## Phonon density of states for ZnO (Wurtzite)

The lattice constants of ZnO in the wurtzite structure are $a=3.25$ Å, $c=5.206$ Å. There are two zinc atoms and two oxygen atoms in the conventional unit cell so the atomic density is $n= 4/((\sqrt{3}/2)*(3.25\times 10^{-10})^2*5.206\times 10^{-10}) = 8.40 \times 10^{28}$ 1/m³. Every atom has three degrees of freedom so there are $3n = 2.52\times 10^{29}$ modes/m³. The integral of the phonon density of states over all frequencies should be $3n$.