Energy band structures of metal-deficient hexagonal diborides M0.75B2 (M = Nb, Zr and Y) were calculated using the full-potential LMTO method. The metal vacancies change the density of states near the Fermi level and this effect is quite different for III-V group transition metal diborides. Contradictory data on superconductivity in diborides may be supposed to be connected with nonstoichiometry of samples. Vacancy formation energies are estimated and analyzed. * E-mail: shein@ihim.uran.ru A recent discovery of superconductivity (SC) in MgB 2 (T c ≈ 39 K) 1 and creation of promising materials based thereon (see reviews [2−5] ) have attracted a great deal of interest in hexagonal transition metal (M) diborides isostructural with MgB 2 [2−5] . Earlier investigations observed no superconductivity in d-metal diborides (Ti, Zr, Hf, V, Ta, Cr, Mo, Nb) with temperatures above 0.6 K 6 . Experimental and theoretical investigations [7−17] showed that the supercoductivity with T c ≈ 40K is unlikely in all undoped diborides except MgB 2 , where the high value of T c is explained by strong electron-phonon coupling and high phonon frequencies and is closely connected with the existence of hole doped boron σ bands.Recently, rather high T c have been reported for ZrB 2 (5.5K) 7 , TaB 2 (9.5K) 8 and NbB2 (5.2K) 9 . On the other hand, Rosner et al showed 10 that SC in TaB 2 was absent down to 1.5 K, and according to 7,8 the SC transition for NbB 2 is not observed to T ∼ 2K, in conformity with earlier data 6 . The weak electron-phonon coupling estimated to be inconsistent with superconductivity in ZrB 2 14 leads to T c ∼ 0.1 K in TaB 2 13 and is responsible only for T c ∼ 3K in NbB 2 12 . So, both experimental and theoretical studies performed to characterize and understand superconductivity in MB 2 yielded contradictory results. It is important also to note that in all the studies [7−17] the composition of transition metal diborides was considered to be strictly stoichiometric (B/M = 2). As is known, lattice vacancies are typical defects, and their presence may change considerably the properties of non-stoichiometric materials in the homogeneity region. For instance, one of the most familiar classes of non-stoichiometric compounds with exclusively wide homogeneity regions (to 30 ∼ 55 at %) includes cubic (B1) III-V group transition metal carbides, nitrides and oxides extensively investigated in numerous works, see 18 . As distinct from the above B1 -carbides, nitrides and oxides, III-V group metal diborides have very narrow homogeneity regions under equilibrium conditions 19 . Therefore the role of non-stoichiometry is usually ignored when their properties are examined. No theoretical studies describing the effect of lattice vacancies on the electronic structure of metal diborides are familiar to us either.
Quite recently, Yamamoto et al20 have carried out a highpressure synthesis of a series of metal-deficient samples of the AlB 2 -type Nb 1−x B 2 , Ta 1−x B 2 (0 < x < 0.48) and Mo 2 B 5 -type borides with the compositions ...