Question

Volume ratio for conventional cell and wigner seitz cell for bcc

Answer 1

Primitive Cell

A primitive cell is a unit cell that contains exactly one lattice point. It is the smallest possible cell.[5] If there is a lattice point at the edge of a cell and thus shared with another cell, it is only counted half. Accordingly, a pointlocated on the corner of a cube is shared by 8 cubes and would count with 1818.

Wigner-Seitz Cell

There is a special type of primitive-cells known as Wigner-Seitz cell. The Wigner-Seitz cell of a lattice point is defined as the volume that encloses all points in space which are closer to this particular lattice point than to any other. It can be constructed as depicted below.[6] [7]

2D-construction of a Wigner-Seitz cell: One chooses any lattice point and draws connecting lines to its closest neighbours. In a second step one constructs the perpendicular bisectors of the connecting lines. The enclosed area is the Wigner-Seitz cell. It forms a unit cell, i.e. is able to build the whole lattice without gaps/overlaps.