Structure-dependent ferroelectricity of niobium clusters (NbN, N=2-52)

The ground-state structures and ferroelectric properties of NbN (N=2-52) have been investigated by a combination of density-functional theory (DFT) in the generalized gradient approximation (GGA) and an unbiased global search with the guided simulated annealing. It is found that the electric dipole moment (EDM) exists in the most of NbN and varies considerably with their sizes. And the larger NbN (N>=25) prefer the amorphous packing. Most importantly, our numerical EDM values of NbN (N>=38) exhibit an extraordinary even-odd oscillation, which is well consistent with the experimental observation, showing a close relationship with the geometrical structures of NbN. Finally, an inverse coordination number (ICN) function is proposed to account for the structural relation of the EDM values, especially their even-odd oscillations starting from Nb38.