  Vanadium is an elemental type-II superconductor which has a pure
superconducting phase, a vortex phase, and a non-superconducting phase. We
designed and carried out a low-budget experiment in our undergraduate physics
lab to measure the magnetic field a close distance from the surface of a pure
Vanadium disk sample isothermally with a Hall sensor across a range of
different temperatures and external magnetic fields. We then used these
measurements to compute the superconducting phase diagram of Vanadium. After
completing measurements at eight temperatures ranging from 2.6K to 5K and
magnetic fields ranging from -0.2T to 0.2T, we were able to detect the Meissner
phase (clearly), and a vortex phase (less clearly). Using the graphs of the
hall bar magnetic field versus external magnetic field, we were able to derive
a rough estimate for the upper critical field and the lower critical field of
Vanadium at the eight temperatures wherein we conducted measurements. The
results are in general accord with the phase diagram of Vanadium found in the
literature, except that the critical temperature appears to be less than 5.43K
and 5.13K (about 4.8K). Further, we observed critical fields lower than those
found in the literature. We hypothesize this is due mostly to impurities in our
Vanadium sample (purchased through Amazon.com), which would reduce the measured
critical temperature below that of pure Vanadium, consistent with our results.
