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What is Homogenous Nucleation?
A spontaneous phase transformation will only occur when the Gibbs free energy has a negative value: ΔG<0
Gibbs "free" energy is energy available to do work (i.e the driving force)
ΔG=ΔH−TΔS
ΔH= change in enthalpy (actual energy of the system)
If ΔH>0, it's endothermic (taking in energy from the surrounding)
If ΔH<0, it's exothermic (giving out energy to the surrounding)
T= temperature of the container (system)
ΔS=entropy (measure of disorder)
ΔG=0: equilibrium
ΔG>0: non-spontaneous
ΔG<0: spontaneous - nuclei will spontaneously start to form
The Process of Homogenous Nucleation?
Solidification of a pure material
Nuclei of solid phase form in the interior of the liquid
Atoms clusters together to form a packing arrangement similar to that found in the solid phase
Each nucleus is spherical with radius r
Nucleation of a spherical
solid particle in a liquid.
There are two energy contributions to the total free energy, ΔG, that accompanies this solidification transformation:
1. Volume free energy ΔGv (the free energy difference between the solid and liquid phase)
ΔGv will be negative if the temperature is below the equilibrium solidification temperature
magnitude is the product of ΔGv and the volume of the spherical nucleus
2. Surface free energy γ (formation fo the solid-liquid phase boundary during solidification transformation)
It's positive
magnitude is the product of γ and the surface area of the nucleus
As a solid particle begins to form as atoms in the liquid cluster together, the free energy increases.
If the radius reaches a specific size, the critical radius r* , it will have the activation free energy ΔG* required to become a stable nucleus and continue growth, where free energy starts to decrease.
If the radius is less than the critical radius r*, it won't become stable, will shrink and re-dissolve.
Nucleus: Cluster that has reached critical radius r*, has activation energy ΔG*, is stable and continues growth.
Embryo: Cluster that has not reached critical radius r*, don't have activation energy ΔG*, and is unstable
Activation free energy, ΔG* : free energy required for the formation of a stable nucleus (or energy barrier to nucleation)
Critical Radius formula
where:
γ = Surface free energy
ΔGv = Volume free energy
Activation free energy ΔG*
where:
γ = Surface free energy
ΔGv = Volume free energy
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