compounds*

We report neutron scattering measurements on single crystals of FeTe_1-xSe_x. Superconductivity (SC) and antiferromagnetic (AFM) order in these compounds can be tuned together by varying Se compositions and/or excess Fe. We show that in systems where long-range magnetic order develops, superconductivity is completely suppressed. The long-range magnetic order is static with long life-time. On the other hand, when the magnetic order is short-range and the system exhibits behaviors of a mixed phase or phase separation between AFM and SC, the energy profile of the magnetic order appears to be quasi-elastic with energy widths around 0.2 meV. We discuss the evolution of the quasi-elastic magnetic scattering with temperature and doping, and their implications on the understanding of the spin-glass/SC mixed phase in FeTe_1-xSe_x systems.