PAS and Symmetry in Fe_4N

For Fe-I (corner site), we find four 3-fold axes (the cubic body diagonals). According to theorem 2, because there are at least two axes of order greater than 3, the EFG vanishes.

For Fe-II (face-centered site), there is a 4-fold rotation axis along the N-Fe-N bond. The z-axis is aligned with the 4-fold rotation axis and according to theorem 1, since there is an axis of order greater than 3, the EFG is axially symmetric, meaning that eta=0.