  A high temperature electrochemical oxidation process has been used to produce
large single crystals of $La_2CuO_{4 + \delta}$ suitable for neutron scattering
experiments. Below room temperature the oxygen-rich phases have structural
superlattice scattering peaks which indicate new periodicities ranging from 2
to 6.6 layers perpendicular to the copper oxide planes. A model structure
originally proposed for $La_2NiO_{4 + \delta}$ can account for the superlattice
peaks as a result of anti-phase domain boundaries between different tilt
directions of the CuO$_6$ octahedra. Within this model, the changes in CuO$_6$
tilt directions are induced by segregated layers of interstitial oxygen which
order in a manner similar to intercalants in graphite. This structural model
thus clarifies previous work and establishes $La_2CuO_{4 + \delta}$ as a unique
lamellar superconducting system with annealed disorder.
