Wurtzite is a hexagonal crystal structure with two atoms in the asymmetric unit and four atoms in the basis. It is related to the hexagonal diamond structure. Many semiconductors such as AlN, BN, CdS, CdSe, GaN, InN, SiC, and ZnO, form the wurtzite structure. Often the bonds between the atoms are partly ionic and there is some charge transfer between the atoms. The Madelung constant of wurtzite is $\alpha = 1.641$.

Crystal structure: Wurtzite
Bravais lattice: hexagonal
Space group: 186 (P6₃/mc),  Strukturbericht: B4,   Pearson symbol: hP4
Point group: 6mm (C_6v)   1 six-fold rotation axis, 6 mirror planes, no inversion

The lattice parameters of the conventional unit cell are:

\[ \begin{equation} a = b; c \ne a, \hspace{0.5cm} \alpha = 90^{\circ} , \,\beta = 90^{\circ} ,\,\gamma = 120^{\circ} . \end{equation} \]

The primitive cell of the hexagonal closed packed (hcp) lattice is given by the three lattice vectors:

$\vec{a}_1=\frac{a}{2}\hat{x}+\frac{-\sqrt{3}a}{2}\hat{y}$,   $\vec{a}_2=\frac{a}{2}\hat{x}+\frac{\sqrt{3}a}{2}\hat{y}$,   $\vec{a}_3=c\hat{z}$.

There are two atoms in the asymmetric unit

Zn1 (⅓,⅔,0),  S1 (⅓,⅔,$z_1$)

The parameter $z_1$ depends on the compound that forms the wurtzite structure. For ZnS $z_1 = 0.3748$.

There are four atoms in the basis

Zn1 (⅓,⅔,0),  S1 (⅓,⅔,$z_1$)  Zn2 (⅔,⅓,½),  S2 (⅔,⅓,$z_1+\frac{1}{2}$)

Space group: 186 (P6₃/mc)
12 symmetry operations:

1	x,y,z	identity
2	-y,x-y,z	C3 axis
3	-x+y,-x,z	C3 axis
4	-x,-y,z+1/2	2-fold screw axis|translation: 0 0 1/2
5	y,-x+y,z+1/2	6-fold screw axis|translation: 0 0 1/2
6	x-y,x,z+1/2	6-fold screw axis|translation: 0 0 1/2
7	-y,-x,z	mirror plane
8	-x+y,y,z	mirror plane
9	x,x-y,z	mirror plane
10	y,x,z+1/2	c-glide plane|translation: 0 0 1/2
11	x-y,-y,z+1/2	c-glide plane|translation: 0 0 1/2
12	-x,-x+y,z+1/2	c-glide plane|translation: 0 0 1/2