Heterogeneous nucleation on substrate

Consider cap$-$shaped nucleus on the substrate.

Neglect the behavior of atoms in the gas phase and on the surface.

Figure $5-3.$ Schematic of basic atomistic processes on substrate surface during vapor

deposition.

$G=a_3{r}^3{G}_V+a_1{r}^2{}_{vf}+a_2{r}^2{}_{fs}-a_2{r}^2{}_{sv}$

How can I derive a$1,$a$2,$a$3?$