  The zero-temperature phase diagrams of imbalanced fermions in 3D optical
lattices are investigated to evaluate the validity of the Fermi-Hubbard model.
It is found that depending on the filling factor, s-wave scattering strength
and lattice potential, the system may fall into the normal($N$) phase,
magnetized superfluid(SF$_M$) or phase separation of $N$ and BCS state. By
tuning these parameters, the superfluidity could be favorable by enhanced
effective couplings or suppressed by the increased band gap. The phase profiles
in the presence of a harmonic trap are also investigated under LDA, which show
some exotic shell structures compared to those without the optical lattice.
