Driving force for solidification
For a pure metal, at the fusion temperature, Tf, the Gibb’s free energy change for fusion, ΔGf, is zero, so that:
ΔGf = ΔHf - Tf ΔSf = 0
ΔHf = Tf ΔSf (1)
where ΔHf is the latent heat of fusion, and ΔSf is the entropy change upon melting.
For a temperature T, other than Tf:
ΔG = ΔH - T ΔS
ΔH and ΔS can be assumed to be constant for small changes is temperature, so for temperatures close to the fusion temperature:
ΔG ≈ ΔHf - Tf ΔSf (2)
Substituting (1) into (2) we get:
ΔG ≈ ΔHf - ΔSf ( Tf - T )
ΔG ≈ ΔSf ΔT
So the Gibb’s free energy change for solidification (also called the driving force) is proportional to the undercooling, ΔT, below the fusion temperature.