Nucleation

1
Nucleation
Don H. Rasmussen Box 5705 Clarkson
University rasmu_at_clarkson.edu
2
Homogeneous Nucleation

• Fluctuations in composition and structure which
  are small in extent but large in degree result in
  small new phase nuclei which are in local
  equilibrium but unstable to growth in an
  undercooled or supersaturated parent phase.

3
How does Homogeneous Nucleation Occur?

• Stable clusters form when their formation
  decreases total free energy.
• Growth of small clusters is limited because new
  particle surface costs more free energy than the
  bulk free energy reduction. Only large clusters
  are stable.
• Clusters grow and decay by monomer
  addition/evaporation and there is in a metastable
  cluster size distribution.
• The larger the supersaturation or undercooling,
  the greater the number and maximum size of the
  existing clusters and the smaller the necessary
  critical cluster size for continued growth.
• For clusters just larger than critical, the
  growth rate increases along with the size in an
  autocatalytic fashion.

4
Numerical Model of Homogeneous Nucleation

• Nucleation Rate, J, is the product of
• q, the net probability of an atom jumping across
  interface and into the critical cluster (per unit
  surface area)
• t, jump frequency of monomer is fluid
• Ac, the surface area of the critical cluster
• nc, the concentration of critical clusters per
  unit volume

5
q is the net rate of diffusion across the surface
of a cluster
where Do is the diffusion coefficient in the
liquid.
and ci and co are the concentration of
crystallizing atoms on the two sides of the
interface of thickness, l.
6
The surface area of a spherical cluster is
The concentration of critical clusters is
7
Nucleation Rate per Unit Volume, J
The pre-exponential factors are almost constant
and approximately 1035 nuclei/cm3sec.
8
Effect of Temperature on Bulk Free Energy Change
9
Free Energy of a Cluster as a Function of Size
10
Influence of increasing Undercooling or
Supersaturation
From 1 to 5 the supersaturation or undercooling
increases which results in a decrease in both
the critical cluster size and the barrier to
nucleation.
11
Conditions for critical cluster or nucleus
12
Critical Cluster Size and Free Energy Barrier
versus Undercooling
13
Temperature Dependence of Nucleation Rate
J(T)
?T
14
Time Temperature Transformation Curves
The delay time is related to the reciprocal of
the nucleation rate and here the delay time is
plotted as a function of the undercooling.
0
DT
200
Time (Seconds)
15
Heterogeneous Nucleation

• Nucleation at the surface of an impurity particle
  or on the walls of the container.
• Catalysts for Nucleation are surfaces which
  significantly lower the barrier to new phase
  formation.
• Heterogeneous nucleation occurs at low
  undercooling and at high rates.

16
Nucleation on a substrate takes less material
liquid
snl
ssl
nucleus
q
ssn
substrate
17
Fraction of the critical cluster which must form
at any specific undercooling
18
Free Energy of Formation of the Nucleus versus
Contact Angle at Fixed Undercooling