Nucleation, Crystallization, and Growth Flashcards
Nucleation
Initial formation of one phase inside another
All nucleation processes have:
Energetic barrier against formation
Two types of nucleation
Homogeneous, heterogeneous
Homogeneous nucleation
Spontaneous particle formation
Heterogeneous nucleation
Formation of particle on a seed of foreign material
Why seed important in heterogeneous nucleation?
Seed provides lower barrier to formation at interface
Majority of nucleation processes are of what type
Heterogeneous
Understanding nucleation rate diagram
Heterogeneous nucleation peaks at a higher temperature so it is easier. Supercooling is required to initiate homogeneous nucleation.
Why nucleation limited on diagram?
Lowered concentration of nucleating material after phase change, and also atoms prefer to grow on existing nuclei.
Weaker bond energies in a material mean (wrt supercooling)
More supercooling is needed to induce homogeneous nucleation
What limits nucleation in slightly undercooled liquids?
Surface tension of small particle radius
What produces nucleation in slightly undercooled liquids?
Bulk fluctuations overcoming surface tension barrier to nucleation
Undercooled liquid is considered to be (wrt stability)
metastable phase – free energy not minimum
The free energy change of nucleation is labeled:
\DeltaG_r
The free energy change of phase formation is labeled:
\DeltaG_v
Critical radius, how labeled
r*
How r* derived
Maximum value of free energy of nucleation
What controls surface tension of particles
Fluctuations in bulk or seed
\sigma in nucleation equations
Surface tension
Nr*/N
Number of particles of critical radius compared to total number of particles
Nr*/N implications for density
Higher density results in less nucleation
Nr*/N implications for phase transformation energy
Higher phase transformation energy change increases particles of critical radius
Nr*/N unincluded effect
More prior particles result in more collisions resulting in more nucleation
Nr*/N implication for temperature
Decrease of temperature increase Nr* because of increase in undercooling which increases phase transformation change in free energy
Example of liquid mobility effect on undercooling
High atom mobility in molten metal means that undercooled metals nucleate rapidly.
Undercooling in glass
Glass is viscous and has low mobility, resulting in fewer clusters forming.
Nucleation rate is labeled:
I
Rate at which atoms reach the critical nucleus is labeled:
R_(r^*)
Crystallization
Phase transition of a disordered fluid to a crystal
When crystallization starts
As soon as nucleation seeds form
Types of crystallization
Cooling, evaporation, precipitation
Cooling crystallization
Result of decrease in temperature dependent solubility of a solute
Evaporation crystallization
Result of evaporation of solvent
Two types of precipitation
Reactive crystallization, anti-solvent
Reactive crystallization
Chemical reacts with solute causing insoluble solid to form
Anti-solvent
A solvent which binds better to a solute than the initial, causing the first solvent to crystallize
Mechanism by which polymers can locally crystallize
Chain folding
What kind of polymer structures crystallize better?
Linear polymer structure
Two types of polymer crystallization
Solution, melt
Solution crystallization
Caused by chain folding
Melt crystallization
Happens across molecules by the lineup of chains
Vi
Rate of crystallization for component i
Rate of crystallization for component i
Vi
Growth in solution vs. growth in melt
Solution growth is slow; melt growth is fast
Why solution growth slow
Large density diff. b/t solution and crystal
Why melt growth fast
Comparable density b/t solution and crystal
What controls growth in solution
Atomic movements from solution to crystal (i.e. diffusion)
What controls growth in melt
Heat flow controls growth in melt
Two examples of crystal growth
Bridgman growth & Czochralski growth
Bridgman growth
Single seed crystal is cooled at one end of a container.
Czochralski growth
Liquid is undercooled; crystal is pulled up at rate of growth. Interface between crystal and melt is effectively stationary.
Growth rate of CZ process determined by
Undercooling at interface
Undercooling at CZ interface controlled by
Heat flow, via conduction heat transfer (crucible) and convection (liquid), heat loss from crystal
Changes occurring during CZ process
Crystal surface area expands, so heat loss from crystal changes, and liquid level drops, so coupling between heater and melt changes
Coarsening growth
Particles smaller than r* shrink and larger than r* grow
What controls surface tension of particles
Fluctuations in bulk or seed
