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Solidification Processing

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The nuclei formed per unit volume and per unit time duration ... the concentration of critical nuclei remains that at predicted by equilibrium ... – PowerPoint PPT presentation

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Title: 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
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