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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!!