In an attempt to clarify conflicting published data, we report new measurements of specific heat, resistivity, magnetic susceptibility, and thermal expansivity up to room temperature for the 6 K superconductor ZrB 12 , using well-characterized single crystals with a residual resistivity ratio Ͼ9. The specific heat gives the bulk result 2⌬͑0͒ / k B T c = 3.7 for the superconducting gap ratio, and excludes multiple gaps and d-wave symmetry for the Cooper pairs. The Sommerfeld constant ␥ n = 0.34 mJ K −2 gat −1 and the magnetic susceptibility = −2.1 ϫ 10 −5 indicate a low density of states at the Fermi level. The Debye temperature D is in the range 1000-1200 K near zero and room temperature, but decreases by a factor of ϳ2 at ϳ35 K. The specific heat and resistivity curves are inverted to yield approximations of the phonon density of states F͑͒ and the spectral electron-phonon scattering function ␣ tr 2 F͑͒, respectively. Both unveil a 15 meV mode, attributed to Zr vibrations in oversized B cages, which gives rise to electron-phonon coupling. The thermal expansivity further shows that this mode is anharmonic, while the vanishingly small discontinuity at T c establishes that the cell volume is nearly optimal with respect to T c .
We measured the specific heat, the magnetization, and the magnetoresistance of a single crystal of ZrB 12 , which is superconducting below T c Х 6 K. The specific heat in zero field shows a BCS-type superconducting transition. The normal-to superconducting-state transition changes from first order ͑with a latent heat͒ to second order ͑without latent heat͒ with increasing magnetic field, indicating that the pure compound is a low-, type-II/1 superconductor in the classification of Auer and Ullmaier ͓Phys. Rev. B 7, 136 ͑1973͔͒. This behavior is confirmed by magnetization measurements. The H-T phase diagram based on specific-heat and magnetization data yields H c2 ͑0͒ = 550 G for the bulk upper critical field, whereas the critical field defined by vanishing resistance is a surface critical field H c3 ͑0͒ϳ1000 G.
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