Elastic scattering and direct reactions have been studied for the collisions induced by the three Beryllium isotopes 9,10,11Be, on a medium mass 64Zn target at energies near the Coulomb barrier. The elastic-scattering angular distribution of the 11Be halo nucleus shows a deviation from the classical Fresnel type diffraction behavior in the Coulomb-nuclear interference peak angular region. The deduced total reaction cross-sections for the 11Be collision is more than a factor of two than the ones measured in the collisions induced by 9;10Be. Moreover, for 11Be a large contribution to the total reaction cross-section due to transfer and break-up processes has been observed.