My question is related to free energy of nucleation in heterogeneous systems and homogeneous systems. I've been given to prove delta_G* (Hetero.)= 27/64 * (delta_G*(Homo)) The stuff I know is : Total (delta G ) = [-4/3 *Pi*r^3* delta Gv] + [4*Pi*r^2*sigma] - [Pi*r^2 * sigma] 1st term is related to energy of volume destroyed in liquid during formation of spherical nucleus 2nd term is surface area created by the sphere which is a positive interfacial energy 3rd term is grain boundary area destroyed as the nucleus forms. (im not quite sure of this though) so total delta G = delta hetero. when i substitute r* =2*sigma/delta Gv I get delta G* het= 1/4 *delta G* homo..... it'd be great if anyone can let me know where I'm going wrong!! Thanx!!