  We report on elastic and inelastic neutron scattering from single-grain
isotopically-enriched samples to elucidate the local magnetic correlations
between Tb$^{3+}$ moments in quasicrystalline i-Tb-Cd. The inelastic neutron
scattering measurements of the CEF excitations demonstrated that the Tb$^{3+}$
moments are directed primarily along the local five-fold axes of the Tsai-type
cluster as was found for the TbCd6 approximant phase. Based on the inelastic
measurements, we consider of a simple Ising-type model for the moment
configurations on a single Tb$^{3+}$ icosahedron and enumerate the lowest
energy moment configurations. We then calculate the diffuse scattering from
these configurations and compare with the experimental magnetic diffuse
scattering measurements to identify the most likely single cluster moment
configurations and find reasonable agreement between the broad features
observed in our scattering simulations. We further consider the role of
higher-order (longer range) intercluster correlations for the magnetic
scattering.
