|HCP(left)-FCC(right) stacking fault|
|The FCC side, note how the 3rd layer's fruits sit on top of voids in the first layer|
|The HCP side. 1st layer and 3rd layers sit on top of each other|
For the second plane, you have two possibilities that are mirror image of each other, a translation, a rotation of 30 degree, etc. In short, this is not a real choice because you have no reference point.
The same alternative has richer consequences in the third plane. Depending on your choice, you end whether with
- 3rd layer's fruits sitting on top of 1st layer's fruits
- 3rd layer's fruits sitting on top of 1st layer's voids
|FCC is left, HCP right, and the grain boundary in the middle (hole in the 3rd layer)|
|FCC is right, HCP left, and the grain boundary in the middle (hole in the 3rd layer)|
If you think about the stacking of a crystal of hard spheres, the price paid to have such a stacking fault is the spheres you could not fit in because of the line. In my very small crystal, I could have fit 2 more spheres without the fault. This is a global penalty.
On the other hand, the space gained to rattle by the spheres neighbouring the fault line increases their (vibrational) entropy and thus decreases their free energy. This is a local gain.
When you balance the global penalty with the local gain, you end up with quite a lot of stacking lines.