(i) Explain why the transformation from y→ α does not occur immediately when a sample is undercooled below the equilibrium transformation temperature. [20%] = Write an equation for the free energy change AG during the homogeneous nucleation of solid-α from liquid-y, given that the free energy of transformation is AGCHEM Gα Gy and the interfacial energy is written σya. From this derive the critical nucleus size. [30%] (iii) Stating assumptions, calculate the activation energy G* for the homogeneous nu- cleation of solid-a from liquid-y given that the free energy change AGCHEM Gα- Gy = -104 Jm³ and the interfacial energy per unit area σyα = 0.1 Jm¯ when a solid particle nucleates from a liquid. (iv) Relate the activation energy for nucleation to the rate of nucleation. -2 [30%] [20%]