The formula to calculate the Critical Free Energy for Nucleation from Volume Free Energy is:
\[ \Delta G = \frac{16 \pi \gamma^3}{3 \Delta G_v^2} \]
Critical Free Energy is the energy required for the formation of stable nuclei. Surface Free Energy is the energy required to create a solid–liquid phase boundary during solidification. Volume Free Energy is the free energy difference between the solid and liquid phases.
Let's assume the following values:
Using the formula:
\[ \Delta G = \frac{16 \pi \cdot 0.2^3}{3 \cdot (-10,000)^2} \approx 1.34041286553165 \times 10^{-9} \]
The Critical Free Energy is approximately \(1.34041286553165 \times 10^{-9}\) Joule.
| Surface Free Energy (Joule per Square Meter) | Volume Free Energy (Joule per Cubic Meter) | Critical Free Energy (Joule) |
|---|---|---|
| 0.1 | -10000 | 0.000000000167552 |
| 0.15 | -10000 | 0.000000000565487 |
| 0.2 | -10000 | 0.000000001340413 |
| 0.25 | -10000 | 0.000000002617994 |
| 0.3 | -10000 | 0.000000004523893 |