Dissemination of IT for the Promotion of Materials Science (DoITPoMS)

# 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

giving:

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.