Primitive cell ↩

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created: 2021-10-31 02:04:59
modified: 2022-01-20 22:17:47

The unit cell that contains exactly one lattice point. This is the smallest possible unit cell.

The volume of the primitive cell is given by the parallelepiped from the primitive vectors of the lattice:

or more simply

Where is the matrix of the lattice1.

Usually, primitive cells in two and three dimensions are chosen to take the shape parallelograms and parallelepipeds, with an atom at each corner of the cell. This choice is not unique, but the volume of primitive cells will always be given by the expression above.

General primitive cell in 2D:

Wigner-Seitz cell

An important type of primitive cell is the Wigner-Seitz cell. It does not take the shape of parallelograms or parallelepipeds, but it can be shown that it is indeed primitive cell.

  1. where the vectors are the primitive vectors of the lattice as column vectors, forming a matrix: .
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