Introduction to Solidification

3. Kinetics

Rongshan QIN

http://cml.postech.ac.kr/rqin

1

In this lecture:

• Homogeneous nucleation

• Heterogeneous nucleation

Solidification

• Two types of solidification

Viscosity vs. temperature in: (a) Glass formation. (b) Metal casting.

Solidification

time

Temperature

Glass formation

Metal casting

Temperature vs. time during solidification

liquid

solid

Solidification

Molecular/atom arrangements in (a) Glass. (b) Crystal.

Metal solidification

• Nucleation

• Growth

rr

Homogeneous nucleation

• No preferred nucleation sites

– Spontaneous

– Random

• Those of preferred sites

– Boundary

– Surface

– Inclusion, …

Local free energy change

1. Liquid to solid 2. Interface

Local free energy change

SLLSbeforeafter AGGVGGG

SLSL rGGrG 23 43

4

Spherical nucleus:

Single nucleus

Critical radius

0/ drGd

SL

SL

GGr

2*

2

3

3

16*

SL

SL

GGG

(GL-GS) vs. supercooling

Free energy density vs. temperature

Parameters

For FCC Copper, r*1 nm, which contains 310 Cu atoms in each nucleus.

System free energy

• Ideal solution: Particle of different sizes

• ni particles with each contains i atoms

• n particles with each contains 1 atom

STGnG ic

ii

ii nn

nn

nn

nnkS lnln

Number of nuclei

• At equilibrium

0/ ic nG

i

i

nn

n

kT

Gln

inn

kT

Gnni exp

kT

Gnni

*exp*

when

Number of nuclei

Boltzmann formula:

Critical nuclei:

Heterogeneous nucleation

• Nucleation site

– Mold walls

– Inclusion

– Interface

– Surface

– Impurity

Heterogeneous nucleation

Liquid

Inclusion

Nucleus IL

NL

IN

R

r

h

a

Heterogeneous nucleation

cosNLINIL

Force equilibrium

where IL, IN and NL are the interface energies of

inclusion-liquid, inclusion-nucleus and nucleus-liquid, respectively. is the nucleus-inclusion wetting angle. The

nucleus is a spherical cap of radius r.

Free energy change

Free energy change

Using cosNLINIL

Thermodynamic barriers

Heterogeneous nucleation barrier

Homogeneous nucleation barrier

Thermodynamic barrier vs. wetting angle

Number of nuclei with critical radius

where ns is the total number of atom around the

incubating agents’ surface in liquid.

Inoculating agents

• Small interface energy

– Similar crystal structure

– Similar lattice distance

– Same physical properties

– Same chemical properties

Effect of surface geometry

Casting refinement

• Adding inoculating agents

– Overheat might melt the agents

• Surface refinement

– Coat agents on mold walls

• Pattern induced solidification

In summary

• Two types of solidification

– Glass formation

– crystallization

• Solidification

– Nucleation

– Growth

• Homogeneous and heterogeneous nucleation

References

1. M.C. Flemings, Solidification processing, 1974.

2. A. L. Greer, Kinetics, Cambridge.