= Solution
The disc <volume> is $\pi d^2h/4$, the combined <area> of its two flat faces is $\pi d^2/2$, and its cylindrical edge <area> is $\pi dh$. With the signed bulk driving term $\Delta G$ per <volume>,
$$
\boxed{W_n=\frac\pi4d^2h\Delta G+\frac\pi2d^2\gamma_f+\pi dh\gamma_e.}
$$
For favourable transformation $\Delta G$ is negative and the interfacial terms are positive. This <classical nucleation theory> expression neglects a separate elastic term; if <coherency strain> is important, its appropriate energy must be added or included explicitly in the effective <volume> term. $W_n$ has energy units, whereas $\Delta G$ here has energy-per-volume units.
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