Single crystals of La 2CuO 4+δ with δ = 0.03 and δ = 0.04 have been studied in the temperature region 10 K ≤ T ≤ 293 K using a high resolution neutron diffractometer. In both crystals, the concentration of excess oxygen is inside the miscibility gap. However, the La 2CuO 4.03 crystal does not undergo a phase separation - homogeneous oxygen distribution was preserved over the entire temperature region studied, while in the La 2CuO 4.04 crystal, the phase separation phenomenon, connected with excess oxygen diffusion was observed. Analysis of the diffraction peak width as a function of interplane spacing allowed us to determine the dimensions of the coherent regions of coexisting phases: 975 ± 22 Å in the direction of the tetragonal axis of the high temperature phase, and (1460 ± 160) Å in the perpendicular direction. Our data provide direct evidence that both the oxygen-rich and oxygen-poor regions have the same Cmca space symmetry.