NTNU

Short Course on solidification at IISc October – November 2012Lars Arnberg, NTNU

1. Introduction – basic concepts 29/10

1. Nucleation - grain refinement 31/10

Crystal morphology

3. Interface stability 5/11

Cells and dendrites

4. Three phase solidification 7/11

Segregation

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NTNUSolidification, Lecture 1

Introduction / Basic concepts

Simple heat flow during solidification

Mushy Zone

Columnar / equiaxed solidification

Curvature effects

Phase diagrams – solute redistribution

 

2

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Microstructure

Solidification of metals is a crystallisation process

Microstructure development Microstructure

Crystal types, phasesCrystal morphologyCrystal sizeChemical composition

Depends on

Composition (constitution)Concentration, CPhase diagram, k, m

Casting conditionsGrowth rate, VTemperature gradient, GCooling rate, G*V

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Microstructure

Increasing concentration

Increasing constitutionalundercooling (Tc)

Increasing morphologicalinstability

Increasing cooling rate (G*V)

Structure refinement

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Heat flow

Reproduced from:W. Kurz & D. J. Fisher:Fundamentals of SolidificationTrans Tech Publications, 1998

€

qA

v= −c

dT

dt+ ΔH

dfs

dt

€

dT

dt= −q

A

vc+

dfs

dt

ΔH

c

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Mushy zone

a

Alloys will solidify over a temperature Interval, ΔTf

M. Z. is where solidificationoccurs

Depending on freezing range and temp gradient

€

a =ΔTf

G

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Controlled solidification

a: Bridgman furnaceIndependent control of G & V. G & V constant

b: Directional chill castingG & V time dependant

dT/dt = GV

s=Kt1/2

Reproduced from:W. Kurz & D. J. Fisher:Fundamentals of SolidificationTrans Tech Publications, 1998

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Growth modesmorphology & temperature distribution

Directional Growth of columnarcrystals

Free growthof equiaxedcrystals

Positive G Negative G

Pure metal

Alloy

Reproduced from:W. Kurz & D. J. Fisher:Fundamentals of SolidificationTrans Tech Publications, 1998

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Structure of castings

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Capillary effects; solid/liquid interface

• Undercooling

• Curvature

2/r for sphere

• Gibbs Thomson

~ 10-7 Km

dAK

dV=

Solidification microstructuresgiven by competition between:

•Curvature : tends to maximise scale

•Diffusion: tends to minimise scale

Reproduced from:W. Kurz & D. J. Fisher:Fundamentals of SolidificationTrans Tech Publications, 1998

€

T = KΓ

€

Γ=σs f

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Phase digram, solute redistribution

Cs C0

T0

C0l

s

T

Cl

Tl

Ts

• Eutectic phase diagram

• Lower solubility of alloying elements in s than in l

• k=Cs/Cl<1 (distribution coefficient)

• m= dTl/dC<0

• k and m constants if solidus & liquidus lines are straight

C

€

T0 = −mΔC0 = −mC0(1 − k)

k

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Al-Fe Al-Mg

Al-MnAl-Si

Eutectic Alphase diagramsfor importantalloyingelements

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Al-Fek=0.03

AlMgk=0.44

Al-Mnk=0.90

Al-Sik=0.14

Al phasediagrams withdifferentpartitioncoefficients

k=Cs/Cl

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Summary/ Conclusions

• Solidification is accomplished by external cooling of a melt. Needed for decreasing the temperature and removing latent heat of fusion

• Metals solidify at a distinct freezing point, alloys have a solidification interval (freezing range)

• Solidification microstructure will depend on both composition, (C0) constitution (k, m) and process (G, V)

• Control of V and G will differ between casting processes• Solidification will occur in mushy zone. Extent of MZ will depend on

temperature gradient and freezing range• Crystal may grow directionally as columnar grains (G>0) or freely from

an undercooled melt as equiaxed grains (G<0)

• Creation of s/l interface will require undercooling. ΔTr will increase with increased curvature (small crystal radii)

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Summary/ Conclusions

• Scale of solidification microstructure will be determined by diffusion (decreasing) and curvature (increasing)

• Solidification of alloys means redistribution of solute between s and l. Determined by distribution coefficient, k.

NTNUSymbols

C: concentration G: temperature gradient, dT/dx K/m

k: distribution coefficient k=Cs/Cl Δsf: entropy of fusion, J/(m3K)

m: liquidus slope, dT/dC σ: solid/liquid interface energy, J/m2

V: growth rate m/s Cl: liquid concentration

T: temperature: K Cs: solid concentration

ΔT: undercooling, K C0: Initial alloy concentration

q: heat flux W/m2

A: area m2

V: volume m3

t: time, s

ΔH: heat of fusion J/m3

c: heat capacity: J/(m3K)

fs: fraction solid

ΔTf: freezing range, K16