The atomic structure of amorphous silicon nitride fibers produced by two different methods is revealed using the technique of neutron scattering. Polymer-derived fibers are found to contain excess crystalline silicon and disordered carbon, and fibers annealed in N-2 for too h contain a cristobalite phase that becomes amorphous under 200-kV electron irradiation. Fibers grown from the gas phase, however, are shown to consist of almost pure amorphous Si3N4, with a small crystalline alpha-Si3N4 component.