Single crystals of the ''1201'' mercury based cuprate have been grown
for the first time. Their structure determination allows the classical
Jahn-Teller distortion of the octahedral copper layer to be confirmed
and gives evidence for the presence of oxygen at the level of the Hg/
Bi layer leading to the formula Hg0.8Bi0.2Ba2CuO4.3. The [Hg0.8Bi0.2Od
elta](infinity) layers can then be described as built up from HgO2 sti
cks that coexist with BiO6 octahedra, bismuth being nearly pentavalent
. The magnetic study of these crystals shows that they exhibit superco
nductivity up to 75 K (T-c(midpoint = 62 K)), with 100% superconductin
g volume fraction at low temperature. Moreover the M(B) loops exhibit
fishtail shapes which were not present for measurements on ceramics. T
he fishtail and irreversibility links of (Hg, Bi)-1201 are studied for
the H parallel to c geometry. These data are compared with those of T
l-single crystals; it appears that (Hg, Bi)-1201 is quite similar to T
l monolayers and differs greatly from Tl bilayers. This underlines the
influence of structural anisotropy in both Hg- and Tl-cuprates on the
ir superconducting properties.