Materials showing long-range two-dimensional hexagonal order (called SBA-15 in the literature) were produced by templating a silica precursor (TEOS) with two Pluronic copolymers, EOxPOyEOx, of nearly the same x/y (0.3) ratio but different y values (x 18, y = 60 and x 20, y = 70, respectively); These materials were hydrothermally treated to increase the condensation of silicate species around the Pluronic aggregates and calcined to liberate the hexagonal array of mesopores. All materials, i.e., before and after hydrothermal treatment and calcination, were investigated by X-ray diffraction (XRD), and all calcined samples were further characterized by transmission electron microscopy and N-2 sorption experiments. The large number and narrow width of the XRD powder diffraction lines demonstrate the good crystallographic quality of the materials. This allows us to quantitatively exploit the XRD reflection intensities and to show that simple structural models of the silica lattice cannot account for them. This means that SBA-15 materials cannot be regarded as an ideal hexagonal lattice of pores imbedded in a uniform silica matrix. The structure of the silica walls is more complex and shows a "corona" region of lower density around the cylindrical organic aggregates.:This corona becomes microporous upon calcination, and we suggest that it arises from the partial occlusion of the PEO chains in the silica matrix. Modeling the XRD intensities allows us, for all the solids of this series::to derive estimates of pore diameters, corona, and wall thicknesses and to examine the influence on these structural parameters of the hydrothermal treatment.