@@ -674,7 +674,7 @@ Now the unit cell contains four carbon atoms which need to be specified in the b

The basis in fractional coordinates is: $\mathrm{C}(0,0), \:\mathrm{C}(1/3, 0), \:\mathrm{C}(1/2, 1/2) \:\mathrm{and} \:\mathrm{C}(1/2, 5/6)$.

### Wigner-Seitz unit cell

There exists a very important alternative type of unit cell - the _Wigner-Seitz cell_.

There exists a very important alternative type of a primitive unit cell - the _Wigner-Seitz cell_.

It is a collection of all points that are closer to one specific lattice point than to any other lattice point.

The cell is formed by taking all the perpendicular bisectrices of lines connecting a lattice point to its neighboring lattice points.

The Wigner-Seitz cell is constructed as follows:

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@@ -696,7 +696,7 @@ It does however, contain multiple atoms, which should be specified in the basis.

Another way to calculate the number of atoms inside the cell is by realizing that there is an atom at the lattice point itself and there is 1/3'rd of an atom at three corners of the cell.

This results in $1+3\times 1/3 = 2$ atoms being inside the unit cell.

The reason why we would want to use the Wigner-Seitz cell over other unit cells becomes clear when we consider the dispersion of electrons in certain crystal structures (following lectures).

The reason why we would want to use the Wigner-Seitz cell over other unit cells becomes clear when we study the reciprocal lattice in next lecture.