Tight-binding simulations of Nb surfaces and surface defects

Abstract

We study the properties of low-index Nb surfaces using the NRL-tightbinding (TB) method. We develop a new TB Hamiltonian for Nb using the basic NRL-TB framework with an expanded fitting database that includes additional bulk structures and frozen phonon calculations. The resulting Hamiltonian is validated by comparing to several bulk-zero-temperature and finite temperature properties. Using this Hamiltonian we simulate the three low-index surfaces, $(001),$ $(110),$ and $(111),$ in slab geometries. We find that substantial slab thickness and Brillouin zone sampling is needed for convergence. Our results show that the surface layer contracts in agreement with experiment, and that the direction of relaxation of the near surface layers oscillates with depth. Both the magnitude of the surface layer contraction and the relaxed surface energies are in good agreement with available experiments and previous simulations. The electronic structure of the surface samples shows distinct surface bands near the Fermi level that are strongly affected by atomic relaxation. The surface phonon spectra show distinct features that correspond to the binding strength of the surface atoms. We also calculate the formation energies of surface defects including adatoms and vacancies. Relaxation around the defects usually involves mainly the first-neighbor atoms, except on the $(111)$ surface where atoms in up to three layers under the defect move significantly.