  We have explored the vortex phase diagram in a spherical single crystal of
niobium (T ~ 9.3 K) via isothermal and temperature dependent dc magnetization
and ac-susceptibility measurements. The crystal has extremely weak pinning that
can be inferred from the reversibility of loops below T_c. However, one can
visualize the peak effect (PE) feature in the isothermal M-H loops up to T = 8
K. The PE is also prominent in isothermal ac-susceptibility data for H > 750
Oe. An interesting observation in the present study is the prominent
fingerprints of surface superconductivity, starting just above the collapse of
pinning at the peak position of the PE and ending at the surface critical field
(H_c3). We have also observed the paramagnetic Meissner effect in field-cooled
magnetization data recorded at relatively large fields in this crystal. A
vortex phase diagram is constructed by marking the peak positions of the PE
(H_p), the upper critical field (H_c2) and the surface critical field (H_c3).
Unlike a previous report which shows the existence of a multi-critical point in
the phase dia-gram of a Nb crystal, where H_p, H_c2 and H_c3 lines meet, we do
not observe a multi-critical point in our weak pinning crystal.
