Many mathematical theories developed for X-ray analysis of interstratified (mixed layer) structure, in which two or more different unit layers are arranged statistically in one dimension, are reviewed and discussed with the determined structure. All the interstratified structures so far reported can be classified into either a regular type or a random one. However, non-integral X-ray superref lections or background elevation often noticed in small angle region can not be explained as due to any one of those types. To solve the problem, a detailed X-ray examination using Kakinoki and Komura's general equation has been tried with reference to its Reichweite and the relevant probability parameters. As the result, it has been disclosed that most of the interstratified minerals are distributed along the line of PBB≅O or PAA≅O on the structure diagram, not along the random line, where PBB and PAA denote the probabilities of B layer next to B layer and A layer next to A layer, respectively. Additional emphasis is put on the extension of the Reichweite in its X-ray analysis as well as the direct observation of layer stacking by a electron microscopy.
Site symmetry of tetrahedral (A) and octahedral (B) sites of the spinel structures in the solid solulion of Fe3O4-Mn3O4 and Fe3O4-Fe2TiO4 varies microscopically with their cation distribution. Variations of the local distortion due to the Jahn-Teller distortion of Mn3+ in B site affect the electric field gradient of cations. This gradient is related to the nuclear quadrupole splitting in the Mossbauer spectra. The above variations also affect lattice vibration, which is recognized by the far-infrared absorption spectra. Factors obtained from these spectra shift continuously over the whole range of Fe3O4-Mn3O4 solid solution. Atomic positional disorder and electron localization by the Jahn-Teller effect give rise to the local distorion, which affects anisotropic temperature factors. From this point of view, X-ray crystal structure analysis can be used for the observation of local displacement of atomic position resulting from the variation of local site symmetry. The structure analysis of Fe3O4-Fe2TiO4 solid solution shows that temperature factors of oxygen considerably varies with the degree of substitution and displacement of oxygen atom results in the local distortion of polyhedra. The observations of these different types of methods give a consistent result for the local site symmetry of the solid solutions.