  A systematic study is presented on the superconductivity (sc) parameters of
the ultrapure niobium used for the fabrication of the nine-cell 1.3 GHz
cavities for the linear collider project TESLA. Cylindrical Nb samples have
been subjected to the same surface treatments that are applied to the TESLA
cavities: buffered chemical polishing (BCP), electrolytic polishing (EP),
low-temperature bakeout (LTB). The magnetization curves and the complex
magnetic susceptibility have been measured over a wide range of temperatures
and dc magnetic fields, and also for di erent frequencies of the applied ac
magnetic field. The bulk superconductivity parameters such as the critical
temperature Tc = 9.26 K and the upper critical field Bc2(0) = 410 mT are found
to be in good agreement with previous data. Evidence for surface
superconductivity at fields above Bc2 is found in all samples. The critical
surface field exceeds the Ginzburg-Landau field Bc3 = 1.695Bc2 by about 10% in
BCP-treated samples and increases even further if EP or LTB are applied. From
the field dependence of the susceptibility and a power-law analysis of the
complex ac conductivity and resistivity the existence of two different phases
of surface superconductivity can be established which resemble the Meissner and
Abrikosov phases in the bulk: (1) coherent surface superconductivity, allowing
sc shielding currents flowing around the entire cylindrical sample, for
external fields B in the range between Bc2 and Bcohc3, and (2) incoherent
surface superconductivity with disconnected sc domains between Bcohc3 and Bc3.
The coherent critical surface field separating the two phases is found to be
Bcoh c3 = 0.81Bc3 for all samples. The exponents in the power law analysis are
different for BCP and EP samples, pointing to different surface topologies.
