Lecture 6

Question 1

What is interfacial energy proportional to for homogenous nucleation?

Answer 1

r^2

Question 2

What is interfacial energy?

Answer 2

The resistance energy to forming a new phase between a new nucleus and the surrounding phase

Question 3

Explain undercooling

Answer 3

Undercooling is when you have to cool a material past it’s “Tm” for it to ACTUALLY solidify because in reality there’s an energy barrier that it has to overcome to start forming nuclei

• the difference between that ACTUAL temp and the Tm is the ΔT=Tm -T and ΔT is undercooling

Question 4

What is the homogenous nucleation rate?

Answer 4

Nhom - the number of stable nuclei formed per second per m^3

Question 5

How do you find the homogenous nucleation rate? What happens if the ΔG*hom increases?

Answer 5

**find C* - the number of nuclei per m^3 that have reached critical size, then plug that number into the Nhom equation

• ΔG*hom increases, nucleation decreases

Question 6

What is a good approximation for reasonable homogenous nucleation? Is nucleation easier at higher or lower temperatures?

Answer 6

Nucleation is easier at higher temperatures if there’s a small enough energy barrier -ΔGhom∗ or great enough Gv (bulk free energy change)

• Gv in denom of formula to calculate ΔGhom*

Question 7

What is different about the nucleation rate formula that you need to use for solidification or freezing (liquid –> solid)?

Answer 7

The A – determines how strongly the nucleation factor depends on cooling

Question 8

When should you use this equation?

Answer 8

1. for solidification
2. working with supercooled liquids
3. problem asks for effect of temp on nucleation
4. determine how much undercooling is required for nucleation

Question 9

For homogenous nucleation, what is ΔHm and how does it affect nucleation? Y sub SL? How does undercooling affect it?

Answer 9

ΔHm is the latent heat of fusion - high ΔHm then easier nucleation

Y sub SL is large - nucleation difficult (small easier)

since its (ΔT)^2 in the formula for Nhom, nucleation rate increases very sharply over a small undercooling temp/window (very steep graph)

Question 10

What is ΔT sub N? What does it look like on a graph?

Answer 10

critical supercooling for detectable nucleation

• the supercooling it needs for nucleation to happen

Question 11

Explain ΔGv

Answer 11

1. ΔGv<0
2. ΔGv is ΔG per volume between S and L
3. bulk free energy change per unit volume at phase transformation
4. driving force of nucleation
5. has to be negative bc nucleation happens when a system lowers its total energy – so that means that the liquid phase has higher energy than the solid

Question 11

How is the Gibbs free energy change for het dif than a hom?

Answer 11

the negative makes it so that the presence of a solid-mould interface reduces the energy barrier