Lecture 5: Nucleation Flashcards
What does a phase diagram show? Not show?
It shows the equilibrium states (phases) at a given condition
Does NOT show kinetic information
What may phase changes involve at the atomic level?
Migration of atoms or atom diffusion
If an atom diffuses from α –>β, what is the activation (barrier) energy?
If an atom diffuses from β –> α?
Q α–>β = Hm-Hα
Q β –>α = Hm-Hb
What is the Arrhenius Equation? What does it help visualize?
ln(Rate) = ln(A) - Q/(kB*T)
measures the relationship between rate, activation energy, and T
What is the Arrhenius plot?
ln(rate) vs. 1/T
slope = -Q/kB
intercept is ln(A)
Q is activation energy
How does the kinetic rate of reaction behave with T (formula)?
It increases exponentially with T
What formulas can you use to calculate diffusivity in dif temperatures?
Ea is activation energy
Does phase transformation happen in one step?
typically no
How does phase transformation usually begin?
It starts from nucleation of many small nuclei, then the nuclei either grow or shrink
Explain the significance of this image?
Even if thermodynamically β is more stable than α, the nucleation needs to overcome a “nucleation barrier” because of the presence of INTERFACIAL ENERGY
What is a nucleation barrier
A point in Gibbs energy where if the corresponding nucleus isn’t at the “critical nucleus size”, then it will shrink, but if it’s larger, it will grow
Describe ΔG L–>S and ΔHm (enthalpy of fusion)?
ΔG L–>S = Gs - GL < 0
** L–>S is favorable
ΔH > 0
which ΔG is favorable vs. not?
negative ΔG is favorable
Where does crystallization from melt (solidification) happen?
T < Tm, because it has the driving for of ΔG
What is a formula for supercooling or undercooling?
ΔT = Tm - T
Where can Nucleation happen?
everywhere (random location), no specific location
What is the volumetric or bulk energy change by nucleating a solid nucleus from the same amount of liquid?
What happens at T < Tm?
a solid nucleus with a spherical radius of r nucleates in a liquid
Why does a nucleus want to grow?
Since a solid is more stable than a liquid at T<Tm
What other energy must the nucleus overcome?
the solid-liquid interface energy
What is the interface energy?
**another thing nucleation must overcome
What is the formula the total energy change after a nucleus forms comprised from?
bulk term (negative)
interface term (positive)
What two energies are competing for a nucleus to form (nucleation barrier)?
bulk and interface
What is the critical r* after a nucleus forms at maximum ΔG for homogenous nucleation?
What is Y SL
solid-liquid interface energy per area >0
What is the ΔG at the nucleation barrier?
What is ΔG v?
free energy difference per volume between bulk solid and bulk liquid (<0 at T<Tm)
How do you make freezing easier?
- smaller nucleation barrier ΔG*
– > smaller r*
– > more negative ΔG v
– > larger undercooling (ΔT)
What happens if r>r*?
nucleus grows
What happens if r < r*?
nucleus shrinks
What does a graph of rate of precipitation vs degree of undercooling look like for the crystallization process? What is the x-axis? What are two properties?
x-axis degree of undercooling (ΔT = T m – T)
at high T (earlier in the graph), there are nucleation difficulties
at low T (later in the graph – after hump), diffusion is slow
How do you graph the crystallization process
rate of precipitation vs degree of undercooling
For the crystallization process, what are the characteristics at high T?
high T = earlier in the graph
- nucleation barrier is high
- so the crystallization rate is slow
For the crystallization process, what are the characteristics at low T?
later the graph
- atom diffusion is slow (slow kinetics)
- so crystallization rate is also low
Where does the maximum nucleation rate occur?
at an optimum T
