  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-crystal X-ray diffraction analysis gives lattice parameters a=3.0851(5)
A and c=3.5201(5) A 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 =38.1-38.3K were obtained in both
magnetization (DTc =0.6K) and resistivity (DTc <0.3K) 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.
