NC#State#UniversityDepartment)of)Materials)Science)and)Engineering 1

MSE#440/540:#Processing#of#Metallic#Materials

Instructors:)Yuntian)ZhuOffice:)308)RBIIPh:)513D0559ytzhu@ncsu.edu

Lecture)2:)Solidification)TheoryHomework:))Problem)from)notes,)

NC#State#UniversityDepartment)of)Materials)Science)and)Engineering 2

Solidification

Nearly#every#metal#product#started#as#a#liquid#at#some#point#in#time.

6What)is)Solidification6 What)is)the)Melting)Point?6 What’s)composition?

NC#State#UniversityDepartment)of)Materials)Science)and)Engineering 3

Nucleation)and)Growth

During#solidification,#solid#nuclei#form#in#the#liquid#and#subsequently#grow#until#the#entire#volume#is#a#solid.;What)is)the)driving)force)for)nucleation)and)growth?

NC#State#UniversityDepartment)of)Materials)Science)and)Engineering 4

Homogeneous)NucleationConsider#free#energy#change#when#small#spherical#nuclei#of#solid#is#formed#in#a#liquid

LS

G#=#H#– TS

ΔG)=)ΔH)– TΔS)

At)Tm,)ΔG))=)0,)ΔH)=)L

ΔS)=)L/Tm

ΔGv(T))=)L– T(L/Tm))

=)L(1GT/Tm)

NC#State#UniversityDepartment)of)Materials)Science)and)Engineering 5

Homogeneous)Nucleation

There#is#a#critical#radius#r*,#at#a#given#undercooling#ΔT#where#embryos#can#grow#and#reduce#the#free#energy.

r*)occurs)at)

HOMEWORK:))Show)that:

r*)=B2!/ΔGv

ΔG)at)r*),)

If)ΔGv)=)LΔT/Tm,)then

=)thermodynamic)barrier)to)nucleation)or)work)of)nucleation

€

ΔG* = 16πγ3TM

2

3L2%

& '

(

) * 1ΔT 2

€

r* = 2γTML

#

$ % &

' ( 1ΔT

€

ΔG* = 16πγ3

3(ΔGV )2

%

& '

(

) *

€

∂ΔG∂r

= 0

Quiz:))What)is)the)physical)origin)of)energy)barrier)for)nucleation?

NC#State#UniversityDepartment)of)Materials)Science)and)Engineering 6

Homogeneous)Nucleation

Note)that)r*)and)ΔGv*)decrease)with)increasing)undercooling

€

ΔG* = 16πγ3TM

2

3L2%

& '

(

) * 1ΔT 2

€

r* = 2γTML

#

$ % &

' ( 1ΔT

Quiz:))The)effect)of) ΔT)on))solidification)speed)and)microstructure.)

https://www.youtube.com/watch?v=IkIOXusTgoUFreeze)beer/2:22

https://www.youtube.com/watch?v=-kIOXusTgoU

NC#State#University

Heterogeneous*Nucleation

Department*of*Materials*Science*and*Engineering 7

€

cosθ =γML − γ SM

γ SL

€

ΔGhet =43πr3ΔGV + 4πr

2γ SL%

& '

(

) * S θ( )

€

r* = − 2γ SLΔGV

=2γ SLTmLV

%

& '

(

) * 1ΔT

€

ΔGhet* = ΔGhom

* S θ( ) = 16πγ SL3

3ΔGV2 S θ( ) =

16πγ SL3 Tm

2

3LV2

&

' (

)

* + 1ΔT 2

S θ( )

€

S θ( ) = 2 + cosθ( ) 1− cosθ( )2

4

NC#State#University

Heterogeneous*Nucleation*Rate

Department*of*Materials*Science*and*Engineering 8

€

Nhet = f1C1e−ΔGhet

*

kT = f1C1e−

AΔT 2

A = 16πγ SL3 Tm

2

3LV2 kT

S θ( )

Innoculants*(seeds):*

Nucleation*of*Melting:*

!SL +*!LV

NC#State#UniversityDepartment)of)Materials)Science)and)Engineering 9

Commercial)Practice

Dynamic#Nucleation

8 Vibrate)melt)to)collapse)internal)cavities8 Fragmentation)of)existing)solids>)breaking)of)dendrite)arms)(crystal)multiplication)8 Electromagnetic)mixing)and)stirring

Nucleation#during#Melting

8 Why)does)melting)usually)occur)at)Tm,)even)at)high)heating)rates?

Most)liquid)metals)wet)their)own)solid,)so)the)wetting)angle)Θ=)0)! no)energy)barrier)for)nucleation) !SL +)!LV

NC#State#UniversityDepartment)of)Materials)Science)and)Engineering 10

Commercial)PracticeCharacteristics#of#a#good#inoculant9 low)interfacial)energy,)γSP,)between)nucleant)and)growing)solid)

9 γSP)decreases)with)decreasing)lattice)mismatch)between)solids)and)nucleant)with)increasing)chemical)affinity)(coherent)interface)

9 Should)be)as)stable)as)possible)in)the)liquid)melt)Tminoc >)Tmmelt

9 possess)a)high)surface)area)(rough)or)pitted))

9Smaller)particles

NC#State#UniversityDepartment)of)Materials)Science)and)Engineering 11

Growth:))Practical)Results

Crystals#grow#in#two#ways#after#nucleating

=Planar)growth)– heat)extraction)through)

the)solid)phase)and)a)smooth)solid/liquid)

interface

=Dendritic)growth)– formation)of)branched)

skeleton)structures.

http://www.youtube.com/watch?v=S07fPo45BvM

http://www.youtube.com/watch?v=S07fPo45BvM

NC#State#University

Reading(Assignment

• Read(Chapter(5

• HW:

Department(of(Materials(Science(and(Engineering 12

1.(Calculate(the(volume(change(from(fcc(γDiron(to(bcc(αDiron.(Hint:(the(atom(radius(is(R,(which(does(not(change(during(phase(transformation.