Kinetics and Microstructural Control

· The diagram illustrates a spherical β-nucleus in a homo-geneous α-liquid.
· For a nucleus of radius, r, the change in the volume energy is given by:
ΔG_Β = (4πr³/3) ΔG_V ;
where ΔG_V = (G_β - G_α)_T .

· The surface energy associated with the formation of the beta-phase is given by: ΔG_S = 4πr² γ_αβ , where γ_αβ = Interfacial Surface Energy/Unit Area.
· The surface energy is positive for all temperatures.
· The total Gibbs function change associated with the formation of the spherical nucleus is given by: ΔG_Total = (4πr³/3) ΔG_V + 4πr² γ_αβ .