Fundamentals of Solidification

Lecture 4: Nucleation and growth

Outline

• Introduction

• Homogeneous nucleation

• Heterogeneous nucleation

• Growth and microstructure

• Summary

Introduction

• There are two types of solidification

– Glass formation

• Physical properties such as viscosity change

smoothly across the solidifying region

– Phase transition

• Some physical properties change abruptly,

such as viscosity, heat capacity

Temperature vs. time in glass solidification and phase transition solidification

Viscosity vs. temperature in glass solidification and phase transition solidification

(a) Glass solidification (b) Phase-transition solidification

Density vs. temperature in glass solidification and phase transition solidification

Heat capacity of Fe

Introduction

• Solidification by phase transition is

modelled as two stage

– Nucleation

• Homogeneous nucleation

• Heterogeneous nucleation

– Growth

Homogeneous nucleation

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

liquid

solid

temperature

Free energy density

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

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.

Heterogeneous nucleation

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

Casting refinement

• Adding inoculating agents

– Overheat might melt the agents

• Surface refinement

– Coat agents on mold walls

• Pattern induced solidification

Growth and microstructure

T. F. Brower and M.C. Flemings, Trans. AIME, 239, 1620 (1967)

H.B. Dong and P.D. Lee, Acta Mater. 53 (2005) 659

Growth and microstructure

Outer chilled zones

Outer chilled zones

Outer chilled zones

Outer chilled zones

Pure metals: Formation of shell because temperature gradient is the key factor in grain growth.

Outer chilled zones

re-melted?

Pouring temperature

survived?

Microstructure of ingot

• Chilled zone

– Fine equiaxed grains.

– Pure substance: Continuous shell.

– Solution: Particles

– Particles flushed away from wall into the

central

• Re-melted

• Survived – nucleus

Intermediate columnar zone

Columnar grains grows

The grain is overtaken by neighbors.

Intermediate columnar zone

Growth and overtaken

Intermediate columnar zone

Columnar growth blocked

Central equiaxed zone

• Equiaxed grain

– Nucleation:

• Supercooling

• Falling particles

• Dendrite fragments– Elevated pouring

temperature:

• Larger equiaxed grains

• More columnar zone

– Anisotropic properties

• Magnetic materials

• Turbo blade.

• More equiaxed zone

– Isotropic properties

– Less segregation

Structure and properties

Summary

• Casting

• Heat management

• Thermodynamics

• Nucleation and growth