One of the subquestions is to create a primitive unit cell for the diamond structure, but I have a hard time to see how you can do this (keeping the condition that it must contain 1 lattice point).
But this would be 1/8th of a cube and If I count the number of latice points it contains 4 times 1/8th latice point and a whole latice point adding up to 1,5 latice points in a primitive unit cell. And for some regions this encloses only 0.5 latice points. These beeing different also points to that how I interpret the lattice that it is not a valid unit cell. I could just be seeing the geometry wrong (most likely), but can someone explain it a bit more in depth
Thank you for your response. I figured out that the shape corresponds to a parallelpiped and not 1/8th cube. But then my second question still remains. Shouldn’t the primitive unit cell always contain 1 latice point by definition. For example using the Wigner-Seitz unit cell.
It is correct that the primitive unit cell only contains one lattice point. Your counting also suggests that something goes wrong because every unit cell must contain an integer number of lattice points.
Try applying what I wrote over here to find the basis using the primitive unit cell.·
Ah, atoms in the basis aren’t lattice points. You can also confirm this by seeing that (1/4, 1/4, 1/4) is not a combination of primitive lattice vectors.
