Question

If the 'cube' embryo nucleates in liquid by homogeneous nucleation,

Please derive the ΔG, r*, ΔG*

r* is the critical radius of nucleus

Answer 1

Let, be the surface energy needed to make the precipitate and assume the surface area for the same to be = 4πr².

Then,

where is the specific interface energy of interaction which is always +(ve) since we are providing it.

Now,

Free energy = volume enclosed by this assumed surface x energy gained per particle volume = where ∆g is the energy gained per particle volume, which is always -(ve) since we are gaining it.

So, upon adding both we get-

or you can denote it by ∆G(r).

Now, differentiate the above equation w.r.t 'r' to determine the critical radius of nucleation. As it comes out to be ;

i.e., obtain the final expression by inserting critical radius back into the ∆G(r).