Metal nitride coating are important for obtaining desirable mechanical properties for metal surface. Please answer the following questions using ZrN ceramic film as the example.

a$)$ Sketch the unit cell sublattices for BCC ZrN below and describe them using words. Explain how your sublattices are consistent with the material stoichiometry. B$)$ For BCC ZrN$,$ what are the formal oxidation states of the Zr and N and the electron configurations of the cation and anion, respectively?