The coexistence of manganoan actinolite and tirodite in samples from four manganese ore deposits has been investigated by an electron probe microanalysis and an X-ray powder method. These amphiboles occur with spessartine, rhodonite, rhodcchrosite and/or alabandite, pyrophanite, quartz. Al₂O₃, TiO₂, Na₂O, and K₂O contents of these amphiboles are very small. Analytical data are plotted on a quadrilateral, Ca₂Mg₅Si₈O₂₂(OH)₂-Ca₂ (Fe, Mn)₅Si₈O₂₂(OH)₂-Mn₂Mg₅Si₈O₂₂(OH)₂-Mn₂(Fe, Mn)₅Si₈O₂₂(OH)₂. X-ray powder patterns of the amphiboles are also given.

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The logical ordering of complex mineral structures has been made to bring out hierarchical nature of their constitutions. The primary structure has neither substructure having other structure type nor pseudo-translations which relate it to other structure type. The types of the secondary structure of a given primary structure A (or B) may be classified into four categories: (1) super structures including simple substitution or distortion derivatives, A*, antiphase domain structures, iA, and structures characterized by commensurable density (or displacive) waves, Â, (2) modulated structure, Ã, (3) patchwork, M (A, B), or intergrowth, I(A, B), both consisting of A and B, and (4) domain structure, D(A), consisting of A with submicroscopic extension. Among these, the primary structures of A* and à are recognized by folding them with their pseudo-translations, and those in the remainings as substructures. The tertiary structure is characterized by the existence in it a substructure having a secondary structure. Likewise, more complex structures can be defined. Examples are: enstatite IV defines a tertiary structure i (A=high clinopyroxene), haüyne a quaternary structure D [I(Ã, B)] (A=nosean, B=haüyne end-member), and e-plagioclase a quinary structure I(iÃ*, B) (A=high anorthite, B=albite). Complex mineral structures are in general characterized by density (and displacive) waves which seem to generate, at their nodes, the boundaries of their substructures.

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Non-crystalline mineral components of soils and sediments have great influence on their physical, chemical and biological properties. These, because the components possess large surface area, are often reagents for cementing and coating surfaces of crystalline particles and change their own reactivities depending on the pH of system involved. In contrast with the striking progress in research of crystalline minerals, studies for non-crystalline minerals have reluctantly been neglected. There is very limited knowledge for their characterization. In this article, several problems encountered due to the lack of knowledge were presented by examples from the studies of Canadian soil minerals. The necessity of basic research was emphasized to gain better understanding of such components.

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A computer software package, RIETAN, has been developed for the Rietveld refinement of angle-dispersive X-ray and neutron data, and TOF neutron data. The program is written in FORTRAN 77 and of modular construction to facilitate changes. RIETAN incorporates data bases of information on space groups, atomic scattering factors, scattering lengths, and anomalous dispersion corrections. It can handle all space groups without additional programming and allows refinement of the diffraction data of samples containing two or more phases. A new profile shape function, which is the sum of a Gauss function and a Lorentz function with unequal peak heights and widths at one-half peak height, has been included for the analysis of angle-dispersive diffraction data. Three different algorithms for nonlinear least squares have been implemented: Gauss-Newton, Marquardt, and conjugate direction methods. One can easily change the method of least squares one after another during refinement. These three methods are combined with an exterior penalty function method so that objective functions can be minimized under equal and unequal constraints which may be linear and/or nonlinear functions with respect to parameters. The program can not only plot the results of Rietveld analysis but also simulate powder diffraction patterns by using user-supplied parameters.

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