What would be the Wigner-Seitz cell of this lattice?

[pepediaz]

Homework Statement

Given the lattice shown in attempt to a solution, consider white circles are atoms (of the same type). What would be the Wigner-Seitz cell of this lattice?

Relevant Equations

Not actually

I know WS cell only contains one lattice point, so we would have to trace bisectors, and obtain some kind of irregular shape.

Anyways, I wanted to check if what I did is okay. It is considering a fictitious point as the center of the (non-primitive) unit cell, which would be one of those hexagons. I don't know if the dotted square would be a WS, or if I should obtain an irregular shape.

 

[Nate810]

Yes, what you have done is okay. The dotted square would be considered a primitive unit cell, while the hexagon would be a non-primitive unit cell. The non-primitive unit cell is made up of multiple primitive unit cells. The irregular shape you obtain when tracing bisectors is a Wigner Seitz cell and it is the smallest unit cell that contains only one lattice point.