Solidification Processing

1
Solidification Processing

• Lecture 11 Kinetics 1

2
Solidification model

• Nucleation
• Homogeneous nucleation
• Heterogeneous nucleation
• Growth

3
Homogeneous nucleation

• No preferred nucleation sites
• Spontaneous
• Random
• Those of preferred sites
• Boundary
• Surface
• Inclusion
• Multiphase

4
Local free energy change
1. Liquid to solid
2. Interface
5
Local free energy change
Spherical nucleus
6
Single nucleus
7
Critical radius
8
Parameters
For FCC Copper, r?1 nm, which contains 310 Cu
atoms in each nucleus.
9
System free energy

• Ideal solution Particle of different sizes
• ni particles with each contains i atoms
• n particles with each contains 1 atom

10
Number of nuclei

• At equilibrium

11
Number of nuclei
when
Boltzmann formula
Critical nuclei
12
Nucleation rate

• The nuclei formed per unit volume and per unit
  time duration
• The rate of formation of nuclei per unit
  volume.

13
Nucleation rate

• Two assumption
• the concentration of critical nuclei remains that
  at predicted by equilibrium considerations even
  after nucleation begins
• The addition of a single atom to a critical
  nucleus makes that nucleus supercritical and able
  to grow rapidly

14
Nucleation rate
? the number of atoms surrounding a critical
nucleus. ?LS the frequency of atom jump across
the liquid-solid interface.
15
Nucleation rate
a the average distance between two
nearest-neighbored atoms in liquid
16
Nucleation rate
where
17
Nucleation rate
18
Nucleation rate