Single crystals of the TlSr2CaCu2O7 superconductor have been grown for
the first time. The structures of an as-grown crystal (T-c = 55 K) an
d an oxygen pressure annealed one (T-c = 15 K) have been refined. The
results are compared to those reported for the polycrystalline phase.
The magnetic study (H parallel to c) of a T-c = 55 K as-grown crystal
allows us to compare the superconducting properties of TlSr2CaCu2O7 wi
th those of other thallium 1212 single crystals.