Quantitative phase analysis of multicomponent mixtures using X-ray powder diffraction data has been approached with a modified version of the Rietveld computer program of Wiles & Young [ J. Appl. Cryst. (1981), 14, 149-151]. This new method does not require measurement of calibration data nor the use of an internal standard; however, the approximate crystal structure of each phase of interest in a mixture is necessary. The use of an internal standard will allow the determination of total amorphous phase content in a mixture. Analysis of synthetic mixtures yielded high-precision results, with errors generally less than 1.0% absolute. Since this technique fits the complete diffraction pattern, it is less susceptible to primary extinction effects and minor amounts of preferred orientation. Additional benefits of this technique over traditional quantitative analysis methods include the determination of precise cell parameters and approximate chemical compositions, and the potential for the correction of preferred orientation and microabsorption effects.

Three peritidal carbonate crusts and associated intercrust sediments (total thickness of ∼30cm; aged <3000 years BP) on Ambergris Cay, Belize, contain 32–100% calcian dolomite (δx=72·5% dolomite) ranging in composition from 40 to 46 mol% MgCO3 (δx=43·3). Dolomite replaced high Mg calcite foraminiferal muds penecontemporaneously with sedimentation, forming partially dolomitized sediments and lithified crusts. Dolomitization probably occurred in normal to moderately evaporated seawater and is apparently continuing at the present. Detailed scanning electron microscope analysis shows a linear increase in mean dolomite crystal size with depth; 0·4 μm near the top of the section to 1·0 μm near the base of the dolomitized section. This size increase is not accompanied by any significant decrease in porosity. Crystal size distributions appear to be log‐normal and become increasingly broad and flat with depth. Rietveld X‐ray pattern‐fitting structure refinements indicate increasing Ca and Mg concentrations on their respective sites (cation ordering) as a function of increasing depth. Most of the ordering occurs within the first 15 cm of the surface. Stoichiometry does not increase with depth indicating no relationship between the Ca/Mg ratio and cation ordering. Strong geochemical trends were observed down‐section in the dolomite, including: (1) increasing Mn content (44 to 274 ppm), and (2) decreasing δ13C values (−0·9 to −5·5‰ PDB). Oxygen isotope values range from δ18O = 1·3‰ PDB in the upper part of the section to 2·6‰ PDB in the lower part of the section and are interpreted to represent two distinct groups of values rather than a continuous trend. Down‐section dolomite crystal size increase and shapes of crystal size distributions are consistent with recrystallization via a surface energy‐driven dissolution‐reprecipitation process (Ostwald ripening). The observed trends in carbon isotopes and Mn content probably result from geochemical re‐equilibration during recrystallization and reflect reducing conditions and an isotopically light, organically derived, carbon source. Oxygen isotope compositions probably reflect relict original dolomite values and are a result of decreasing evaporation due to rising sea level.

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The structural characteristics of Sr1−x Lax TiO3+δ (0≤x≤0.4) at 1400 °C have been investigated as a function of ambient oxygen partial pressure. A modified Rietveld pattern-fitting structure-refinement program [H. M. Rietveld, J. Appl. Crystallogr. 2, 65 (1969)] was used to determine the nature of the distortions of the fundamental perovskite unit cell, the degree of lattice perfection, and the cation vacancy concentrations. Specimens equilibrated in forming gas displayed a linear relation between x, the lattice parameters, and the degree of lattice perfection while those samples annealed in air and oxygen deviated significantly from linearity. A monoclinic distortion of the perovskite structure was seen in the samples at low oxygen partial pressures while a second phase or layer type of distortion appeared in samples with x&gt;0.2 under oxidizing conditions.

Convolution products Were obtained by folding a specimen-related function into another function representing the intrinsic profile of the diffractometer used in this study. The instrumental contributions were modeled with three split-Pearson VII functions: one for each of the a~, a2 and o~ 3 components in the Cu Ka spectral distribution. The positions and intensities of the a 2 and og 3 lines were based on those of the a~ line while their shapes were constrained to follow that of the a~. Values of the variable parameters of these functions, obtained from a 'defect-free' specimen, were fit with polynomials to establish four discrete curves from which the instrument profiles could be synthesized at any diffraction angle. Both a normalized Lorentzian and a Gaussian function were evaluated for use in representing the specimen contributions. The integral breadth (/3) of the specimen function was adjusted until the instrument-specimen convolution product best matched the observed profile. In specimens with small crystallite size, the angular dependence of/3 for the specimen profile followed the Scherrer relation while, in a strained specimen, the angular dependence followed the simple 4e tan 0 relation. In both cases, the specimen contributions were best modeled by a Lorentzian-type function.