Here we report the growth of sub-millimeter MgB2 single crystals of various shapes under high pressure in Mg-B-N system. Structure refinement using a single-crysial X-ray diffraction analysis gives lattice parameters a = 3.0851(5) Å and c = 3.5201(5) Å with small reliability factors Rw = 0.025, R = 0.018), which enables us to analyze the Fourier and Fourier difference maps. The maps clearly show the B sp2 orbitals and covalency of the B-B bonds. The sharp superconducting transitions at Tc = 38.1-38.3 K were obtained in both magnetization ΔTc = 0.6 K) and resistivity (ΔTc < 0.3 K) measurements. Resistivity measurements with magnetic fields applied parallel and perpendicular to the Mg and B sheets reveal the anisotropic nature of this compound, with upper critical field anisotropy ratio of about 2.7.
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