Vacancies and small vacancy clusters in BCC transition metals : calculation of binding energy, atomic relaxation and electronic and vibrational densities of states

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Abstract
A tight-binding type electronic theory is used to calculate the binding energy Ebin, atomic relaxation, and electronic and vibrational densities of states (DOS), ρi(E) and gi(ω), for vacancy-type lattice defects in BCC transition metals : The short-range repulsive energies between neighbouring atomic sites are simulated by a Born-Mayer potential. Binding energies of di-vacancies and small vacancy clusters (up to tetra-vacancies) are obtained using the direct energy minimization procedure, and compared with the available experimental results. Atomic vibrations and d-electron DOS on atoms near the lattice defects are also investigated using the recursion method by Haydock et al. In general, atomic relaxation around the lattice defects plays a dominant role in determining the binding energies and vibrational properties (local vibrational DOS) of the defects. Furthermore, it is shown that E bin and electronic DOS ρi(E) are very sensitive to the structure of atomic defects (configuration of vacancies) : The prominent resonance peak appears near the centre of d-band, similar to the surface state peak observed for W(001) or α-Fe(001) surfaces, for the tetra-vacancy aggregated on the (001) plane

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