We have carried out magnetic measurements and transmission electron microsc
opy (TEM) study on over-doped Tl2Ba2CuO6+delta (Tl-2201) single crystal sam
ples with a range of different oxygen content. Magnetic measurements show t
he existence of an irreversibility line that is considerably lower than the
upper critical field B-c2 and displays a positive upward curvature. We pro
pose that the critical field determined from magnetoresistive transitions f
or strongly over-doped sample is not the true upper critical field but the
irreversibility field instead. TEM study has shown that phase separation du
e to oxygen inhomogeneity is presented in the strongly overdoped samples th
at have very low T-c value and exhibit unusual temperature dependence of th
e upper critical field.