  The Fe1+yTe1-xSex series of materials is one of the prototype families of
Fe-based superconductors. To provide further insight into these materials we
present systematic inelastic neutron scattering measurements of the low energy
spin excitations for x=0.27, 0.36, 0.40, 0.49. These measurements show an
evolution of incommensurate spin excitations towards the (1/2 1/2 0) wave
vector with doping. Concentrations (x=0.40 and 0.49) which exhibit the most
robust superconducting properties have spin excitations closest to (1/2 1/2 0)
and also exhibit a strong spin resonance in the spin excitation spectrum below
Tc. The resonance signal appears to be closer to (1/2 1/2 0) than the
underlying spin excitations. We discuss the possible relationship between
superconductivity and spin excitations at the (1/2 1/2 0) wave vector and the
role that interstitial Fe may play.
