  The effects of high-temperature vacuum-annealing induced Mg deficiency in
MgB2 single crystals grown under high pressure were investigated. As the
annealing temperature was increased from 800 to 975 C, the average Mg content
in the MgB2 crystals systematically decreased, while Tc remains essentially
unchanged and the superconducting transition slightly broadens from 0.55 K to
1.3 K. The reduction of the superconducting volume fraction was noticeable
already after annealing at 875 C. Samples annealed at 975 C are partially
decomposed and the Mg site occupancy is decreased to 0.92 from 0.98 in as-grown
crystals. Annealing at 1000 C completely destroys superconductivity. X-ray
diffraction analysis revealed that the main final product of decomposition is
polycrystalline MgB4 and thus the decomposition reaction of MgB2 can be
described as 2MgB2(s) = MgB4(s) + Mg(g). First-principles calculations of the
Mg1-x(VMg)xB2 electronic structure, within the supercell approach, show a small
downshift of the Fermi level. Holes induced by the vacancies go to both sigma
and pi bands. These small modifications are not expected to influence Tc, in
agreement with observations. The significant reduction of the superconducting
volume fraction without noticeable Tc reduction indicates the coexistence,
within the same crystal, of superconductive and non-superconductive electronic
phases, associated with regions rich and poor in Mg vacancies.
