internal” time scale ≈ “external” time scale

Endo.

Exo.heating

Glass SCL crystal Liquid

Glass Supercooledliquid

liquid

coolingTmTg

Tx

Tp

Ts TL

Glass transition: Endo.

Crystallization: Exo.

melting: Endo.

C+L

< Thermal map >

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